A method for monitoring and early warning of the distribution evolution of non-compliant stores based on spatiotemporal sequences.

Abstract

This application discloses a method for monitoring and trend early warning of the distribution evolution of non-compliant stores based on spatiotemporal sequences, belonging to the fields of big data, artificial intelligence, and data analysis. By integrating environmental driving mechanisms, cross-scale propagation analysis, and critical state identification, it achieves proactive monitoring and trend early warning of the distribution evolution of non-compliant stores. This method overcomes the limitation of related technologies that can only passively respond to violations, providing forward-looking early warnings before large-scale outbreaks of violations. By synthesizing a multidimensional environmental pressure index and driving spatiotemporal distribution extrapolation, combined with cross-scale situation generation and bidirectional modulation, as well as critical signal strength identification, it effectively captures early signals of system instability. Verification through physical consistency constraints ensures the reliability of the early warning results, thereby supporting preventive intervention decisions.

Description

Technical Field

[0001] This application relates to the fields of big data, artificial intelligence, and data analysis, and in particular to a method for monitoring and trend early warning of the distribution evolution of illegal stores based on spatiotemporal sequences. Background Technology

[0002] In related technologies, monitoring methods for non-compliant stores mainly focus on the identification and detection of existing violations, typically based on single-dimensional user behavior data or store operation data for anomaly judgment. These methods can only respond to established violations and cannot provide proactive warnings before large-scale outbreaks of violations, nor do they consider the driving role of external environmental conditions in the evolution of violations.

[0003] The root of these limitations lies in the fact that the relevant technologies lack the ability to model the dynamic relationship between environmental factors and violations, and cannot depict the cross-scale propagation of violations from individual shops to the entire city under environmental pressure. Furthermore, the technologies lack the ability to identify critical states of the system, failing to capture early signs of system instability before violations erupt. This leaves early warning efforts in a reactive, reactive state for a long time, with insufficient lead time to support preventative intervention decisions.

[0004] In summary, the core challenge facing these technologies is how to integrate environmentally driven mechanisms, cross-scale propagation analysis, and critical state identification into the monitoring of non-compliant stores, so as to achieve proactive monitoring and trend warning of the distribution and evolution of non-compliant stores. Summary of the Invention

[0005] This application provides a method for monitoring and predicting the distribution evolution of non-compliant stores based on spatiotemporal sequences. The technical solution is as follows: On the one hand, a method for monitoring and trend early warning of the distribution evolution of non-compliant stores based on spatiotemporal sequences is provided, the method comprising: In response to the task of monitoring the evolution of the distribution of illegal shops, a multidimensional synthesis is performed on the environmental monitoring data and socio-economic indicators of the selected area to obtain an environmental pressure index. Then, using the environmental pressure index as the driving force, the spatiotemporal distribution of the density of illegal shops in the selected area is deduced based on the specific critical pressure threshold and carrying capacity constraints of the area. Cross-scale propagation analysis is performed on the spatiotemporal distribution to generate store-level propagation trends, business district-level infection trends, and city-level evolution trends. During the analysis, bidirectional modulation is performed to correct the store-level state recovery rate with the business district-level infection trend and the store-level propagation rate with the city-level evolution trend. Based on the results of the cross-scale propagation analysis, a critical signal strength is generated. The critical signal strength is compared with a dynamic threshold to determine whether the selected area is approaching the critical state of a violation outbreak and to estimate the critical arrival time, thereby generating a critical early warning message. The critical warning information is verified using entropy increase constraints and energy conservation constraints, and the verified critical warning information is output as the trend warning result for the selected region. Attached Figure Description

[0006] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0007] Figure 1 This is a flowchart of a method for monitoring and predicting the distribution evolution of non-compliant stores based on spatiotemporal sequences, provided in an embodiment of this application. Figure 2 This is a flowchart of another method for monitoring and predicting the distribution evolution of non-compliant stores based on spatiotemporal sequences, provided in an embodiment of this application. Figure 3 This is a flowchart of another method for monitoring and predicting the distribution evolution of non-compliant stores based on spatiotemporal sequences, provided in an embodiment of this application. Figure 4 This is a flowchart of another method for monitoring and predicting the distribution evolution of non-compliant stores based on spatiotemporal sequences, provided in an embodiment of this application. Figure 5 This is a flowchart of another method for monitoring and predicting the distribution evolution of non-compliant stores based on spatiotemporal sequences, provided in an embodiment of this application. Detailed Implementation

[0008] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0009] In this application, the terms "first," "second," etc., are used to distinguish identical or similar items with essentially the same function. It should be understood that there is no logical or temporal dependency between "first," "second," and "n," nor is there any limitation on the quantity or execution order.

[0010] It should be noted that the information (including but not limited to user device information, user personal information, etc.), data (including but not limited to data used for analysis, data stored, data displayed, etc.) and signals involved in this application are all authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0011] Current methods for monitoring non-compliant stores primarily focus on identifying existing violations, typically relying on single-dimensional data for anomaly detection. These methods can only passively respond to established violations, failing to provide proactive warnings before large-scale outbreaks and neglecting to consider the driving force of external environmental conditions on the evolution of violations. Furthermore, these technologies lack the ability to model the dynamic relationship between environmental factors and violations, making it difficult to characterize the cross-scale propagation of violations and identify critical system states. This results in a long-term passive response state for early warning systems, with insufficient lead time.

[0012] To address this issue, this application proposes a spatiotemporal sequence-based method for monitoring and trend warning of the distribution evolution of illegal shops. By responding to monitoring tasks, a multidimensional synthesis of environmental monitoring data and socioeconomic indicators for a selected area is performed to obtain an environmental pressure index, which drives the deduction of the spatiotemporal distribution of illegal shop density. Cross-scale propagation analysis is performed on this spatiotemporal distribution to generate shop-level, business district-level, and city-level situations, and bidirectional modulation is applied. Based on the propagation analysis results, a critical signal strength is generated, compared with a dynamic threshold to determine whether it is approaching a critical state for illegal activity and to estimate the arrival time, generating critical warning information. The warning information is verified using entropy increase constraints and energy conservation constraints, and trend warning results are output, thereby achieving proactive monitoring and trend warning of the distribution evolution of illegal shops.

[0013] For ease of understanding, the following explains some key terms in this embodiment: Environmental Stress Index: This index quantifies the external environmental stress that may result from violations within a selected area. Its generation may involve a comprehensive consideration and synthesis of various environmental monitoring data and socioeconomic indicators to reflect the overall stress level of the region.

[0014] Spatiotemporal distribution of non-compliant store density: This distribution describes the dynamic changes in the number or proportion of non-compliant stores within a selected area over a specific time and spatial dimension. Its projection aims to predict the clustering or diffusion trends of non-compliant stores in different regions and at different times.

[0015] Cross-scale propagation analysis: This analytical method aims to reveal the propagation and evolution patterns of violations across different spatial scales (e.g., from micro-stores to meso-business districts to macro-cities). Through hierarchical modeling, it captures the mutual influence of violations at different levels.

[0016] Store-level dissemination trend: This trend reflects the potential changing trend of a store's violation status or the possibility of spreading violations to other stores. It is typically generated based on the store's historical behavior, its surrounding environment, and its connections with other stores.

[0017] Business District-Level Contagion Situation: This situation describes the overall contagion risk and spread trend of violations within a specific business district. Its generation can aggregate the spread situation of individual shops within the business district to reflect the collective violation risk of the business district as a meso-level unit.

[0018] City-level evolutionary trend: This trend depicts the macro-evolutionary trend and risk level of violations across the entire city. Its generation can be based on the contagion patterns of various business districts, while also considering overall driving factors at the city level, to provide a comprehensive early warning perspective.

[0019] Two-way modulation: This mechanism refers to the mutual influence and correction between situations at different scales during cross-scale propagation analysis. For example, situation feedback from a higher scale (business district or city) corrects parameters at a lower scale (store) to improve the accuracy and consistency of the model.

[0020] Critical signal strength: This strength is an early warning indicator used to characterize a system approaching a critical state of violation. Its generation is typically based on sensitivity analysis after applying perturbations to the system's propagation pattern, in order to capture signals of system instability.

[0021] Dynamic threshold: This threshold is a reference value used for comparison with the critical signal strength. Its value is adjusted based on historical data, regional characteristics, or real-time monitoring. When the critical signal strength exceeds this threshold, it indicates that the system may be entering a critical state.

[0022] Critical Warning Information: This information is generated by the system after determining that a selected area is approaching a critical state for a violation to occur. It typically includes the determination of the critical state and the estimated arrival time of the critical state to support timely intervention.

[0023] Entropy increase constraint: This constraint is based on the principle of the second law of thermodynamics and is used to verify the physical consistency of the system's evolution process. In the context of the spread of violations, the system's entropy should generally increase monotonically with time; otherwise, the warning information may be unreasonable.

[0024] Energy conservation constraint: This constraint is used to verify the balance of energy within a system (such as input energy from the environment and dissipated energy). By comparing the input and dissipated energy, it is determined whether the system evolution conforms to physical laws, thereby improving the reliability of early warning results.

[0025] This application provides a method for monitoring and trend early warning of the distribution evolution of non-compliant stores based on spatiotemporal sequences. See [link to relevant documentation]. Figure 1 The specific implementation method includes the following steps: 101. In response to the task of monitoring the distribution and evolution of illegal shops, perform multidimensional synthesis of environmental monitoring data and socioeconomic indicators for selected areas to obtain an environmental pressure index. Using this environmental pressure index as a driving force, and based on the specific critical pressure threshold and carrying capacity constraints of the region, deduce the spatiotemporal distribution of the density of illegal shops within the selected area.

[0026] For example, the generation of the environmental stress index involves a simple weighted summation of environmental monitoring data and socioeconomic indicators within a selected area. For instance, a fixed weight is set, and environmental monitoring data such as air quality index, noise level, and population density are directly added to socioeconomic indicators such as regional GDP and consumer price index to obtain a preliminary environmental stress index. When extrapolating the spatiotemporal distribution of illegal shop density, a fixed critical stress threshold is set. When the environmental stress index exceeds this threshold, the density of illegal shops is considered to increase linearly. A fixed carrying capacity upper limit is preset; when the density of illegal shops reaches this upper limit, its growth stops. The extrapolation process uses a simple difference equation, adding the current illegal shop density to a linear function of the environmental stress index to obtain the density at the next time step.

[0027] 102. Perform cross-scale propagation analysis on the above spatiotemporal distribution to generate store-level propagation trends, business district-level infection trends, and city-level evolution trends. During this analysis, bidirectional modulation is performed, using the business district-level infection trend to correct the store-level state recovery rate, and the city-level evolution trend to correct the store-level propagation rate.

[0028] For example, cross-scale propagation analysis is conducted separately. The generation of store-level propagation trends is based on each store's historical violation records, simply calculating its violation frequency. The generation of district-level contagion trends involves averaging the violation frequencies of all stores within the district. The generation of city-level evolutionary trends involves averaging the average violation frequencies of all districts. Two-way modulation employs a simple linear correction. For instance, the store-level state recovery rate is directly multiplied by a fixed proportional factor of the district-level contagion trend. Similarly, the store-level propagation rate is directly multiplied by another fixed proportional factor of the city-level evolutionary trend. This correction is preset and does not adjust with the dynamic changes of specific trends.

[0029] 103. Based on the results of the above cross-scale propagation analysis, a critical signal strength is generated, and this critical signal strength is compared with a dynamic threshold. By comparing the two, it is determined whether the selected area is approaching the critical state of a violation outbreak, and the critical arrival time is estimated, thereby generating a critical early warning information.

[0030] For example, the generation of critical signal strength involves a simple threshold judgment of the city-level evolution trend in the cross-scale propagation analysis results. For instance, when the violation density growth rate in the city-level evolution trend exceeds a preset fixed threshold, the system is considered to be in a critical state, and this growth rate is directly used as the critical signal strength. The dynamic threshold is a preset fixed value that does not adjust with time or environmental changes. When the critical signal strength exceeds this fixed threshold, it is determined to be approaching a critical state. The prediction of the critical arrival time is simply calculated by dividing the difference between the current critical signal strength and the preset outbreak threshold by a fixed average rate of change. The critical warning information only includes a simple "yes / no" judgment result.

[0031] 104. Verify the above critical warning information using entropy increase constraints and energy conservation constraints. The verified critical warning information is output as the trend warning result for the selected region.

[0032] For example, entropy increase constraint verification is a simple check of the overall number of non-compliant stores in the system. For instance, if the warning message indicates a significant decrease in the number of non-compliant stores, but historical data shows that violations are typically widespread, then the verification fails. Energy conservation constraint verification is a rough comparison of the macroscopic trend between the environmental stress index and the density of non-compliant stores. For instance, if the environmental stress index continues to rise, but the warning message shows a significant decrease in the density of non-compliant stores, and there is no obvious dissipation mechanism to explain the difference, then the warning message fails the energy conservation verification.

[0033] This application achieves proactive monitoring and trend early warning of the distribution evolution of non-compliant stores by integrating environment-driven mechanisms, cross-scale propagation analysis, and critical state identification. This method overcomes the limitations of related technologies that can only passively respond to violations, providing forward-looking warnings before large-scale outbreaks of violations. By synthesizing a multi-dimensional environmental pressure index and driving spatiotemporal distribution extrapolation, combined with cross-scale situation generation and bidirectional modulation, and critical signal strength identification, it effectively captures early signals of system instability. Verification through physical consistency constraints ensures the reliability of the early warning results, thereby supporting preventative intervention decisions.

[0034] In some of the above-mentioned schemes in this application, an environmental pressure index is proposed to be obtained by multidimensional synthesis of environmental monitoring data and socioeconomic indicators of selected areas, which is used as a driving force for the spatiotemporal extrapolation of the density of illegal shops. However, in its implementation process, the specific synthesis path of the environmental pressure index is not clearly defined, and it is impossible to effectively separate and integrate heterogeneous environmental monitoring data and socioeconomic data. It is also impossible to accurately quantify the pressure generated by the evolution of illegal shops from the natural environment and socioeconomic levels, which may easily lead to the calculation of the environmental pressure index not conforming to the actual situation of the region, thereby affecting the accuracy of subsequent extrapolation of illegal shop density, cross-scale propagation analysis and critical early warning.

[0035] For this, see Figure 2 This application further proposes a method for obtaining an environmental stress index by performing multidimensional synthesis of environmental monitoring data and socioeconomic indicators in a selected area in response to the task of monitoring the distribution and evolution of non-compliant shops. The steps include: 201. Extract temperature and humidity data for the selected area from environmental monitoring data. Based on the deviations between the temperature data and temperature reference values, and the deviations between the humidity data and humidity reference values, generate a meteorological pressure index. The temperature and humidity reference values ​​are determined by statistical analysis of historical monitoring data.

[0036] 202. Extract employment rate fluctuation data and regional operation status index from socio-economic indicators for selected regions, and generate a social stress index based on employment rate fluctuation data and regional operation status index.

[0037] 203. Determine the environmental stress index based on the meteorological stress index and the social stress index.

[0038] For example, when extracting temperature and humidity data for a selected area from environmental monitoring data, the aim is to obtain basic meteorological information reflecting the region's natural environmental conditions. Temperature and humidity data are key meteorological elements affecting human activities and the business environment; their abnormal fluctuations can directly or indirectly affect business operations and potential violations. This can be achieved, for example, by real-time data collection through a network of meteorological sensors deployed within the selected area, or by obtaining historical and real-time data from third-party meteorological service platforms. Furthermore, remote sensing satellite data can be inverted and combined with ground calibration point data to obtain temperature and humidity distribution data for a large area.

[0039] When generating a meteorological stress index based on the deviations between temperature data and temperature reference values, and humidity data and humidity reference values, the aim is to quantify the degree to which current meteorological conditions deviate from normal, thereby assessing the "stress" they exert on violations. A larger deviation indicates more abnormal meteorological conditions, potentially creating greater external pressure on business operations and increasing the risk of violations. For example, the absolute difference between temperature data and temperature reference values ​​is calculated, and similar processing is applied to humidity data and humidity reference values. These two deviation values ​​are then combined using a weighted average or a non-linear function to generate the meteorological stress index. Alternatively, statistical methods are employed, such as calculating the percentile of current temperature and humidity in historical distributions, or using Z-score standardization to convert the degree of deviation into a dimensionless stress index. Temperature and humidity reference values ​​serve as benchmarks for measuring whether current meteorological data is abnormal. These reference values ​​reflect the typical meteorological characteristics of the selected area under normal conditions, ensuring that the calculation of the meteorological stress index accurately reflects the actual situation in the region and avoids assessment distortion due to regional differences. For example, by statistically analyzing temperature and humidity data for the same period (e.g., the same month, season, or day) over the past few years (e.g., 5-10 years) in a selected area, the average, median, or specific quantiles are calculated as reference values. In addition, more complex statistical models, such as seasonal time series models, are used to model historical data to predict the normal temperature and humidity range for a future period, and the central value or interval boundary is used as a reference value.

[0040] When extracting employment rate fluctuation data and regional operational status indices from socioeconomic indicators for selected regions, the aim is to obtain key indicators reflecting the region's socioeconomic vitality. Employment rate fluctuation data directly reflects the stability of the labor market and residents' income expectations, while the regional operational status index comprehensively reflects the overall health of the regional economy and the activity of the business environment. Abnormal changes in these indicators may indicate socioeconomic pressures, thereby affecting store operating strategies and compliance. For example, employment rate fluctuation data is obtained from monthly or quarterly employment reports released by government statistical departments, calculated by measuring month-on-month or year-on-year change rates. The regional operational status index is calculated by comprehensively considering macroeconomic indices (such as PMI, GDP growth rate, and consumer confidence index) released by the government or professional institutions. In addition, employment-related information is extracted from non-traditional data sources such as recruitment platform data, business registration and deregistration data, and commercial real estate vacancy rates through big data analysis, and combined with traffic flow, electricity consumption, and mobile payment data to construct the regional operational status index.

[0041] The social stress index, generated based on employment rate fluctuation data and regional operational status index, aims to quantify the pressure exerted on store operations by the socio-economic environment. Significant fluctuations in the employment rate or a poor regional operational status index indicate an unstable socio-economic environment, potentially leading to difficulties in store operations and increasing their incentive to engage in illegal activities. For example, the social stress index can be generated by weighted summation or logical combination of employment rate fluctuation data (e.g., the magnitude of employment rate decline) and the regional operational status index (e.g., the index falling below a certain threshold). Alternatively, machine learning models, such as regression models or neural networks, can be used as training samples, along with historical employment rate fluctuation data, the regional operational status index, and corresponding data on stores engaging in illegal activities, to learn and predict the social stress index.

[0042] An environmental pressure index is determined based on meteorological and social pressure indices. This step aims to integrate pressures from both the natural environment and socioeconomic dimensions to form a comprehensive environmental pressure index. This comprehensive index can more fully reflect the driving force of the external environment on the evolution of non-compliant shops, providing more accurate input for subsequent projections of violation density. For example, a weighted average of the meteorological and social pressure indices is used, with weights determined based on historical data analysis or expert experience, to reflect the relative importance of different pressure sources on non-compliant behavior. Furthermore, multi-factor decision-making models, such as the analytic hierarchy process (AHP) or fuzzy comprehensive evaluation, are employed, using the meteorological and social pressure indices as inputs to comprehensively assess and determine the environmental pressure index.

