Mathematical model modeling method based on data analysis operation processing

Abstract

The invention relates to the technical field of mathematical modeling, in particular to a mathematical model modeling method based on data analysis operation processing. The method comprises the following steps: collecting metal pollution data of a target water area by using a multi-parameter water quality sensor array; performing time sequence alignment on the metal pollution data to generate a standardized pollution data set; constructing a metal migration model based on fluid dynamics and chemical adsorption coupling; inputting the standardized pollution data set into the metal migration model for three-dimensional space interpolation calculation, and generating a metal pollutant diffusion cloud picture; pollution source reverse analysis is carried out on the metal pollutant diffusion cloud picture, and a potential pollution source coordinate set and pollution contribution degree sorting are generated. According to the method, by integrating multi-parameter water quality sensor data, fluid dynamics and chemical models and multispectral analysis, the modeling precision of the water pollution diffusion mathematical model is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mathematical modeling, and particularly relates to a mathematical model modeling method based on data analysis operation processing. BACKGROUND

[0002] Traditional water quality monitoring and heavy metal pollution assessment methods mainly rely on chemical analysis and laboratory testing. Although these methods are accurate, they are often time-consuming, costly, and difficult to achieve large-scale real-time monitoring. Therefore, a mathematical model modeling method based on data analysis operation processing has emerged. With the rapid development of computer technology and data science, the application of mathematical models in water body heavy metal pollution analysis has gradually attracted widespread attention. Initially, research focused on simple statistical analysis methods such as regression analysis and correlation analysis to reveal the distribution of heavy metals in water bodies. With the increase in data volume, especially the application of remote sensing technology and the Internet of Things, data sets gradually become large and complex, and the limitations of traditional methods begin to appear. With the introduction of advanced data analysis methods such as machine learning and deep learning, more accurate and efficient mathematical models have been developed. However, current traditional metal pollution analysis is usually limited to static measurement or based on simple linear models, which cannot accurately reflect the dynamic migration and diffusion process of pollutants in water bodies, and the positioning of pollution sources often relies on empirical judgment or simplified assumptions, making it difficult to accurately identify potential pollution sources, thereby resulting in low model accuracy of mathematical modeling. SUMMARY

[0003] Therefore, it is necessary to provide a mathematical model modeling method based on data analysis operation processing to solve at least one of the above technical problems.

[0004] To achieve the above-mentioned purpose, a mathematical model modeling method based on data analysis operation processing, the method comprising the following steps:

[0005] Step S1: collecting metal pollution data of a target water area by using a multi-parameter water quality sensor array; performing time series alignment on the metal pollution data to generate a standardized pollution data set;

[0006] Step S2: constructing a metal migration model based on fluid dynamics and chemical adsorption coupling; inputting the standardized pollution data set into the metal migration model for three-dimensional space interpolation calculation to generate a metal pollutant diffusion cloud map;

[0007] Step S3: performing reverse analysis of the metal pollutant diffusion cloud map to generate a potential pollution source coordinate set and a pollution contribution degree ranking; performing multi-spectral collection on the potential pollution source coordinate set and extracting metal fingerprint features in the corresponding spectrum;

[0008] Step S4: setting a pollution concentration threshold; analyzing the water body heavy metal concentration based on the metal fingerprint feature and the pollution contribution degree ranking to generate water body heavy metal concentration data; using the pollution concentration threshold to dynamically warn the water body heavy metal concentration data, and predicting the pollution diffusion trajectory of the metal pollutant diffusion cloud map according to the warning result, to construct a water body pollution diffusion mathematical model.

[0009] The present application can obtain multi-dimensional metal pollution data in real time through the multi-parameter water quality sensor array, and effectively eliminate the space-time deviation through time series alignment processing, to construct a unified standardized pollution data set, and provide reliable data basis for subsequent modeling. The metal migration model is constructed by combining fluid dynamics and chemical adsorption mechanism, which can more truly reflect the diffusion, adsorption and settlement behaviors of metal ions in water body, realize three-dimensional space interpolation with more physical meaning, generate dynamic diffusion cloud map, and significantly improve the prediction accuracy. Through reverse analysis of the diffusion cloud map combined with the pollution contribution degree ranking, the position of the potential pollution source can be accurately identified; further using multispectral technology to extract metal fingerprint features, the spectral feature matching and verification of the pollution source are realized, and the accuracy and reliability of the pollution source positioning are enhanced. By setting the pollution concentration threshold, combining the pollution contribution degree and the metal fingerprint feature, the water body heavy metal concentration analysis is carried out, the high-risk area is automatically identified, and the pollution event is intervened in advance through the dynamic warning mechanism, to improve the water quality safety management ability. Based on the warning result and the diffusion trajectory prediction, the water body pollution diffusion mathematical model is constructed, which can serve the simulation analysis of the present pollution, and provide theoretical support for the pollution trend evolution prediction under different future scenarios, with good expansibility and practical application value. Therefore, the present application improves the precision of the water body pollution diffusion mathematical modeling by integrating multi-parameter water quality sensor data, fluid dynamics and chemical model, and multispectral analysis.

[0010] Preferably, step S1 comprises the following steps:

[0011] Step S11: arranging a multi-point water quality monitoring area of the target water area to generate sensor arrangement data, wherein a grid division strategy is used for sensor arrangement, and the size of each grid is 100m*100m;

[0012] Step S12: sampling the multi-parameter metal pollutants of the target water area according to the sensor arrangement data to generate original metal pollution data;

[0013] Step S13: filling in the missing values in the original metal pollution data to obtain missing filling data; removing the outliers of the missing filling data to obtain cleaned metal pollution data;

[0014] Step S14: time stamp standardization is performed on the cleaned metal pollution data to generate time-unified data; and the time-unified data is used to perform multi-sensor time sequence alignment and normalization on the cleaned metal pollution data, thereby generating a standardized pollution data set.

[0015] The present application ensures uniform monitoring of the target water area through the grid division strategy for sensor deployment, avoids data blind spots, and improves the spatial coverage and representativeness of sampling. This grid deployment scheme can provide accurate multi-point data support for different pollution conditions in different regions. Based on the sensor deployment data, multi-parameter metal pollutant sampling is performed on the water area to generate raw metal pollution data, ensuring the comprehensiveness and multidimensionality of data collection and providing rich basic data for subsequent pollution analysis. The filling of missing values and the elimination of outliers in the raw data can effectively improve the quality and reliability of the data, ensuring that the analysis results will not be biased due to incomplete or inaccurate data in the subsequent analysis process. The cleaned metal pollution data is more representative and meets the input requirements of the analysis model. Through time stamp standardization and multi-sensor time sequence alignment technology, the time deviation between different sensors can be eliminated, ensuring the consistency of multiple sensor data in the same time dimension. The normalization operation further eliminates errors between different sensors, forming a unified standardized pollution data set. The generated standardized pollution data set not only has high comparability, but also provides high-quality data support for subsequent metal pollutant migration models, pollution source analysis, and concentration analysis. The high accuracy and standardized processing of this data set greatly improve the credibility of subsequent analysis.

[0016] Preferably, step S12 comprises the following steps:

[0017] Step S121: determining the sampling area and the deployment sensor coordinates according to the sensor deployment data;

[0018] Step S122: setting the types of metal pollutants to be detected, wherein the types of metal pollutants include lead, mercury, cadmium, chromium, and arsenic. Specifically, the detection sensitivity of lead is set to 0.001 mg / L, and the early warning threshold is set to 0.05 mg / L; the detection sensitivity of mercury is set to 0.0001 mg / L, and the early warning threshold is set to 0.001 mg / L; the detection sensitivity of cadmium is set to 0.0005 mg / L, and the early warning threshold is set to 0.005 mg / L; the detection sensitivity of chromium is set to 0.002 mg / L, and the early warning threshold is set to 0.1 mg / L; the detection sensitivity of arsenic is set to 0.001 mg / L, and the early warning threshold is set to 0.01 mg / L;

[0019] Step S123: Based on the type of metal pollutants to be detected, the sampling area is arranged with sensors at a coordinate of every 10 minutes for water sampling and metal data collection. The sampling depth is divided into 0-0.5m, 0.5-5m, and 5-10m, and the original metal pollution data is generated.

[0020] The present application determines the sampling area and the sensor arrangement coordinate according to the sensor arrangement data, ensures that the spatial distribution of the sampling area is scientific and reasonable, effectively avoids the blank area and overlapping area in the data collection process, and improves the representativeness and spatial coverage of the sampling data. By setting specific types of metal pollutants and their sensitivity and warning thresholds, different metal pollutants in the water body can be accurately identified, including lead, mercury, cadmium, chromium and arsenic, etc. This targeted detection can effectively monitor harmful metal pollution in the water body, timely detect pollution exceeding the warning threshold, and improve the accuracy and timeliness of monitoring. The sampling depth is divided into multiple levels such as 0-0.5m, 0.5-5m, and 5-10m, which can capture metal pollution data at different depths of the water body. Through this multi-level sampling method, not only the surface pollution of the water body can be identified, but also the pollution of the middle and deep layers of the water body can be reflected, and the spatial distribution of pollution can be comprehensively evaluated. Water sampling and metal data collection are carried out every 10 minutes, ensuring the high frequency and timeliness of data collection, which can timely reflect the trend of water pollutant concentration, and plays a key role in tracing and trend analysis of pollution sources. By accurately setting the detection sensitivity and warning threshold of metal pollutants, the detection of each type of metal pollutant can neither miss low-concentration pollution nor be disturbed by small fluctuations. This significantly improves the accuracy and effectiveness of the sampling data, and enhances the reliability and early warning capability of the water quality monitoring system.

[0021] Preferably, step S2 comprises the following steps:

[0022] Step S21: Collecting historical data from the standardized pollution data set to obtain a historical pollution data set;

[0023] Step S22: Extracting the hydrodynamic characteristics and chemical adsorption characteristics in the historical pollution data set to generate water hydrodynamic parameters and metal pollution chemical adsorption characteristic data;

[0024] Step S23: Numerical modeling and fitting modeling are performed on the water hydrodynamic parameters and metal pollution chemical adsorption characteristic data respectively to generate fluid dynamics modeling data and chemical adsorption modeling data;

[0025] Step S24: Mathematically coupling the fluid dynamics modeling data and the chemical adsorption modeling data to generate a metal migration model; inputting the standardized pollution data set into the metal migration model for three-dimensional spatial interpolation calculation to generate a metal pollution diffusion cloud map.

