Method and device for simulating spatial level of urban economy

Abstract

The application provides a city economic level space simulation method and device, first, multiple source space data are acquired, the research area is divided into a plurality of sub-regions according to the spatial distribution characteristics of the city economic level, and a driving factor data set is constructed by taking a regular space unit as a basic simulation unit;Then, based on the historical city economic level total data, the total quantity constraint model of the city economic level evolution with time is constructed on the sub-region scale;Combined with the attribute information of the space unit, the city economic level grade change probability model of the space unit is established, and the probability of the city economic level grade change of each space unit in a given time stage is calculated;Under the total quantity constraint condition of the city economic level, the dynamic expansion mechanism of the city economic level grade system is introduced, and the city economic level grade of the space unit is distributed and updated;The simulation results of each sub-region are spatially integrated, so that the simulation results meet the overall scale total quantity constraint, so that the city economic level space simulation result is obtained.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and device for spatial simulation of urban economic levels. Background Technology

[0002] Urban economic level is used to characterize the economic development status of urban spatial units within a certain period, reflecting the intensity and scale of their economic activities. It is of great significance in urban planning, regional economic analysis, and spatial governance decisions. With the continuous advancement of urbanization, urban economic activities exhibit significant agglomeration and differentiation in space, and the distribution of economic levels among different spatial units shows obvious non-equilibrium characteristics.

[0003] In the actual process of urban economic development, influenced by factors such as location, resource endowment, and infrastructure level, urban economic activities exhibit different development characteristics at different spatial scales. However, existing spatial simulation methods for urban economic levels mostly consider only the single scale of spatial units and construct unified transfer rules to model the economic evolution process of spatial units. This makes it difficult to effectively characterize the differences and synergistic effects between economic driving mechanisms at different spatial scales, thus making it difficult to accurately reflect the spatiotemporal process of urban economic development.

[0004] Furthermore, existing spatial simulation methods for urban economic levels mostly focus on short-term simulations, typically assuming that the numerical range of urban economic levels is fixed within the extreme range of historical statistical data, and constructing a relatively static economic hierarchy based on this. However, against the backdrop of sustained and rapid urban economic development, the total urban economic output continues to grow, and the economic levels of different regions gradually exceed the range of values ​​from the historical statistical period, causing the numerical range of urban economic levels to expand over time. In long-term spatial simulations of urban economic levels, if a fixed numerical range or static hierarchy is still used to constrain the economic levels, the simulation results are easily limited by artificial upper limits in later stages, resulting in unreasonable truncation or saturation, thus failing to truly reflect the spatial evolution characteristics of urban economic levels after they exceed historical ranges. Summary of the Invention

[0005] This application proposes a spatial simulation method and device for urban economic levels, which can solve one of the problems existing in the background technology.

[0006] To achieve the above objectives, this application adopts the following technical solution:

[0007] Firstly, a spatial simulation method for urban economic levels is provided, including:

[0008] Obtain multi-source driving factor data and economic level statistics of urban economic level of each spatial unit in time series. Several spatial units constitute a sub-region, and all sub-regions constitute the regional whole of the city.

[0009] The driving factor feature vector is obtained from the driving factor data, and the economic level is obtained from the economic level statistics.

[0010] Based on the aforementioned economic level statistics, a time series prediction model for the total economic level is constructed at both the sub-regional and overall regional scales to characterize the evolution of the total economic level.

[0011] Based on the economic level, a spatial unit economic level development probability model is constructed to characterize the probability of changes in the economic level of a spatial unit within a given time period.

[0012] Based on the constructed multi-scale collaborative cellular automaton model, the spatial distribution of economic level grades of each spatial unit is obtained. The cellular automaton model uses the total economic level as a constraint and the probability of change in economic level grades as the input to the spatial unit state transition probability.

[0013] Based on the spatial distribution results of the economic level of each spatial unit, the economic level of each spatial unit is converted into a continuous economic level value of the spatial unit, and the simulated total of the city's economic level is obtained from the continuous economic level value of each spatial unit.

[0014] Based on the above technical solution, firstly, multi-source spatial data is acquired and preprocessed. The study area is divided into several sub-regions according to the spatial distribution characteristics of urban economic levels, and a driving factor dataset is constructed using regular spatial units as basic simulation units. Subsequently, based on historical total urban economic level data, a total constraint model of urban economic level evolution over time is constructed at the sub-region scale. On this basis, a probability model of changes in urban economic level levels within spatial units is established by combining spatial unit attribute information, calculating the probability of changes in urban economic level levels in each spatial unit within a given time period. Under the constraint of total urban economic level, a dynamic expansion mechanism for the urban economic level system is introduced, and spatial neighborhood effects and historical development inhibition factors are comprehensively considered to improve the assessment of urban economic levels within spatial units. The ranking system is assigned and updated to form spatial simulation results of urban economic levels at the sub-regional scale. Finally, the simulation results of each sub-region are spatially integrated, and the consistency of the total urban economic level is corrected at the overall scale of the study area to ensure that the simulation results meet the overall scale constraints. This yields spatial simulation results of urban economic levels at the study area scale. By establishing a collaborative constraint relationship between the overall scale, sub-regional scale, and spatial unit scale of the study area, this solves the problem that existing methods cannot reflect the linkage between different spatial levels by modeling at a single spatial scale. At the same time, by introducing a dynamic expansion mechanism of the ranking system, the limitations of a fixed ranking system on the evolution of urban economic levels during long-term simulations are effectively avoided, thereby improving the rationality and stability of the spatial simulation results of urban economic levels.