[0043] The above technical solution decomposes the environmental pressure driving the evolution of illegal shops into two parts: meteorological pressure (natural environment dimension) and social pressure (society and economy dimension). These are then quantified separately and synthesized into a comprehensive environmental pressure index. This solves the problems of unclear synthesis path, difficulty in integrating heterogeneous data, and inaccurate pressure quantification. For example, by extracting temperature and humidity data from environmental monitoring data and generating a meteorological pressure index based on their deviation from historically determined temperature and humidity reference values, the degree to which current meteorological conditions deviate from normal conditions can be accurately reflected, quantifying the pressure driving illegal activities caused by natural environmental conditions and avoiding assessment biases that may result from directly using raw data. Similarly, by extracting employment rate fluctuation data and regional operational status indices from socioeconomic indicators and generating a social pressure index based on these, unstable factors at the socioeconomic level can be accurately captured, and the pressure driving illegal activities caused by socioeconomic conditions can be reasonably quantified, ensuring the relevance and accuracy of social pressure calculation. Determining the environmental pressure index based on the meteorological and social pressure indices achieves a comprehensive integration of both natural and socioeconomic pressures, enabling the resulting environmental pressure index to accurately reflect the actual driving intensity of the distribution and evolution of illegal shops. This multidimensional synthesis method provides a more accurate and reliable driving force for subsequent spatiotemporal distribution projection of non-compliant store density, cross-scale propagation analysis, and critical warning. It improves the accuracy and effectiveness of the entire monitoring and early warning system from the source, thereby enabling earlier and more accurate identification of the critical state of non-compliance outbreaks and supporting preventive intervention decisions.

[0044] In some of the embodiments described above in this application, a meteorological pressure index is proposed to be generated based on the deviation between temperature data and temperature reference values, and the deviation between humidity data and humidity reference values, in order to support the calculation of the environmental pressure index and provide a driving basis for the spatiotemporal extrapolation of the density of illegal stores. However, in its implementation, the actual impact of temperature and humidity deviations on the evolution of regional violations varies under different store distribution densities. The meteorological pressure index calculated using fixed weights cannot fit the actual situation of different regions, which will lead to deviations in the calculation of the environmental pressure index, and thus affect the accuracy of subsequent extrapolation of the density of illegal stores and trend warning results.

[0045] To address this, this application further proposes a step for generating a meteorological stress index based on the deviations of the temperature data and the temperature reference value, and the deviations of the humidity data and the humidity reference value. This step includes: extracting the store distribution density of the selected area from the environmental monitoring data; determining temperature weighting coefficients and humidity weighting coefficients based on the store distribution density; calculating the temperature deviation between the temperature data and the temperature reference value; weighting the temperature deviation using the temperature weighting coefficients; calculating the humidity deviation between the humidity data and the humidity reference value; weighting the humidity deviation using the humidity weighting coefficients; and generating the meteorological stress index based on the weighted temperature deviation and the weighted humidity deviation.

[0046] For example, "extracting the store distribution density of the selected area from the environmental monitoring data" refers to obtaining the geographical location information of each store within the selected area from environmental monitoring data sources such as Geographic Information System (GIS) data, Point of Interest (POI) data, or satellite remote sensing imagery, and calculating the number of stores per unit area or the degree of store clustering based on this location information. For instance, a gridding method can be used to divide the selected area into several grid cells of a preset size, and the number of stores contained in each grid cell can be counted to obtain the gridded store distribution density. Alternatively, the Kernel Density Estimation (KDE) method can be used, with each store as the center, combining a kernel function and bandwidth parameters to calculate the store distribution density at any location within the selected area.

[0047] Building upon this, "determining temperature and humidity weighting coefficients based on store distribution density" refers to dynamically adjusting the influence of temperature and humidity deviations on the meteorological pressure index calculation according to the density of store distribution within the selected area. For example, a pre-defined weighting function can be used, taking store distribution density as input and outputting corresponding temperature and humidity weighting coefficients. For instance, higher store distribution density results in larger weighting coefficients, and vice versa. Alternatively, a piecewise linear function or lookup table can be used to directly assign corresponding weighting coefficients based on the interval in which the store distribution density falls.

[0048] "Calculating the temperature deviation between the temperature data and the temperature reference value, and then weighting the temperature deviation with a temperature weighting coefficient" refers to quantifying the degree to which the actual temperature deviates from the normal or ideal temperature, and correcting it according to the store distribution density. The temperature deviation is expressed as the absolute difference between the temperature data and the temperature reference value, or their squared difference. The weighting process typically involves multiplying the temperature deviation by a pre-determined temperature weighting coefficient to reflect the actual contribution of the temperature deviation to meteorological stress at a specific store distribution density.

[0049] "Calculating the humidity deviation between the humidity data and the humidity reference value, and then weighting the humidity deviation with a humidity weighting coefficient" refers to quantifying the degree to which the actual humidity deviates from the normal or ideal humidity, and correcting it according to the store distribution density. The humidity deviation is expressed as the absolute difference between the humidity data and the humidity reference value, or their squared difference. The weighting process typically involves multiplying the humidity deviation by a predetermined humidity weighting coefficient to reflect the actual contribution of the humidity deviation to meteorological stress at a specific store distribution density.

[0050] "Generating the meteorological pressure index based on the weighted temperature deviation and the weighted humidity deviation" refers to integrating the effects of temperature and humidity, after correction for store distribution density, to form a unified meteorological pressure index. For example, this could be achieved by simply summing the weighted temperature deviation and the weighted humidity deviation, or by performing a weighted average, where the weights are preset based on the relative importance of temperature and humidity on violations. Alternatively, a non-linear function, such as the sigmoid function or an exponential function, could be used to fuse the two factors to more precisely characterize the meteorological pressure index.

[0051] The above technical solution fully considers the differences in store density within a region when calculating the meteorological pressure index. For example, by extracting the store density of a selected area from environmental monitoring data, and dynamically determining the temperature and humidity weighting coefficients based on this, the deviations between temperature data and temperature reference values, as well as the deviations between humidity data and humidity reference values, can be adaptively adjusted according to the degree of store clustering within the region during weighted processing. In areas with high store density, small deviations in temperature and humidity may have a more significant impact on the evolution of violations; assigning higher weighting coefficients in these areas can more accurately capture this sensitivity. Conversely, in areas with low store density, the weights are correspondingly reduced to avoid overreaction. This dynamic weighting mechanism allows the generated meteorological pressure index to more realistically and precisely reflect the actual meteorological pressure experienced by different regions, thus solving the problem of calculation errors caused by fixed weights in related technologies. In view of this, this application provides a more reliable basic input for the accurate calculation of the environmental stress index, thereby improving the accuracy of the spatiotemporal extrapolation of the density of non-compliant stores, enhancing the reliability and effectiveness of the monitoring and trend early warning results of the distribution evolution of non-compliant stores, and providing a more accurate basis for preventive intervention decisions.

[0052] In some of the embodiments described above in this application, a social pressure index is generated based on employment rate fluctuation data and regional operational status index, which is then combined with meteorological pressure index to synthesize environmental pressure index, serving as a driving force for the spatiotemporal distribution of illegal store density. However, in this process, directly using the original employment rate fluctuation data cannot intuitively extract the direction and intensity of the driving force of employment rate changes on illegal behavior, nor can it adjust the corresponding magnitude of social pressure in conjunction with the operational status of the selected area. This can easily lead to the generated social pressure index deviating from the actual situation, thereby affecting the accuracy of the environmental pressure index and reducing the reliability of the monitoring and trend warning results of the distribution evolution of illegal stores.

[0053] To address this, this application further proposes a method for generating a social stress index based on employment rate fluctuation data and a regional operational status index. This method includes: performing a difference operation on the employment rate fluctuation data to obtain the direction and magnitude of employment rate changes; determining a state adjustment coefficient based on the regional operational status index; and multiplying the direction and magnitude of the employment rate changes with the state adjustment coefficient to obtain the social stress index.

[0054] For example, performing differencing on the employment rate fluctuation data yields the direction and magnitude of changes in the employment rate, aiming to extract its dynamic characteristics from the original data. Difference is a commonly used time series analysis method; by calculating the differences between data points in consecutive time periods, it can effectively reveal the trend and intensity of data changes. For instance, using first-order differencing calculates the difference between the current employment rate and the previous employment rate. A positive difference indicates an increase in the employment rate, and a negative difference indicates a decrease. The absolute value of the difference represents the magnitude of the change. Another approach is to use percentage differencing, which calculates the percentage change in the current employment rate relative to the previous employment rate, thus more intuitively reflecting the relative intensity of the employment rate change. This method transforms the raw, potentially noisy, employment rate data into more interpretable data on the direction and magnitude of change, providing clear and meaningful input for subsequent calculations of social stress indices.

[0055] The purpose of determining the state adjustment coefficient based on the regional operational status index is to incorporate the region's own macroeconomic performance into the calculation of the social stress index, reflecting the differences in the resilience of different regions to fluctuations in the same employment rate. The regional operational status index is a comprehensive indicator, weighted and aggregated from multiple dimensions such as regional economic growth rate, consumer price index, and industrial structure stability, used to characterize the overall health and resilience of the region. The determination of the state adjustment coefficient is based on a pre-defined mapping rule or function. For example, when the regional operational status index is high (indicating good regional performance), a lower state adjustment coefficient is set, indicating that the region is more resistant to fluctuations in the employment rate and has relatively less social stress. Conversely, when the regional operational status index is low, a higher state adjustment coefficient is set, indicating that the region is more sensitive to fluctuations in the employment rate and has greater social stress. Another approach is to use a machine learning model to train a regression model using historical data, taking the regional operational status index as input and outputting the corresponding state adjustment coefficient, thereby achieving more refined adjustment. The introduction of this state adjustment coefficient allows the calculation of the social stress index to fully consider the endogenous characteristics of the region, avoiding a "one-size-fits-all" calculation method and improving the accuracy and regional adaptability of social stress assessment.

[0056] The social stress index is obtained by multiplying the direction and magnitude of the employment rate change with the state adjustment coefficient. This aims to organically combine the dynamic characteristics of the employment rate with the region's endogenous adjustment capacity, forming a comprehensive indicator reflecting social stress. This multiplicative approach effectively integrates information from different dimensions. For example, the direction of the employment rate change can be encoded as +1 (increasing) or -1 (decreasing), and then multiplied by the magnitude of the change and the state adjustment coefficient. When the employment rate decreases (direction -1) and the magnitude is large, while the regional operational state index is low (state adjustment coefficient is large), the resulting social stress index will be a large negative value, indicating increased social stress. Conversely, when the employment rate increases (direction +1) and the magnitude is large, while the regional operational state index is high (state adjustment coefficient is small), the resulting social stress index will be a small positive value, indicating relatively low or alleviated social stress. Another approach is to introduce weighting factors to perform a weighted product of the direction, magnitude, and state adjustment coefficient of the employment rate change, highlighting the relative importance of different factors in the formation of social stress. Through this multiplicative process, the resulting social stress index not only reflects the trend and intensity of changes in the employment environment, but also incorporates the region's own responsiveness to these changes, thus providing a more comprehensive, accurate, and region-specific assessment of social stress.

[0057] The aforementioned technical solution enables differential calculations on raw employment rate fluctuation data, clearly separating the direction and magnitude of employment rate changes. This solves the problem that raw data cannot intuitively reflect the driving force of changes in the employment environment on illegal behavior, providing a clear and effective foundation for the subsequent calculation of the social pressure index. By determining the state adjustment coefficient based on the regional operational status index, the calculation of the social pressure index can be adjusted to reflect the overall operational situation of the region, avoiding biases caused by uniform calculations and ensuring that the social pressure index is adapted to the actual situation of the region. Multiplying the direction and magnitude of employment rate changes with the state adjustment coefficient integrates three types of core information. This reflects both the direction and intensity of the driving force of changes in the employment environment on illegal activities and incorporates the adjusting effect of the region's own operational status, allowing the resulting social pressure index to accurately reflect the actual pressure brought by the social level of the selected region to the evolution of illegal shops. This improves the accuracy of the social pressure index, thus providing solid support for the accurate synthesis of the environmental pressure index and enhancing the reliability of the monitoring and trend warning results of the distribution evolution of illegal shops.

[0058] This application proposes a method for extrapolating the spatiotemporal distribution of the density of illegal shops within a selected area. This method uses the environmental pressure index as a driving force and is based on the region's specific critical pressure threshold and carrying capacity constraints. (See [link to relevant documentation]). Figure 3 Specifically, it includes the following steps: 301. Determine the excess pressure amount when the environmental pressure index exceeds the critical pressure threshold, and use this excess pressure amount as the effective environmental driving force.

[0059] This step aims to identify and quantify the environmental pressures that truly drive the growth of non-compliant businesses. The environmental pressure index is a comprehensive indicator derived from environmental monitoring data and socioeconomic indicators, reflecting the external pressures faced by the region. The critical pressure threshold is a pre-set benchmark value, indicating the level of environmental pressure required to trigger an increase in non-compliant behavior. Excess pressure is the portion of the environmental pressure index that exceeds this critical pressure threshold. Using it as an effective environmental driver means that only when environmental pressure accumulates to a certain level, exceeding the region's tolerance capacity, will it substantially promote the evolution of non-compliant businesses. This excess pressure is calculated using a simple difference calculation, taking the maximum value (not less than zero) of the difference between the environmental pressure index and the critical pressure threshold. Alternatively, a non-linear function, such as the Sigmoid or ReLU function, can be used to map the difference between the environmental pressure index and the critical pressure threshold to more precisely characterize the contribution of excess pressure to the driving force.

[0060] 302. Based on the effective environmental driving force and the current density of non-compliant stores in the selected area, generate the non-compliance density growth rate.

[0061] This step calculates the potential increase in the density of non-compliant stores within a selected area under the current effective environmental driving forces. The increase in violation density reflects the trend of new violations based on specific environmental pressures and existing non-compliant stores. The current density of non-compliant stores is the number or proportion of non-compliant stores already existing in the area at the time of projection, providing a basis for the further spread of violations. This increase in violation density is calculated by multiplying the effective environmental driving forces by the current density of non-compliant stores and then multiplying by a preset growth coefficient. Alternatively, a regression model trained on historical data can be constructed, taking the effective environmental driving forces and the current density of non-compliant stores as input, and outputting the predicted increase in violation density.

[0062] 303. Based on the carrying capacity constraint and the current density of non-compliant stores, determine the saturation inhibition factor, and use the saturation inhibition factor to correct the increase in the non-compliant density to obtain the suppressed growth.

[0063] This step introduces a constraint on regional carrying capacity to prevent the unlimited growth of illegal shop density, ensuring it conforms to the actual physical or social carrying capacity limit. The carrying capacity constraint refers to the maximum density of illegal shops that a region can accommodate in terms of economic, social, and environmental factors. A saturation inhibition factor is a coefficient between 0 and 1 used to reduce the growth rate of illegal shop density. This factor decreases significantly when the current illegal shop density approaches the carrying capacity limit, thus inhibiting growth. The inhibited growth is the actual growth after correction for the carrying capacity constraint. This saturation inhibition factor is determined based on the ratio of the current illegal shop density to the carrying capacity constraint, for example, by calculating 1 minus the ratio of the current illegal shop density to the carrying capacity limit, ensuring it is not less than 0. Alternatively, more complex nonlinear functions, such as the Logistic function or the Gompertz function, can be used to simulate the saturation inhibition process, making the inhibition more significant as the carrying capacity limit approaches.

[0064] 304. Based on the current density of non-compliant stores and the preset recovery rate benchmark, determine the recovery attenuation amount. Based on the suppressed growth amount and the recovery attenuation amount, obtain the spatiotemporal distribution of the density of non-compliant stores in the selected area.

[0065] This step considers the natural attenuation process of non-compliant shops potentially recovering to a compliant state through rectification, closure, or other means. The recovery attenuation represents the reduction in the density of non-compliant shops due to recovery activities within a certain period. The preset recovery rate benchmark is a basic recovery ratio set based on historical data or experience. By combining the suppressed growth with the recovery attenuation, a more realistic net change in the density of non-compliant shops is obtained, thereby deduce the spatiotemporal distribution of non-compliant shop density within the selected area. This recovery attenuation is simply calculated by multiplying the current density of non-compliant shops by the preset recovery rate benchmark. Alternatively, the preset recovery rate benchmark can be a dynamic value, adjusted according to factors such as the region's regulatory intensity and economic conditions; for example, the greater the regulatory intensity, the higher the recovery rate benchmark.

[0066] The above technical solution addresses the problems of previous derivation methods in extrapolating the spatiotemporal distribution of non-compliant store density, namely, failing to distinguish between effective driving forces and ineffective environmental pressures, failing to constrain non-compliant growth by incorporating regional carrying capacity limitations, and failing to account for the natural recovery and attenuation of existing non-compliant stores. For example, by identifying the excess pressure amount exceeding the critical pressure threshold and using it as the effective environmental driving force, this application can accurately screen out the environmental pressure components that truly drive the evolution of non-compliant behavior, eliminating ineffective pressure interference that does not meet the driving conditions. This makes the calculation of the driving force more consistent with the actual logic of non-compliant occurrence and improves the accuracy of the derivation. The non-compliant density growth is generated based on the effective environmental driving force and the current density of non-compliant stores within the selected area. This calculation combines the existing non-compliant base with the effective environmental driving force, conforming to the objective law that the larger the existing non-compliant base during the non-compliant propagation and expansion process, the more new non-compliant behaviors are generated by environmental driving forces, ensuring the rationality of the growth calculation. Based on carrying capacity constraints and the current density of non-compliant shops, a saturation suppression factor is determined. This factor is then used to correct the growth rate of non-compliant density, resulting in suppressed growth. By incorporating the upper limit of non-compliant shops that the region can accommodate, saturation suppression is introduced, avoiding unreasonable results where the non-compliant density exceeds the region's actual carrying capacity. This ensures the simulation results conform to actual carrying capacity limitations. Based on the current density of non-compliant shops and a preset recovery rate benchmark, a recovery attenuation is determined. Combining the suppressed growth and recovery attenuation, the spatiotemporal distribution of non-compliant shop density is obtained, incorporating the compliance recovery process existing in existing non-compliant shops. This recreates the true process of simultaneous growth and attenuation in the evolution of non-compliance, further improving the accuracy of the spatiotemporal distribution simulation results. In summary, this application, through a hierarchical decomposition simulation process, introduces effective driving force screening, saturation growth constraints, and recovery attenuation correction, obtaining accurate spatiotemporal density distribution results that conform to the dynamic laws of non-compliance evolution. This provides reliable and accurate basic data for subsequent cross-scale propagation analysis and early warning, thereby improving the overall effectiveness and reliability of monitoring and trend early warning of non-compliant shop distribution evolution.

[0067] This application further proposes a method for generating the increase in violation density based on effective environmental driving forces and the current density of non-compliant stores within a selected area. The method includes: determining a driving force response value based on the effective environmental driving force through a driving force response mapping, wherein the driving force response mapping is jointly calibrated by historical environmental pressure data and historical violation density change data; multiplying the driving force response value by the current density of non-compliant stores to obtain an initial increase; determining a regional growth rate coefficient based on historical violation density data for the selected area; and correcting the initial increase using the regional growth rate coefficient to obtain the actual increase in violation density.

[0068] For example, this driver-response mapping is a function or model used to describe the relationship between input drivers (i.e., effective environmental drivers) and system responses (i.e., the trend or intensity of violation density growth), transforming abstract drivers into concrete, quantifiable response values. This mapping is constructed using machine learning models (e.g., neural networks, support vector regression), where historical environmental stress data serves as input features and historical violation density change data serves as output labels, learning the mapping relationship between the two through training. Alternatively, it can be constructed using nonlinear regression analysis or piecewise functions; for example, fitting an S-shaped or exponential curve based on historical data, with effective environmental drivers as independent variables and driver response values ​​as dependent variables. The historical environmental stress data refers to a set of data related to environmental stress experienced by a selected area over a past period, such as historical meteorological stress indices and social stress indices. This data is typically stored in time series format and associated with geographic location information. Historical violation density change data refers to recorded data on the change of violation store density in a selected area over a period of time. This includes, for example, sequence data statistically recorded at different points in time regarding the violation store density in the selected area, or the increase or decrease in violation store density obtained through differencing, smoothing, or other processing. Joint calibration refers to the process of using historical environmental pressure data and historical violation density change data as inputs or references to train, calibrate, or determine the driving force response mapping parameters, ensuring that the mapping relationship accurately reflects the actual causal or correlation between environmental pressure and violation density changes. The driving force response value is a quantitative value transformed through the driving force response mapping, representing the potential growth tendency or intensity of violation store density under the current environmental driving force. It is a dimensionless proportionality factor or a growth potential value with a specific unit. The preliminary growth amount is a preliminary estimate of the violation store density growth amount based on the environmental driving force response and the current violation store density. It is usually obtained by multiplying the driving force response value by the current violation store density, reflecting the characteristic that the spread of violations is often proportional to the existing scale. The regional growth rate coefficient is a correction factor reflecting the historical characteristics of violation growth in a selected region. It is determined by analyzing the average growth rate, volatility, or trend of non-compliant store density over a past period, such as calculating the compound annual growth rate of non-compliant store density over the past N periods. The revised initial growth amount is calculated by multiplying the initial growth amount by the regional growth rate coefficient to more accurately reflect the actual potential for violation density growth in the selected region. The most common method is to multiply the initial growth amount by the regional growth rate coefficient. The resulting violation density growth amount is the expected growth of non-compliant store density within the selected region at the current time step, determined after calibration based on environmentally driven responses and regional characteristics.