[0026] The present application can accumulate and utilize past pollution data by collecting historical data from standardized pollution data sets, providing historical data support for modeling the migration of metal pollutants. These historical data can reveal long-term trends and patterns of water pollution diffusion, helping to improve the accuracy and stability of the model. By extracting hydrodynamic characteristics and chemical adsorption properties from the historical pollution data set, hydrodynamic parameters and metal pollution chemical adsorption property data are generated, providing a scientific basis for subsequent model construction. This process ensures that key physical and chemical parameters required for modeling are fully and accurately considered. Numerical modeling and fitting modeling are performed on the hydrodynamic parameters and metal pollution chemical adsorption property data, respectively, to generate fluid dynamics modeling data and chemical adsorption modeling data. This process ensures the accuracy of the metal migration model under the dual mechanisms of physics and chemistry, and can simulate the complex behavior of metal pollutants in water, including diffusion, deposition, and adsorption. By mathematically coupling the fluid dynamics modeling data and the chemical adsorption modeling data, a metal migration model is generated. This model can consider the dynamic changes of water flow and the chemical behavior of pollutants in water, providing accurate predictions of the migration path and concentration distribution of metal pollutants. The standardized pollution data set is input into the metal migration model, and a metal pollutant diffusion cloud map is generated through three-dimensional spatial interpolation calculation. This process provides clear visualization of the spatial and temporal changes of pollution diffusion, allowing for intuitive display of the diffusion trend and impact range of pollutants in water, facilitating precise pollution monitoring and response by decision-makers.

[0027] Preferably, the step S24 of inputting the standardized pollution data set into the metal migration model for three-dimensional spatial interpolation calculation comprises:

[0028] inputting the standardized pollution data set into the metal migration model for three-dimensional gridding to generate pollution grid point data;

[0029] extracting local spatial vortex features from the pollution grid point data to generate vortex field perception data;

[0030] reconstructing the flow field structure from the vortex field perception data to generate vortex structure mapping data;

[0031] performing spatial interpolation projection on the vortex structure mapping data to generate three-dimensional interpolated pollution field data;

[0032] reconstructing the pollution concentration isosurface data from the three-dimensional interpolated pollution field data;

[0033] rendering the pollution concentration isosurface data in color layers to generate a metal pollutant diffusion cloud map.

[0034] The application generates pollution grid point data by inputting a standardized pollution dataset into a metal migration model for three-dimensional gridding, which can convert water pollution data into standardized spatial grid data, facilitating subsequent calculation and analysis. This gridding method improves the accuracy and structure of data processing, and clearly represents the spatial distribution of pollutants. Local spatial vortex feature extraction is performed on the pollution grid point data to generate vortex field perception data, which can capture vortex flow characteristics in the water body and reveal the influence of water flow on pollutant diffusion, especially the propagation of metal pollutants in complex water flow environments. By extracting vortex features, it helps to understand the movement and distribution dynamics of pollutants in water flow. Based on the vortex field perception data, the flow field structure is reconstructed to generate vortex structure mapping data. This can accurately reconstruct the fine structure of water flow and help further analyze how pollutants are affected by water flow and vortices, thereby providing more accurate diffusion predictions. Accurate modeling of the flow field structure can enhance the physical credibility of the metal migration model. Spatial interpolation projection is performed on the vortex structure mapping data to generate three-dimensional interpolated pollution field data, which can calculate the pollution distribution in unknown areas based on known pollution data, making the spatial distribution of pollutants more continuous and accurate. The generation of three-dimensional interpolated pollution field data provides high-quality spatial data for subsequent visualization and analysis. By performing isosurface reconstruction on the three-dimensional interpolated pollution field data, pollution concentration isosurface data is generated, which can visually present the distribution and changes of pollutant concentration in three-dimensional space and clearly indicate high concentration areas of pollution. Through color layer rendering, the visualization effect of isosurface data can be further enhanced, facilitating intuitive display of the diffusion process of metal pollutants in water bodies. Through the final color layer rendering, a metal pollutant diffusion cloud map is generated, which can visually display the diffusion path, concentration distribution and change trend of metal pollutants in water bodies. This visualization result not only improves the efficiency of pollution monitoring, but also provides strong support for decision-makers, facilitating the development of more effective pollution control measures.

[0035] Preferably, the pollution source reverse analysis of the metal pollutant diffusion cloud map in step S1 comprises:

[0036] Time series slicing is performed on the metal pollutant diffusion cloud map to generate dynamic diffusion evolution data;

[0037] Flow vector field inversion is performed on the dynamic diffusion evolution data to generate pollutant reverse migration path data;

[0038] Bayesian space reasoning is performed on the pollutant reverse migration path data to generate potential source area probability distribution data;

[0039] Boundary inversion homotopy focusing is performed on the potential source area probability distribution data to generate a set of potential pollution source coordinates;

[0040] Trace the potential pollution source coordinate set to the block classification, and generate pollution source contribution area data;

[0041] Calculate the weight of the pollution source contribution area data, and sort the pollution contribution degree of the pollution source contribution area data according to the weight, thereby generating the pollution contribution degree sorting.

[0042] The application can reveal the diffusion evolution of pollutants at different time points by slicing the metal pollutant diffusion cloud chart in time sequence, thereby providing dynamic information in time for subsequent pollution source analysis, which helps to understand the spatiotemporal variation characteristics of pollutant diffusion, especially the influence range of pollution sources in different time periods. The pollution source reverse migration path data is generated by performing flow vector field inversion on the dynamic diffusion evolution data, which calculates the diffusion trajectory of the pollutant by using the flow vector field, and can inversely deduce the source area of the pollutant, thereby providing a reliable basis for the positioning of the pollution source, which helps to determine the position of the pollution source and analyze how the pollutant diffuses in the water body. The potential source area probability distribution data is generated by performing Bayesian space reasoning on the pollutant reverse migration path data. The Bayesian space reasoning method can comprehensively consider various uncertainty factors (such as water flow, pollutant degradation, etc.), and reveal the possibility of the pollution source area through probability distribution, which makes the inference of the pollution source more scientific and reliable. The potential pollution source coordinate set is generated by performing boundary inversion and homotopy focusing on the potential source area probability distribution data. This process improves the accuracy of the pollution source area by using boundary inversion and homotopy focusing technology, avoids the misjudgment of a single source point, and can more accurately determine the regional range of the pollution source. The pollution source contribution area data is generated by performing trace source block classification on the potential pollution source coordinate set, which helps to identify the influence degree of the pollution source in different water body areas and reveal the different contribution degrees of the pollution source to water quality. Through trace source block classification, the influence range of the pollution source can be clearly delimited, and targeted governance measures can be developed according to the range. The pollution contribution degree sorting is generated by calculating the weight of the pollution source contribution area data and sorting the pollution contribution degree of the pollution source contribution area data according to the weight, which can reveal the contribution degree of each pollution source area to the overall pollution diffusion, and provide data support for subsequent environmental governance. The areas with high contribution degree can be given priority to pollution control and repair, thereby improving the efficiency of pollution control.

[0043] Preferably, in step 1, the potential pollution source coordinate set is collected by multi-spectrum, and the metal fingerprint characteristics in the corresponding spectrum are extracted, including:

[0044] The potential pollution source coordinate set is configured with ground multi-spectrum equipment parameters to generate multi-spectrum collection parameter data;

[0045] The multispectral acquisition parameter data is subjected to on-site spectral scanning to generate original multispectral data of the pollution source area;

[0046] The spectral bands of the original multispectral data are calibrated, and the calibrated spectral bands are subjected to background reflection elimination to generate background-removed spectral data;

[0047] The metal characteristic bands in the background-removed spectral data are extracted, and the metal characteristic bands are subjected to element characteristic vector matching to obtain metal fingerprint characteristics.

[0048] The present application configures the parameters of the ground multispectral equipment for the set of potential pollution source coordinates to generate multispectral acquisition parameter data. This process provides targeted technical support for spectral acquisition, ensuring that the equipment parameters (such as spectral range, acquisition time, resolution, etc.) in the acquisition process meet the actual conditions on site, thereby obtaining higher quality original multispectral data. By subjecting the multispectral acquisition parameter data to on-site spectral scanning, original multispectral data of the pollution source area is generated. This step can comprehensively capture the spectral information of the potential pollution source area from different spectral bands, which helps to accurately identify the metal pollution characteristics of the pollution source area. By collecting original data, comprehensive monitoring and analysis of the pollution source area can be ensured. By calibrating the spectral bands of the original multispectral data and eliminating the background reflection of the calibrated spectral bands, background-removed spectral data is generated. Background reflection elimination can effectively eliminate the interference caused by environmental light, ground reflection, etc., thereby improving the accuracy of the data. The background-removed spectral data provides more authentic pollution source characteristics, providing a reliable basis for subsequent metal feature extraction and analysis. By extracting the metal characteristic bands in the background-removed spectral data and matching the element characteristic vectors in these metal characteristic bands, metal fingerprint characteristics are obtained. By matching the element characteristic vectors in the metal characteristic bands, the metal components in the pollution source can be accurately identified. This method can accurately identify different metal pollutants, providing strong support for quantitative analysis and source tracing of pollution sources. After extracting and matching the metal fingerprint characteristics, the types and concentrations of various metal pollutants in the pollution source can be more accurately determined. Through high-resolution multispectral data and fingerprint feature matching, trace metal pollution in water bodies can be effectively identified, improving the recognition accuracy and reliability of pollution sources. Through multispectral acquisition and metal fingerprint extraction, information about the pollution source can be obtained in multiple spectral dimensions, providing more comprehensive pollution source characteristics than traditional single detection methods. This provides multi-angle data support for subsequent pollution source analysis, pollution control, and environmental monitoring, which helps to more accurately assess the source, type, and diffusion potential of pollutants.

[0049] Preferably, the parameter configuration of the ground multispectral equipment for the set of potential pollution source coordinates comprises:

[0050] The ground multi-spectral equipment parameters of the potential pollution source coordinate set are configured, wherein the spatial resolution of the ground multi-spectral equipment is set to 0.3-1 meter, 8-16 spectral bands can be supported, the band coverage range is 400-2500 nanometers, the single band width is set to 10-30 nanometers, the spectral resolution is controlled to be between 3-10 nanometers, the imaging frame rate is 3-10 frames / second, the field of view angle range is 20-40 degrees, the equipment ground installation height is set to 3-6 meters, and the data sampling interval is 10-30 minutes.