[0015] In one possible design approach of the first aspect, the driving factor feature vector is obtained by standardizing the driving factor data; the economic level level is obtained from the economic level statistics, specifically including:

[0016] Let G be the economic level of spatial unit i at time t. i Let (t) be the discretized hierarchical threshold sequence obtained within its sub-region:

[0017]

[0018] Discretized economic level Represented as:

[0019] Among them, the hierarchical threshold sequence contains a total of Each threshold corresponds to a set of values. A range of economic levels.

[0020] In one possible design approach of the first aspect, the time-series forecasting model for the total economic level is an S-curve model:

[0021]

[0022] in, Indicates time The corresponding total economic level; This is an upper bound parameter used to characterize the evolution trend of the total economic level; its value is obtained by fitting historical statistical data. and It is a curve shape control parameter used to adjust the growth direction and growth rate of the total economic level over time.

[0023] In one possible design approach of the first aspect, the development probability model for the economic level of the spatial unit is a random forest model:

[0024]

[0025]

[0026] in, spatial unit In time The corresponding driving factor feature vector; d is the number of driving factors; This is the current forecast time point; The probability of development of the economic level of a spatial unit; The number of base learners; Indicates the first The classification output of each base learner; This is an indicator function. It takes the value 1 when the base learner determines that the economic level of the spatial unit has changed, and takes the value 0 otherwise.

[0027] In one possible design approach of the first aspect, based on the constructed multi-scale cooperative cellular automata model, the spatial distribution results of the economic level of each spatial unit are obtained, specifically including:

[0028] Based on the aforementioned time-series forecasting model for total economic level, the upper bound of the highest level in the economic level classification system is dynamically expanded.

[0029] Under the premise of satisfying the total economic level constraint, spatial units within the sub-region are ranked according to the comprehensive development probability of spatial units. The comprehensive development probability is defined by the economic level development probability of the spatial unit, the neighborhood effect factor, and the development inhibition factor.

[0030] Spatial units are selected sequentially from high to low in order of comprehensive development probability for iterative updates of economic level.

[0031] In one possible design approach of the first aspect, based on the aforementioned economic level aggregate time series forecasting model, the upper bound of the highest level of the economic level classification system is dynamically expanded, specifically including:

[0032] Assume the economic level hierarchy is set according to a preset time interval. Update, among which Indicates the time span between two consecutive level expansion operations; at time nodes At that time, the economic level hierarchy within each sub-region consists of a finite number of discrete levels, and the spatial unit... The range of economic level grades is as follows:

[0033]

[0034] in, Indicates time node The corresponding highest level number;

[0035] At each preset time interval At the end, a dynamic expansion operation is performed on the economic level hierarchy system, assuming the [number]th [level] is [value]. The time point corresponding to the secondary expansion is:

[0036]

[0037] Let the upper bound of the highest level corresponding to the time of the previous level expansion be . Then the upper bound of the highest level corresponding to the current level expansion time. Update as follows:

[0038]

[0039] in, For time intervals [ The total economic growth rate of cities within the region is specifically expressed as follows:

[0040]

[0041] in, Indicates at a time node The corresponding target economic level total, Indicates at a time node The corresponding target economic level;

[0042] When satisfied At that time, at the highest level of the existing economic level hierarchy. Add a new highest level based on the existing level The value range corresponding to this newly added level is defined as follows: .

[0043] In one possible design approach of the first aspect, spatial units are selected sequentially in descending order of the comprehensive development probability for iterative updates of the economic level, specifically including:

[0044] For the selected spatial unit Not exceeding the highest level of the current year Under the constraints, its economic level was changed from Complete a level update;

[0045] After each spatial unit is selected and updated, the total economic level of the current sub-region is calculated in real time based on the updated spatial unit level results. Let the current year's economic level be B. The upper and lower thresholds corresponding to level B are respectively and Then its grade representative value is defined as:

[0046]

[0047] Record the time node within the current sub-region. The number of spatial units belonging to level B is:

[0048]

[0049] The total economic level of this sub-region in the current year is then expressed as:

[0050]

[0051] The current economic level of the sub-region With the time series forecasting model of total economic level at time nodes The target economic level of the corresponding sub-region The comparison is made, and the error is defined as:

[0052]

[0053] When error Less than the preset tolerance threshold If the sub-region is determined to have met the total economic level constraint in the current year, the spatial unit level update within the sub-region is stopped; otherwise, the next spatial unit is selected from the sorting sequence and the above process is repeated.

[0054] In one possible design approach of the first aspect, based on the spatial distribution results of the economic level levels of each spatial unit, the economic level level of the spatial unit is converted into a continuous economic level value of the spatial unit, and the simulated total urban economic level is obtained from the continuous economic level values ​​of each spatial unit, specifically including:

[0055] Let the first Each sub-region at a time node The economic level threshold sequence is as follows:

[0056]

[0057] in, The threshold number is the number of spatial units. Belongs to the Each sub-region, at a specific time point The city's economic level is categorized as follows:

[0058]

[0059] The continuous economic level value corresponding to this spatial unit is defined as:

[0060]

[0061] in, Representing spatial units At the time point Continuous values ​​of economic level;

[0062] By summing up the continuous economic level values ​​of all spatial units, the simulated total economic level of the city is calculated:

[0063]

[0064] in, The total number of spatial units within the study area;

[0065] Calculate the ratio between the simulated total urban economic level and the target total urban economic level:

[0066]

[0067] in, To be at the time node The target total amount of urban economic development;

[0068] when At that time, the continuous economic level values ​​of all spatial units are adjusted proportionally in a uniform manner:

[0069]

[0070] in, This represents a continuous value of the economic level of a spatial unit after proportional adjustment.

[0071] By adjusting the above proportions, the simulated total urban economic level is made to meet the overall scale target constraints, namely:

[0072]

[0073] Where M represents the number of spatial units within the study area.