[0069] The above technical solution determines the driving force response value by jointly calibrating a driving force response mapping based on historical environmental pressure data and historical violation density change data. This effectively fits the actual correspondence between environmental pressure and violation density growth within a specific region. This allows for a more accurate quantification of the actual driving effect of environmental pressure on violation growth, avoiding quantification biases and improving the accuracy of the driving force response value. Multiplying this driving force response value by the current density of violating shops yields the initial growth amount. This step combines the degree of environmental influence on violation growth with the existing scale of violating shops in the region, aligning with the actual evolutionary logic of violation behavior spreading and growing based on existing violation foundations. This ensures that the initial growth amount reflects the diffusion characteristics of violation behavior. A regional growth rate coefficient is determined based on historical violation density data for the selected region, and this coefficient is used to correct the initial growth amount. Utilizing the region's own historical violation growth characteristics to correct the initial growth amount adapts to the unique violation growth characteristics of different regions, effectively correcting potential biases in the initial growth amount. In summary, this application addresses the inaccuracy in calculating the increase in violation density in the original scheme by introducing response relationships calibrated from historical data and regional characteristics, resulting in violation density growth figures that better reflect the actual situation in the region. This provides more accurate foundational data for subsequent extrapolation of the spatiotemporal distribution of violation store density, thereby improving the reliability and accuracy of monitoring and trend warning of the evolution of violation store distribution, and making the warning results more instructive.

[0070] This application further proposes a method to determine a saturation suppression factor based on carrying capacity constraints and the current density of non-compliant stores. Specifically, this includes: extracting the upper limit of carrying capacity for a selected area from the carrying capacity constraints; calculating the ratio of the current density of non-compliant stores to the upper limit of carrying capacity to obtain the carrying capacity occupancy ratio; and determining the saturation suppression factor based on the carrying capacity occupancy ratio through a saturation mapping, where the saturation mapping causes the value of the saturation suppression factor to decrease monotonically as the carrying capacity occupancy ratio approaches 1.

[0071] The extraction of the carrying capacity limit for a selected area from the carrying capacity constraints aims to clarify the maximum density or number of illegal shops that the selected area can tolerate under specific conditions. This carrying capacity limit is a critical value resulting from the combined effects of various factors such as the regional environment, socio-economic conditions, and regulatory capacity, and its setting is crucial for accurately assessing the risk of illegal activities in the area. In practice, the extraction of the carrying capacity limit is achieved through various methods. For example, it can be determined by comprehensively analyzing historical data on illegal shops, regional population density, commercial facility saturation, and relevant policies and regulations, combined with expert experience or machine learning models for prediction and setting. Another method is to directly obtain or calculate the maximum number or density of illegal shops that the area can accommodate within a specific time period based on regional carrying capacity assessment reports issued by urban planning departments or environmental management departments.

[0072] The ratio of the current density of non-compliant shops to the maximum carrying capacity is calculated to obtain the carrying capacity occupancy ratio. This ratio quantifies the extent to which the current size of non-compliant shops is utilizing the area's maximum carrying capacity. It directly reflects how close the current non-compliant status is to the area's carrying capacity limit and is a key indicator for assessing the level of non-compliance pressure in the area. The carrying capacity occupancy ratio is typically calculated by directly dividing the currently monitored density of non-compliant shops by a pre-set maximum carrying capacity value. Furthermore, for ease of subsequent processing, this ratio is normalized, for example, using a sigmoid function or Min-Max normalization method, mapping it to a standardized interval to facilitate uniform processing of subsequent saturation mapping.

[0073] Based on this, a saturation inhibition factor is determined through a saturation mapping based on the capacity occupancy ratio. This saturation mapping causes the value of the saturation inhibition factor to decrease monotonically as the capacity occupancy ratio approaches 1. This step is the core of this scheme, aiming to transform the capacity occupancy ratio into an inhibitory effect on the growth of non-compliant stores. The characteristics of the saturation mapping ensure that when the capacity occupancy ratio is low, the inhibitory effect is not obvious, and the saturation inhibition factor is close to 1. However, as the capacity occupancy ratio gradually increases and approaches 1, the inhibitory effect is sharply enhanced, and the saturation inhibition factor decreases rapidly until it approaches 0. This mapping relationship is implemented using various mathematical models. For example, a piecewise linear function is used, setting different inhibition slopes in different capacity occupancy ratio ranges. Alternatively, a nonlinear function is used, such as an exponential decay function (e.g., exp(-a×capacity occupancy ratio), where a is a positive coefficient) or an inverse sigmoid function, so that the inhibitory effect exhibits stronger nonlinear characteristics when the capacity occupancy ratio approaches 1, thereby more accurately simulating the nonlinear inhibitory effect when the system reaches saturation in reality.

[0074] The above technical solution incorporates the actual limitations of regional carrying capacity into the deduction process of illegal store density. By extracting the upper limit of carrying capacity from the constraints, accurate basic data is provided for subsequent quantification of carrying capacity occupancy. The carrying capacity occupancy ratio is obtained by calculating the ratio of the current illegal store density to the upper limit of carrying capacity, intuitively quantifying the remaining space between the current scale of violations and the regional carrying capacity limit, providing a reasonable calculation basis for determining the specific value of the saturation inhibition factor. More importantly, the saturation inhibition factor is determined through saturation mapping based on the carrying capacity occupancy ratio, and its value monotonically decreases as the carrying capacity occupancy ratio approaches 1. This allows the saturation inhibition factor to accurately reflect the constraining effect of regional carrying capacity on the growth of illegal store density. When the carrying capacity occupancy ratio is higher and the scale of violations is closer to the regional carrying capacity limit, the space for adding new illegal stores is smaller, the growth is more strongly inhibited, and the corresponding value of the saturation inhibition factor is smaller, thus reasonably correcting the growth rate of violation density. This avoids the problem of the simulation results of violation density deviating from the actual situation, and makes the spatiotemporal distribution of the density of violation shops obtained by simulation more in line with the actual carrying capacity of the region. This provides more accurate and reliable basic data for subsequent cross-scale propagation analysis and trend early warning, thereby improving the accuracy and practicality of the entire early warning method.

[0075] This application further proposes a method for obtaining the spatiotemporal distribution of the density of non-compliant shops within a selected area based on the suppressed growth and the recovery decay, which includes: The difference between the suppressed growth and the recovery attenuation is calculated to obtain the net change in violation density.

[0076] Add the current density of non-compliant stores to the net change in non-compliant store density to obtain the updated density of non-compliant stores in the current projection step.

[0077] The updated density of non-compliant stores in the current simulation step is associated with the current simulation timestamp to form a time slice of the spatiotemporal distribution of the density of non-compliant stores in the selected area in the current simulation step. Together with the time slices generated in the historical simulation steps, this constitutes the spatiotemporal distribution of the density of non-compliant stores in the selected area.

[0078] For example, when calculating the difference between the suppressed growth and the recovery decline to obtain the net change in violation density, the aim is to accurately reflect the actual change in the density of violating stores within the current projection step. One implementation is to directly perform a subtraction operation, i.e., the net change in violation density equals the suppressed growth minus the recovery decline. Another implementation is to introduce weighting factors, considering that different factors may have different weights on the net change. For example, the net change in violation density equals a preset weight multiplied by the suppressed growth, and then subtracts another preset weight multiplied by the recovery decline, where the weighting factors are adjusted based on historical data or expert experience.

[0079] When adding the current density of non-compliant shops to the net change in non-compliant density to obtain the updated density of non-compliant shops in the current time step, the aim is to achieve iterative updates of the density of non-compliant shops, gradually advancing the density extrapolation process. One implementation is to directly accumulate the current density of non-compliant shops with the calculated net change in non-compliant density to obtain the density of non-compliant shops in the next time step. Another implementation is to introduce boundary condition checks during accumulation, for example, ensuring that the updated density of non-compliant shops is not lower than zero, or does not exceed the carrying capacity limit of the area, to guarantee the physical rationality of the extrapolation results.

[0080] When the density of non-compliant stores updated in the current projection step is associated with the current projection timestamp to form a time slice of the spatiotemporal distribution of non-compliant store density within the selected area, together with the time slices generated in previous projection steps, the aim is to integrate discrete spatial density distribution data calculated at different time points into a continuous spatiotemporal dataset with temporal evolution characteristics, thereby providing complete basic data for subsequent dynamic analysis and trend prediction. One implementation method is to use a time series database or a specially designed data structure for storage. For example, the density of non-compliant stores updated in each projection step (usually represented as a numerical distribution on a spatial grid or geographical area) is treated as a "time slice" and assigned a unique timestamp. These time slices are stored in chronological order in a list, array, or as a dimension of a multidimensional tensor, thus forming a complete spatiotemporal cube data model. Another implementation method is to store the spatial density distribution data generated in each projection step as an independent data file or database record, and associate it with the corresponding projection timestamp through metadata (such as time information in the file name, timestamp field in the database table). When spatiotemporal analysis is required, the system retrieves and aggregates these independent time slices based on timestamps, dynamically constructing a complete spatiotemporal distribution.

[0081] The above technical solution enables the construction of a complete spatiotemporal distribution of non-compliant store density, encompassing both spatial and temporal attributes, by iteratively updating density results and integrating multiple rounds of simulation results with timestamps. For example, the net change in non-compliant density is obtained by calculating the difference between suppressed growth and recovery decay. Combining the scale of non-compliant density growth driven by environmental pressure (reflected by suppressed growth) and the density reduction resulting from non-compliant stores returning to compliance (reflected by recovery decay), the net change is accurately reflected, reflecting the actual change in non-compliant store density within the current simulation step. This avoids the bias caused by statistically analyzing changes in only one direction, ensuring the accuracy of density change statistics. Adding the current non-compliant store density to the net change in non-compliant density yields the updated non-compliant store density for the current simulation step. The updated result, based on the original current density and the actual net change, conforms to the iterative logic of density simulation, progressively advancing the density update process and ensuring the accuracy of each simulation result, providing reliable single-step results for subsequent integration of spatiotemporal distribution. By associating the updated density of non-compliant stores with the current timestamp of the current simulation step to form a time slice for the current step, and combining it with the time slices generated in previous simulation steps, a complete spatiotemporal distribution is formed. By associating the spatial density results of each simulation step with the timestamp, the density results at different simulation moments can be integrated in an orderly manner according to the time dimension. This not only preserves the spatial distribution characteristics of the density of non-compliant stores, but also adds the dimension of temporal evolution. This perfectly meets the needs of subsequent cross-scale propagation analysis for basic data in the spatiotemporal dimension, and can effectively support the subsequent analysis and early warning work on the evolution process of the distribution of non-compliant stores.

[0082] This application further proposes performing cross-scale propagation analysis on this spatiotemporal distribution to generate store-level propagation trends, business district-level infection trends, and city-level evolution trends. During the analysis, bidirectional modulation is performed, using the business district-level infection trend to correct the store-level state recovery rate and the city-level evolution trend to correct the store-level propagation rate. See [link to relevant documentation]. Figure 4 Specifically, it includes: 401. Based on the current status of each store in the spatiotemporal distribution and the propagation relationship between stores, generate the store-level propagation situation. The propagation relationship between stores is a static connection relationship that is predetermined based on the spatial distance between stores and the similarity of business types.

[0083] 402. Aggregate the store-level propagation trend by business district to generate the business district-level spread trend, and use the business district-level spread trend to adjust the store-level status recovery rate.

[0084] 403. Based on the business district-level transmission trend and the transmission relationship between business districts, the city-level evolution trend is deduced and generated, and the store-level transmission rate is corrected based on the city-level evolution trend.

[0085] This cross-scale propagation analysis of spatiotemporal distribution refers to an in-depth analysis of the evolution of the density of non-compliant shops at different spatial scales (such as shops, business districts, and cities) and temporal dimensions. Its purpose is to reveal the mechanisms of propagation, diffusion, and mutual influence of violations at different levels. In practice, a multi-agent simulation model is used, treating each shop as an independent agent. By defining the interaction rules and state transition logic between agents, the propagation process of violations at different scales is simulated. Alternatively, a diffusion model based on complex networks can be constructed, abstracting shops, business districts, and cities as network nodes. The connection strength between nodes reflects the propagation relationship, and network dynamics methods are then used to analyze the diffusion path and speed of violations.

[0086] This generation of store-level dissemination trends refers to assessing, at the micro level, the current violation status, the degree of external influence, and the future tendency or spread of violations for each individual store. This helps to precisely understand the potential risks of each store. For example, a risk index can be calculated for each store, taking into account its historical violation records, the influence of the surrounding environment, and its business type characteristics to quantify its violation tendency. Alternatively, a state transition probability model can be built for each store to predict the likelihood of it transitioning from a compliant state to a non-compliant state or recovering from a non-compliant state to a compliant state in the next time step.

[0087] This concept of generating a business district-level transmission trend refers to aggregating store-level transmission information at the meso-level to reflect the overall level and trend of violation transmission risk within a specific business district. This helps identify areas with high incidence of violations. For example, by statistically analyzing the number or proportion of stores in a specific business district that are in violation or have a high tendency to violate regulations, the transmission risk index of that business district can be quantified. Alternatively, based on the transmission network structure between stores within the business district, the average transmission speed or infection rate within the business district can be calculated to characterize its transmission trend.

[0088] This city-level evolutionary trend analysis refers to the overall evolutionary trend of illegal behavior in the entire urban area by comprehensively considering the contagion patterns of all business districts and the interactions between them at the macro level. This provides city managers with a holistic perspective. Specifically, the overall city-level violation index is obtained by weighted averaging or summing the contagion risk indices of each business district. Alternatively, a macro-dynamic model at the city scale can be constructed, treating business districts as interacting units to simulate the growth, saturation, and decline processes of the overall urban violation density.

[0089] This two-way modulation refers to the fact that, in the process of cross-scale propagation analysis, not only is there information aggregation from the micro to the macro level, but a feedback adjustment mechanism is also introduced from the macro or meso level back to the micro level. This mechanism allows situational information at different scales to influence and correct each other, making the model closer to reality. For example, propagation parameters (such as propagation rate and recovery rate) at the micro-level of individual shops can be dynamically adjusted to align with the overall situation of the meso-level business district or the macro-level city. Alternatively, adaptive algorithms can be designed to update the parameters or rules of the lower-level model in real time based on changes in the higher-level situation.

[0090] The adjustment of store-level recovery rates based on the spread of the virus within a business district means that the more severe the spread (i.e., the higher the risk of violation) in a business district, the more difficult it is for stores within that district to recover from a non-compliant state, resulting in a lower recovery rate. This adjustment reflects the constraints of the regional environment on individual behavior. For example, a base store-level recovery rate can be set, and then a correction coefficient can be introduced based on the spread risk index of the business district to which the store belongs. This coefficient decreases as the spread risk index increases, resulting in the corrected store-level recovery rate. Alternatively, the corresponding store-level recovery rate can be directly selected from a pre-defined recovery rate lookup table based on the level of spread within the business district.

[0091] The correction of the store-level propagation rate based on city-level evolution trends means that the more severe the overall violation trend in a city (i.e., the higher the overall violation density or the faster the growth), the greater the likelihood that an individual store will be induced or actively participate in violation activities, resulting in a higher propagation rate. This correction reflects the driving role of the macro environment on micro-level propagation behavior. For example, a base store-level propagation rate can be set, and then a correction coefficient can be introduced based on the city's violation density or growth rate reflected in the city-level evolution trend. This coefficient increases as the city's violation trend worsens, resulting in the corrected store-level propagation rate. Alternatively, the threshold parameters in the store-level propagation model can be dynamically adjusted according to the severity of the city-level evolution trend, making it easier to trigger the propagation of violations.

[0092] This method, based on the current state of each store in a spatiotemporal distribution and the propagation relationships between stores, generates a store-level propagation situation and serves as the starting point for cross-scale analysis. It utilizes the real-time status information of each store and pre-established inter-store interaction mechanisms. The current state of a store includes whether it has violated regulations, the degree of violation, and the frequency of historical violations. The propagation relationships between stores define which stores have potential paths for the propagation of violations.

[0093] The inter-store propagation relationships are static connections predetermined based on spatial distance and business type similarity. This means that before the analysis begins, a network reflecting the likelihood of mutual influence has been constructed based on the stores' geographical location and business category. For example, a spatial distance threshold is set; stores within that threshold are connected. The similarity of store business types (e.g., catering, retail, entertainment) is calculated; stores with similarity above a certain threshold are also connected. These connections are binary (present or absent) and weighted (connection strength is related to distance and similarity).

[0094] This method aggregates store-level dissemination trends by business district to generate business district-level contagion trends. It involves summarizing individual store information at the micro level to the meso-level business district level. This typically involves statistically analyzing, averaging, or weighted summing the dissemination trends of all stores within the business district to form an indicator that can represent the characteristics of the entire business district.

[0095] Based on the contagion patterns at the business district level and the contagion relationships between business districts, this model extrapolates to generate city-level evolutionary trends, further aggregating business district information from the meso-level to the macro-city level. This not only considers the contagion risk of each business district itself but also the potential mutual influence between different business districts (e.g., the cross-business district spread of violations due to the flow of people, goods, and information), thus providing a more comprehensive depiction of the overall urban trend of violation evolution.

[0096] The aforementioned technical solution overcomes the limitations of previous analytical methods. By generating hierarchical propagation trends at the store, business district, and city levels, this application clearly distinguishes the hierarchical characteristics at different scales, leading to a more comprehensive and in-depth understanding of violations. A two-way modulation mechanism is introduced, using the business district-level contagion trend to correct the store-level recovery rate and the city-level evolution trend to correct the store-level propagation rate, achieving effective interaction and feedback between information at different scales. This mechanism allows core parameters at the micro-store level to dynamically reflect the overall environmental impact at the meso-level business district and macro-level city levels, thus avoiding biases caused by fixed parameters or unidirectional aggregation. For example, when the overall violation risk of a business district is high, the recovery difficulty of its internal stores will increase accordingly, which is reflected in the correction of the store-level recovery rate by the business district-level contagion trend. When the overall violation trend of the city deteriorates, the tendency of individual stores to spread violations will also increase, which is reflected in the correction of the store-level propagation rate by the city-level evolution trend. This two-way modulation allows the model to better fit the actual laws of violation propagation, improving the accuracy and reliability of cross-scale propagation analysis results. This provides a more accurate and solid data foundation for subsequent critical warnings, thereby enabling more effective support for preventive intervention decisions.

[0097] This application further proposes a step for generating the store-level propagation situation based on the current state of each store in the spatiotemporal distribution and the propagation relationship between stores. This step includes: determining the connection weights of the propagation relationship between stores based on spatial distance and business type similarity; for each compliant store, determining the propagation impact on the compliant store based on the current state of the non-compliant stores with which it has a propagation relationship, the connection weights, and the store-level propagation rate; and determining the state transition trend of the compliant store based on the propagation impact and the current state of the compliant store, and using the set of state transition trends of all stores as the store-level propagation situation.