[0051] By setting the spatial resolution of the ground multi-spectral equipment to be between 0.3-1 meter, the present application can ensure that high-precision spatial information is obtained in the pollution source area, and this high resolution helps to accurately identify the specific location, distribution and pollution concentration changes of the pollution source, avoiding missing important details due to low resolution. The equipment can support 8-16 spectral bands, with a band coverage range of 400-2500 nanometers, which can cover multiple bands from visible light to near-infrared and short-wave infrared, which enables simultaneous capture of pollution source information in multiple spectral ranges, especially metal pollutants in water, the reflection and absorption characteristics under different spectral ranges will be fully displayed, which helps to improve the identification accuracy of the pollution source. The single band width is set to 10-30 nanometers, and the spectral resolution is controlled to be between 3-10 nanometers, which helps to capture subtle spectral differences, making the equipment have strong ability in identifying metal fingerprint features. The fine spectral resolution improves the detection sensitivity of metal pollutants, especially the identification ability of low-concentration pollutants. The imaging frame rate is 3-10 frames / second, which can effectively ensure the monitoring of rapidly changing pollution sources, especially when monitoring the pollution diffusion process, high-frequency spectral data can be obtained in real time, thereby ensuring the detailed capture of dynamic changes and adapting to rapidly changing pollution environments. The field of view angle range is 20-40 degrees, and the equipment can adjust the field of view angle according to the specific monitoring requirements, thereby flexibly monitoring pollution sources of different sizes. This configuration not only provides wide coverage, but also ensures observation details, especially when monitoring a wide range of water, it can effectively cover a large range of pollution source areas. The equipment ground installation height is set to be between 3-6 meters, which can ensure that the equipment can obtain sufficient coverage range and maintain appropriate resolution, avoiding the influence of too high or too low installation position on the clarity of the image and the accuracy of the data. Reasonable installation height can also reduce the interference of the surrounding environment on the measurement results. The data sampling interval is 10-30 minutes, which enables the equipment to periodically sample within a reasonable time, ensuring data continuity while avoiding unnecessary storage and processing pressure caused by too frequent data collection. This time interval can be adjusted according to the change rate of the pollution source to flexibly meet the monitoring needs in different scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 A schematic diagram of the step flow of a mathematical model modeling method based on data analysis operation processing is shown in the figure;

[0053] Figure 2 A schematic diagram of the step flow of a mathematical model modeling method based on data analysis operation processing is shown in the figure; Figure 1 A detailed implementation step flow schematic diagram of step S2 in the method is shown in the figure;

[0054] Figure 3 A detailed implementation step flow schematic diagram of step S4 in the method is shown in the figure; Figure 1 A detailed implementation step flow schematic diagram of step S4 in the method is shown in the figure;

[0055] The implementation, functional features and advantages of the present application will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0056] The technical method of the present application will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0057] In addition, the accompanying drawings are only schematic illustrations of the present application and are not necessarily drawn to scale. Identical reference numerals in the drawings represent identical or similar parts, and thus repeated descriptions thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities, which do not necessarily correspond to physically or logically independent entities. The functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different network and / or processor methods and / or microcontroller methods.

[0058] It should be understood that although the terms "first", "second" and the like can be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, without departing from the scope of the exemplary embodiments, a first element can be referred to as a second element, and similarly a second element can be referred to as a first element, and the term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0059] To achieve the above-mentioned purpose, please refer to Figures 1 to 3 A mathematical model modeling method based on data analysis operation processing, the method comprising the following steps:

[0060] Step S1: collecting metal pollution data of a target water area by using a multi-parameter water quality sensor array; performing time series alignment on the metal pollution data to generate a standardized pollution data set;

[0061] Step S2: constructing a metal migration model based on coupling of fluid dynamics and chemical adsorption; inputting a standardized pollution data set into the metal migration model for three-dimensional space interpolation calculation to generate a metal pollutant diffusion cloud map;

[0062] Step S3: performing pollution source reverse analysis on the metal pollutant diffusion cloud map to generate a potential pollution source coordinate set and a pollution contribution degree ranking; performing multi-spectral collection on the potential pollution source coordinate set and extracting metal fingerprint features in the corresponding spectrum;

[0063] Step S4: setting a pollution concentration threshold; performing water heavy metal concentration analysis on the pollution contribution degree ranking based on the metal fingerprint features to generate water heavy metal concentration data; performing dynamic early warning on the water heavy metal concentration data using the pollution concentration threshold, and predicting the pollution diffusion trajectory of the metal pollutant diffusion cloud map according to the early warning result to construct a water pollution diffusion mathematical model.

[0064] The present application can obtain multi-dimensional metal pollution data in real time through a multi-parameter water quality sensor array, effectively eliminate the space-time deviation through time series alignment processing, construct a unified standardized pollution data set, and provide reliable data basis for subsequent modeling. The metal migration model constructed by combining fluid dynamics and chemical adsorption mechanism can more realistically reflect the diffusion, adsorption and sedimentation behaviors of metal ions in water, realize three-dimensional space interpolation with more physical meaning, generate a dynamic diffusion cloud map, and significantly improve the prediction accuracy. Through reverse analysis of the diffusion cloud map combined with the pollution contribution degree ranking, the position of the potential pollution source can be accurately identified; further, the metal fingerprint features are extracted using multi-spectral technology to realize spectral feature matching and verification of the pollution source, and the accuracy and reliability of the pollution source positioning are enhanced. By setting a pollution concentration threshold, combining pollution contribution degree and metal fingerprint features, water heavy metal concentration analysis is carried out, high-risk areas are automatically identified, and pollution events are intervened in advance through a dynamic early warning mechanism to improve water quality safety management capability. Based on the early warning result and diffusion trajectory prediction, a water pollution diffusion mathematical model is constructed, which can serve the simulation analysis of the present pollution and provide theoretical support for the pollution trend evolution prediction under different future scenarios, and has good expansibility and practical application value. Therefore, the present application improves the modeling precision of the water pollution diffusion mathematical model by integrating multi-parameter water quality sensor data, fluid dynamics and chemical model, and multi-spectral analysis.

[0065] In the embodiment of the present application, reference is made to FIG. 1, which is a step flowchart of a mathematical model modeling method based on data analysis and operation processing, and in the present example, the mathematical model modeling method based on data analysis and operation processing comprises the following steps: Figure 1

[0066] ​Step S1: Collecting metal pollution data of the target water area by using a multi-parameter water quality sensor array; performing time series alignment on the metal pollution data to generate a standardized pollution data set;

[0067] In the embodiment of the present application, a multi-parameter water quality sensor array suitable for monitoring metal pollutants is selected to ensure that the sensor can simultaneously monitor multiple metal ions (such as lead, mercury, cadmium, etc.). The sensor array is arranged at different positions of the target water area to ensure comprehensive coverage of the water area, and appropriate sensor positions are selected according to the flowability or water depth. The sensor array starts to collect metal pollutant concentration data in the water area in real time, including but not limited to the concentration of metal ions, pH value, temperature, dissolved oxygen, and other environmental factors. A reasonable sampling frequency (for example, collecting data once an hour or once a minute) is set, and an appropriate sampling frequency is selected according to the time scale of the monitoring target. The collected raw data is preprocessed to remove noise and correct data outliers. If there are missing values or incorrect data in the sensor data, interpolation or other appropriate correction methods are used for data filling or repair. Since different sensors have different sampling times or frequencies, the data of each sensor needs to be time series aligned to ensure that all data are compared under the same time reference. Interpolation or resampling methods are used to align data with inconsistent collection time points to ensure that all data cover the same time period and the sampling interval is uniform. For data of different metal pollutants, standardization processing is needed due to different units and magnitudes. Common standardization methods include min-max normalization and Z-score standardization, and appropriate methods are selected according to data distribution. For example, Z-score standardization is used, and the formula is: where X is the original data, μ is the data mean, σ is the data standard deviation, and Z is the standardized data. After standardizing the data of all metal pollutants, they are integrated into a standardized pollution data set.

[0068] Step S2: Constructing a metal migration model based on coupling of fluid dynamics and chemical adsorption; inputting the standardized pollution data set into the metal migration model for three-dimensional space interpolation calculation to generate a metal pollutant diffusion cloud map;

[0069] In the embodiments of the present application, by describing the fluid flow characteristics in the water body, using models such as Navier-Stokes equation, Euler equation or Reynolds averaged equation, the flow law of water flow in the water body is simulated, considering the influence of flow velocity, flow rate and water area structure. Based on the adsorption-desorption process and the chemical reaction of metal ions, combined with the adsorption kinetics model (such as Langmuir adsorption isotherm or Freundlich adsorption isotherm), the adsorption-desorption process of metal ions in the water body with the water bottom sediments or other particulate matters is simulated. Combined with the transport characteristics of water flow and the adsorption behavior of metal ions, a coupling model is constructed. The model describes the flow of metal ions through the fluid dynamics equation, while the adsorption and desorption process of metal ions in the water body is considered through the adsorption kinetics equation. The coupling model can be represented as a diffusion-migration-adsorption equation set, which is specifically: where C is the metal concentration, D is the diffusion coefficient, v is the water flow velocity, and R(C) is the chemical adsorption term, representing the adsorption and desorption process of metal ions with sediments. According to the actual monitoring data, the parameters required by the model are obtained, such as water flow velocity, diffusion coefficient, adsorption constant, etc. They can be estimated through field measurement or data in literature, and parameter calibration is carried out using reverse modeling or optimization method. The standardized pollution data set (metal pollutant data collected from sensors) is input as the initial condition into the metal migration model, which is the metal pollution concentration at different times in each point of the water area. The model initializes the metal migration simulation according to the geographical information of the water body (such as the depth of the water body, the distribution of flow velocity, etc.). Three-dimensional spatial interpolation methods such as Kriging interpolation, Spline interpolation or other spatial interpolation methods are used to calculate the three-dimensional spatial interpolation of metal pollution data. Spatial interpolation can help to extend the data of local measurement points to the entire water area, so as to generate the spatial distribution of metal pollutants in the entire three-dimensional water area. The interpolated data contains the metal pollutant concentration of each point in the water body, covering the depth, lateral and longitudinal coordinates of the water body. Based on the interpolated data, a visualization tool (such as MATLAB, Python's Matplotlib or Paraview, etc.) is used to generate a three-dimensional metal pollutant diffusion cloud chart. The diffusion cloud chart shows the concentration distribution of metal pollutants in the water body and its expansion over time, and color and transparency are usually used to represent different concentrations of metal pollutants. When generating the diffusion cloud chart, the following parameters can be considered: according to the time series data, the metal pollutant diffusion chart at different times is generated to observe the expansion trend of the pollutants. Through the pollutant distribution at different depths and in the lateral and longitudinal directions of the water area, the spatial expansion of the pollutants in the water body is displayed.