[0074] In a second aspect, an electronic device is provided, comprising: a processor, and a memory coupled to the processor, the memory for storing a computer program; the processor for executing the computer program stored in the memory such that the electronic device performs the urban economic level spatial simulation method as described in any possible implementation of the first aspect. Attached Figure Description

[0075] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0076] Figure 1 This is a flowchart of the multi-scale collaborative urban economic level spatial simulation method provided in the embodiments of this application;

[0077] Figure 2 This is a spatial error distribution map between the simulation results of this application example and the actual urban economic level provided in the embodiments of this application. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0079] It should be noted that although functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification and the above-mentioned figures are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0080] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0081] This embodiment provides a multi-scale collaborative spatial simulation method for urban economic levels, addressing the shortcomings of existing urban economic spatial simulation methods in reflecting the collaborative relationships between different spatial scales under single-spatial-unit-scale modeling conditions, and the limitation imposed by fixed numerical intervals on economic growth during long-term simulations. To achieve the above objectives, this embodiment proposes a spatial simulation method for urban economic levels based on a multi-scale collaborative constraint mechanism and a dynamic expansion mechanism of the hierarchical system.

[0082] The proposed method establishes hierarchical linkages between the study area scale (e.g., the entire province), sub-region scale (e.g., cities and counties), and spatial unit scale, constructing a multi-scale collaborative cellular automata model. It then constrains the spatial simulation process using a time-evolution model of urban economic output. Furthermore, by introducing a dynamic expansion mechanism for the economic hierarchy, the upper bound of the economic hierarchy automatically adjusts with the growth of total economic output, thereby avoiding the limitations imposed by a fixed hierarchy on later simulation results and improving the rationality and stability of urban economic spatial simulation results.

[0083] This embodiment provides a multi-scale collaborative spatial simulation method for urban economic levels, comprising the following steps:

[0084] S1: Acquire and preprocess multi-source driving factor data for spatial simulation of urban economic levels within the study area. Divide the study area into sub-regions based on the spatial distribution characteristics of urban economic development, and construct spatial units within each sub-region using a unified standard. Use these spatial units as the basic simulation units for organizing multi-source driving factor data. Simultaneously, discretize the continuous values ​​of urban economic levels in each spatial unit to construct a hierarchical system of urban economic levels.

[0085] S2: Based on the time series of historical urban economic level statistics, a time series prediction model for the total urban economic level is constructed at both the overall scale and the sub-regional scale of the study area. This model is used to determine the target constraint values ​​for the overall urban economic level of the study area and each sub-region at different time points, thereby forming a multi-scale "top-down" total constraint condition for spatial simulation.

[0086] S3: Based on the multi-source driving factor data corresponding to spatial units, a bottom-up spatial simulation model of urban economic level based on random forest is constructed to calculate the probability of changes in the urban economic level of each spatial unit in a certain period of time. This model is used to characterize the development trend of spatial units in the process of urban economic evolution and serves as the state transition probability in the multi-scale cooperative cellular automaton model.

[0087] S4: Under the constraint of the total economic level target of the sub-region obtained in step S2, a multi-scale collaborative cellular automata model is constructed, with spatial units as cellular state units. Within each simulation time stage, under the combined effect of the total scale constraint of the sub-region and the state transition rules of the spatial unit, and combined with the probability of change of the urban economic level of the spatial units obtained in step S3, the spatial simulation and state update of the urban economic level of the spatial units within each sub-region are performed. This yields the spatial distribution results of the urban economic level of each sub-region in that time stage, and the simulation continues into the next time stage.

[0088] S5: Based on step S4, the simulation results of each sub-region are merged to form the spatial distribution results of the urban economic level at the overall scale of the study area. The simulation results are then uniformly adjusted according to the urban economic level target constraints at the overall scale of the study area, thereby obtaining the spatial simulation results of the urban economic level at the spatial unit scale within the study area.

[0089] Step S1 specifically includes the following steps:

[0090] First, multi-source driving factor data for spatial simulation of urban economic levels are acquired within the study area, and the data is preprocessed. The preprocessing includes operations such as coordinate system unification, data reprojection, spatial clipping, resampling, and raster alignment to align the spatial resolution and spatial extent of data from different sources.

[0091] Based on the spatial distribution characteristics of urban economic development, the study area is divided into sub-regions, thereby constructing a multi-scale spatial hierarchy within the study area, consisting of the overall scale of the study area, the sub-region scale, and the spatial unit scale. The overall scale of the study area is used to characterize the scale of overall economic development in the region; the sub-region scale is used to depict the spatial differences in economic development within the region; and the spatial unit scale is used for spatial simulation calculations of urban economic levels.

[0092] A regular spatial grid is constructed within the sub-region, and the spatial grid unit is used as the basic spatial unit for simulating the urban economic level, which carries the information of driving factors and the status of the urban economic level.

[0093] The driving factors include natural environmental conditions, land use characteristics, population and economic activity intensity, and transportation accessibility. Using a spatiotemporal alignment method, data from different sources are mapped onto a spatial grid, forming a spatial unit driving factor dataset.

[0094] Furthermore, the multi-source driving factors are standardized to serve as input features for the model. For the k-th driving factor, its standardization formula is expressed as:

[0095]

[0096] In the formula, and The first The attribute value and its standardized eigenvalue of the k-th driving factor corresponding to each spatial unit. and Let represent the maximum and minimum values ​​of the k-th driving factor, respectively. For each spatial unit, its feature vector can be represented by the standardized eigenvalues ​​of each driving factor, and the input feature sample set is the set of feature vectors of all spatial units.