[0098] This method, based on spatial distance and business type similarity between stores, determines the connection weights of the propagation relationships between them. The aim is to quantify the potential intensity or likelihood of the spread of violations between different stores. For example, stores that are spatially closer tend to have more frequent interactions such as personnel flow and information exchange, increasing the likelihood of mutual influence on violations. Stores with higher business type similarity have more similar business models and target customer groups, making them more prone to "copycat" or mutual imitation violations. Multiple methods are used to determine the connection weights. For instance, spatial proximity is represented by the reciprocal of the Euclidean distance or geographically weighted distance between stores; the closer the distance, the greater the weight. Business type similarity is calculated using the hierarchical structure of industry classification codes or by analyzing store business scope descriptions using natural language processing techniques; the higher the similarity, the greater the weight. The connection weights are the product or weighted combination of spatial proximity and business type similarity measures, and are also learned by training machine learning models using historical propagation data.

[0099] For each compliant store, the propagation impact is determined based on the current state of violating stores with propagation relationships to that compliant store, the connection weight, and the store-level propagation rate. This aims to accurately assess the propagation pressure a compliant store receives from its surrounding violating stores. The current state of the violating stores reflects the activity level or severity of the violation from the propagation source itself. The connection weight reflects the strength of the propagation path. The store-level propagation rate is a macro-level parameter representing the overall propagation activity of the violation throughout the store network. To determine the propagation impact, a weighted summation method is used: multiplying the "violation status value" (e.g., a value between 0 and 1 representing the severity of the violation) of each violating store with a propagation relationship to the target compliant store by its corresponding connection weight, then multiplying by the store-level propagation rate, and finally summing the results for all relevant violating stores to obtain the total propagation impact on the compliant store. Alternatively, a probability-based propagation model can be constructed, taking into account the above factors, to calculate the probability that the compliant store will transition to a violating state in the next time step, and using this probability as the propagation impact.

[0100] Based on the propagation impact and the current status of the compliant store, this method determines the state transition trend of the compliant store, aiming to judge whether a compliant store will change to a non-compliant state. This considers not only external propagation pressure but also the store's own internal attributes. One way to determine the state transition trend is to compare the calculated propagation impact with a preset "non-compliance tendency threshold." If the propagation impact exceeds this threshold, the compliant store's state transition trend is determined to be towards a non-compliant state. Conversely, it remains compliant. Another more refined approach is to combine, in addition to the propagation impact, the compliant store's own historical violation frequency, operational stability, credit rating, and other internal factors (these factors are combined into a "susceptibility coefficient"), and use a comprehensive function or classification model (such as logistic regression or support vector machine) to determine its state transition trend.

[0101] This approach uses the collection of state transition trends from each store as the store-level propagation profile. The aim is to aggregate the individual state change predictions of all micro-stores, forming a holistic and refined micro-propagation landscape. This collection is a data structure, such as a list, array, or matrix, where each element corresponds to a store and stores the predicted state transition trend for that store at the current time step (e.g., "maintain compliance," "tend towards violation"). In this way, it clearly reflects which stores face higher violation risks under the current environment and propagation conditions, as well as the specific direction and intensity distribution of violation propagation at the store level.

[0102] The above technical solution clarifies the specific steps for generating store-level propagation trends, progressing step-by-step from quantifying propagation relationships between stores to calculating propagation impact and then judging state transitions, thus solving the problem of inaccurate store-level propagation trend generation. For example, determining the connection weights of propagation relationships between stores based on spatial distance and business type similarity simultaneously considers both physical proximity and operational similarity, making the connection weights more aligned with actual violation propagation patterns and accurately distinguishing the strength of propagation relationships between different store pairs. Based on this, for each compliant store, the propagation impact on the compliant store is determined by combining the current state of violating stores with propagation relationships, connection weights, and store-level propagation rate. This quantifies the differences in impact between different violating stores on the target compliant store and, combined with the intensity of the violation source and overall propagation activity, provides a reliable quantitative basis for subsequent judgment of state transitions. Based on the obtained propagation impact and the current state of the compliant store, the state transition trend of that store is determined, and these are aggregated as the store-level propagation trend. This ensures that the results clearly reflect the propagation trend of violations at the store level, and the state changes of each store are accurately quantified. This provides an accurate and reliable foundation for subsequent aggregation by business district to obtain the business district-level contagion trend and to correct parameters such as store-level status recovery rate and store-level transmission rate, thereby improving the accuracy and reliability of the entire method for monitoring and trend early warning of the distribution evolution of non-compliant stores.

[0103] This application further proposes the following steps for determining the state transition trend of the compliant store: extracting historical violation frequency data from the current state of the compliant store, and determining the susceptibility coefficient of the compliant store based on the historical violation frequency data. Based on the propagation impact, the store-level propagation rate, and the susceptibility coefficient, determining the violation tendency value of the compliant store. Comparing the violation tendency value with a preset tendency threshold, if the violation tendency value exceeds the preset tendency threshold, determining that the state transition trend of the compliant store is a tendency towards a violation state; if the violation tendency value does not exceed the preset tendency threshold, determining that the state transition trend of the compliant store is to maintain a compliant state.

[0104] For example, historical violation frequency data refers to the number or frequency of violations committed by a specific compliant store over a past period. This data is obtained from multiple sources, such as publicly available penalty records from government regulatory departments, which count the number of times a store has been administratively penalized for violating relevant regulations. Alternatively, it can be obtained from reports provided by third-party business credit rating agencies, which typically summarize store complaint records, negative public opinion, and other information, quantifying them as violation frequency. This data objectively reflects the accumulation of potential violation risks in a store's business operations. The susceptibility coefficient is an indicator that quantifies the sensitivity of a compliant store to the impact of external violation propagation. Its determination is based on various designs using historical violation frequency data. For example, a linear or nonlinear mapping function can be used to normalize the historical violation frequency data to a specific range (e.g., 0 to 1) as the susceptibility coefficient. The higher the frequency, the larger the susceptibility coefficient, indicating that the store is more susceptible to the impact of external violation propagation. Alternatively, multiple tiered thresholds can be set based on historical violation frequency data to classify stores into different susceptibility levels (e.g., low, medium, high), and each level can be assigned a preset susceptibility coefficient value. For example, stores with historical violation frequencies below a certain threshold might have a susceptibility coefficient of 0.2, while stores with frequencies above another threshold might have a susceptibility coefficient of 0.8. The violation tendency value is a quantitative indicator that assesses the likelihood of a compliant store transitioning to a violation status after comprehensively considering external dissemination impact, overall dissemination capability, and the store's own susceptibility. Its determination typically involves mathematical operations on the dissemination impact, store-level dissemination rate, and susceptibility coefficient. For example, a multiplicative model can be used, multiplying the dissemination impact, store-level dissemination rate, and susceptibility coefficient to obtain the violation tendency value. Alternatively, a weighted summation model can be constructed, assigning different weights to these three parameters, then performing a weighted summation, and finally mapping it to a specific range using an activation function to obtain the violation tendency value. The preset tendency threshold is a critical value used to distinguish the status transition trend of compliant stores. The setting of this threshold needs to comprehensively consider historical data analysis, expert experience, and actual business needs. For example, by statistically analyzing the violation tendency values ​​of historically non-compliant stores, an empirical threshold that maximizes classification accuracy can be selected, such as determining the optimal cutoff point through ROC curve analysis. Alternatively, a fixed threshold can be set by expert experience based on industry regulatory policies and risk control objectives; for example, stores with a violation tendency value higher than 0.6 are considered to be trending towards non-compliance. This threshold is a static value but can also be dynamically adjusted based on region, industry, or time. State transition trend refers to the probability that a compliant store's operating status will either shift towards a non-compliant status or remain compliant within the current monitoring period. When the violation tendency value exceeds the preset tendency threshold, it indicates that the store is significantly affected by external factors and has high inherent susceptibility, making a shift towards a non-compliant status highly likely; therefore, its trend is determined as trending towards non-compliance. Conversely, when the violation tendency value does not exceed the preset tendency threshold, the store is considered to remain compliant.This trend assessment provides micro-level state input for subsequent cross-scale propagation analysis and forms the basis for constructing store-level propagation trends.

[0105] The above technical solution fully considers the historical violation data of each compliant store when determining its status transition trend, thus avoiding bias caused by uniformly judging violation tendencies. For example, by extracting historical violation frequency data from the current status of compliant stores and determining a store-specific susceptibility coefficient based on this data, each store's susceptibility coefficient can more accurately reflect its inherent violation risk level, avoiding bias caused by uniformly setting susceptibility coefficients. Furthermore, the dissemination impact, store-level dissemination rate, and this susceptibility coefficient are combined to jointly determine the violation tendency value. This step combines information from three dimensions: the impact of external violation dissemination, the overall dissemination probability level, and the store's own susceptibility to violation dissemination. This allows for a more comprehensive and accurate quantification of the actual violation tendency of compliant stores, preventing the violation tendency value from deviating from the true situation due to the lack of information on the store's own risk dimensions. By comparing this violation tendency value with a preset tendency threshold, the status transition trend of compliant stores can be determined more accurately, reducing the occurrence of misjudgments or omissions. This refined determination of state transition trends lays the foundation for generating more reliable store-level dissemination patterns, thereby improving the accuracy and reliability of the entire method for monitoring and trend warning of the distribution evolution of non-compliant stores. This allows the warning results to be closer to the actual situation and provides more effective support for preventive intervention decisions.

[0106] This application further proposes the following steps for aggregating store-level spread trends by business district to generate business district-level contagion trends: Based on the business district to which each store belongs, the store-level communication trend is grouped by business district to obtain a set of store status transition trends within each business district.

[0107] For each business district, count the number of stores whose status transition trend is towards a non-compliant status, calculate the proportion of such stores to the total number of stores in the business district, and obtain the infection risk index of the business district.

[0108] By correlating the infection risk index of each business district with the spatial boundary of the corresponding business district, the infection status at the business district level can be obtained.

[0109] For example, when grouping the store-level propagation trends by business district, based on pre-built Geographic Information System (GIS) data containing the precise geographic coordinates of each store and the boundary information of its respective business district, the system automatically categorizes the propagation trends of each store into its corresponding business district through spatial query functions. Alternatively, administrative division or commercial functional zoning data can be used to match the store's registered address or business address with this zoning information to determine its business district, and then group the store-level propagation trends accordingly, forming a set of store status transition trends within each business district. This grouping method ensures that micro-level store information can be accurately aggregated at the mid-level business district level, laying the foundation for subsequent business district-level analysis.

[0110] After obtaining the set of store status transition trends within each business district, a quantitative analysis of each business district is needed to generate its contagion risk index. Specifically, this involves iterating through the set of store status transition trends within each business district, counting the number of stores judged to be "tending towards a violation status," and then dividing this number by the total number of stores in that business district. This yields a proportion between 0 and 1, representing the contagion risk index for that business district. Alternatively, a database query language (such as SQL) can be used to group and aggregate the stored store status data, directly calculating the proportion of stores trending towards violations within each business district. This proportion calculation effectively eliminates the impact of differences in the size of different business districts, making the contagion risk comparable between different business districts and thus more accurately assessing the overall violation risk level of the business district.

[0111] Building upon this foundation, to enable spatial visualization and analysis of the infectious disease situation at the business district level, it is necessary to correlate the calculated infectious disease risk index of each business district with its corresponding spatial boundaries. For example, the infectious disease risk index can be stored as attribute data within the vector polygon data representing each business district in a Geographic Information System (GIS), ensuring that each business district's geographical area carries its corresponding infectious disease risk value. Alternatively, thematic maps can be generated, rendering business districts with different risk indices using different colors or textures to visually represent the spatial distribution of the infectious disease situation at the business district level. This correlation method transforms risk information from abstract numerical values ​​into entities with clearly defined geographical locations and extents, facilitating intuitive risk assessment and spatial decision-making by management personnel.

[0112] The above technical solution clarifies the specific path for generating a meso-level business district-level contagion trend from a micro-level store-level propagation trend, solving the problem of lacking a clear implementation method for the aggregation of micro-level information to the meso-level in cross-scale propagation analysis. For example, grouping stores based on their respective business districts ensures the reasonable attribution of store status transition trend sets and avoids information confusion. By statistically analyzing the number of stores trending towards violations and calculating their proportion of the total number of stores in the business district, this solution provides a standardized and comparable business district contagion risk index, overcoming the impact of differences in the size of different business districts on risk assessment, and enabling the accurate quantification of the violation contagion risk of the business district. Correlating this contagion risk index with the spatial boundary of the corresponding business district gives the business district-level contagion trend a clear spatial attribute, providing a data foundation for subsequent spatial analysis and visualization.

[0113] This clear and quantifiable business district-level contagion pattern enhances the accuracy and reliability of the entire method for monitoring and trend warning of the distribution evolution of non-compliant stores. For example, in the process of performing cross-scale propagation analysis and bidirectional modulation on the aforementioned spatiotemporal distribution, when correcting the store-level state recovery rate with this business district-level contagion pattern, the accuracy of the business district-level contagion pattern can more accurately reflect the inhibitory or promoting effect of the business district environment on the store's return to compliance, thus making the correction of the store-level state recovery rate more reasonable. When extrapolating the city-level evolution pattern based on this business district-level contagion pattern and the contagion relationship between business districts, the accurate business district-level data provided by this solution as input ensures that the extrapolation results of the city-level evolution pattern are closer to reality, thereby providing more solid data support for the generation of critical warning information and improving the timeliness and effectiveness of the warning.

[0114] This application further proposes a specific method for correcting the store-level recovery rate based on the business district-level infection situation, including: extracting the infection risk index of the business district to which the store belongs from the business district-level infection situation; determining a recovery rate correction coefficient based on the infection risk index, wherein the value of the recovery rate correction coefficient increases as the infection risk index increases; and multiplying the base value of the store-level recovery rate by the recovery rate correction coefficient to obtain the corrected store-level recovery rate.

[0115] For example, extracting the contagion risk index of a store's business district from the business district-level contagion situation aims to obtain the actual level of violation transmission risk in that business district. The business district-level contagion situation represents the macro-level state of violation transmission, while the contagion risk index quantifies this risk. By extracting this index, it is ensured that subsequent adjustments to the store's recovery rate accurately reflect the impact of its surrounding business environment. In practice, each store is pre-associated with a specific business district. When a store needs to be processed, its corresponding contagion risk index is directly queried and extracted from the data structure storing the business district-level contagion situation (e.g., a database table or hash map containing the contagion risk indices of each business district) using the identifier of its business district. Alternatively, if the business district is defined by geographical boundaries (e.g., a polygonal region), a spatial query is performed using the store's geographical coordinates (e.g., a point-within-a-polygon test) to determine its business district and obtain its contagion risk index.

[0116] Based on the infection risk index, a recovery rate correction coefficient is determined, and the value of the recovery rate correction coefficient increases with the increase of the infection risk index. This step aims to establish a dynamic relationship between the risk level of the business district and the recovery ability of stores. The recovery rate correction coefficient is a multiplier or addend used to adjust the basic recovery rate of stores. Its value increases with the increase of the infection risk index, meaning that the higher the violation risk of the business district, the greater the impact of the correction coefficient on the recovery rate, making it more difficult for stores in high-risk business districts to recover to a compliant state. This correction coefficient is determined in several ways. For example, a linear function model is used, expressing the correction coefficient as a linearly increasing function of the infection risk index, i.e., correction coefficient = a × infection risk index + b, where a is a positive number to ensure an increasing trend, and b is a constant offset. In addition, nonlinear functions, such as exponential functions or sigmoid functions, are also used to capture more complex risk response patterns, such as correction coefficient = exp(k × infection risk index), where k is a positive number. Another approach is to use piecewise functions or lookup tables to pre-determine correction coefficient values ​​for different infection risk index ranges. For example, when the infection risk index is in the low-risk range, the correction coefficient is 1.0; when it is in the medium-risk range, the correction coefficient is 1.2; and when it is in the high-risk range, the correction coefficient is 1.5.

[0117] Multiplying the base value of the store-level recovery rate by the recovery rate correction factor yields the corrected store-level recovery rate. This is a crucial calculation step for actually adjusting the store recovery rate. The base value of the store-level recovery rate represents the store's inherent or default recovery capability when unaffected by the external business environment. By multiplying it by the previously determined recovery rate correction factor, a more realistic corrected store-level recovery rate, adjusted for environmental risk, is obtained. For example, if the store's base recovery rate is 0.1, and the correction factor determined based on the risk of its business district is 1.2, then the corrected recovery rate is 0.1 × 1.2 = 0.12. This multiplicative relationship intuitively reflects the amplifying or inhibiting effect of business district risk on the store's recovery capability. To ensure the corrected recovery rate is within a reasonable range, an upper limit constraint is applied after the multiplication operation. For example, the corrected store-level recovery rate = min(base value × correction factor, maximum recovery rate) to prevent it from exceeding the practically feasible maximum recovery rate.

[0118] The aforementioned technical solution allows for dynamic adjustment of the store-level recovery rate, ensuring it fully considers the actual contagion risk within the business district where the store is located. This correction ensures that the store-level recovery rate parameter accurately reflects the impact of the overall violation atmosphere within the business district on the recovery ability of individual stores, thus avoiding analytical biases caused by parameter settings that do not conform to actual propagation patterns. The corrected store-level recovery rate, as a more context-aware parameter, improves the modeling accuracy of store-level propagation trends, business district-level contagion trends, and city-level evolution trends in subsequent cross-scale propagation analysis. Especially in high-risk business districts, increasing the correction coefficient makes it more difficult for stores to recover to a compliant state, which aligns with the actual violation propagation mechanism. This allows the model to more accurately predict the persistence and spread trends of violations, providing a more reliable and refined data foundation for monitoring and trend warning of the distribution evolution of violating stores, thereby supporting more timely and accurate identification and warning of critical states.

[0119] This application further proposes a method for extrapolating city-level evolutionary trends based on the contagion situation at the business district level and the contagion relationships between business districts. Specifically, this method includes: determining the contagion weights of the contagion relationships between business districts based on the intensity of pedestrian interaction and the similarity of their commercial functions; calculating the contagion contribution of each business district to the overall city based on its contagion risk index in the business district-level contagion situation and the contagion weights between it and other business districts; and extrapolating city-level evolutionary trends based on the contagion contributions of each business district and the city's violation growth rate.

[0120] In determining the contagion weights for the contagion relationships between business districts, the intensity of pedestrian interaction refers to the scale and frequency of population movement between different business districts, which is quantified based on multiple data sources. For example, by analyzing anonymized mobile communication signaling data, the migration trajectories and dwell times of users between different business districts can be statistically analyzed to calculate the frequency and intensity of pedestrian interaction between business districts. Another approach is to utilize public transportation card swipe data or shared mobility data to identify commuting and travel patterns between different business districts, thereby assessing the intensity of pedestrian interaction. The similarity of business functions refers to the degree of similarity between different business districts in terms of business formats, service types, or target customer groups. For example, by analyzing the industry classification data of registered shops within each business district, the similarity coefficient of business format distribution between different business districts can be calculated, such as using cosine similarity or Jaccard similarity for quantification. Furthermore, the similarity in business functions is also assessed by analyzing the business scope, product categories, or consumer profile data of merchants within the business district. After obtaining the intensity of pedestrian interaction and the similarity of business functions, the contagion weights are determined through various methods. One approach is to use a weighted summation model, multiplying the standardized intensity of pedestrian interaction and the similarity of business functions by preset weight coefficients and then summing them to obtain the contagion weight. These weight coefficients can be set based on historical data or expert experience. Another approach is to build a machine learning-based predictive model, taking features such as pedestrian interaction intensity and business function similarity as input, and outputting the contagion weight between business districts. This model can be trained and optimized using historical data on the spread of violations.