[0070] Step S3: reverse analysis of the metal pollutant diffusion cloud map to generate a set of potential pollution source coordinates and a pollution contribution degree ranking; multispectral collection of the set of potential pollution source coordinates and extraction of metal fingerprint features in the corresponding spectrum;

[0071] In the embodiments of the present application, the source of the pollutant is analyzed using the inverse algorithm of the diffusion model according to the metal pollutant diffusion cloud chart, which can determine the pollution source by inversely deducing the diffusion path of metal ions, combining the water flow pattern and the trend of pollutant concentration change over time. The position of the pollution source is calculated using the inverse solution method of the diffusion equation (such as the Lagrangian method or the Eulerian method) based on the existing metal pollutant concentration distribution data. The potential position of the pollution source is calculated using numerical back simulation technology in combination with the flow field of the water body and the pollutant concentration data. Based on the time series data of the pollutant diffusion cloud chart, the position of the pollution source can be calculated by backtracking or gradient descent method. An optimization method such as genetic algorithm or particle swarm algorithm is used to find the optimal solution of the pollution source coordinates to minimize the error between the simulated pollution diffusion chart and the measured pollution cloud chart. According to the inverse analysis result, the position coordinate set of the potential pollution source is obtained, and these positions are the emission source or the pollution source area of the metal pollutant. The contribution of each potential pollution source to the overall pollution diffusion cloud chart is calculated. Common methods include calculating the distance between the pollution source and each point in the pollution cloud chart, and evaluating the contribution of each pollution source to the pollutant concentration in a specific area based on the position of the pollution source and the mode of pollutant diffusion. According to the pollution contribution of each potential pollution source, from high to low, the contribution ranking of the pollution source is generated. The potential pollution source coordinates and their contribution are displayed through a visualization tool to help decision-makers understand the distribution and impact of the pollution source and develop subsequent pollution control strategies. A multispectral sensor or remote sensing device (such as a multispectral camera carried by a drone, a ground multispectral sensor, etc.) is used to collect multispectral data in the target pollution source area. Multispectral sensors can usually capture spectral information in different wavebands, covering visible light, near-infrared, etc. According to the potential pollution source coordinate set generated in step S3, the area around the pollution source is selected for multispectral collection. The collection area should include the pollution source and its surrounding environment to detect the radiation characteristics of the pollution source. Each metal pollutant will exhibit unique absorption peaks or reflection characteristics in the spectrum, which are referred to as the "spectral fingerprint" of the metal. For example, metals such as lead, cadmium, and mercury have distinct absorption or reflection peaks at specific wavelengths. The collected multispectral data is preprocessed to eliminate environmental interference, such as denoising, radiation correction, and geometric correction. According to the known characteristic wavebands of metal pollutants, appropriate spectral wavebands are selected for analysis. Common wavebands include the near-infrared waveband (NIR) and the mid-infrared waveband (MIR), which usually contain the absorption characteristics of metal ions. The characteristic spectral peaks of metal pollutants are extracted from the multispectral data through spectral unmixing methods, which can be used for quantitative analysis of the types and concentrations of metals in the water body. The metal fingerprint characteristics extracted from the spectral data are combined with the pollution source coordinates to verify the metal pollution type of the pollution source.By comparing the metal fingerprint characteristics with the standard metal spectrum database, the types of metal pollutants existing in the pollution source are determined, which provides a basis for pollution source classification and further treatment.

[0072] Step S4: setting a pollution concentration threshold; analyzing the water body heavy metal concentration based on the metal fingerprint characteristics and the pollution contribution degree ranking to generate water body heavy metal concentration data; using the pollution concentration threshold to dynamically warn the water body heavy metal concentration data, and predicting the pollution diffusion trajectory of the metal pollutant diffusion cloud map according to the warning result, so as to build a water body pollution diffusion mathematical model.

[0073] In the embodiments of the present application, by defining the pollution threshold, the pollution concentration threshold should be set based on water quality standards and environmental protection requirements. Common water quality standards include metal pollutant concentration limits in World Health Organization (WHO), national environmental protection standards (such as GB / T, EPA), which are usually defined according to the toxicity of metals, the impact on the ecological environment and the risk to human health. According to the historical data of the target water area, the standard concentration limit of heavy metals, ecological health data and other factors, set the pollution concentration threshold. The threshold should be refined into multiple levels (for example: low risk, medium risk, high risk) to deal with different pollution levels. For example: lead (Pb): 10 μg / L, cadmium (Cd): 5 μg / L, mercury (Hg): 0.1 μg / L, arsenic (As): 10 μg / L. According to different seasons, climate change, water flow conditions and other dynamic adjustments, ensure sensitivity and accuracy. Through the metal fingerprint feature data extracted in the foregoing steps, combined with the pollution contribution degree ranking, the concentration analysis of water body heavy metals is carried out. Through multispectral data, the spectral characteristics of each metal pollutant are extracted, and these characteristics are associated with the concentration of metals. Using known spectral fingerprints and pollution source data, the actual concentration of each heavy metal in the water body is calculated by inversion algorithm (such as least squares method or machine learning regression method). According to the contribution degree ranking of pollution sources, the sources with greater contribution to water pollution are selected for concentration analysis and calculation of their spatial distribution and concentration in the water body. Through the above analysis, the heavy metal concentration data in different positions of the water body is generated, covering metal types, concentration values, time changes and other information. Using three-dimensional maps, spatial interpolation and other methods, the metal concentration data is mapped to the water space to generate detailed water heavy metal concentration map. The set pollution concentration threshold is compared with the water heavy metal concentration data in real time to judge whether there is excessive heavy metal pollution in the water body. According to the real-time or periodic monitoring data flow, the change of heavy metal concentration in the water body is continuously tracked and compared with the preset threshold. When the concentration of some heavy metals in the water body exceeds the threshold, the early warning system is automatically triggered. The warning information can include the type of pollution, concentration, pollution area and potential threat to the environment and health. According to different pollution concentration levels (for example, light, medium and heavy pollution), a multi-level warning mechanism is designed. Each warning level will trigger different response measures. Combined with sensor data, stream data analysis technology is used to predict the trend of metal concentration changes in the water body in real time, and quickly respond to pollution events. According to the flow characteristics of the water body, the physical and chemical properties of metal pollutants and other factors, select the appropriate diffusion model. Common diffusion models include two-dimensional or three-dimensional fluid dynamics diffusion model, random walk model, particle swarm model, etc. Based on the position of the pollution source, the pollution concentration and the water flow velocity, the diffusion trajectory of the metal pollutant is predicted. The model will consider the diffusion rate, settling rate, adsorption process and other factors of the metal pollutant to simulate dynamically.The time series data of the pollution source, such as the pollution start time, diffusion rate, etc., are input into the diffusion model for step-by-step calculation to predict the diffusion path of the pollutants. The trajectory of the pollutant diffusion is combined with the water body area division to generate a dynamic cloud chart of pollution diffusion. The chart can show the concentration change of the pollutants and their spatial distribution in the water body. According to historical data and real-time monitoring results, optimization algorithms are used to adjust the model parameters to improve the accuracy and timeliness of the prediction. For example, Kalman filter, Particle filter, etc. can be used to optimize the prediction of the diffusion trajectory of the pollutants. A water pollution diffusion model based on fluid dynamics is constructed, using diffusion equations, convection equations, pollutant adsorption and sedimentation equations, etc., considering the influence of water flow, temperature, sediment, etc. on the diffusion of pollutants. Multiple factors such as flow field, pollutant concentration field and chemical reaction process are coupled into a unified mathematical model to accurately describe the diffusion behavior of pollutants in the water body. The model is discretized and solved by numerical methods such as finite element method, finite difference method, etc. The prediction results of the model are compared with the actual monitoring data to verify its accuracy. If the error is large, the model needs to be further optimized or the parameters need to be adjusted. According to the prediction results and the water heavy metal concentration data, the severity of the current pollution and its impact on the environment and ecological system are evaluated.

[0074] Preferably, step S1 comprises the following steps:

[0075] Step S11: The multi-point water quality monitoring area of the target water area is laid out to generate sensor layout data, wherein a grid division strategy is used for sensor layout, and the size of each grid is 100m x 100m;

[0076] Step S12: Multi-parameter metal pollutant sampling is performed on the target water area according to the sensor layout data to generate original metal pollution data;

[0077] Step S13: Missing values in the original metal pollution data are filled to obtain missing filled data; the missing filled data is subjected to outlier removal to obtain cleaned metal pollution data;

[0078] Step S14: The cleaned metal pollution data is subjected to timestamp standardization to generate time-unified data; the cleaned metal pollution data is subjected to multi-sensor time series alignment and normalization using the time-unified data to generate a standardized pollution data set.

[0079] In the embodiments of the present application, by selecting the monitoring area range, the water area boundary data (such as aerial photographs, satellite images, etc.) is imported into the GIS system. Using the grid division function in the GIS software, the monitoring area is divided into regular 100m x 100m grid cells. The center point of each grid cell is used as the layout position of the sensor. After determining the layout point, the geographic coordinates (latitude, longitude, altitude, etc.) of each layout point are recorded as sensor layout data. Select appropriate water quality sensors, such as metal pollution sensors, dissolved oxygen sensors, etc., to meet the different monitoring needs of the water area. The selection of the layout point takes into account factors such as water flow, depth, etc., and preferentially selects areas with large changes in water flow and areas with pollution sources. At the designated grid layout point, the concentration of metal pollutants in the water body is sampled by the sensor at regular intervals. Each sensor collects and records data within a set time interval (such as every hour, every day). The recorded data should include time stamp, sensor location (grid coordinates), pollutant concentration, etc. The sampling results are arranged into an original data set, where each data contains time, location, pollutant concentration, etc. Through time series data analysis, the time period of missing data and the adjacent data points are determined. Use time series analysis methods (such as linear interpolation, spline interpolation, etc.) to fill in the missing data and maintain the continuity of the data. Use statistical methods such as 3σ rule, box plot analysis (IQR), etc. to identify outliers. By analyzing the distribution of data, identify abnormal data that exceeds a certain standard deviation range, and remove or correct it. Through filling and outlier removal, the cleaned metal pollution data set is obtained, which represents the metal pollution situation of each sampling point in the target water area. Unify the time format of all data, such as converting all time stamps to UTC time (world standard time) or local standard time, and unify the time accuracy (such as to hours, minutes, seconds). Align the data collected by different sensors to the same time point to ensure the consistency and comparability of different sensor data. Use interpolation methods (such as linear interpolation, spline interpolation) to align the data of sensors with different sampling frequencies, ensuring the completeness of the data at each time point. For example, for sensor A data with a time stamp of 10:00, if sensor B data is collected at 10:05, an interpolation method can be used to estimate the value of B at 10:00. Use common normalization methods (such as min-max normalization, Z-score standardization, etc.) to convert the metal pollutant concentration data of each sensor to a unified standard scale. For example, for the concentration data of sensor A and sensor B, they can be converted to values in the [0, 1] interval through normalization processing. After completing the time unification, alignment and normalization processing, all sensor data is summarized into a standardized pollution data set.