[0097] Furthermore, statistical data characterizing the city's economic level are obtained, and this data is discretized to construct a city economic level hierarchy for spatial simulation. The discretization process employs the natural breakpoint method to classify the city's economic level, and independently determines the corresponding classification threshold within each sub-region.

[0098] Let G be the urban economic level corresponding to spatial unit i at time t. i Let (t) be the discretized hierarchical threshold sequence obtained within its sub-region:

[0099]

[0100] The threshold sequence contains a total of A threshold, thus forming a corresponding... The city's economic level range is then discretized. It can be represented as:

[0101] Furthermore, the urban economic level is aligned with the spatial grid corresponding to the aforementioned driving factors, so that each spatial unit simultaneously corresponds to a unique driving factor feature vector and an urban economic level.

[0102] In step S2, based on the time series of historical urban economic statistics, time series prediction models for the total urban economic level are constructed at both the overall scale and the sub-regional scale of the study area to model the evolution of the total urban economic level.

[0103] Specifically, at the overall scale of the study area, the statistical data on urban economic levels at each time point within the study area are summed to obtain the overall urban economic level sequence of the study area; at the sub-region scale, the statistical data on urban economic levels at corresponding time points in each sub-region are summed to obtain the overall urban economic level sequence of each sub-region.

[0104] Based on the aforementioned time series data, time evolution models of total urban economic level are constructed at both the overall and sub-regional scales of the study area to calculate the total economic level of the target city at different time points.

[0105] Considering that urban economic development typically exhibits phased characteristics of slow initial growth, rapid mid-term growth, and eventual stabilization, this embodiment employs an S-curve model to characterize the temporal evolution of the total urban economic level. Specifically, an S-curve is used to model the evolution of the total urban economic level over time, and its mathematical expression is as follows:

[0106]

[0107] in, Indicates time The corresponding total economic level of the city; This is the upper bound parameter in the S-curve model used to characterize the evolution trend of the total urban economic level. Its value is obtained by fitting historical statistical data and is used to reflect the changing characteristics of the overall urban economic development scale within a given statistical interval. and These are curve shape control parameters used to adjust the growth direction and speed of the city's total economic level over time.

[0108] Based on historical data on the total economic level of cities, the least squares fitting method is used to adjust the parameters in the S-curve model. , and Estimate the data to minimize the error between the total urban economic level calculated by the model and historical observations, thereby obtaining a time evolution model that can reflect the overall evolution trend of the urban economy.

[0109] Using the aforementioned time evolution model, the overall target total urban economic level of the study area and the target total urban economic level of each sub-region can be calculated at different time points. In the subsequent spatial simulation process, the overall target total urban economic level of the study area is used to constrain the overall economic development scale of the region; the target total urban economic level of each sub-region is used to constrain the economic distribution process of spatial units within the region.

[0110] By adopting the above approach, a multi-scale collaborative total constraint mechanism is established between the overall scale of the study area and the sub-regional scale, providing multi-scale constraint conditions for subsequent spatial simulation of urban economic levels.

[0111] Step S3 is used to construct a spatial unit urban economic level development probability model based on historical urban economic level change information, calculate the probability of urban economic level change in a spatial unit within a given time period, and thus serve as the state transition probability in the multi-scale cooperative cellular automaton model, providing input for spatial simulation and state update in step S4.

[0112] Specifically, set and For different historical time points, and For each spatial unit Based on its time interval Whether the economic level of the city has changed is used as a monitoring label, and time is used as the time. The corresponding driving factor data are used as input features to construct the sample dataset. The supervision label is defined as a binary classification label:

[0113]

[0114] in Representing spatial units In time The city's economic level. Representing spatial units In the time interval Has the economic level of the city changed?

[0115] Set spatial unit In time The corresponding driving factor feature vector is:

[0116]

[0117] Where d is the number of driving factors. The sample dataset can then be represented as:

[0118]

[0119] in, The total number of samples.

[0120] To mitigate the bias caused by the imbalance between positive and negative samples during model training, the sample dataset was sampled in equal proportions to construct a balanced sample set, which was then divided into a training set and a test set. A random forest classification model was used to train the model on the training set, establishing a mapping relationship between driving factors and changes in the economic level of spatial unit cities. The model performance was then validated using the test set.

[0121] After completing model training and validation, in time As the current prediction time point, time Corresponding driving factor feature vector Input into the trained random forest model to predict spatial units In time The probability of changes in the city's economic level during subsequent simulation phases, starting from this point, is used as the development probability of spatial units. .

[0122] The spatial unit evolution probability is calculated based on the classification results of the random forest model, and its expression is as follows:

[0123]

[0124] in, This represents the number of base learners in the random forest model. Indicates the first The classification output of each base learner This is an indicator function. It takes the value 1 when the corresponding base learner determines that the spatial unit has changed its urban economic level, and takes the value 0 otherwise.

[0125] Thus, the time of each spatial unit is obtained. This is the set of probabilities of changes in the city's economic level in the subsequent stages of the current node. This set of probabilities is used as the input of the spatial unit state transition probability in the subsequent multi-scale cooperative cellular automata model, thereby providing basic probabilistic conditions for the spatial simulation of the city's economic level.

[0126] Step S4 is used to allocate and update the urban economic level at the spatial unit level under the constraint of the total urban economic level determined in step S2, based on the multi-scale collaborative cellular automata model, taking spatial units as cellular state units, integrating the probability of change of urban economic level of spatial units calculated in step S3, and combining the influence of spatial neighborhood and historical development inhibition factors, so as to obtain the spatial distribution result of urban economic level of spatial units in each sub-region.

[0127] Specifically, at the time node As the starting point for the spatial simulation of urban economic level, the upper bound of the highest level of the urban economic level system is dynamically expanded based on the time evolution model of the total urban economic level constructed in step S2. This avoids the failure of the fixed level system to constrain the upper bound of the economic level during the long-term simulation process, which would lead to a limited distribution of economic level in the later simulation stages and thus weaken the differences between different stages.