[0121] When calculating the contribution of a business district to the overall city's spread of illegal activities, the business district's spread risk index within that business district measures the risk of such spread within that district. The spread weight between that business district and other business districts reflects the potential intensity of the spread of illegal activities from that business district to other business districts. Calculating the spread contribution aims to comprehensively consider both the business district's own risk and its external spread capabilities. One calculation method is to multiply each business district's own spread risk index by the sum of its spread weights to all other business districts, thus obtaining its overall contribution to the city's spread. This represents the total influence of the business district's internal risk spreading to the entire city through its external connections. Another calculation method is to construct a network graph of all business districts in the city, where business districts are nodes and the spread weights between business districts are edge weights. Then, using centrality measures in network analysis, such as the PageRank algorithm or eigenvector centrality, the importance and influence of each business district in the illegal spread network are evaluated, which is then used as its overall contribution to the city's spread.

[0122] When extrapolating the city-level evolution trend, the contagion contribution of each business district reflects the external driving effect of cross-business district transmission on the overall density of illegal shops in the city, while the city's illegal shop growth rate represents the endogenous growth trend of illegal shop density at the city level. This city illegal shop growth rate is obtained by analyzing historical city-level illegal shop density data, for example, by predicting its baseline growth rate using time series analysis methods (such as the ARIMA model), or by dynamically estimating it using a regression model built in conjunction with urban macroeconomic indicators (such as GDP growth rate, unemployment rate, etc.). One method for extrapolating the city-level evolution trend is to simply sum up the contagion contributions of all business districts and superimpose them with the city's illegal shop growth rate to obtain the overall trend of change in the city's illegal shop density. Another more refined method is to construct a city-scale dynamic system model. This model uses the contagion contribution of each business district as an external input, the city's illegal shop growth rate as an endogenous growth term, and may introduce constraints such as urban carrying capacity, simulating the spatiotemporal evolution of the city's illegal shop density through iterative calculations.

[0123] The aforementioned technical solutions enable a more accurate quantification of the propagation impact of violations between business districts, avoiding biases caused by simple averaging or ignoring actual interaction characteristics. For example, by introducing the intensity of pedestrian interaction and the similarity of commercial functions to determine the contagion weight between business districts, the weight setting is made more consistent with the actual patterns of cross-business district propagation of violations, thus providing a more realistic and reliable basis for subsequent calculations of contagion contribution. Based on this, by combining the business district's own contagion risk index and its external propagation weight to calculate the contagion contribution of the business district to the city as a whole, the role of each business district in the evolution of urban violations can be precisely assessed, differentiating the magnitude of the influence of different business districts and avoiding the limitations of generalizing to all business districts. Combining the contagion contribution of each business district with the city's violation growth rate, a city-level evolutionary trend is generated. This not only considers the external drivers of cross-business district propagation but also takes into account the city's own endogenous growth patterns, making the obtained city-level evolutionary trend closer to reality. This multi-dimensional and refined deductive process provides an accurate macro-based basis for subsequent adjustments to the store-level dissemination rate, thereby ensuring the accuracy and reliability of the early warning results on the distribution and evolution trend of non-compliant stores, and improving the precision and foresight of the early warning work.

[0124] This application further proposes a method for calculating the infectious contribution of this business district to the city as a whole, including: Based on the geographical proximity between this business district and other business districts, the contagion weight is adjusted to obtain the adjusted contagion weight.

[0125] Multiply the infection risk index of the business district by the revised infection weight to obtain the one-way infection component of the business district to other business districts.

[0126] The unidirectional transmission components of this business district to all other business districts are summed to obtain the overall transmission contribution of this business district to the city.

[0127] This method involves adjusting the contagion weight based on the geographical proximity of the business district to other business districts, resulting in a revised contagion weight. This aims to incorporate geospatial factors to more accurately reflect the actual intensity of illegal activity spread between business districts. Geographical proximity is an indicator of the spatial closeness between two business districts. It is generally believed that the closer the geographical locations of business districts, the more frequent their interactions in terms of pedestrian flow, information, and business activities, thus increasing the likelihood of mutual influence on illegal activities. For example, geographical proximity can be quantified by calculating the Euclidean distance between the geometric centers of each business district or by using the shortest path distance based on the actual road network. During the correction process, a decay function is designed so that the closer the geographical distance, the larger the correction coefficient, and vice versa. The original contagion weight (based on the intensity of pedestrian interaction and the similarity of business functions) is then multiplied by this correction coefficient to obtain the revised contagion weight. Another implementation method is to divide the relationship between business districts into different proximity levels (such as "directly adjacent," "secondarily adjacent," etc.) based on geographical distance, and pre-set a correction factor for each level. The original contagion weight is then multiplied by the corresponding level's correction factor.

[0128] Multiplying the contagion risk index of a business district by the modified contagion weight yields the one-way contagion component of that business district to other business districts. This step quantifies the impact of a specific business district on the spread of violations to other individual business districts. The contagion risk index reflects the likelihood or activity level of a violation outbreak within that business district, while the modified contagion weight represents the intensity of the spread of violations from that business district to other business districts. By multiplying these two, a comprehensive indicator, the one-way contagion component, is obtained, which more accurately characterizes the actual impact of violations from one business district to another. For example, a direct multiplication operation can be used, where the one-way contagion component equals the contagion risk index multiplied by the modified contagion weight. Alternatively, more complex nonlinear functions can be employed, such as a sigmoid function or an exponential function, to map the contagion risk index and the modified contagion weight, thereby better simulating the actual contagion dynamics and obtaining the one-way contagion component.

[0129] The contribution of a particular business district to the overall city's violations is calculated by summing the one-way contagion components of that business district to all other business districts. This aims to comprehensively assess the overall influence of a specific business district in the evolution of violations throughout the city. By summing the one-way contagion components of that business district to all other business districts, the contribution of that business district as a source or propagation node to the overall violation situation in the city is fully reflected. For example, the contribution to the overall city's violations can be obtained by directly summing the one-way contagion components calculated between that business district and all other business districts. In another implementation, each one-way contagion component is assigned a different weight based on the size, importance, or centrality of other business districts in the city network, and then a weighted sum is performed to obtain a more refined contribution.

[0130] The above technical solution incorporates geographical proximity between business districts to correct the original transmission weights when calculating the contribution of business districts to the overall city's transmission. This correction allows the transmission weights between business districts to more accurately reflect the actual spread patterns of violations in geographic space, avoiding the overestimation of the transmission impact of distant business districts and the underestimation of the transmission impact of nearby business districts that might result from only considering pedestrian interaction and similarity of business types. The corrected transmission weights, combined with the transmission risk index of each business district, generate a more accurate unidirectional transmission component, which, through accumulation, yields a more realistic contribution of business districts to the overall city's transmission. Given that the aforementioned city-level evolutionary trend will be used to correct the store-level transmission rate, this solution, by providing a more accurate city-level evolutionary trend, improves the accuracy of the entire cross-scale transmission analysis, making the correction of the store-level transmission rate more reasonable. This provides a more reliable foundation for subsequent critical signal strength generation, violation outbreak critical state determination, and critical warning information output, enhancing the overall accuracy and practicality of the monitoring and trend warning method for the distribution evolution of violating stores.

[0131] This application further proposes a method for extrapolating the city-level evolutionary trend based on the infectious contribution of each business district and the city's violation growth rate. This method includes: weighted summation of the infectious contributions of each business district to obtain the total city-level infectious drive, where the summation weight of each business district is determined by its economic share within the city; generating the city's endogenous growth based on the city's violation growth rate and the current urban violation density within the selected area; and superimposing the total city-level infectious drive with the city's endogenous growth, while applying urban carrying capacity constraints to obtain the city-level evolutionary trend.

[0132] For example, in the process of weighted summation of the infection contributions of each business district to obtain the total city-level infection-driven amount, where the summation weight of each business district is determined by its economic share in the city, this infection contribution is an indicator measuring the degree of influence of each business district on the overall spread of violations in the city. The specific calculation method can refer to the implementation method described above. This weighted summation refers to accumulating the infection contributions of each business district according to preset weights to reflect the differentiated impact of different business districts on the overall violation situation in the city. The total city-level infection-driven amount is a comprehensive indicator reflecting the overall urban violation growth trend driven by the infection mechanism between business districts after weighted aggregation. The summation weight is determined by the economic share of each business district in the city, where the economic share refers to the proportion of each business district in the overall economic activity of the city, such as measured by indicators like GDP contribution, commercial sales, number of registered enterprises, or employment population. For example, by collecting annual economic statistics of each business district and calculating its proportion in the total urban economy as the weight. Alternatively, a business big data platform can be used to analyze real-time data such as transaction volume, customer traffic, or commercial density in various business districts to dynamically assess their economic activity and determine their weights. By introducing economic share as a weight, the dominant role of business districts with significant economic influence in the spread of illegal activities can be more accurately reflected.

[0133] In generating endogenous urban growth based on the city's violation growth rate and the current urban violation density within a selected area, the city's violation growth rate refers to the city's inherent violation growth trend, independent of contagion between business districts. It may be influenced by various factors such as the macroeconomic environment, policy and regulatory changes, and seasonality. For example, a baseline growth rate can be predicted by performing time-series analysis on historical urban violation data, using models such as ARIMA or exponential smoothing. Alternatively, a default growth rate reflecting the overall urban violation trend can be set based on expert experience or industry reports published by government departments. The current urban violation density within the selected area refers to the proportion of the number or area of ​​all violating shops within the selected area to the total number of shops or total commercial area at the current moment. For example, it can be obtained from city-level violation shop density data aggregated from the spatiotemporal distribution. Alternatively, it can be directly queried from a real-time violation monitoring database. This endogenous urban growth is the growth generated by the combined effect of the city's own violation trend and current violation level, compensating for the shortcomings of considering only external contagion drivers. For example, it can be calculated by multiplying the city's violation growth rate by the current urban violation density within the selected area. Alternatively, a more complex nonlinear model, such as the logistic growth model, can be used to simulate endogenous growth, causing it to slow down as the city approaches its carrying capacity.

[0134] In the process of superimposing the total amount of city-level infectious growth with the city's endogenous growth and imposing urban carrying capacity constraints to obtain the city-level evolutionary trend, the superposition refers to merging the total amount of city-level infectious growth driven by inter-business districts with the city's own endogenous growth to obtain the overall potential for illegal growth in the city. For example, the two can be directly added together. Alternatively, they can be weighted and superimposed according to the actual situation to highlight the role of a certain aspect. The urban carrying capacity constraint refers to the upper limit of the number of illegal shops or the density of illegal activities that the city can accommodate within a specific period. Exceeding this limit will lead to system instability or trigger strong intervention measures. For example, it can be determined based on the historical highest illegal density record, the commercial carrying capacity limit set by the urban planning department, or the resource restrictions of the law enforcement department. Alternatively, it can be adjusted in real time based on dynamic indicators such as urban population density and commercial facility density. Imposing urban carrying capacity constraints means that after calculating the initial urban illegal growth, it is compared with the upper limit of the urban carrying capacity to ensure that the city-level evolutionary trend does not exceed the actual tolerable range. For example, if the superimposed illegal density exceeds the upper limit of the urban carrying capacity, the illegal density is limited to the upper limit value. Alternatively, a saturation function can be used so that the growth rate gradually approaches zero as the violation density nears its upper limit. This city-level evolutionary trend is a comprehensive result derived from the deduction, reflecting the overall trend of the distribution of illegal shops in the city. It provides a macro-level basis for subsequent early warning and decision-making.

[0135] The above technical solutions enable a more accurate projection of the evolution of illegal shops at the city level. By weighted summing of the contagion contributions from each business district and determining the summation weight based on the economic share of each business district in the city, the system more realistically reflects the driving force of different business districts on the overall urban contagion of illegal activities, avoiding the bias caused by averaging calculations and thus making the calculation of the total urban-level contagion drive more accurate. Generating the city's endogenous growth based on the urban illegal growth rate and the current urban illegal density within the selected area covers the inherent growth characteristics of the city's illegal evolution itself, compensating for the omissions caused by considering only the contagion drive between business districts, and making the calculation of the overall urban illegal growth drive more complete. Superimposing the total urban-level contagion drive with the city's endogenous growth and imposing urban carrying capacity constraints not only integrates the combined effects of external business district contagion and internal endogenous growth, more completely reflecting the driving sources of urban illegal growth, but also ensures that the projection results conform to the upper limit of illegal shops that the city can accommodate through carrying capacity constraints, avoiding unreasonable projection results that exceed the actual carrying capacity. In summary, the city-level evolution trend obtained in this application is more accurate and reliable, providing a solid and precise input foundation for subsequent store-level propagation rate correction and critical early warning analysis, and improving the reliability and practicality of the entire method for monitoring and trend early warning of the distribution evolution of non-compliant stores.

[0136] This application further proposes a method for adjusting store-level dissemination rates based on city-level evolution trends, the method including: Extracting urban violation density from city-level evolution trends.

[0137] Based on the density of violations in the city, a propagation rate correction coefficient is determined. The value of this propagation rate correction coefficient increases monotonically as the density of violations in the city increases.

[0138] Multiply the propagation rate correction factor by the base value of the store-level propagation rate to obtain the corrected store-level propagation rate.

[0139] For example, the city violation density can be extracted from the city-level evolution trend. This density is a macro-level indicator that measures the overall density of non-compliant shops within a selected area, reflecting the trend of violation spread at the city level. Extracting this density provides a macro-level basis for correcting the shop-level propagation rate. One implementation calculates the city violation density by weighted averaging or summing the violation densities of each business district within the city-level evolution trend, then dividing by the total city area or total number of shops. The weights are determined based on factors such as the economic size and number of shops in the business district. Another implementation may involve the city-level evolution trend itself directly containing the overall city's non-compliant shop density data; in this case, this data is directly read as the city violation density.

[0140] Based on urban violation density, a propagation rate correction coefficient is determined. This coefficient is a dynamically adjusted factor used to quantify the impact of the overall urban violation level on the potential for micro-level store propagation. Its value monotonically increases with urban violation density, ensuring that the higher the macro-level violation level, the larger the micro-level propagation rate correction, consistent with actual propagation patterns. One implementation uses a linear or piecewise linear function to define the relationship between the propagation rate correction coefficient and urban violation density. For example, the correction coefficient can be set to 1 plus a positive number multiplied by the urban violation density, or multiple thresholds can be set, using different correction slopes in different density ranges. Another implementation uses a non-linear function, such as an exponential or sigmoid function, to more precisely characterize this relationship. For example, the correction coefficient can be an expression relating the exponential or sigmoid function to urban violation density, where the function parameters are obtained by fitting historical data.

[0141] The corrected store-level propagation rate is obtained by multiplying the propagation rate correction coefficient by the base value of the store-level propagation rate. This is a specific calculation method that applies a macro-level correction factor to the micro-level propagation rate. Through multiplication, the inherent propagation characteristics of the store are preserved while the influence of the overall urban environment is added. In one implementation, the multiplication operation is performed directly, meaning the corrected store-level propagation rate equals the propagation rate correction coefficient multiplied by the base value of the store-level propagation rate. In another implementation, an upper or lower limit constraint is applied on top of the multiplication to prevent the corrected propagation rate from being too high or too low, keeping it within a reasonable physical range. For example, the corrected store-level propagation rate equals the minimum value between the corrected value and the maximum propagation rate.

[0142] The above technical solution extracts core characteristic parameters, namely urban violation density, from the macro-level city-level evolution trend. Based on this, the micro-level store propagation rate parameter is dynamically adjusted, thereby achieving reasonable modulation of micro-level propagation parameters by the macro-evolutionary trend and ensuring the effectiveness of cross-scale bidirectional modulation. Urban violation density is chosen as the correction basis because it directly and accurately reflects the overall degree of illegal store spread at the city level. Furthermore, this density data integrates the propagation influence between different business districts, ensuring that the correction basis aligns with the actual overall situation of violation evolution and avoiding correction bias caused by irrelevant parameters. The propagation rate correction coefficient is determined based on urban violation density, and the value of the correction coefficient increases monotonically with increasing urban violation density. This setting conforms to the actual dynamic law of violation propagation; that is, the higher the overall urban violation density, the easier it is for the overall environment for violation propagation to facilitate the spread of illegal behavior between stores, and the corresponding probability of propagation at the micro-level stores should also increase accordingly. This rule fits the actual logic of violation propagation, ensuring that the corrected parameters conform to the actual propagation trend. Multiplying the propagation rate correction coefficient by the base value of the store-level propagation rate is a simple and intuitive calculation method. While retaining the inherent propagation attributes of the store as embodied in the original base propagation rate, it also incorporates the influence of macro-level urban evolution trends. This method preserves the original characteristics of micro-stores while integrating dynamic adjustments at the macro level, ensuring the rationality and feasibility of the correction. Therefore, this application can improve the accuracy of violation propagation analysis, making the store-level propagation rate parameters more consistent with actual evolutionary patterns. This, in turn, improves the accuracy of predicting the distribution evolution of violating stores and providing trend warnings, meeting the need for forward-looking early warning of violation outbreaks.

[0143] In some of the solutions described above in this application, a critical signal strength is generated to determine whether a selected area is approaching a critical state of violation outbreak. However, in its implementation, there is a lack of a signal generation method that can effectively capture the characteristics of the distribution system of violating stores approaching critical instability. Conventional signal generation methods cannot reflect the sensitivity characteristics of the violating system when it is close to an outbreak, and it is difficult to accurately reflect the distance between the system and the critical state of violation outbreak, thus failing to provide a reliable basis for subsequent critical state determination and early warning.

[0144] In response, this application further proposes a method for generating critical signal strength based on the results of cross-scale propagation analysis, see [link to relevant documentation]. Figure 5 The method includes: 501. Apply simulated perturbations to the results of cross-scale propagation analysis to obtain the propagation situation after perturbation.

[0145] 502. Based on the results of cross-scale propagation analysis and the propagation trend after disturbance, determine the spatiotemporal distribution variation of the density of illegal shops in the selected area.

[0146] 503. Based on the ratio of the change amplitude to the intensity of the simulated disturbance, determine the disturbance sensitivity metric, and use the disturbance sensitivity metric as the critical signal intensity.

[0147] For example, "applying simulated perturbations to the results of the cross-scale propagation analysis to obtain the propagation situation after the perturbation" aims to assess the system's stability or sensitivity by introducing controllable external disturbances to observe the system's response to the disturbances. For instance, various methods can be used to simulate the perturbations. One method is to superimpose a pre-defined, small-amplitude perturbation onto the input parameters of the cross-scale propagation analysis, such as increasing or decreasing parameters like the environmental stress index, store-level propagation rate, or state recovery rate by a fixed percentage, or randomly flipping a small proportion of the initial violation status of some stores. Another method is to modify certain parameters in the cross-scale propagation analysis model, such as adjusting the propagation weights or recovery rates between stores, and then rerun the model to obtain the propagation situation after the perturbation. In this way, a response state of the system under a specific perturbation is obtained, providing a basis for subsequent sensitivity analysis.

[0148] Based on this, the aim of "determining the magnitude of change in the spatiotemporal distribution of illegal shop density within the selected area based on the results of this cross-scale propagation analysis and the propagation trend after the disturbance" is to quantify the difference in the system's state before and after the disturbance, so as to intuitively reflect the system's response to the disturbance. Specifically, the magnitude of change is determined by calculating the difference in the spatiotemporal distribution of illegal shop density before and after the disturbance. For example, the difference in illegal shop density at each spatial location and time step is calculated, and then the absolute values ​​of these differences are statistically summarized, such as by summing or averaging, to obtain the overall magnitude of change. In addition, the magnitude of change is also determined by comparing the statistical characteristics of the illegal shop density distribution before and after the disturbance, such as changes in mean, variance, or kurtosis.