[0080] Preferably, step S12 comprises the following steps:

[0081] Step S121: determining the sampling area and the layout sensor coordinates according to the sensor layout data;

[0082] Step S122: setting the types of metal pollutants to be detected, wherein the types of metal pollutants include lead, mercury, cadmium, chromium and arsenic, and the detection sensitivity of lead is set to 0.001 mg / L, the pre-warning threshold is set to 0.05 mg / L; the detection sensitivity of mercury is set to 0.0001 mg / L, the pre-warning threshold is set to 0.001 mg / L; the detection sensitivity of cadmium is set to 0.0005 mg / L, the pre-warning threshold is set to 0.005 mg / L; the detection sensitivity of chromium is set to 0.002 mg / L, the pre-warning threshold is set to 0.1 mg / L; the detection sensitivity of arsenic is set to 0.001 mg / L, and the pre-warning threshold is set to 0.01 mg / L;

[0083] Step S123: based on the types of metal pollutants to be detected, the water body sampling and metal data collection are performed every 10 minutes according to the layout sensor coordinates for the sampling area, the sampling depth is divided into 0-0.5 m, 0.5-5 m and 5-10 m, and the original metal pollution data is generated.

[0084] In the embodiments of the present application, the water area is divided into multiple sampling areas by using a geographic information system (GIS) to analyze the geographic coordinates of the sensor deployment points. The area around each sensor deployment point will become the sampling range, ensuring that each sampling point is representative and covers the entire water area. The coordinate data of the deployed sensors, including longitude, latitude, and depth, are entered into a database as a basis for subsequent data analysis and processing. For each sensor, in combination with the geographic information of the target water area, the depth position in the water body is recorded (such as 0-0.5m, 0.5-5m, 5-10m, etc. water layer). According to the water quality monitoring requirements and pollution source analysis, the types of metal pollutants to be detected are selected. The detection sensitivity and warning threshold of each metal pollutant are listed to ensure that the monitoring can respond to the changes in the concentration of metal pollutants in the water body in a timely manner. The detection sensitivity and warning threshold of different metals are set according to environmental standards or actual needs. The following are the recommended settings: the detection sensitivity of lead is set to 0.001mg / L, and the warning threshold is set to 0.05mg / L; the detection sensitivity of mercury is set to 0.0001mg / L, and the warning threshold is set to 0.001mg / L; the detection sensitivity of cadmium is set to 0.0005mg / L, and the warning threshold is set to 0.005mg / L; the detection sensitivity of chromium is set to 0.002mg / L, and the warning threshold is set to 0.1mg / L; the detection sensitivity of arsenic is set to 0.001mg / L, and the warning threshold is set to 0.01mg / L; for each metal pollutant, a suitable sensor is selected to match the above sensitivity requirements, and a warning threshold is set for each pollutant. In actual operation, the sensitivity parameters are determined according to the technical indicators of the sensor (such as minimum detection limit, accuracy, etc.). Sampling is performed by the sensor every 10 minutes, and after each sampling is completed, the timestamp, sampling location, metal pollutant concentration, and other data are automatically recorded. The sensor can upload data in real time to a data storage system or cloud platform through wireless communication. Corresponding sensors are set at each depth level to ensure that the pollution conditions of each water layer can be completely collected. During each sampling, the sensor will indicate its working depth (e.g., shallow, deep, bottom), ensuring the accuracy of data at each level. After each sampling is completed, the sensor will save the sampling results and upload the data to the monitoring platform through the wireless network, ensuring real-time monitoring and data traceability. The collected raw data includes time, location (sensor coordinates), pollutant concentration (unit: mg / L), sampling depth, and other information, forming a raw metal pollution data set.

[0085] As an example of the present application, reference is made to Fig. 1, which shows a schematic diagram of a water quality monitoring system according to an embodiment of the present application. In this example, the step S2 includes: Figure 2

[0086] Step S21: Historical data collection on the standardized pollution data set to obtain a historical pollution data set;

[0087] ​Step S22: extract the hydrodynamic characteristics and chemical adsorption characteristics in the historical pollution data set to generate water body hydrodynamic parameters and metal pollution chemical adsorption characteristic data;

[0088] Step S23: respectively perform numerical modeling and fitting modeling on the water body hydrodynamic parameters and the metal pollution chemical adsorption characteristic data to generate fluid dynamics modeling data and chemical adsorption modeling data;

[0089] Step S24: mathematically couple the fluid dynamics modeling data and the chemical adsorption modeling data to generate a metal migration model; input the standardized pollution data set into the metal migration model for three-dimensional space interpolation calculation to generate a metal pollutant diffusion cloud map.

[0090] In the embodiments of the present application, pollution data for a corresponding time period, such as pollution data for the past year, is extracted from historical data storage to construct a long-term trend analysis model. Data cleaning and normalization algorithms are used to convert raw pollution data into a standardized format, ensuring data quality and consistency. A database (such as a SQL or NoSQL database) is used to manage the historical pollution data set, ensuring data queryability and traceability. Based on water flow simulation models (such as SWAN, MIKE21) and field monitoring data, hydrodynamic parameters such as water flow velocity and direction are extracted. Numerical methods (such as finite difference method, finite element method) are used to extract water body turbulence intensity, mixed layer depth, etc. Based on experimental data or literature, the adsorption isotherm of metal pollutants in water (such as Langmuir, Freundlich, etc. Model) is extracted, and the adsorption rate constant is calculated. Combined with the chemical composition of the water body, pH value, etc., the chemical adsorption characteristics of the metal pollutants are extracted. A numerical fluid dynamics (CFD) model based on the Navier-Stokes equation is used, combined with water flow velocity, direction, turbulence, etc. to establish a hydrodynamic model. Numerical simulation is performed to solve the velocity field, pressure field, etc. during water flow. Langmuir adsorption model or Freundlich model, etc. are used to model the adsorption behavior of metal pollutants, and the distribution and concentration change of pollutants in the water body are obtained. The adsorption constant in the model is fitted with experimental data to accurately describe the adsorption process of the pollutants. The modeling results of hydrodynamics and chemical adsorption are stored as a data set for subsequent coupling analysis. By coupling the flow equation of the water body and the adsorption kinetics equation of the metal pollutants, a metal migration model is established. Specifically, the migration, diffusion, sedimentation and adsorption processes of metal pollutants in the water body are considered. Numerical methods (such as finite difference method or finite element method) are used to discretize the coupled model to solve the spatial distribution and change of metal pollutants in the water body. Based on the metal migration model, interpolation calculation is performed in the three-dimensional space of the water body to simulate the spatial distribution of metal pollutants. The interpolation method can use Kriging interpolation or inverse distance weighting (IDW) method to obtain high-precision spatial distribution map. Using GIS software or special visualization tools, the diffusion cloud map of metal pollutants is generated based on the calculation results of the metal migration model. The concentration change of pollutants at different times and spatial positions is shown in the figure.

[0091] Preferably, the step S24 of inputting the standardized pollution data set into the metal migration model for three-dimensional spatial interpolation calculation comprises:

[0092] The standardized pollution data set is input into the metal migration model for three-dimensional gridding to generate pollution grid point data;

[0093] The pollution grid point data is subjected to local spatial vortex feature extraction to generate vortex field perception data;

[0094] The vortex field perception data is subjected to flow field structure reconstruction to generate vortex structure mapping data;

[0095] The vortex structure mapping data is subjected to spatial interpolation projection to generate three-dimensional interpolated pollution field data;

[0096] The three-dimensional interpolated pollution field data is subjected to isosurface reconstruction to generate pollution concentration isosurface data;

[0097] The pollution concentration isosurface data is subjected to color layer rendering to generate a metal pollution diffusion cloud chart.

[0098] In the embodiments of the present application, the pollution concentration data of each monitoring point in the standardized pollution dataset is used as input to define a three-dimensional space of the water body. The water body space is divided into multiple uniform small cells using a gridding method, and the grid size is determined according to the scale of the water body and the required accuracy. The corresponding pollution data is saved in each small grid cell. Specifically, the monitoring point data is inserted into the corresponding grid points using methods such as Kriging interpolation or inverse distance weighting (IDW) to generate pollution grid point data. Through numerical fluid dynamics simulation, combined with the flow information of the water body, the flow characteristics in the pollution grid point data are extracted, especially the vortex structure in the fluid. A turbulence model (such as k-ε model) is used to analyze the vortex of the fluid to obtain the vortex characteristics of the local space. The vortex intensity, vortex direction, and vortex density of each pollution grid point are calculated to form vortex field perception data, providing spatial flow information of the pollutants. Using the vortex field perception data, combined with the fluid mechanics model, the flow field structure is reconstructed. According to the spatial distribution and flow pattern of the vortex, the overall flow field of the fluid is reconstructed. Through the reconstruction of the flow field, the variation law of the pollutants in the flow field can be further obtained, especially the propagation trend under different flow conditions. Through vector field and streamline analysis, the spatial layout of the vortex is reconstructed to generate vortex structure mapping data, representing the flow field structure in the water body and its relationship with the pollutants. The vortex structure mapping data is projected using spatial interpolation to calculate the pollution concentration distribution in different regions of the water body. Interpolation methods such as Kriging interpolation and inverse distance weighting (IDW) are used to refine the vortex structure mapping data in three-dimensional space and generate pollution field data. Spatial interpolation projection can provide concentration data of metal pollutants in each spatial unit to form three-dimensional interpolation pollution field data. Based on the three-dimensional interpolation pollution field data, the pollution concentration data is processed using the isosurface algorithm. The isosurface refers to the surface formed by connecting points with the same concentration value in three-dimensional space. Methods such as Marching Cubes algorithm or volume rendering are used to convert the pollution field data into isosurface data of the pollution concentration. The isosurface can clearly show the variation trend of the pollution concentration and the distribution of the pollutants in the water body. Based on the generated isosurface data of the pollution concentration, visualization techniques such as OpenGL, VTK, and other three-dimensional visualization tools are used for color layer rendering of the data. Different pollution concentration thresholds are set for color mapping of the pollution concentration data. For example, low concentration areas use green, higher concentration areas use yellow, and the highest concentration area uses red. Through color layer rendering, a pollution diffusion cloud chart with hierarchical sense is generated, which can intuitively show the spatial diffusion trend of metal pollutants in the water body. Professional visualization platforms such as Unity3D and Paraview are used to generate the final metal pollutant diffusion cloud chart.