[0128] Assume a city economic level ranking system is established according to a preset time interval. Update, among which This indicates the time span between two consecutive level expansion operations. At the time node... At that time, the urban economic level hierarchy system within each sub-region consists of a finite number of discrete levels, and the spatial unit... The range of values ​​for the city's economic level is as follows:

[0129]

[0130] in, Indicates time node The corresponding highest level number.

[0131] In subsequent simulations, at each preset time interval At the end, a dynamic expansion operation is performed on the urban economic level hierarchy system. Let the [number]th [unit] be [value]. The time point corresponding to the secondary expansion is:

[0132]

[0133] Let the upper bound of the highest level corresponding to the time of the previous level expansion be . Then the upper bound of the highest level corresponding to the current level expansion time. Update as follows:

[0134]

[0135] in, For time intervals [ The overall economic growth rate of cities within the region. Specifically, it is expressed as:

[0136]

[0137] in, This indicates that step S2 is at time node. The corresponding total economic level of the target city This indicates that step S2 is at time node. The corresponding total economic level of the target city.

[0138] When satisfied At that time, at the highest level of the original urban economic level hierarchy system Add a new highest level based on the existing level The value range corresponding to this newly added level is defined as follows:

[0139]

[0140] By limiting the addition of a maximum of one level at any given time during expansion, drastic changes to the hierarchical system within a short period can be avoided, thus maintaining the continuity and stability of the hierarchical structure over time. The thresholds for other existing level classifications remain unchanged. This approach allows the urban economic level hierarchy to gradually expand along with the overall growth of the city's economic level, providing new hierarchical space for subsequent upgrades of urban economic level in spatial units.

[0141] When the target simulation time point is ,and At that time, by time node As the starting point of the simulation, the spatial evolution of the city's economic level is simulated year by year. Specifically, the time interval is... The simulation is divided into multiple consecutive phases based on the year. Within each corresponding simulation phase, the probability of change in the economic level of spatial unit cities is calculated based on the result obtained in step S3. Furthermore, by combining the current state of the spatial neighborhood and the historical development status of the spatial units, the neighborhood effect factor and development inhibition factor are dynamically updated, thereby constructing a comprehensive development probability for each spatial unit, which is used to characterize the possibility of changes in the urban economic level of the spatial unit in the current year.

[0142] During the current annual simulation phase, let's assume... Indicates the time point corresponding to the current year, spatial unit The comprehensive development probability is defined as:

[0143]

[0144] in, Representing spatial units The overall development probability within the current year, The probability of change in the economic level of a spatial unit city, calculated in step S3, represents the probability of the basic development potential of the spatial unit. It is used to characterize its long-term relative development tendency and remains unchanged over time in subsequent annual simulations. The neighborhood effect factor is obtained based on the spatial neighborhood state update within the current year. This refers to the development inhibition factor updated based on historical development status within the current year.

[0145] The neighborhood effect factor This is used to characterize the developmental and enhancing effect of spatial units within a spatial neighborhood that have already undergone updates in urban economic level on the target spatial unit. Let spatial units be... Centered Neighborhood set is During the current annual simulation phase, let the set of spatial units that have undergone updates to their urban economic level be denoted as... The number of updated spatial units in the neighborhood is defined as follows:

[0146] And based on this, the neighborhood effect factor is calculated:

[0147]

[0148] in, It is a single-neighborhood enhancement intensity parameter used to characterize the spatial agglomeration and diffusion effects of urban economic development.

[0149] The developmental inhibitory factor This technique is used to characterize the reduced probability of a spatial unit experiencing a change in its urban economic level during subsequent years of simulation, once that change has occurred. This reflects the phased characteristics of spatial unit evolution during urban economic development and avoids frequent level changes in spatial units during consecutive years of simulation. Let spatial units be... The indicator for whether a change in the city's economic level occurred during the historical annual simulation period is:

[0150]

[0151] The growth inhibition factor in the current year is defined as:

[0152]

[0153] in, The intensity parameter is used to prevent repeated changes in the urban economic level of spatial units during consecutive annual simulation phases.

[0154] Within the sub-region, under the premise of meeting the overall economic level constraints of the city, the first consideration is the comprehensive development probability of the spatial units. The spatial units within the sub-region are sorted, and then iteratively updated by selecting spatial units in descending order of comprehensive development probability. For each iteration, a spatial unit is selected from the sorted sequence as the current update object, and an urban economic level update operation is performed.

[0155] For the selected spatial unit Within the highest level of the current year's simulation phase Under the constraints, its urban economic level was changed from

[0156]

[0157] Complete a level update.

[0158] After each spatial unit is selected and updated, the total urban economic level within the current sub-region is calculated in real time based on the updated spatial unit level results. Let the urban economic level level in the current year's simulation phase be:

[0159]

[0160] grade The corresponding upper and lower thresholds are respectively and Then its grade representative value is defined as:

[0161]

[0162] Record the time node within the current sub-region. The number of spatial units belonging to level B is:

[0163]

[0164] Under the current year's simulation conditions, the total urban economic level corresponding to this sub-region is expressed as:

[0165]

[0166] The total urban economic level currently simulated for the sub-region The time evolution model in step S2 at time nodes Total economic level of the target city in the corresponding sub-region The comparison is made, and the error is defined as:

[0167]

[0168] When error Less than the preset tolerance threshold If the sub-region is determined to have met the total urban economic level constraint during the current year's simulation phase, the spatial unit level update within the sub-region is stopped; otherwise, the next spatial unit is selected from the sorting sequence and the above level update and total quantity verification process is repeated.