[0149] The aim of "determining a disturbance sensitivity metric based on the ratio of the change magnitude to the intensity of the simulated disturbance, and using this metric as the critical signal strength" is to standardize the system's response to disturbances, obtaining an index that objectively reflects the system's sensitivity, and using it as a warning signal for critical states. For example, the calculated change magnitude can be directly divided by the intensity of the simulated disturbance to obtain a raw sensitivity ratio. For instance, if the simulated disturbance intensity is a percentage change in the environmental pressure index, and the change magnitude is the total change in the density of violating shops, then the sensitivity metric is the quotient of the total change and the percentage change. Furthermore, logarithmic ratios are also used, or nonlinear functions are introduced to map the ratio, to better capture the characteristics of different sensitivity ranges, thereby more accurately characterizing the system's sensitivity.

[0150] The above technical solution utilizes the dynamic characteristic that the system's sensitivity to disturbances increases when it approaches a critical state, effectively solving the problem of the lack of signal generation methods in related technologies that can capture the near-critical instability characteristics of the distribution system of illegal shops. For example, by applying a controllable simulated disturbance to the results of cross-scale propagation analysis, the system can rely on the existing propagation trend to introduce artificially generated disturbances of controllable intensity, thus providing an accurate comparative basis for subsequent calculations of the system's response to disturbances. Compared to directly using the natural fluctuations of existing monitoring data to calculate sensitivity, the intensity of artificially simulated disturbances is controllable, and the resulting response better reflects the inherent sensitivity characteristics of the system itself. Based on this, by comparing the state differences of the system before and after disturbance, the spatiotemporal distribution variation of the density of illegal shops in the selected area can be determined, which can intuitively quantify the degree of state change of the system after being disturbed, accurately reflecting the system's response to the magnitude of the disturbance. The disturbance sensitivity metric is determined based on the ratio of the variation amplitude to the simulated disturbance intensity, and this ratio is used as the critical signal intensity. This ratio eliminates the interference of the disturbance intensity itself on the response amplitude, and the resulting sensitivity metric accurately reflects the system's sensitivity to disturbances. As the system gets closer to the critical state of a violation outbreak, the higher its sensitivity to disturbances, the intensity of the obtained critical signal accurately reflects the distance of the system from the critical state, providing accurate and reliable input for subsequent critical state determination and early warning output, thereby realizing proactive monitoring and trend early warning of the distribution evolution of violating stores.

[0151] In some embodiments described above in this application, a simulated perturbation is applied to the results of cross-scale propagation analysis to obtain the propagation state after the perturbation, which is then used to calculate the perturbation sensitivity metric to obtain the critical signal strength. However, in its implementation, there is no clear and reasonable method for determining the perturbation object and the perturbation amplitude. If the perturbation is applied arbitrarily, it will either cause the system state after the perturbation to deviate from the actual operating logic, or it will fail to effectively stimulate the system's sensitive response, resulting in inaccurate critical signal strength calculated subsequently, and failing to provide a reliable basis for critical state determination.

[0152] In response, this application further proposes a method for applying simulated perturbations to the results of the cross-scale propagation analysis to obtain the perturbed propagation situation, including: The environmental pressure index is extracted from the results of the cross-scale propagation analysis, and a preset proportion of the environmental pressure index is used as the perturbation amplitude.

[0153] The disturbance amplitude is superimposed on the environmental pressure index to obtain the disturbed environmental pressure index.

[0154] The cross-scale propagation analysis was re-executed using the environmental pressure index after the disturbance to obtain the propagation trend after the disturbance.

[0155] For example, the results of this cross-scale propagation analysis refer to the store-level propagation trend, business district-level contagion trend, and city-level evolution trend generated after performing cross-scale propagation analysis on the spatiotemporal distribution of non-compliant store density within a selected area, as well as the spatiotemporal distribution of non-compliant store density inferred in the process. These results are typically stored in a multi-dimensional data structure (e.g., datasets containing time series, spatial grids, or graph structures), comprehensively reflecting the evolution of non-compliant stores at different scales. The environmental pressure index is the core factor driving the evolution of the distribution of non-compliant stores, and its value reflects the comprehensive environmental pressure experienced by the selected area. This index is a single numerical value, and also a field quantity that varies over time as a sequence or spatial distribution. The preset ratio refers to the proportional coefficient used to determine the perturbation amplitude; its value is a fixed percentage (e.g., 5%, 10%), or a range value dynamically adjusted based on historical data or expert experience (e.g., randomly selected between 2% and 15%). The perturbation amplitude is the specific perturbation amount calculated based on the environmental pressure index and the preset ratio; it is a positive value (increasing pressure) or a negative value (decreasing pressure), used to simulate small fluctuations in the external environment. The superposition operation refers to combining the calculated perturbation amplitude with the original environmental pressure index, for example, through simple arithmetic addition or subtraction, to generate a new, perturbed environmental pressure index. This perturbed environmental pressure index, obtained after the superposition operation and incorporating simulated perturbations, serves as input for subsequent re-execution of the cross-scale propagation analysis. Re-execution of this cross-scale propagation analysis involves using the same or similar models and algorithms as the original analysis, but with the perturbed environmental pressure index as the driving input, to re-evaluate the evolution of the distribution of non-compliant stores. This may involve recalculating the store-level propagation trend, the business district-level contagion trend, and the city-level evolution trend, as well as updating the spatiotemporal distribution of non-compliant store density. The perturbed propagation trend is the output obtained after re-executing the cross-scale propagation analysis; it reflects the new state that the non-compliant store distribution evolution system may exhibit under simulated perturbations.

[0156] The above technical solutions allow for the selection of appropriate perturbation targets and the determination of perturbation amplitude based on the proportion of the original core driving forces. This ensures that the propagation state after perturbation conforms to the actual evolutionary laws without disrupting the original system operating logic, providing a reliable foundation for accurate calculation of the critical signal strength. For example, the environmental pressure index can be extracted from the cross-scale propagation analysis results as the target of perturbation. Since the environmental pressure index is itself a core driving force in the evolution of the distribution of illegal shops, perturbing this driving force accurately reflects the system's true sensitivity to perturbations, conforming to the inherent logic of critical state identification. This avoids the sensitivity response distortion problem caused by perturbing non-driving links, ensuring that the subsequent perturbation response reflects the system's true critical proximity. Using a preset proportion of the environmental pressure index as the perturbation amplitude ensures that the perturbation amplitude matches the original system's driving level, avoiding the drawbacks of fixed-amplitude perturbations. Specifically, a perturbation that is too small to elicit a system response when the driving level is high, or a perturbation that is too large when the driving level is low, causing the system state to deviate from the actual operating range, ensures that the perturbation remains within a reasonable range. The perturbation amplitude is superimposed on the environmental pressure index to obtain the perturbed environmental pressure index. This operation retains the original environment-driven framework, adding only a small perturbation, and does not change the overall logic of the system's original operation, ensuring that the post-perturbation state conforms to the basic laws of actual evolution. Based on this, cross-scale propagation analysis is re-performed using the perturbed environmental pressure index to obtain the post-perturbation propagation trend. This operation can obtain complete and logically consistent post-perturbation system operation results, ensuring that subsequent calculations of system change amplitudes are based on the complete propagation evolution logic, thus improving the accuracy of subsequent critical signal strength calculations.

[0157] In some embodiments described above in this application, the variation range of the spatiotemporal distribution of the density of non-compliant shops within a selected area is used to calculate the critical signal strength, providing a data basis for subsequent determination of the critical state of a violation outbreak. However, in its implementation, the specific calculation method for the variation range is not clearly defined. Different calculation logics will yield significantly different variation range results, failing to guarantee the accuracy of the variation range calculation. This, in turn, will lead to deviations in the critical signal strength calculated subsequently, affecting the accuracy of the determination of the critical state of a violation outbreak and the early warning results, and failing to meet the need for forward-looking and accurate early warning.

[0158] In response, this application further proposes to determine the spatiotemporal distribution variation of the density of non-compliant shops within the selected area, specifically including the following steps: The spatiotemporal distribution of the density of the first non-compliant store is extracted from the results of this cross-scale propagation analysis, and the spatiotemporal distribution of the density of the second non-compliant store is extracted from the propagation trend after the disturbance.

[0159] The difference between the spatial and temporal distribution of the density of the first non-compliant store and the spatial and temporal distribution of the density of the second non-compliant store is calculated to obtain the density deviation at each spatial location.

[0160] By statistically summarizing the density deviations at various spatial locations, the spatiotemporal distribution variation of the density of the non-compliant shops can be obtained.

[0161] In detail, the core of the steps in extracting the spatiotemporal distribution of the first non-compliant store density from the results of the cross-scale propagation analysis, and extracting the spatiotemporal distribution of the second non-compliant store density from the perturbed propagation state, lies in acquiring the spatiotemporal data of the non-compliant store density under two different states: the unperturbed baseline state and the response state after simulated perturbation. This step aims to provide clear, accurate, and comparable raw data for subsequent calculations of the magnitude of change. For example, the pre-calculated cross-scale propagation analysis results are retrieved from the storage medium via a data interface or file read, and the spatiotemporal distribution data of the first non-compliant store density is parsed from it. The perturbed propagation state data is received from another storage location or via real-time data stream, and the spatiotemporal distribution of the second non-compliant store density is extracted. Furthermore, specific data processing modules or functions are invoked, which are responsible for filtering and formatting the required spatiotemporal distribution data of the non-compliant store density from the raw simulation output. For example, by specifying the time range and spatial resolution, the required spatiotemporal distributions of the first and second non-compliant store densities are accurately extracted from the large-scale simulation results.

[0162] The step of calculating the difference between the spatial distributions of the first and second non-compliant shop densities to obtain the density deviation at each spatial location aims to quantify the local impact of the simulated disturbance on the density of non-compliant shops at each specific spatial location within a selected area. Precise spatial correspondence ensures the effectiveness and accuracy of the comparison. For example, using a point-by-point (or grid-by-grid) comparison method, for each spatial unit (e.g., a geographic grid or a business district) in the spatiotemporal distribution of the first non-compliant shop density, the corresponding spatial unit in the spatiotemporal distribution of the second non-compliant shop density is found. Then, the non-compliant shop density values ​​of these two units are subtracted to obtain the density deviation for that spatial unit. Furthermore, the spatial analysis functions of a Geographic Information System (GIS) are utilized to overlay the two spatiotemporal distributions as layers and perform raster calculations or vector data attribute table difference operations. For example, for each geographic coordinate point or region, the numerical difference in non-compliant shop density before and after the disturbance is directly calculated, generating a new data layer containing the density deviation at each spatial location.

[0163] In the step of statistically summarizing the density deviations at various spatial locations to obtain the spatiotemporal distribution variation of the density of the violating shops, its role is to integrate local, discrete density deviation information into a quantitative indicator that reflects the overall responsiveness of the entire selected area. This summarization method allows for a comprehensive assessment of the system's sensitivity to disturbances. For example, the absolute values ​​of the density deviations at all spatial locations can be summed, or statistical indicators such as the average, maximum, and variance can be calculated to quantify the overall variation. For instance, the L1 or L2 norm of the density deviations of all spatial units can be calculated as a measure of the overall variation. Furthermore, a weighted average method is also used for statistical summarization, where the weights are determined based on factors such as the importance of the spatial location, its area size, or population density. For example, higher weights are assigned to the density deviations in urban centers to more accurately reflect the contribution of changes in key areas to the overall variation.

[0164] The above technical solution clarifies the specific calculation steps for the spatiotemporal distribution variation of illegal store density. By extracting the first and second spatiotemporal distributions of illegal store density from the original cross-scale propagation analysis results and the propagation trend after disturbance, the density data of the original state and the state after disturbance are clearly distinguished, avoiding data source confusion and providing a clear and accurate original data foundation for subsequent calculations. The difference between the illegal store densities at corresponding spatial locations in the two distributions is calculated, obtaining the density deviation at each spatial location. This point-by-point comparison method avoids calculation errors caused by spatial misalignment, accurately reflects the change in illegal density at each spatial location caused by the simulated disturbance, and ensures the accuracy of local change calculations. The density deviations at all spatial locations are statistically summarized to obtain the overall variation of the spatiotemporal distribution of illegal store density within the entire selected area. The local changes are integrated into a quantitative result that reflects the overall change, providing accurate input for subsequent calculations of disturbance sensitivity (i.e., critical signal strength). Therefore, this application can ensure the accuracy of the variation calculation, providing reliable support for the accurate calculation of the subsequent critical signal strength, thereby improving the reliability of the early warning results and meeting the needs of forward-looking and accurate early warning.

[0165] In some of the solutions described above in this application, a disturbance sensitivity metric is proposed to be determined based on the ratio of the change amplitude to the intensity of the simulated disturbance. This disturbance sensitivity metric is then used as a critical signal strength to determine the critical state of a violation outbreak. However, in its implementation, only the ratio of the change amplitude to the disturbance intensity is considered. The sensitivity metric is not corrected for the degree of occupancy of the carrying capacity by the current density of violating shops in the selected area. This ignores the objective law that the closer the violation density is to the area's carrying capacity limit, the closer the system itself is to an unstable critical state, and the higher its sensitivity to disturbances should be. This leads to the obtained disturbance sensitivity metric deviating from the actual system stability state, resulting in an inaccurate critical signal strength and affecting the accuracy of subsequent critical state determination and early warning.

[0166] In response, this application further proposes a method for determining the disturbance sensitivity measure based on the ratio of the change amplitude to the intensity of the simulated disturbance, including: Divide the magnitude of the change by the intensity of the simulated disturbance to obtain the original sensitivity ratio.

[0167] A sensitivity correction coefficient is determined based on the ratio of the current density of non-compliant stores to the maximum carrying capacity within the selected area. The value of this sensitivity correction coefficient increases as the ratio of the current density of non-compliant stores to the maximum carrying capacity within the selected area increases.

[0168] Multiply the original sensitivity ratio by the sensitivity correction coefficient to obtain the disturbance sensitivity measure.

[0169] For example, the magnitude of change refers to the overall difference or fluctuation in the spatiotemporal distribution of non-compliant shop density within a selected area before and after the application of a simulated disturbance. It quantifies the system's response strength to external disturbances. This magnitude of change is obtained by calculating the sum or average of the absolute differences in non-compliant shop density across all spatial locations before and after the disturbance, or by calculating the statistical distance (e.g., Euclidean distance, KL divergence, etc.) between the distributions of non-compliant shop density before and after the disturbance. The intensity of the simulated disturbance refers to the quantified value of the external disturbance applied to the system, used to simulate external shocks that may lead to the evolution of the non-compliant shop distribution. This intensity is set as a fixed percentage of the environmental stress index; for example, an increase or decrease of 5% in the environmental stress index is taken as the disturbance intensity. Alternatively, based on historical data analysis, the intensity of the simulated disturbance can be set as the standard deviation or maximum fluctuation range of the environmental stress index within a specific time window. Dividing the magnitude of change by the intensity of the simulated disturbance yields the original sensitivity ratio. The original sensitivity ratio initially reflects the system's response to a unit disturbance intensity. It is calculated by directly dividing the change amplitude by the simulated disturbance intensity, or by calculating on a logarithmic scale, i.e., by calculating the difference between the logarithmic value of the change amplitude and the logarithmic value of the simulated disturbance intensity.

[0170] Building upon this, this application further considers the ratio of the current density of non-compliant shops within the selected area to the upper limit of carrying capacity. The current density of non-compliant shops within the selected area refers to the number or proportion of non-compliant shops per unit area or unit business district within the selected area at the current monitoring time. This is calculated by statistically analyzing real-time or recent monitoring data to determine the ratio of the total number of non-compliant shops to the total area of ​​the area, or by spatially aggregating shop location data within the area using a Geographic Information System (GIS) to calculate the density of non-compliant shops in each grid or sub-area. The upper limit of carrying capacity refers to the maximum density of non-compliant shops that the selected area can accommodate without systemic instability or severe negative impacts. This is set based on historical data analysis as the highest historical value that the density of non-compliant shops within the area has never exceeded, or by predicting it through a regression model between regional socio-economic, environmental, and other indicators and the density of non-compliant shops. Based on this ratio, a sensitivity correction coefficient is determined. This sensitivity correction coefficient is an adjustment factor used to correct the original sensitivity ratio, making it more accurately reflect the true sensitivity of the system under different carrying pressures. This coefficient is designed as a non-linear function, such as an exponential or sigmoid function. Its input is the ratio of the current density of non-compliant shops within the selected area to the maximum carrying capacity, and its output is a correction coefficient. This function should ensure that the correction coefficient increases as the ratio increases. Alternatively, a piecewise linear function can be used, setting different growth slopes for the correction coefficient based on different intervals of the ratio. Multiplying the original sensitivity ratio by this sensitivity correction coefficient yields the disturbance sensitivity measure. This disturbance sensitivity measure is a system sensitivity index corrected for carrying capacity constraints; it comprehensively considers the system's response strength to external disturbances and the system's current carrying capacity pressure state.

[0171] Through the above technical solution, the calculation of disturbance sensitivity measurement not only considers the system's direct response to disturbances but also incorporates the system's current carrying capacity stress. For example, by introducing a sensitivity correction coefficient and increasing its value as the ratio of the current density of illegal shops in the selected area to the upper limit of carrying capacity increases, this application can accurately capture the objective law that the system's sensitivity to external disturbances increases when the density of illegal shops approaches the carrying capacity limit. This correction mechanism enables the obtained disturbance sensitivity measurement to more realistically and precisely reflect the early signals of system instability, avoiding the problem of inaccurate critical signal strength caused by ignoring carrying capacity stress. Therefore, the disturbance sensitivity measurement as the critical signal strength is more accurate, thereby improving the accuracy of subsequent determinations of whether the selected area is approaching the critical state of illegal outbreak and the prediction of the critical arrival time, providing a more reliable basis for timely and effective preventive intervention decisions.

[0172] In some of the embodiments described above in this application, a method is proposed to compare the critical signal strength with a dynamic threshold, determine whether a selected area is approaching the critical state of a violation outbreak, and estimate the critical arrival time to generate critical early warning information to complete the trend warning of the distribution evolution of violating stores. However, in its implementation, there is a lack of clear judgment rules and critical arrival time prediction logic, which makes it impossible to obtain clear and reliable early warning results, and it is also difficult to provide clear critical arrival time to support preventive intervention decisions. It is easy to have problems such as inaccurate judgment and large prediction time deviation, which cannot meet the actual needs of proactive early warning.

[0173] In response, this application further proposes to compare the critical signal strength with a dynamic threshold to determine whether the selected area is approaching a critical state for a violation to occur and to estimate the critical arrival time, generating the critical warning information, including: When the intensity of the critical signal exceeds the dynamic threshold, the selected area is determined to be approaching the critical state of a violation outbreak. When the intensity of the critical signal does not exceed the dynamic threshold, the selected area is determined not to be approaching the critical state of a violation outbreak.

[0174] When determining that the selected area is approaching the critical state of a violation outbreak, the remaining time required for the critical signal strength to reach the preset outbreak threshold is estimated based on the rate of change of the critical signal strength over continuous monitoring time, and this is taken as the critical arrival time.

[0175] The determination result of the critical state approaching the outbreak of violation is combined with the critical arrival time to generate the critical warning information.

[0176] The critical signal strength is a quantitative indicator that measures how close the system's current state is to the threshold of a violation outbreak and how sensitive the system is to external disturbances. It reflects the degree to which the system's internal structure and dynamic characteristics respond to external environmental pressures. This critical signal strength is calculated based on the system's response to simulated disturbances, for example, by the ratio of the magnitude of the system state change to the intensity of the disturbance after applying a small disturbance. Furthermore, it is also constructed by analyzing the volatility, correlation, or nonlinearity of key internal system parameters (such as the density of violating shops and the propagation rate). When these characteristics exhibit abnormal changes, the critical signal strength increases accordingly.

[0177] This dynamic threshold serves as a reference boundary for determining whether the system has entered a critical state. Its value is not fixed but adaptively adjusts based on external environmental conditions, historical data, or the system's own state. This dynamic threshold is dynamically generated through a machine learning model by statistically analyzing the distribution of critical signal intensity during historical violation outbreaks and combining this with factors such as the current region's environmental pressure index and carrying capacity. Alternatively, it can be adjusted in real-time based on the system's stability characteristics under different operating modes, by monitoring the statistical properties of system parameters (such as mean, variance, and trend) to ensure the threshold accurately reflects the current system's actual critical state.