[0099] Preferably, the reverse analysis of the pollution source on the metal pollutant diffusion cloud chart in step S1 comprises:

[0100] The metal pollutant diffusion cloud chart is time-series sliced to generate dynamic diffusion evolution data;

[0101] The dynamic diffusion evolution data is flow vector field inversed to generate pollutant reverse migration path data;

[0102] The pollutant reverse migration path data is Bayesian space reasoning to generate potential source area probability distribution data;

[0103] The potential source area probability distribution data is boundary inversion homotopy focusing to generate potential pollution source coordinate set;

[0104] The potential pollution source coordinate set is traced to block classification to generate pollution source contribution area data;

[0105] The weight of the pollution source contribution area data is calculated, and the pollution source contribution area data is sorted according to the weight, so as to generate pollution contribution degree sorting.

[0106] In the embodiment of the application, the metal pollutant diffusion cloud chart is sliced according to the time dimension to obtain a series of continuous time frames, each frame representing the distribution of metal pollutants in the water body at a certain time. The pollution concentration of each time frame is extracted using a time series data processing method to generate dynamic diffusion evolution data. The time series data of the metal pollution cloud chart can be processed using data analysis tools (such as pandas and NumPy in Python) and visualization platforms (such as Matplotlib and Paraview). The flow direction and rate of pollutant diffusion are calculated by using fluid dynamics model or Lagrangian analysis method to inverse the flow vector field of dynamic diffusion evolution data. The reverse tracking method is used to calculate the migration path of the pollutant from the target pollution area. The specific inversion method can be based on particle tracking algorithm, combined with the flow information (such as flow rate and flow direction) of the water body to determine the reverse migration path of the pollutant. The Lagrangian particle tracking model (such as Eulerian-Lagrangian method) is used to inverse the migration path of the pollutant. The Bayesian inference method is used to combine the reverse migration path data to infer the probability of the potential pollution source. The Bayesian inference calculates the spatial probability distribution of the pollution source according to the historical data and the conditions of pollutant diffusion. The position of the pollution source can be estimated by constructing Bayesian network or applying Markov Chain Monte Carlo (MCMC) algorithm. The specific Bayesian inference formula is: Where P(S|D) is the posterior probability of the spatial location S of the pollution source given the observed data D, P(D|S) is the likelihood function of the pollutant diffusion path, P(S) is the prior probability of the pollution source, and P(D) is the total probability of the observed data. The boundary inversion method is used to process the probability distribution data of potential source areas obtained from Bayesian inference, and homotopy focusing is used to further refine the pollution source regions. Homotopy focusing, through optimization algorithms, gradually approximates the boundary of the most likely pollution source region, thereby accurately determining the set of spatial coordinates of the pollution source. Optimization algorithms (such as gradient descent and genetic algorithms) can be used to invert and optimize the boundary of the potential source region to obtain the precise coordinates of the potential pollution sources. Based on the set of potential pollution source coordinates, the pollution sources are classified and divided into different source tracing blocks. Each source tracing block represents the influence range of the pollution source. Spatial analysis methods (such as Voronoi diagrams and k-means clustering) are used to divide and classify the potential pollution source regions, generating contribution region data of the pollution sources. Each region represents the magnitude of the influence of different pollution sources. For each block, its contribution to the metal pollution diffusion process is assessed based on pollutant concentration and flow characteristics. Weights are assigned to each pollution source area according to its size, pollution concentration, and diffusion characteristics. The weights are calculated based on the region's pollutant concentration, impact range, and its relationship to the time series. For example, areas with larger impacts or higher concentrations will be assigned higher weights. Finally, the pollution source contribution areas are ranked according to their weights to obtain a pollution contribution ranking, thereby assessing the degree of contribution of each potential pollution source to water pollution. The weight calculation formula is: W i =α·C i ·A i ;W i Let C be the weight of the i-th pollution source. i Let A be the concentration in the i-th pollution source area. i Let be the area of ​​the i-th pollution source region, and α be the weighting coefficient.

[0107] Of particular importance, boundary inversion homotopy focusing on potential source region probability distribution data also includes:

[0108] Identify the probability distribution boundary of the potential source region probability distribution data to obtain boundary candidate region data;

[0109] Perform higher-order boundary mapping on the candidate boundary region data to generate homotopy mapping candidate region data;

[0110] Nonlinear coordinate adjustment is performed on the homotopy mapping candidate region data to generate inversion coordinate set data;

[0111] The inverted coordinate set data is focused in coordinate space to generate high-precision pollution source area data;

[0112] The high-precision pollution source area data is refined by boundary inversion to generate a potential pollution source coordinate set.

[0113] In the embodiments of the present application, by the numerical characteristics of the probability distribution, image processing or geographic information analysis techniques are used to identify the probability boundaries in the potential source area probability distribution data. These boundaries represent the diffusion area of the pollution source, and are usually cut based on the threshold value of the probability value. According to the statistical characteristics of the probability distribution, such as mean, standard deviation or percentile, a suitable threshold value is selected to determine the boundary. Common methods include Otsu threshold method or edge detection algorithm based on local maximum value. Through contour extraction, cluster analysis and other techniques, the boundary candidate region data of the pollution source is obtained, which contains the location of the potential pollution source. High-order mapping algorithm is used for spatial transformation of the boundary candidate region data, usually using homotopy mapping technology, which can effectively handle complex and irregular boundary shapes. Through homotopy mapping of the candidate region data, a more regular and smooth region structure is obtained, which can be realized by numerical simulation algorithm or spatial geometric transformation method, ensuring that the transformed region data still maintains the core characteristics of the original data. Through homotopy mapping, a candidate region can be obtained, which is very helpful for spatial coordination and detail capture in the subsequent analysis process. Nonlinear coordinate transformation (such as high-order Bezier curve fitting, radial basis function transformation, etc.) is used to adjust the coordinates of the mapped region data. The main purpose of this step is to correct the errors caused by geometric irregularity or boundary effect. Algorithms such as finite element method (FEM) or smooth constraint algorithm are used to adjust the coordinates non-linearly, ensuring that they conform to the actual geographical characteristics of the potential source area, generating coordinate set data that accurately reflect the spatial characteristics of the pollution source area, ensuring that the transformed data can better reflect the actual pollution source space. Coordinate focusing algorithms (such as principal component analysis, clustering algorithm or multi-scale transformation) are used to focus the inversion coordinate data in space, reducing the redundancy of spatial data and improving the positioning accuracy. Local weighting algorithms or local linear regression methods are applied to fine-tune the coordinates in the local space, highlighting the core area of the pollution source area. This processing helps to improve the spatial accuracy of the pollution source area and eliminate irrelevant or low-probability areas. Through the coordinate focusing algorithm, highly concentrated pollution source areas are extracted, and high-precision pollution source area data is finally obtained, which provides accurate positioning basis for subsequent pollution source analysis. Through inversion refinement technology, the boundary of the high-precision pollution source area data is further modified, which can be refined by iterative optimization methods, Monte Carlo simulation and other techniques to improve the detail level and spatial accuracy of the pollution source area. Through the inversion algorithm, the fuzzy part of the boundary is gradually corrected in the iterative process, and the error or overlapping area is eliminated. Ensure that the generated potential pollution source coordinate set is as accurate as possible, which can reflect the actual location of the pollution source, and provide reliable data support for subsequent pollution source analysis and monitoring.

[0114] Preferably, the step 1 of performing multi-spectral collection on the potential pollution source coordinate set, and extracting the metal fingerprint features in the corresponding spectrum includes:

[0115] The ground multi-spectral equipment parameters of the potential pollution source coordinate set are configured to generate multi-spectral collection parameter data;

[0116] The multi-spectral collection parameter data is subjected to on-site spectral scanning to generate original multi-spectral data of the pollution source area;

[0117] The spectral band of the original multi-spectral data is calibrated, and the calibrated spectral band is subjected to background reflection elimination to generate background-removed spectral data;

[0118] The metal characteristic band in the background-removed spectral data is extracted, and the metal characteristic band is subjected to element characteristic vector matching to obtain metal fingerprint features.

[0119] In the embodiments of the present application, a suitable ground multi-spectral device (such as a portable spectrometer or a multi-spectral sensor carried by a drone) is configured according to the location and environmental characteristics of the potential pollution source coordinate set. When configuring the device, the following parameters are considered: according to the absorption characteristics of metal pollutants, a suitable waveband range is selected, usually the visible light, near-infrared (NIR) and short-wave infrared (SWIR) wavebands are selected. According to the requirements and accuracy requirements of the on-site environment, set the appropriate spatial resolution to ensure coverage of the entire pollution source area. Set the frequency of multi-spectral acquisition in order to capture the dynamic changes of the pollution source, generate multi-spectral acquisition parameter data, which specifically includes device type, waveband configuration, sampling time, resolution, etc. At the coordinate position of the potential pollution source, perform on-site spectral scanning according to the configured multi-spectral device parameters. Use the configured spectral instrument to collect the target area, ensuring that the data collection covers the pollution source and the surrounding area. During the scanning process, ensure that the device can record the spectral data of the target area in real time, and the collected spectral data includes the values of reflectance at different wavelengths, constituting the original multi-spectral data. The collected spectral data includes multiple spectral bands from the visible light band to the near-infrared and short-wave infrared band, each band corresponds to different spectral information. The original multi-spectral data deviates due to device errors or external environmental interference. By comparing the known standard reflectance data or using a reflectance standard plate for calibration, the deviation in the original data is corrected to ensure the accuracy of the reflectance values of each band. Background reflection includes the reflection spectrum of non-metal pollution sources such as ground, vegetation or water surface. In the data processing process, use background removal algorithms (such as regional reflectance ratio method, spectral feature extraction method, etc.) to remove the background of the original data. After background removal, the background-removed spectral data is obtained, which removes the interference of non-pollution source parts by comparing the pre-set background model, making the spectral characteristics of the pollution source more obvious. In the background-removed spectral data, based on the spectral absorption characteristics of metal pollutants, extract the relevant metal characteristic wavebands. For example: lead (Pb) usually has obvious absorption characteristics in the 320-500nm waveband range. Mercury (Hg) has specific absorption characteristics in the 200-300nm waveband range. Cadmium (Cd) shows absorption characteristics in the 600-700nm waveband. Match the extracted metal characteristic waveband data with the known metal fingerprint spectral feature library. The feature library contains typical spectral fingerprints of various metals (such as lead, mercury, cadmium, etc.). The spectral matching algorithm (such as dynamic time warping DTW or correlation coefficient matching) can be used to compare the to-be-tested spectral data with the standard metal spectral characteristics in the fingerprint library. Through element feature vector matching, the fingerprint characteristics of each metal pollutant are obtained, including the concentration distribution, spatial distribution and influence area of the metal in the environment.