[0169] The spatial unit level update process for the aforementioned annual simulation phase is executed independently in each sub-region until completion from the time node. To the target time point The annual simulations yielded the results for each sub-region at the target time point. The corresponding spatial unit city economic level distribution results.

[0170] Step S5 is used to convert the discrete level results formed at the sub-region scale into continuous urban economic level values ​​at the spatial unit scale based on the distribution results of urban economic level levels of spatial units obtained in step S4, and to perform consistency correction on the total urban economic level at the overall scale of the study area, thereby realizing multi-scale coordination between the sub-region level system, spatial unit simulation results and the overall total constraint of the study area.

[0171] Specifically, since the urban economic level grading system in step S1 is constructed independently within each sub-region based on its own grading threshold, the range of urban economic level values ​​corresponding to the same grading number is not consistent across different sub-regions. To calculate the simulated total urban economic level at the overall scale of the study area, it is necessary to first convert the discrete grading results of the spatial units into continuous urban economic level values.

[0172] Let the first Each sub-region at a time node The threshold sequence for urban economic level is as follows:

[0173]

[0174] in, The number of threshold units. If spatial units... Belongs to the Each sub-region, at a specific time point The city's economic level is categorized as follows:

[0175]

[0176] The continuous urban economic level value corresponding to this spatial unit is defined as:

[0177]

[0178] in Representing spatial units At the time point The continuous value of the city's economic level.

[0179] Based on this, the continuous values ​​of urban economic level of all spatial units within the study area are summarized, and the simulated total urban economic level at the overall scale of the study area is calculated:

[0180]

[0181] in This represents the total number of spatial units within the study area.

[0182] To ensure that the simulation results meet the overall urban economic level constraint at the study area scale, the proportionality coefficient between the simulated total and the target total is calculated:

[0183]

[0184] in The overall scale of the study area obtained in step S2 at the time node The target total amount of urban economic development. When At that time, the urban economic level values ​​of all spatial units within the study area were adjusted proportionally:

[0185]

[0186] in This represents the economic level of a spatial unit city after the proportion adjustment.

[0187] Through the above proportional correction, the simulated total urban economic level at the overall scale of the study area meets the overall scale target constraint, namely:

[0188]

[0189] Where M represents the number of spatial units within the study area.

[0190] This yields simulation results of the spatial distribution of urban economic levels in spatial units, satisfying the overall constraint of the urban economic level of the study area. Through the above process, the urban economic level hierarchy constructed at the sub-regional scale and the simulation results at the spatial unit scale are unified and coordinated under the overall constraint of the study area, thereby ensuring the consistency and synergistic constraint relationship of the spatial simulation results of urban economic levels across different spatial scales.

[0191] Specific application examples

[0192] This application example uses a province as the research area to specifically illustrate the spatial simulation method for urban economic levels proposed in this application. In this application example, Gross Domestic Product (GDP) is used as a representative indicator of urban economic levels.

[0193] (1) Study area and acquisition of basic data

[0194] At the overall scale of the study area, a province was selected as the study area, and basic data for multiple consecutive years within the province were obtained, including county-level GDP data, land use data, digital elevation model (DEM) data, population density data, nighttime light data, point of interest (POI) data, and road network vector data for each year of 2010, 2015, and 2020. The above data were then spatially cropped and uniformly processed according to the administrative boundaries of the province.

[0195] At the sub-regional scale, the study area is divided into multiple sub-regions based on the administrative units of a certain province, county, and district, and a regular spatial grid is constructed within each sub-region.

[0196] At the spatial unit scale, regular spatial grid units are used as the basic spatial units for simulating urban economic levels, carrying information on driving factor characteristics and urban economic level grades. Specifically, the spatial grid adopts a 1 km × 1 km uniform-scale square grid. Through this method, a multi-scale spatial representation structure is constructed between the overall scale of the study area, the sub-regional scale, and the spatial unit scale, providing fundamental data support for subsequent spatial simulations of urban economic levels.

[0197] (2) Data preprocessing and driving factor construction

[0198] Preprocessing operations such as unifying the coordinate system, reprojection, resampling, and raster alignment are performed on the multi-source driving factor data to unify the spatial resolution and construct a regular spatial grid. The spatial grid cell serves as the smallest spatial unit for simulating the urban economic level in this application example, and is used to carry driving factor characteristics and GDP level information.

[0199] Based on the completed data preprocessing, multi-source driving factors for characterizing the spatial evolution of GDP are extracted, focusing on natural environmental conditions, socio-economic activity intensity, and spatial accessibility characteristics, thus constructing a set of driving factors for spatial units. Specifically, elevation, slope, population density, and nighttime light intensity—a total of four driving factors—are extracted from digital elevation models, population data, and nighttime light data to characterize the natural conditions and population and economic activity intensity of spatial units.

[0200] For road network vector data, highway and provincial road elements are extracted separately, and corresponding Euclidean distance fields are constructed. Based on this, four driving factors are extracted within the spatial grid: highway length, provincial road length, Euclidean distance to the nearest highway, and Euclidean distance to the nearest provincial road. These factors are used to characterize the traffic accessibility level of the spatial unit.

[0201] Based on land use data, information on land use types such as forest land, cultivated land, and building land is extracted, and the proportions of cultivated land, forest land, and building land within the spatial grid are calculated, totaling four driving factors, which are used to characterize the land use structure features of spatial units.

[0202] In addition, for Points of Interest (POI) data, elements in the categories of living services, transportation facilities, and catering services were selected, and the kernel density estimation method was used to calculate the corresponding kernel density values, resulting in three driving factors: kernel density of living services, kernel density of transportation facilities, and kernel density of catering services. These factors are used to characterize the degree of aggregation of human activities within spatial units.