[0178] The step of determining whether a selected area is approaching a critical state for a violation outbreak aims to perform a binary classification of the current system state, clearly determining whether the selected area has entered a critical zone requiring high attention, thus providing a basis for subsequent early warning and intervention decisions. This determination is achieved by directly comparing the real-time calculated critical signal strength with the current dynamic threshold. If the former is greater than the latter, it is determined to be approaching a critical state; otherwise, it is determined not to be approaching. To improve the robustness of the determination, a certain hysteresis or smoothing mechanism is also introduced. For example, it is only determined to be approaching a critical state when the critical signal strength exceeds the dynamic threshold for multiple consecutive monitoring cycles, or exceeds the dynamic threshold by a certain magnitude, to avoid false alarms.

[0179] The rate of change of the critical signal strength over continuous monitoring time reflects the speed and direction of its evolution over time, and is a key indicator for assessing the trend of system state evolution. This rate of change is obtained by calculating the ratio of the difference between the critical signal strengths at two adjacent monitoring times to the time interval, i.e., the first-order difference. Furthermore, more complex time series analysis methods, such as moving average, exponential smoothing, or Kalman filtering, are used to process the critical signal strength sequence to obtain a more stable and representative rate of change.

[0180] The preset outbreak threshold is the critical signal strength value at which the system is considered to have fully entered a violation outbreak state; it serves as a warning line set by the early warning system. This preset outbreak threshold is set based on the maximum or average critical signal strength recorded during historical large-scale violation outbreak events, combined with expert experience. Alternatively, it can be determined through simulation experiments or stress tests to identify the critical signal strength at which an irreversible violation outbreak will occur, thereby establishing the threshold.

[0181] This estimation of the remaining time required for the critical signal strength to reach a preset burst threshold serves as a quantitative time window, indicating how much time is left before the system fully erupts, thus providing valuable time for regulatory authorities to formulate preventative intervention measures. The estimation is based on the current critical signal strength, the preset burst threshold, and the current rate of change, and is performed using linear extrapolation. Furthermore, nonlinear regression models or time series forecasting models are also used, combined with historical data and current trends, to predict the future trajectory of the critical signal strength, thereby providing a more accurate estimate of the remaining time.

[0182] The step of combining the determination result of the approaching critical state of a violation outbreak with the critical arrival time to generate a critical warning message aims to integrate discrete determination results and continuous time estimates into a complete and easy-to-understand warning report, allowing users to quickly obtain key information and take action. This combination encapsulates the determination result (e.g., "approaching critical state" or "not approaching critical state") with the estimated critical arrival time (e.g., "expected to reach the outbreak threshold in X hours / days") in a structured text or data format. Furthermore, it includes additional information such as confidence intervals, risk levels, and recommended intervention measures, forming a multi-dimensional and actionable warning report.

[0183] The above technical solution clearly defines whether the evolution of the distribution of violating stores is approaching a critical state and provides a quantitative estimate of the critical arrival time, thus solving the problems of vague critical state determination rules and unreasonable prediction logic in related technologies. For example, by comparing the critical signal strength with a dynamic threshold, the system can adaptively determine the violation risk level of the current area based on real-time data and environmental changes. When the critical signal strength exceeds the dynamic threshold, it is immediately determined to be approaching a critical state of violation outbreak. This allows the early warning system to promptly capture early signals of system instability, avoiding misjudgments or missed reports caused by fixed thresholds. After determining that it is approaching a critical state, based on the rate of change of the critical signal strength over continuous monitoring time, the remaining time required for the critical signal strength to reach the preset outbreak threshold, i.e., the critical arrival time, can be dynamically estimated. This prediction method based on the real-time rate of change makes the prediction results closer to the actual evolution process, providing regulatory authorities with a precise time window to take preventive intervention measures before a large-scale outbreak of violations, thus improving the timeliness and accuracy of early warnings. By combining the judgment result of the critical state approaching the outbreak of violations with the critical arrival time, a complete critical early warning information including state judgment and time prediction is generated. This provides decision-makers with a comprehensive and clear early warning basis, greatly enhancing the practicality and guidance of the monitoring and trend early warning method for the distribution and evolution of violating stores, and realizing the transformation from passive response to proactive prevention.

[0184] In some of the embodiments described above in this application, a method for estimating the critical arrival time is proposed to obtain early warning information of the critical state of a violation outbreak. However, in the process of estimating the critical arrival time, the simple linear estimation is based only on the current rate of change to derive the remaining time, without considering the changing trend of the critical signal strength with the process of violation spread. During the spread of violation, the rate of change of the critical signal strength often gradually accelerates as the scale of violation expands. The estimation result obtained by simple linear extrapolation has a large error and cannot obtain an accurate critical arrival time, which will affect the reliability of the early warning and is not conducive to carrying out preventive intervention in advance.

[0185] In response, this application further proposes a method for estimating the remaining time required for the critical signal strength to reach a preset burst threshold based on the rate of change of the critical signal strength over continuous monitoring time, as the critical arrival time. This method specifically includes the following steps: The critical signal strength sequence is extracted from the critical signal strength sequence of continuous monitoring time, and the change in critical signal strength between these two time points is calculated as the current rate of change. This step aims to obtain the instantaneous rate of change of the violation outbreak trend in the current state of the system. By focusing on the two most recent monitoring time points, it ensures that the calculated rate of change best reflects the current dynamic evolution and avoids interference from earlier data in judging the current trend. In practice, the critical signal strength sequence is managed through timestamp indexes or queue data structures. For example, the system maintains a fixed-length sliding window. Each time a new critical signal strength value is detected, it is added to the window, the oldest value is removed, and then the two newest values ​​are taken from the window for difference calculation. Alternatively, a database query can be used to select the two newest records from the stored historical critical signal strength data, sorted by timestamp, for calculation each time a calculation is needed.

[0186] The difference between the preset outbreak threshold and the critical signal strength at the current monitoring moment is divided by the current rate of change to obtain the linearly extrapolated remaining time. This step provides a preliminary estimate of the time required to reach the preset outbreak threshold based on the current rate of change. It offers a basic, linear time prediction as a starting point for subsequent adjustments. This calculation is performed directly through arithmetic operations; for example, dividing the difference between the preset outbreak threshold and the current critical signal strength by the current rate of change. The preset outbreak threshold is a pre-defined critical value representing the outbreak of a violation, determined based on expert experience, historical data analysis, or simulation experiments.

[0187] Based on the changing trend of the rate of change over continuous monitoring time intervals, an acceleration factor is determined. This acceleration factor is then used to correct the remaining time of the linear extrapolation, yielding the critical arrival time. This step is one of the core technical concepts of this application, aiming to overcome the limitations of simple linear extrapolation. By analyzing the changing trend of the rate of change itself and introducing an acceleration factor, the actual situation of the rate potentially accelerating during the spread of violations can be more accurately reflected, thereby correcting the deviation of the linear prediction and obtaining a more realistic critical arrival time. The changing trend of the rate of change is obtained by calculating the second derivative or difference of the rate of change over multiple consecutive time intervals. For example, the changing rate sequence of the most recent three or more monitoring time intervals is calculated, and then the trend of these rates (whether it is accelerating, decelerating, or remaining constant) is analyzed. The acceleration factor is set according to this trend. For example, if the rate shows an accelerating growth trend, the acceleration factor is greater than 1, resulting in a shorter estimated time. If the rate shows a decelerating trend, the acceleration factor is less than 1, resulting in a longer estimated time. In addition, a nonlinear model (such as an exponential model or a polynomial model) is constructed by fitting historical changing rate data to predict future changing rates, and the acceleration factor is determined based on the difference between this model and the linear prediction.

[0188] By employing the aforementioned technical solutions, the inaccuracy of simple linear extrapolation in predicting critical arrival times is addressed. By incorporating historical trends in critical signal strength to correct the linear prediction results, a more accurate critical arrival time that aligns with actual evolutionary patterns can be obtained, thus improving the reliability of early warning results. For example, by selecting signals from the two most recent monitoring times to calculate the current rate of change, the latest violation propagation trend can be reflected, avoiding interference from earlier historical data and ensuring that the current rate of change matches the latest violation evolution. Based on this, a basic prediction result is first obtained through linear extrapolation, retaining the fundamental advantage of the simplicity and ease of implementation of the linear extrapolation method. Furthermore, an acceleration factor is determined based on the changing trend of the rate of change between continuous monitoring times, and this acceleration factor is used to correct the remaining time of the linear extrapolation. This fully considers the objective law that the rate of change of critical signal strength often accelerates as the scale of violation expands during the spread of violation, correcting the prediction error caused by simple linear extrapolation. This makes the obtained critical arrival time more consistent with the actual violation evolution trend, thereby improving the accuracy of the prediction results. This provides a more precise time reference for preventative intervention before a violation outbreak, helping decision-makers to take more timely and effective measures to prevent large-scale outbreaks of violations.

[0189] In some of the embodiments described above in this application, it is proposed that after generating critical warning information, it is necessary to verify it before outputting trend warning results. However, in this process, there is a lack of verification methods that combine the physical laws of the evolution system of illegal stores. It is impossible to rule out erroneous warning results that do not conform to the laws of dynamics due to model deviation and calculation error in the process of cross-scale propagation analysis and critical state determination. Erroneous warning information will interfere with preventive intervention decisions and cannot guarantee the accuracy and reliability of warning results.

[0190] To address this, this application further proposes verifying the critical early warning information using entropy increase constraints and energy conservation constraints, including: extracting the spatial distribution of the density of non-compliant stores within the selected area from the results of the cross-scale propagation analysis; calculating the system entropy value based on the spatial distribution; and comparing the direction of change of the system entropy value over continuous monitoring time. When the system entropy value monotonically decreases with time, the critical early warning information is determined to have failed the entropy increase verification. Based on the environmental pressure index and the density of non-compliant stores within the selected area, the environmental input energy is calculated. Based on the corrected store-level state recovery rate and the density of non-compliant stores within the selected area, the dissipated energy is calculated. The environmental input energy and the dissipated energy are compared; when the difference between the environmental input energy and the dissipated energy exceeds a preset tolerance, the critical early warning information is determined to have failed the energy conservation verification. When the critical early warning information simultaneously passes both the entropy increase verification and the energy conservation verification, the critical early warning information is determined to have passed the physical consistency verification.

[0191] For example, when verifying the critical warning information, the spatial distribution of the density of non-compliant shops within the selected area is extracted from the results of the cross-scale propagation analysis. This spatial distribution aims to obtain the geographical distribution of non-compliant shops within the selected area, represented as a gridded density map, where each grid cell represents the density of non-compliant shops within it. Alternatively, it can be represented as vector data based on a Geographic Information System (GIS), where each shop or sub-region is assigned a corresponding non-compliance density value. For instance, the selected area is divided into several sub-regions, and the number or density of non-compliant shops in each sub-region is counted, thus forming a discrete spatial distribution data. Another approach is to convert the discrete shop data into a continuous density field using an interpolation algorithm.

[0192] The system entropy is calculated based on this spatial distribution. System entropy is an indicator that measures the degree of disorder or information uncertainty within a system. Various methods are used to calculate system entropy. For example, based on this spatial distribution, the selected area is divided into N non-overlapping sub-regions, and the proportion p_i of the density of illegal shops in each sub-region to the total density is calculated. Then, the system entropy is calculated using the Shannon entropy formula H = -Σp_i × log(p_i). Alternatively, generalized entropy forms such as Renyi entropy or Tsallis entropy are also used to accommodate the quantification requirements of disorder for different system characteristics.

[0193] The direction of change of the system's entropy value is compared over continuous monitoring periods. This step utilizes the fundamental physical law of entropy increase during the evolution of open systems. During continuous monitoring, the system records its current entropy value. By comparing the current entropy value with the previous entropy value, the direction of entropy change is determined. For example, if the current entropy value is less than the previous entropy value, it indicates that the system entropy value is monotonically decreasing over time. If a monotonically decreasing entropy value is observed across multiple continuous monitoring periods, the evolutionary trend is considered inconsistent with the principle of entropy increase, thus determining that the critical warning information has failed entropy increase verification. Another comparison method is to calculate the average rate of change of the entropy value within a certain time window. If the average rate of change is negative and exceeds a preset threshold, verification is deemed unsuccessful.

[0194] Based on the environmental pressure index and the density of non-compliant shops within the selected area, the environmental input energy is calculated. The environmental input energy characterizes the driving force of the external environment on the evolution of the non-compliant shop system. The calculation of the environmental input energy is determined by the product of the environmental pressure index and the density of non-compliant shops within the selected area, or by a more complex functional relationship. For example, the selected area is divided into multiple sub-regions. For each sub-region, the environmental pressure index is multiplied by the local density of non-compliant shops in that sub-region to obtain the local environmental input energy. Then, the local environmental input energies of all sub-regions are summed to obtain the total environmental input energy. Alternatively, a nonlinear response function can be constructed, using the environmental pressure index and the density of non-compliant shops as inputs, to output the environmental input energy, thus providing a more refined characterization of the environmental driving force.

[0195] Based on this, dissipated energy is calculated using the corrected store-level state recovery rate and the density of non-compliant stores within the selected area. Dissipated energy characterizes the energy consumed by the system through store state recovery. The calculation of dissipated energy is determined based on the product of the corrected store-level state recovery rate and the density of non-compliant stores within the selected area, or a more complex functional relationship. For example, the violation status value of each store is extracted from the density of non-compliant stores within the selected area. For each store, the corrected store-level state recovery rate is multiplied by the store's violation status value to obtain the store's local dissipation. Then, the local dissipation values ​​of all stores are summed to obtain the dissipated energy. Another calculation method is to perform a weighted summation based on the area-averaged corrected store-level state recovery rate and the total density of non-compliant stores in the area to obtain the area-level dissipated energy.

[0196] The environmental input energy is compared with the dissipated energy. This step aims to verify the system's energy balance. The preset tolerance is an allowable range of energy differences used to determine if the system is in an energy conservation state. For example, the absolute difference between the environmental input energy and the dissipated energy is calculated; if this absolute difference exceeds a preset fixed tolerance, the verification fails. Alternatively, the relative difference between the environmental input energy and the dissipated energy is calculated (e.g., the difference divided by the input energy); if this relative difference exceeds a preset percentage tolerance, the verification fails. When the difference between the environmental input energy and the dissipated energy exceeds the preset tolerance, the critical warning information is deemed to have failed the energy conservation verification.

[0197] When the critical warning information passes both the entropy increase verification and the energy conservation verification, it is determined that the critical warning information has passed the physical consistency verification. This step is a comprehensive judgment. Only when the critical warning information simultaneously satisfies the entropy increase constraint and the energy conservation constraint is it considered to meet physical consistency, that is, the warning information is reliable and conforms to the system evolution law. This means that if any verification fails, even if the other verification passes, the physical consistency verification result is still considered to have failed.

[0198] The above technical solution addresses the lack of physical verification methods for critical early warning information in related technologies, improving the accuracy and reliability of early warning results. For example, by extracting the spatial distribution of the density of non-compliant shops within a selected area from the results of cross-scale propagation analysis, and calculating the system entropy value based on this, and then comparing the direction of change of the system entropy value over continuous monitoring time, this application utilizes the basic law of entropy increase in open systems to promptly identify abnormal early warning results that violate natural evolutionary trends. When the system entropy value monotonically decreases with time, it is determined that the critical early warning information has failed the entropy increase verification, thus effectively filtering out erroneous early warnings that do not conform to the macroscopic evolutionary laws. This application further calculates the environmental input energy based on the environmental pressure index and the density of non-compliant shops within the selected area, and calculates the dissipated energy based on the corrected shop-level state recovery rate and the density of non-compliant shops within the selected area. By comparing the environmental input energy and the dissipated energy, when the difference between the two exceeds the preset tolerance, it is determined that the critical early warning information has failed the energy conservation verification. This mechanism ensures the rationality of the non-compliant shop evolution system at the energy level and eliminates energy imbalance early warnings caused by model bias or calculation errors. Only when a critical early warning message passes both entropy increase verification and energy conservation verification is it deemed to have passed physical consistency verification. This dual verification mechanism, combining the entropy change law of macroscopic systems and the energy balance law of microscopic systems, can comprehensively and robustly verify the physical rationality of early warning information, avoiding misjudgments that may occur with single verification. This makes the output trend warning results more consistent with the actual laws of the evolution of non-compliant stores, providing a more accurate and reliable basis for subsequent preventive intervention decisions, avoiding interference from erroneous warnings, and thus enhancing the practical value and decision support capability of the entire method for monitoring and trend warning of the distribution evolution of non-compliant stores.

[0199] In some of the embodiments described above in this application, the energy input of the computing environment is proposed to complete the energy conservation verification of critical early warning information. However, in its implementation, it is not clear how to accurately calculate the total energy input of the environment in combination with the spatial differences in the distribution of violations. If the whole-domain calculation method is directly adopted, it cannot reflect the differentiated driving effect of environmental pressure in different regions on the evolution of violations, which can easily lead to the energy calculation results deviating from the actual situation, thereby affecting the accuracy of the verification results of critical early warning information.

[0200] To address this, this application further proposes a method for calculating environmental input energy, which includes: dividing a selected area into multiple sub-regions, and extracting the local non-compliant store density of each sub-region from the non-compliant store density within the selected area. For each sub-region, multiplying the environmental pressure index by the local non-compliant store density of the sub-region to obtain the local environmental input energy of the sub-region. The local environmental input energies of all sub-regions are then summed to obtain the total environmental input energy.

[0201] For example, the subdivision of a selected area aims to break down a large geographical area into smaller, more homogeneous units for management or analysis. This subdivision is achieved through various strategies, such as using a gridding method to uniformly divide the selected area into a series of regular rectangular or hexagonal grid cells. Alternatively, it can be based on existing geographic information such as administrative boundaries, commercial functional zoning, and population density distribution. Or, clustering algorithms can be used to dynamically generate interconnected sub-regions based on the similarity of shop distribution, transportation networks, or socioeconomic characteristics. This fine-grained subdivision allows for better capture of the heterogeneity within the area, laying the foundation for subsequent refined analysis.

[0202] After the selected area is divided into multiple sub-regions, it is necessary to obtain the density information of non-compliant stores within each sub-region. The extraction of local non-compliant store density is achieved through various methods. For example, it can be obtained by directly counting the number of non-compliant stores in each sub-region and dividing by the area of ​​that sub-region or the total number of stores. Spatial interpolation techniques, such as Kriging interpolation or inverse distance weighting, are also used to estimate the average non-compliant store density of the sub-region based on the non-compliant store density data of known points within and around the sub-region. Furthermore, the non-compliant status values ​​of all stores within a sub-region are aggregated and normalized by combining them with the area of ​​the sub-region. This step ensures that the non-compliant status of each sub-region can be accurately quantified, thereby reflecting the local spatial characteristics of the non-compliant behavior.

[0203] For each sub-region, the environmental stress index is multiplied by the density of locally violating shops within that sub-region to quantify the driving effect of environmental stress on the evolution of local violations. The environmental stress index represents the potential driving strength of the external environment on violations, while the density of locally violating shops reflects the actual scale of violations within that sub-region. Multiplying the two can be intuitively understood as the "energy" input generated by environmental stress at a specific scale of violations. In addition to simple multiplication, weighted multiplication is employed, such as assigning different weights based on the area or importance of the sub-region. Alternatively, a nonlinear function can be designed to combine the environmental stress index and the density of locally violating shops in a more complex way to better simulate the actual driving mechanism. In this way, the environmental driving energy experienced by each sub-region can be accurately calculated, reflecting its contribution to the overall system energy.