[0120] Preferably, the ground multi-spectral device parameter configuration for the potential pollution source coordinate set includes:

[0121] The ground multi-spectral equipment parameters of the potential pollution source coordinate set are configured, wherein the spatial resolution of the ground multi-spectral equipment is set to 0.3-1 meter, 8-16 spectral bands can be supported, the band coverage range is 400-2500 nanometers, the single band width is set to 10-30 nanometers, the spectral resolution is controlled to be between 3-10 nanometers, the imaging frame rate is 3-10 frames / second, the field of view angle range is 20-40 degrees, the equipment ground installation height is set to 3-6 meters, and the data sampling interval is 10-30 minutes.

[0122] Preferably, the metal characteristic band in the background-removed spectral data is extracted, and element characteristic vector matching is performed on the metal characteristic band, including:

[0123] The band energy distribution in the background-removed spectral data is analyzed to obtain candidate metal characteristic band data;

[0124] The signal-to-noise ratio of the candidate metal characteristic band data is enhanced to generate high-resolution metal band data;

[0125] Principal component analysis is performed on the high-resolution metal band data to obtain a metal characteristic band;

[0126] The background-removed spectral data is input into a preset spectral library by using the metal characteristic band to perform element spectral line retrieval to obtain preliminary element spectral line matching data;

[0127] The characteristic vector similarity of the preliminary element spectral line matching data is calculated, and the preliminary element spectral line matching data is filtered according to the confidence degree to generate a metal fingerprint characteristic.

[0128] In the embodiments of the present application, the spectral reflectance values of each waveband are normalized and the energy distribution is calculated. The energy can be obtained by integrating the reflectance values of each waveband or by wavelength-weighted averaging. Based on the typical absorption characteristics of different metals and known spectral data, the waveband range related to metal pollutants (such as lead, mercury, cadmium, etc.) is screened out. For example, the typical absorption waveband of lead is usually in the range of 300-500 nm, while the absorption waveband of mercury is in the range of 250-350 nm. After obtaining these waveband ranges, potential metal characteristic waveband data is screened out as candidate metal characteristic waveband data. Gaussian filtering or other smoothing filtering operations are performed on the candidate metal characteristic waveband data to reduce the influence of noise. Wavelet transform is used for denoising the data, and by selecting a suitable wavelet basis function, the low-frequency part of the signal is extracted while the noise is removed. The mean smoothing technique is applied to the signal of each waveband to enhance the stability of the waveband signal and further reduce the noise. After enhancing the signal-to-noise ratio, high-resolution metal waveband data is generated, making the metal characteristic waveband more clear and reliable, which is convenient for subsequent analysis. By performing principal component analysis on the high-resolution metal waveband data, the most representative metal characteristic waveband is extracted: the high-resolution metal waveband data is regarded as a multi-dimensional data matrix, and PCA processing is performed to extract the main components. The goal of PCA is to map high-dimensional waveband data to a low-dimensional space, thereby retaining most of the data variability and reducing redundant wavebands. The first few principal components in the principal component analysis are selected, which can effectively represent the spectral characteristics of the metal. Through this step, metal characteristic wavebands with significant information are obtained. The extracted metal characteristic waveband data is input into a pre-set metal element spectral library for comparison. The spectral library contains known spectral line data of different metal elements. Spectral line matching algorithms (such as dynamic time warping (DTW), least squares fitting, etc.) are used to match the background-removed spectral data with the metal element spectral lines in the spectral library. According to the spectral matching results, the preliminary matching data of each element is obtained, which includes the concentration and spatial distribution of the corresponding element. The features of the preliminary element spectral line matching data are vectorized, and the spectral features of each element can be converted into a high-dimensional feature vector. Common similarity measurement methods (such as cosine similarity, Euclidean distance, etc.) are used to calculate the similarity between different element spectral lines. Based on the feature vector similarity, a confidence threshold is set to filter the results with low matching degree. Statistical methods (such as standard deviation, confidence interval, etc.) can be used to evaluate the reliability of the matching to ensure that only high-confidence matching results are retained. According to the screened high-confidence matching data, the spectral fingerprint features of each metal element are extracted. Each metal fingerprint feature includes the typical spectral waveband, absorption characteristics, and concentration value of the metal. Finally, the generated metal fingerprint features can be used as the key basis for pollution source analysis, pollution source tracing, and water pollution early warning.

[0129] As an example of the present application, reference is made toFigure 3 As shown, in this example, the step S4 includes:

[0130] Step S41: setting a pollution concentration threshold; performing sensitivity analysis on the pollution contribution degree ranking data based on the metal fingerprint characteristics to generate heavy metal concentration influence factor data;

[0131] Step S42: associating modeling the metal fingerprint characteristic data and the heavy metal concentration influence factor data to generate pollution concentration fitting parameter data;

[0132] Step S43: performing concentration inversion calculation on the pollution concentration fitting parameter data to generate water body heavy metal concentration data;

[0133] Step S44: using the pollution concentration threshold to compare the water body heavy metal concentration data, when the pollution concentration threshold is greater than or equal to the water body heavy metal concentration data, then the water body heavy metal concentration data is dynamically warned, and the warning result is obtained;

[0134] Step S45: predicting the pollution diffusion trajectory of the metal pollutant diffusion cloud according to the warning result to construct a water body pollution diffusion mathematical model.

[0135] In the embodiments of the present application, the pollution concentration threshold is set according to the water body environment standard and historical pollution data. The threshold setting can consider the following factors: combining ecological research, setting the impact threshold on aquatic organisms, referring to public health standards to ensure human drinking water safety and food chain safety, for example, the pollution concentration threshold of lead is set to 0.05 mg / L, mercury to 0.001 mg / L, cadmium to 0.005 mg / L, etc. Using metal fingerprint characteristic data, sensitivity analysis is performed to evaluate the impact of each pollution source on metal concentration changes. Variance analysis method is used to evaluate the sensitivity of different metal characteristic wave bands and pollution sources to pollution concentration, and to identify key influencing factors. Regression analysis is performed on metal fingerprint characteristic data and pollution contribution ranking data to find out the key factors affecting pollution concentration in contribution ranking data. Based on the regression analysis results, the metal pollution sources are ranked according to the degree of influence, and the heavy metal concentration influence factor data is generated. Based on the metal fingerprint characteristic data and the heavy metal concentration influence factor data, a multiple regression model, support vector regression (SVR), random forest, etc. Data model is established to quantify the relationship between metal fingerprint characteristics and pollution concentration. Through polynomial regression, ridge regression, etc. Method, a mathematical model between metal fingerprint characteristics and pollution concentration is established, and the pollution concentration fitting parameter data is output. Support vector machine (SVM), neural network, etc. Machine learning algorithm is applied, combined with training data, to generate a prediction model. Through model training, the fitting parameters between metal fingerprint characteristics and pollution concentration are obtained, which can include: metal pollutant concentration fitting coefficient: the contribution of the concentration of each metal pollutant to the overall pollution degree. Influence factor weight: reflects the influence degree of pollution source on water pollution. Spatial and temporal variation coefficient: describes the change trend of pollution concentration in space and time. Apply pollution concentration fitting parameter data to metal fingerprint characteristic data, and calculate the concentration of each metal in the water body through inversion algorithm (such as least squares method, inverse calculation algorithm, etc.). According to the known pollution contribution factor and fitting parameter, the concentration value of each heavy metal is obtained through inverse calculation. Based on the concentration inversion calculation, the metal pollutant concentration of each measurement point is reconstructed, and the water body heavy metal concentration data is generated. Compare the heavy metal concentration data in the water body with the set pollution concentration threshold, and compare the pollution concentration data in different time periods with the set threshold. If the pollution concentration exceeds the set threshold, the early warning mechanism is triggered. Real-time monitoring of metal pollutants in water body concentration, and automatic comparison with set threshold, timely discovery of over-standard pollution. When the pollution concentration reaches or exceeds the set threshold, the system automatically generates an early warning result, including: output of the area where the pollutant concentration exceeds the standard, the type of over-standard metal, the concentration value and the time point. Based on the pollution concentration, different warning levels (such as yellow warning, orange warning, red warning, etc.) are generated. Based on the water flow field, pollutant concentration and diffusion law, a mathematical model of metal pollutant diffusion is constructed to predict the diffusion path of the pollutant.Using existing hydrodynamic models, consider meteorological factors such as water flow, wind speed, and precipitation, to predict the trajectory of pollutant diffusion. Use finite difference or finite element methods to numerically simulate the diffusion behavior of pollutants in water, generating spatial and temporal diffusion maps of pollutants. Based on the diffusion trajectory data, combined with the location of known pollution sources, pollutant concentration, flow characteristics, and other information, construct a mathematical model of pollution diffusion. By comparing and calibrating the actual monitoring data, adjust the parameters in the model to ensure the accuracy of the prediction results. According to the actual changes and early warning data, continuously optimize the prediction accuracy of the diffusion model.

[0136] Especially important is that step S45 further comprises the following steps:

[0137] Perform time series evolution analysis on the early warning result data to obtain pollution evolution driving factors;

[0138] Model the spatial diffusion trend of the pollution evolution driving factors to generate diffusion trend model data;

[0139] Extract the trajectory features of the metal pollutant diffusion cloud map and perform spatio-temporal fusion with the diffusion trend model data to generate pollution diffusion trajectory prediction data;

[0140] Construct a mathematical model of water pollution diffusion based on the pollution diffusion trajectory prediction data.