[0203] In summary, this application example constructs 15 driving factors to comprehensively describe the characteristics of spatial units from multiple aspects such as natural environment, land use, transportation accessibility, and socio-economic activities.

[0204] The above driving factors are standardized to eliminate the influence of different dimensions. The standardization formula is as follows:

[0205]

[0206] in, and They represent the first The original attribute values ​​and standardized feature values ​​of each spatial unit. and Driving factors Maximum and minimum values ​​across all spatial units within the study area.

[0207] (3) GDP status construction and discretization

[0208] This study obtains GDP data for each district and county in a province for 2010 and 2015, using GDP as a specific indicator of urban economic level. Using 2015 district-level GDP data as the base year, the district-level GDP information is mapped to the corresponding spatial unit scale. Within each sub-region, the GDP values ​​are discretized using the natural breakpoint method to determine the threshold for GDP level classification, and continuous GDP values ​​are converted into a finite category of development status.

[0209] In subsequent simulations, the threshold for the lowest level of GDP classification was kept unchanged based on the GDP classification system established in 2015. Only the threshold for the highest level of GDP classification was dynamically expanded over time to ensure the consistency of the GDP classification mapping relationship in different years.

[0210] (4) GDP time evolution modeling

[0211] An evolutionary model of GDP over time is constructed based on historical GDP statistics of a certain province. In this application example, GDP data from 2000 to 2020 are obtained from statistical yearbooks as historical samples to depict the overall evolutionary trend of GDP over time. Specifically, the total GDP of the province is calculated at the overall scale of the study area, while the total GDP of each district and county is calculated at the sub-regional scale, thus constructing GDP time evolution models at the overall scale and the sub-regional scale respectively.

[0212] Considering that GDP evolution typically exhibits phased characteristics of slow initial growth, rapid growth in the middle stage, and a tendency to stabilize in the later stage, an S-curve model is used to characterize the time evolution of GDP, and its expression is:

[0213]

[0214] in, Indicates time The corresponding GDP Indicates the year. The upper bound parameter, obtained by fitting historical GDP total data, is used to characterize the evolution trend of total GDP within a given statistical interval. and It is a curve shape control parameter used to adjust the growth direction and growth rate of GDP over time.

[0215] By fitting the parameters of the above model using the least squares method, the total GDP target for different years can be obtained.

[0216] (5) Calculation of the probability of change in GDP level of spatial unit

[0217] Using changes in GDP levels within a historical timeframe as supervisory information and spatial unit driving factor features as input, a model for calculating the probability of changes in GDP levels for spatial units is constructed. In this application example, 2010-2015 is selected as the historical training phase. Within each district / county sub-region, for each spatial unit, it is determined whether its GDP level changed during 2010-2015, and this is used as the supervisory label.

[0218] Using the spatial unit driving factor features corresponding to 2010 as model input, a training sample dataset was constructed. A random forest model was used for training, and the model performance was validated using an independent test set. After model training, the spatial unit driving factor features corresponding to 2015 were used as input to predict the probability of GDP level changes in spatial units during subsequent simulation phases starting from 2015. The calculation method is as follows:

[0219]

[0220] in, Representing spatial units In time The base probability of GDP level change corresponding to the time. In the random forest model, the first... The classification results of the decision trees, Representing spatial units The corresponding driving factor eigenvector in 2015.

[0221] (6) Calculation of the comprehensive development probability of multi-scale cellular automata and dynamic expansion of GDP level system

[0222] In this application example, a multi-scale cooperative cellular automata model is used to simulate the spatial evolution of urban economic levels. In this model, spatial units are used as cellular state units, and the spatial evolution of GDP is realized under the combined effect of sub-regional scale total constraints and spatial unit scale state update rules.

[0223] First, the GDP ranking system is dynamically expanded. In this application example, the GDP ranking system is dynamically expanded every 5 years. 2015 is taken as the starting point for the dynamic expansion of the ranking system. The corresponding upper limit of GDP level is In subsequent simulations, for each condition that satisfies...

[0224]

[0225] At specific time points, the upper limit of the highest level in the GDP rating system will be updated.

[0226] Let the upper bound of the GDP level corresponding to the previous level expansion time be . Then the current level expansion time The corresponding GDP level upper bound is updated as follows:

[0227]

[0228] in, The relative growth rate of a stage, calculated from the target GDP total series, is defined as:

[0229]

[0230] After completing the expansion of the GDP grading system, the basic probability of changes in the GDP grading of spatial units is calculated using step (5). As the fundamental transition probabilities in the cellular automata model, during the yearly spatial simulation, the neighborhood effect factor and development inhibition factor are dynamically updated based on the spatial neighborhood state and the historical development state of the spatial unit in each year, thereby constructing the comprehensive development probability of the spatial unit in each year:

[0231]

[0232] in, This indicates the current year, corresponding to 2016-2020; and Representing spatial units In time The corresponding neighborhood effect factor and development inhibition factor are identified. Through this method, cellular state transition probabilities are constructed at the spatial unit scale, providing a basis for subsequent GDP spatial allocation and state updates.

[0233] The neighborhood effect factor This is used to characterize the developmental and enhancing effect of spatial units within a spatial neighborhood that have already undergone updates in urban economic level on the target spatial unit. Let spatial units be... Centered Neighborhood set is During the current annual simulation phase, let the set of spatial units that have undergone updates to their urban economic level be denoted as... The number of updated spatial units in the neighborhood is defined as follows:

[0234] And based on this, the neighborhood effect factor is calculated:

[0235]

[0236] in, This is a single-neighborhood enhancement intensity parameter used to characterize the spatial agglomeration and diffusion effects of urban economic development. In this application example, it is set as follows: Neighborhood, The value is 1.125.