[0204] After calculating the local environmental input energy of all sub-regions, these local energies need to be aggregated to obtain the total environmental input energy of the entire selected region. The most direct method is to perform a simple arithmetic summation, directly adding the local environmental input energies of all sub-regions. Alternatively, a weighted summation method can be used, assigning different weights based on factors such as the area, population, and economic activity of each sub-region to reflect the differences in the contribution of different sub-regions to the overall environmental input energy. This accumulation process ensures that, considering spatial heterogeneity, the total environmental driving energy received by the entire selected region can be accurately obtained, providing comprehensive and accurate data for subsequent energy conservation verification.

[0205] The above technical solution addresses the issue of insufficient consideration of spatial differences in violation distribution when calculating environmental input energy. For example, by dividing the selected area into multiple sub-regions and extracting the local density of violating shops in each sub-region, this application can precisely capture the spatially uneven distribution characteristics of violations, avoiding the drawback of smoothing out local differences that may occur with global calculations. Based on this, multiplying the environmental pressure index by the local density of violating shops for each sub-region accurately quantifies the driving effect of environmental pressure on violations at the local scale, making the calculation of local environmental input energy closer to the actual dynamic process. By summing the local environmental input energy of each sub-region, this application can obtain an accurate and spatially representative total environmental input energy for the entire selected area. This method of calculating and summarizing by region improves the accuracy of environmental input energy calculation, thus providing more reliable data support for the energy conservation verification of the aforementioned critical warning information, and further enhancing the accuracy and credibility of the critical warning information verification results.

[0206] In some of the embodiments described above in this application, the calculation of dissipated energy is proposed to complete the energy conservation verification of the early warning information. However, in its implementation, the original solution does not specify the specific calculation method of dissipated energy, but only provides a conceptual explanation of the calculation. It does not combine the corrected state recovery rate with the violation status data of the store level for accurate statistics, which can easily lead to deviations in the dissipated energy calculation results, thereby affecting the accuracy of the early warning information verification results and failing to provide a reliable physical consistency verification basis for subsequent early warning output.

[0207] To address this, this application further proposes a method for calculating dissipated energy based on the corrected store-level state recovery rate and the density of non-compliant stores within a selected area. The specific steps include: extracting the violation state value of each store from the density of non-compliant stores within the selected area; multiplying the corrected store-level state recovery rate by the store's violation state value for each store to obtain the store's local dissipation; and summing the local dissipation of each store to obtain the dissipated energy.

[0208] To address the aforementioned issues, this application extracts the violation status value of each store from the density of non-compliant stores within a selected area when calculating dissipated energy. This non-compliant store density data is typically stored in a gridded or region-aggregated format. Extracting the violation status value of each store involves parsing this density data and reversing it to deconstruct it into records of the individual stores constituting that density. For example, if the density data is based on a Geographic Information System (GIS) layer, each store may correspond to a point feature with attributes (such as whether it is non-compliant and the degree of non-compliance), which can be directly retrieved by querying these point features. Alternatively, the non-compliant store density data may come directly from a database containing detailed information on all stores. In this database, each store has a unique identifier and a corresponding violation status field (e.g., 0 for compliance, 1 for minor violation, and 2 for serious violation). By traversing this database, the violation status value of each store can be extracted. This step aims to obtain micro-level violation status information for each individual store, laying the foundation for subsequent refined calculations.

[0209] For each store, the corrected store-level state recovery rate is multiplied by the store's violation status value to obtain the store's local dissipation. This corrected store-level state recovery rate is a value between 0 and 1, representing the store's tendency or speed of recovery from a violation status to a compliant status, which may be influenced by the contagion effect at the business district level. The store's violation status value is both discrete (e.g., 0 / 1, representing compliance / violation) and continuous (e.g., a violation index from 0 to 100). Multiplying the two, for example, if the violation status value is 1 (violation) and the recovery rate is 0.2, the local dissipation is 0.2. If the violation status value is 0 (compliance), the local dissipation is 0. Furthermore, the multiplication operation can also be understood as a weighted summation or dot product operation, matching the components of the recovery rate with the components of the violation status to obtain a comprehensive local dissipation. This step quantifies the dissipation contribution of an individual store, considering its individual violation degree and recovery capability.

[0210] The local dissipation of each store is summed to obtain the total dissipated energy. This summation operation is implemented directly using a simple summation algorithm. For example, in a loop, all stores are traversed, and the local dissipation calculated for each store is added to a sum variable to obtain the total dissipated energy. If the store data is stored in a distributed system, the summation operation is also implemented using a parallel computing framework (such as MapReduce). Each computing node is responsible for calculating the local dissipation of a portion of the stores, and then the results are aggregated to the central node for summation. This step aggregates the dissipation contributions of all individual stores to form the total system dissipated energy for the entire selected area.

[0211] The above technical solution clarifies the specific calculation path for dissipated energy. By statistically analyzing dissipation from a single-store perspective and then aggregating the results, the calculated dissipated energy can match the actual evolutionary state of the system, providing an accurate data foundation for energy conservation verification and thus improving the reliability of early warning information verification results. For example, the violation status value of each store is extracted from the density of violating stores within a selected area. Based on the single-store status information contained in the violation store density, the basic violation status data of each store is obtained. Compared with the general method of statistical analysis based on the entire region, this method can preserve the status differences of individual stores and avoid the status information being averaged out, providing an accurate basic input for subsequent accurate calculation of the dissipation of each store. For each store, the corrected store-level status recovery rate is multiplied by the store's violation status value to obtain the store's local dissipation. Here, the status recovery rate after cross-scale situational correction is combined to match the actual violation evolution recovery capability of the current region. At the same time, based on the calculation of the violation status of each store, it accurately reflects the actual dissipation contribution of a single store, avoiding the incorrect amortization of dissipation from stores in different states, and ensuring that the calculation of the local dissipation of each store conforms to the actual evolutionary law. By summing up the local dissipation amounts of each store, the dissipated energy is obtained. This store-by-store aggregation method comprehensively covers the dissipation contribution of all stores within the selected area, ensuring no local areas or individual stores are overlooked. The resulting dissipated energy accurately reflects the actual dissipation level of the entire system, providing accurate calculation results for subsequent energy conservation comparisons and guaranteeing the accuracy of early warning verification. This refined method of dissipated energy calculation, combined with the environmental input energy calculation method described above, can more accurately assess the system's energy balance, thus providing a more solid physical consistency verification basis for critical early warnings of violations and enhancing the reliability and credibility of the early warning results.

[0212] The following example will provide a more detailed explanation of the above technical solution: Suppose we need to monitor and provide trend forecasts for the distribution and evolution of non-compliant shops in a specific area of ​​a city (e.g., a commercial center). This area contains a large number of businesses, and historical data shows that violations are related to environmental factors and socioeconomic conditions. Current technologies typically only identify violations after they occur, failing to provide early warnings or effectively integrate multi-dimensional data or consider the cross-scale propagation characteristics of violations.

[0213] This method responds to the task of monitoring the distribution and evolution of non-compliant shops. The system continuously collects environmental monitoring data and socioeconomic indicators for the selected area. For example, environmental monitoring data may include real-time temperature and humidity data for the area, while socioeconomic indicators may include employment rate fluctuation data and regional operational status index. The system performs synthetic processing on these multidimensional data to obtain an environmental stress index. For instance, the system extracts temperature and humidity data from the environmental monitoring data and generates a meteorological stress index based on their deviations from historically determined temperature and humidity reference values. It also extracts employment rate fluctuation data and the regional operational status index from the socioeconomic indicators and generates a social stress index based on these data. For example, it performs a difference operation on the employment rate fluctuation data to obtain the direction and magnitude of employment rate changes, and combines this with a state adjustment coefficient determined by the regional operational status index to generate a social stress index. By combining the meteorological stress index and the social stress index, the environmental stress index for the selected area is determined. This process differs from related technologies that rely solely on a single data source for anomaly detection; instead, it comprehensively considers multiple external driving factors.

[0214] The system uses the environmental pressure index as a driving force and, based on the specific critical pressure threshold and carrying capacity constraints of the region, extrapolates the spatiotemporal distribution of the density of non-compliant shops within the selected area. For example, the system calculates the excess pressure amount when the environmental pressure index exceeds the critical pressure threshold, using this as an effective environmental driving force. Based on this effective environmental driving force and the current density of non-compliant shops, the system generates the increase in non-compliant density. Based on carrying capacity constraints (e.g., the upper limit of the carrying capacity of shops in the region) and the current density of non-compliant shops, a saturation inhibition factor is determined and used to correct the increase in non-compliant density, resulting in a suppressed increase. Combining the current density of non-compliant shops with the recovery attenuation amount determined by a preset recovery rate benchmark value, the spatiotemporal distribution of the density of non-compliant shops within the selected area is obtained. This extrapolation process can dynamically simulate the evolution of the density of non-compliant shops, compensating for the lack of dynamic modeling capabilities for non-compliant behavior under environmental driving forces in related technologies.

[0215] The system performs cross-scale propagation analysis on the extrapolated spatiotemporal distribution, generating store-level propagation trends, business district-level contagion trends, and city-level evolutionary trends. During the analysis, the system performs bidirectional modulation. For example, based on the current state of each store in the spatiotemporal distribution and pre-determined propagation relationships between stores (based on spatial distance and business type similarity), a store-level propagation trend is generated. Then, the store-level propagation trends are aggregated by business district to generate business district-level contagion trends, and these business district-level trends are used to adjust the store-level state recovery rate. For example, if a business district has a high contagion risk index, the state recovery rate of stores within that business district will be lowered, reflecting that stores are more difficult to restore to compliance in adverse environments. Based on the business district-level contagion trends and the contagion relationships between business districts, a city-level evolutionary trend is extrapolated, and this city-level evolutionary trend is used to adjust the store-level propagation rate. For example, if the overall violation density of the city is high, the propagation rate between stores will be higher, reflecting that violations are more easily spread at the city level. This cross-scale analysis and bidirectional modulation mechanism effectively characterizes the propagation process of violations from the micro to the macro level, a feature not found in other related technologies.

[0216] Based on the results of cross-scale propagation analysis, the system generates a critical signal strength. Specifically, the system applies a simulated perturbation to the results of the cross-scale propagation analysis; for example, it uses a preset proportion of the environmental pressure index as the perturbation amplitude and re-executes the cross-scale propagation analysis to obtain the propagation pattern after the perturbation. Then, by comparing the ratio of the spatiotemporal distribution change in the density of illegal shops before and after the perturbation to the intensity of the simulated perturbation, a perturbation sensitivity metric is determined and used as the critical signal strength. This critical signal strength reflects the system's sensitivity to external perturbations and is key to identifying the system's critical state.

[0217] The system compares the critical signal strength with a dynamic threshold to determine whether the selected area is approaching a critical state for a violation to erupt, and estimates the critical arrival time, generating a critical warning message. When the critical signal strength exceeds the dynamic threshold, the system determines that the area is approaching a critical state. In determining if it is approaching a critical state, the system estimates the remaining time required to reach a preset outbreak threshold based on the rate of change of the critical signal strength over continuous monitoring time, using this as the critical arrival time. For example, by calculating the change in the critical signal strength between the two most recent monitoring times and combining the change trend to determine an acceleration factor, the system corrects the linear extrapolation of the remaining time. This process transforms early warning work from a passive response to proactive prediction, providing sufficient advance warning time to support preventative intervention decisions, and is superior to related technologies.

[0218] The system verifies the critical early warning information using entropy increase constraints and energy conservation constraints. For example, it extracts the spatial distribution of the density of non-compliant stores from cross-scale propagation analysis results, calculates the system entropy value, and compares its direction of change over continuous monitoring time. If the system entropy value monotonically decreases with time, the early warning information is deemed to have failed the entropy increase verification. The system calculates the environmental input energy based on the environmental pressure index and the density of non-compliant stores, and calculates the dissipated energy based on the corrected store-level state recovery rate and the density of non-compliant stores, comparing the difference between the two. If the difference exceeds a preset tolerance, the early warning information is deemed to have failed the energy conservation verification. Only critical early warning information that passes both entropy increase and energy conservation verifications is deemed to have passed the physical consistency verification and is output as the trend early warning result for the selected area. This physical consistency verification mechanism ensures the reliability and scientific validity of the early warning information, further improving the accuracy of the early warning.

[0219] All the above-mentioned optional technical solutions can be combined in any way to form optional embodiments of this application, and will not be described in detail here.

[0220] The above are merely optional embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for monitoring and trend early warning of the distribution evolution of non-compliant stores based on spatiotemporal sequences, characterized in that, The method includes: In response to the task of monitoring the evolution of the distribution of illegal shops, a multidimensional synthesis is performed on the environmental monitoring data and socio-economic indicators of the selected area to obtain an environmental pressure index. Then, using the environmental pressure index as the driving force, the spatiotemporal distribution of the density of illegal shops in the selected area is deduced based on the specific critical pressure threshold and carrying capacity constraints of the area. Cross-scale propagation analysis is performed on the spatiotemporal distribution to generate store-level propagation trends, business district-level infection trends, and city-level evolution trends. During the analysis, bidirectional modulation is performed to correct the store-level state recovery rate with the business district-level infection trend and the store-level propagation rate with the city-level evolution trend. Based on the results of the cross-scale propagation analysis, a critical signal strength is generated. The critical signal strength is compared with a dynamic threshold to determine whether the selected area is approaching the critical state of a violation outbreak and to estimate the critical arrival time, thereby generating a critical early warning message. The critical warning information is verified using entropy increase constraints and energy conservation constraints, and the verified critical warning information is output as the trend warning result for the selected region.

2. The method according to claim 1, characterized in that, The task of monitoring the distribution and evolution of non-compliant shops involves performing multi-dimensional synthesis of environmental monitoring data and socio-economic indicators for selected areas to obtain an environmental stress index, including: Temperature and humidity data for the selected area are extracted from the environmental monitoring data. A meteorological pressure index is generated based on the deviations between the temperature data and the temperature reference value, and the deviations between the humidity data and the humidity reference value. The temperature reference value and the humidity reference value are determined by statistical analysis of historical monitoring data. Employment rate fluctuation data and regional operation status index of the selected region are extracted from the socio-economic indicators. Based on the employment rate fluctuation data and regional operation status index, a social stress index is generated. The environmental stress index is determined based on the meteorological stress index and the social stress index.

3. The method according to claim 1, characterized in that, The process of using the environmental pressure index as a driving force and, based on the region-specific critical pressure threshold and carrying capacity constraints, extrapolating the spatiotemporal distribution of the density of illegal shops within the selected area includes: Determine the excess pressure amount when the environmental pressure index exceeds the critical pressure threshold, and use the excess pressure amount as the effective environmental driving force. Based on the effective environmental driving force and the current density of non-compliant stores in the selected area, a non-compliance density growth rate is generated. Based on the carrying capacity constraint and the current density of non-compliant stores, a saturation inhibition factor is determined, and the increase in non-compliant density is corrected using the saturation inhibition factor to obtain the suppressed increase. Based on the current density of non-compliant stores and the preset recovery rate benchmark, the recovery attenuation amount is determined. Based on the suppressed growth amount and the recovery attenuation amount, the spatiotemporal distribution of the density of non-compliant stores in the selected area is obtained.

4. The method according to claim 3, characterized in that, The process of obtaining the spatiotemporal distribution of the density of non-compliant stores within the selected area based on the suppressed growth and the recovery decay includes: The difference between the suppressed growth and the recovery decay is calculated to obtain the net change in violation density; Add the current density of non-compliant stores to the net change in non-compliant store density to obtain the updated density of non-compliant stores in the current projection step; The updated density of non-compliant stores in the current simulation step is associated with the current simulation timestamp, which serves as the spatiotemporal distribution of the density of non-compliant stores in the selected area in the time slice of the current simulation step. Together with the time slices generated in the historical simulation steps, they constitute the spatiotemporal distribution of the density of non-compliant stores in the selected area.

5. The method according to claim 1, characterized in that, The process involves performing cross-scale propagation analysis on the spatiotemporal distribution to generate store-level propagation trends, business district-level infection trends, and city-level evolution trends. During the analysis, bidirectional modulation is performed to correct the store-level state recovery rate using the business district-level infection trend and the store-level propagation rate using the city-level evolution trend. This includes: Based on the current state of each store in the spatiotemporal distribution and the propagation relationship between stores, the store-level propagation situation is generated. The propagation relationship between stores is a static connection relationship that is predetermined based on the spatial distance between stores and the similarity of business types. The store-level propagation trends are aggregated by business district to generate the business district-level infection trends, and the store-level state recovery rate is corrected based on the business district-level infection trends. Based on the aforementioned business district-level transmission trend and the transmission relationship between business districts, the city-level evolution trend is deduced and generated, and the store-level transmission rate is corrected using the city-level evolution trend.

6. The method according to claim 5, characterized in that, The process of generating the store-level propagation situation based on the current state of each store in the spatiotemporal distribution and the propagation relationship between stores includes: The connection weights of the propagation relationships between stores are determined based on the spatial distance between stores and the similarity of business types. For each compliant store, the amount of propagation impact on the compliant store is determined based on the current status of the non-compliant stores that have a propagation relationship with the compliant store, the connection weight, and the store-level propagation rate. Based on the propagation impact and the current status of the compliant stores, the state transition trend of the compliant stores is determined, and the set of state transition trends of each store is taken as the store-level propagation situation.

7. The method according to claim 5, characterized in that, The process of generating the city-level evolutionary trend based on the business district-level transmission pattern and the transmission relationship between business districts includes: Based on the intensity of pedestrian interaction and the similarity of commercial functions between business districts, the contagion weight of the contagion relationship between the business districts is determined; For each business district, based on the infection risk index of the business district in the business district-level infection situation, and the infection weight between the business district and other business districts, the infection contribution of the business district to the city as a whole is calculated. Based on the infection contribution of each business district and the city's violation growth rate, the city-level evolution trend is deduced.

8. The method according to claim 1, characterized in that, The generation of the critical signal strength based on the results of the cross-scale propagation analysis includes: The results of the cross-scale propagation analysis are subjected to simulated perturbation to obtain the propagation situation after perturbation; Based on the results of the cross-scale propagation analysis and the propagation trend after the disturbance, the spatiotemporal distribution variation of the density of non-compliant shops in the selected area is determined; Based on the ratio of the change amplitude to the intensity of the simulated disturbance, a disturbance sensitivity metric is determined, and the disturbance sensitivity metric is used as the critical signal intensity.

9. The method according to claim 1, characterized in that, The comparison of the critical signal strength with the dynamic threshold determines whether the selected area is approaching a critical state for a violation to occur and estimates the critical arrival time, generating critical warning information, including: When the critical signal strength exceeds the dynamic threshold, the selected area is determined to be approaching the critical state of a violation outbreak; when the critical signal strength does not exceed the dynamic threshold, the selected area is determined not to be approaching the critical state of a violation outbreak. When determining that the selected area is approaching the critical state of a violation outbreak, the remaining time required for the critical signal strength to reach the preset outbreak threshold is estimated based on the rate of change of the critical signal strength over continuous monitoring time, and this is taken as the critical arrival time. The determination result of the critical state approaching the outbreak of violation is combined with the critical arrival time to generate the critical warning information.

10. The method according to claim 1, characterized in that, The verification of the critical warning information using entropy increase constraints and energy conservation constraints includes: The spatial distribution of the density of non-compliant shops within the selected area is extracted from the results of the cross-scale propagation analysis. The system entropy value is calculated based on the spatial distribution, and the direction of change of the system entropy value over continuous monitoring time is compared. When the system entropy value decreases monotonically with time, it is determined that the critical warning information has not passed the entropy increase verification. Based on the environmental pressure index and the density of non-compliant stores in the selected area, the environmental input energy is calculated; based on the corrected store-level state recovery rate and the density of non-compliant stores in the selected area, the dissipated energy is calculated; the environmental input energy and the dissipated energy are compared, and when the difference between the environmental input energy and the dissipated energy exceeds the preset tolerance, it is determined that the critical warning information has failed the energy conservation verification. When the critical warning information passes both the entropy increase verification and the energy conservation verification, it is determined that the critical warning information has passed the physical consistency verification.

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