[0141] In the embodiments of the present application, the pollution concentration dynamic early warning results are organized according to the time dimension to construct a time series data set. Multivariate time series analysis (such as ARIMA, LSTM or Bayesian time network) is used to fit the pollution early warning trend, identify the key change nodes and trend patterns of the pollution concentration change over time. Through grey correlation analysis, factor decomposition or principal component analysis, the core factors driving the evolution of pollution are identified, including water flow rate, water temperature, rainfall, terrain slope, inflow source composition, etc., to generate pollution evolution driving factor data. Using pollution evolution driving factors as input variables, combined with geographic spatial information, a trend model of metal pollutant diffusion in water is established by geostatistical modeling (such as Kriging interpolation), random field modeling, or diffusion simulation method based on physical mechanism. Nonlinear mapping relationship between driving factors and pollution concentration diffusion can also be constructed using random forest regression, support vector machine regression or neural network model to generate diffusion trend model data describing the diffusion rate, concentration gradient, directionality and other trend information of pollutants at different spatial locations. Image processing and feature extraction are performed on the existing metal pollutant diffusion cloud map to obtain diffusion trajectory curve, velocity vector, direction field and other information. Methods including optical flow analysis, vector field estimation, feature line tracking, etc. can be used. The extracted trajectory features are fused with the diffusion trend model data to generate time-continuous and spatial-consistent pollutant diffusion trajectory prediction results by using spatio-temporal convolutional neural network (ST-CNN), Kalman filter fusion, or Bayesian fusion strategy. The pollution diffusion trajectory prediction data reflecting the propagation path, range and rate of metal pollutants in water over time are formed. Partial differential equation-based model: such as two-dimensional / three-dimensional Advection-Diffusion (advection-diffusion) equation, considering factors such as velocity field, diffusion coefficient, pollution source intensity. Deep learning or graph neural network is used to model the trajectory data to automatically learn the diffusion law. The existing observation data is used to fit the parameters in the mathematical model, and the historical data is used to verify and adjust the model to improve the prediction accuracy. The water pollution diffusion mathematical model capable of predicting the distribution and concentration of pollutants at any time in the future is constructed, which provides a theoretical basis for water resource early warning, management and scheduling.

[0142] Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, the scope of the present application being defined by the appended claims and not by the above description, therefore all variations falling within the meaning and scope of the equivalent elements of the application file are intended to be included in the present application.

[0143] The foregoing is considered as illustrative only of the principles of the application. Numerous modifications and changes will readily occur to those skilled in the art, and it is intended to embrace all such modifications and changes that fall within the scope of the application. Accordingly, the application is not to be restricted in scope to the specific embodiments disclosed herein but is to be accorded the full scope that the principles and novel features request appropriately granted.

Claims

1. A mathematical modeling method based on data analysis and computation, characterized in that, Includes the following steps: Step S1: Collect metal pollution data of the target water area using a multi-parameter water quality sensor array; Time-series alignment of metal pollution data is performed to generate a standardized pollution dataset; Step S2: Construct a metal migration model based on the coupling of fluid dynamics and chemisorption; input the standardized pollution dataset into the metal migration model for three-dimensional spatial interpolation calculation to generate a diffusion cloud map of metal pollutants; Step S3: Perform reverse analysis of the metal pollutant diffusion cloud map to generate a set of potential pollution source coordinates and a ranking of pollution contribution; perform multispectral acquisition on the set of potential pollution source coordinates and extract the metal fingerprint features in the corresponding spectra; Step S4: Set pollution concentration threshold; rank pollution contribution based on metal fingerprint characteristics to analyze water body heavy metal concentration, generate water body heavy metal concentration data; use pollution concentration threshold to dynamically warn of water body heavy metal concentration data, and predict pollution diffusion trajectory of metal pollutant diffusion cloud map based on the warning results, so as to construct a mathematical model of water pollution diffusion.

2. The mathematical modeling method based on data analysis and computation processing according to claim 1, characterized in that, Step S1 includes the following steps: Step S11: Deploy multiple water quality monitoring points in the target water area and generate sensor deployment data. The sensor deployment is carried out using a grid division strategy, with each grid being 100m × 100m in size. Step S12: Based on the sensor deployment data, perform multi-parameter metal pollutant sampling on the target water area to generate raw metal pollution data; Step S13: Fill in the missing values ​​in the original metal contamination data to obtain the missing data; remove outliers from the missing data to obtain the cleaned metal contamination data; Step S14: Timestamp standardize the cleaned metal contamination data to generate time-unified data; use the time-unified data to perform multi-sensor time series alignment and normalization on the cleaned metal contamination data to generate a standardized contamination dataset.

3. The mathematical modeling method based on data analysis and computation processing according to claim 7, characterized in that, Step S12 includes the following steps: Step S121: Determine the sampling area and the coordinates of the deployed sensors based on the sensor deployment data; Step S122: Set the types of metallic pollutants to be detected, including lead, mercury, cadmium, chromium, and arsenic. Specifically, the detection sensitivity for lead is set to 0.001 mg / L, and the warning threshold is set to 0.05 mg / L; the detection sensitivity for mercury is set to 0.0001 mg / L, and the warning threshold is set to 0.001 mg / L; the detection sensitivity for cadmium is set to 0.0005 mg / L, and the warning threshold is set to 0.005 mg / L; the detection sensitivity for chromium is set to 0.002 mg / L, and the warning threshold is set to 0.1 mg / L; the detection sensitivity for arsenic is set to 0.001 mg / L, and the warning threshold is set to 0.01 mg / L. Step S123: Based on the type of metal pollutant to be detected, water samples and metal data are collected every 10 minutes in the sampling area according to the coordinates of the deployed sensors. The sampling depth is divided into 0-0.5m, 0.5-5m, and 5-10m to generate raw metal pollution data.

4. The mathematical modeling method based on data analysis and computation processing according to claim 1, characterized in that, Step S2 includes the following steps: Step S21: Collect historical data from the standardized contamination dataset to obtain the historical contamination dataset; Step S22: Extract hydrodynamic features and chemical adsorption characteristics from historical pollution datasets to generate hydrodynamic parameters of water bodies and chemical adsorption characteristics of metal pollution. Step S23: Perform numerical modeling and fitting modeling on the hydrodynamic parameters of the water body and the chemical adsorption characteristics of metal pollution, respectively, to generate fluid dynamics modeling data and chemical adsorption modeling data; Step S24: Mathematically couple the fluid dynamics modeling data and the chemical adsorption modeling data to generate a metal migration model; input the standardized pollution dataset into the metal migration model for three-dimensional spatial interpolation calculation to generate a metal pollutant diffusion cloud map.

5. The mathematical modeling method based on data analysis and computation processing according to claim 4, characterized in that, Step S24, which involves inputting the standardized pollution dataset into the metal migration model for three-dimensional spatial interpolation calculation, includes: The standardized pollution dataset is input into the metal migration model for three-dimensional meshing to generate pollution grid point data. Local spatial vortex features are extracted from the pollution grid data to generate vortex field sensing data. The flow field structure is reconstructed from the vortex field sensing data to generate vortex structure mapping data; Spatial interpolation projection is performed on the vortex structure mapping data to generate three-dimensional interpolated pollution field data; Contour surface reconstruction is performed on the three-dimensional interpolated pollution field data to generate pollution concentration contour surface data; Color-layered rendering is applied to the isosurface data of pollution concentration to generate a cloud map of metal pollutant diffusion.

6. The mathematical modeling method based on data analysis and computation processing according to claim 1, characterized in that, Step S1 involves reverse analysis of the pollution source in the diffusion cloud map of metal pollutants, including: Time-series slices were created from the diffusion cloud map of metal pollutants to generate dynamic diffusion evolution data; The flow direction vector field is inverted from the dynamic diffusion evolution data to generate pollutant reverse migration path data; Bayesian spatial inference is performed on the pollutant reverse migration path data to generate potential source region probability distribution data; Boundary inversion homotopy focusing is performed on the probability distribution data of potential source areas to generate a set of coordinates of potential pollution sources; The coordinate set of potential pollution sources is classified into source-tracing blocks to generate pollution source contribution area data. Calculate the weights of the pollution source contribution area data, and sort the pollution contribution area data according to the weights to generate a pollution contribution ranking.

7. The mathematical modeling method based on data analysis and computation processing according to claim 1, characterized in that, Step 1 involves multispectral acquisition of the coordinate set of potential pollution sources and extraction of metal fingerprint features from the corresponding spectra, including: Configure the ground-based multispectral equipment parameters for the set of potential pollution source coordinates to generate multispectral acquisition parameter data; On-site spectral scanning is performed on the multispectral acquisition parameter data to generate raw multispectral data of the pollution source area; The spectral bands of the original multispectral data are calibrated, and background reflectance is removed from the calibrated spectral bands to generate background-free spectral data. Metal feature bands are extracted from the background spectral data, and element feature vector matching is performed on the metal feature bands to obtain metal fingerprint features.

8. The mathematical modeling method based on data analysis and computation processing according to claim 7, characterized in that, Configuring ground-based multispectral equipment parameters for the coordinate set of potential pollution sources includes: The parameters of the ground-based multispectral equipment were configured for the coordinate set of potential pollution sources: the spatial resolution of the ground-based multispectral equipment was set to 0.3–1 meter, it could support 8–16 spectral bands, the band coverage range was 400–2500 nanometers, the width of a single band was set to 10–30 nanometers, the spectral resolution was controlled between 3–10 nanometers, the imaging frame rate was 3–10 frames / second, the field of view range was 20–40 degrees, the ground installation height of the equipment was set to 3–6 meters, and the data sampling interval was 10–30 minutes.

9. The mathematical modeling method based on data analysis and computation processing according to claim 7, characterized in that, Extracting metal feature bands from background-de-spectral data and performing elemental feature vector matching on these bands includes: By analyzing the band energy distribution in the background-removed spectral data, the characteristic band data of candidate metals are obtained; Signal-to-noise ratio enhancement is performed on candidate metal characteristic band data to generate high-resolution metal band data; Principal component analysis was performed on high-resolution metal band data to obtain the characteristic bands of the metals; Using the metal characteristic band, the background-de-background spectral data is input into a preset spectral library for elemental spectral line retrieval to obtain preliminary elemental spectral line matching data; Calculate the feature vector similarity of the preliminary elemental spectral line matching data, and perform confidence filtering on the preliminary elemental spectral line matching data based on the feature vector similarity to generate metal fingerprint features.

10. The mathematical modeling method based on data analysis and computation processing according to claim 1, characterized in that, Step S4 includes the following steps: Step S41: Set pollution concentration threshold; perform sensitivity analysis on pollution contribution ranking data based on metal fingerprint characteristics to generate heavy metal concentration influence factor data; Step S42: Perform correlation modeling on the metal fingerprint feature data and the heavy metal concentration influencing factor data to generate pollution concentration fitting parameter data; Step S43: Perform concentration inversion calculation on the pollution concentration fitting parameter data to generate water heavy metal concentration data; Step S44: Use the pollution concentration threshold to compare the heavy metal concentration data of water body with the threshold. When the pollution concentration threshold is greater than or equal to the heavy metal concentration data of water body, then perform dynamic early warning on the heavy metal concentration data of water body and obtain the early warning result. Step S45: Based on the early warning results, predict the pollution diffusion trajectory of the metal pollutant diffusion cloud map to construct a mathematical model for water pollution diffusion.

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