[0237] The developmental inhibitory factor This describes the characteristic that, after a spatial unit has undergone changes in its economic development during the urban economic process, the likelihood of its economic level changing again in subsequent years decreases. Let the spatial unit be... The indicator for whether a change in the city's economic level occurred during the historical annual simulation period is:

[0238]

[0239] The growth inhibition factor in the current year is defined as:

[0240]

[0241] in, To suppress intensity parameters, this is used to avoid repeated changes in urban economic level among spatial units during consecutive annual simulation phases. In this application example... Defined as 0.99.

[0242] (7) Spatial distribution and annual updates of GDP

[0243] At the sub-regional scale of districts and counties, the spatial evolution of GDP is simulated using a cellular automata iterative method at the spatial unit scale, with the total GDP of each district and county as a constraint.

[0244] Using 2015 as the starting point of the simulation, the spatial simulation process is advanced year by year between two adjacent GDP level expansion points.

[0245] In each year Within the district / county area, under the premise of meeting the total GDP constraint, the first consideration is the comprehensive development probability of the spatial unit. The spatial units within the sub-region are sorted, and then selected iteratively for updating in descending order of comprehensive development probability. For each iteration, a spatial unit is selected from the sorted sequence as the current update target, and a GDP level update operation is performed. The selected spatial unit... Within the highest level of the current year's simulation phase Under the constraints, its urban economic level was changed from

[0246]

[0247] Complete a level update.

[0248] After each spatial unit GDP level update, the total GDP at the district / county level for the current year is calculated in real time. Let the... At what time point? The total GDP is The target GDP obtained in step (4) is When the following relative error constraint condition is met:

[0249]

[0250] If so, the update of the GDP level of spatial units within the district / county area within that year is stopped; otherwise, spatial units that meet the conditions are selected and the above update process is repeated.

[0251] Through the above methods, under the constraint of the total GDP of districts and counties, the GDP level update at the spatial unit scale is gradually completed, thereby realizing the gradual distribution of GDP at the spatial unit scale and obtaining the GDP of each district and county in a province at a certain time node. The spatial unit GDP level distribution results.

[0252] (8) Integration of provincial-level results and overall total correction

[0253] After completing the spatial simulation of GDP at the sub-regional scale for each district and county in a province, the spatial unit GDP level results within each district and county are spatially integrated to form the spatial unit GDP level distribution results at the overall scale of the province.

[0254] Because the GDP grading system within each district and county is independently constructed based on its own grading thresholds, the GDP value range corresponding to the same grading number is not consistent across different districts and counties. To calculate the total GDP at the provincial level, it is necessary to first convert the discrete GDP grading results of spatial units into continuous GDP values. Let the... At what time point? The GDP level threshold sequence is as follows:

[0255]

[0256] If spatial unit Belongs to the Each district and county, and its GDP level is:

[0257]

[0258] The continuous GDP value corresponding to this spatial unit is defined as:

[0259]

[0260] in, Representing spatial units At the time point The continuous value of GDP.

[0261] Based on this, the continuous GDP values ​​of all spatial units within a province are aggregated to calculate the simulated total urban economic level of the province:

[0262]

[0263] in This represents the total number of spatial units in a certain province.

[0264] To ensure that the simulation results meet the GDP constraint of a certain province, calculate the ratio between the simulated total and the target total:

[0265]

[0266] in For a certain province at a certain time point The total GDP target. When At that time, the economic level values ​​of all cities in all spatial units within a province were adjusted proportionally.

[0267]

[0268] in This represents the GDP value of a spatial unit after proportional adjustment.

[0269] Through the above proportional correction, the simulated total GDP of a certain province meets the overall scale target constraint, that is:

[0270]

[0271] Where M represents the number of spatial units within a certain province.

[0272] (9) Comparative experiment and effect evaluation

[0273] To verify the effectiveness and superiority of the spatial simulation method for urban economic level proposed in this application example, a comparative experiment was conducted between the method in this application example and the existing Random Forest-Cellular Automata (RF-CA) method under the same study area, the same basic data and the same time range.

[0274] In the comparative experiment, both methods used a province as the study area and employed consistent basic data, spatial resolution, and GDP classification schemes. The RF-CA method directly performs spatial modeling and simulation at the overall provincial scale, constructing unified spatial transfer rules and executing spatial evolution processes within the province. The method in this application example, however, divides the study area into sub-regions based on county-level administrative units, introduces time constraints on urban economic output and a dynamic level expansion mechanism at the sub-region scale, and integrates the results at the provincial scale after completing the sub-region simulation.

[0275] Both methods use 2015 as the base year and 2015-2020 as the simulation period to obtain spatial simulation results of the urban economic level in 2020. The spatial distribution of actual GDP in 2020 is used as the true value to evaluate the accuracy of the simulation results of the two methods.

[0276] Overall accuracy (OA) and the Kappa coefficient are selected as evaluation indicators, and their calculation methods are as follows:

[0277] ; ;

[0278] In the formula, This represents the total number of spatial units within the study area. The number of categories representing GDP levels. Let Sk represent the number of cells that correctly predicted the GDP level for the k-th category, and Sk be the number of cells in the k-th category. Based on the above definition, Used to measure the overall consistency between simulation results and actual results at the spatial unit level. This represents the expected probability that the simulation results will match the actual results under random assignment conditions, while The coefficients, after eliminating the influence of random consistency, are used to comprehensively evaluate the level of consistency between simulation results and actual results.

[0279] The comparison results are shown in Table 1. Under the condition of direct modeling at the overall scale of a province, the application example method is superior to the RF-CA method in both OA and Kappa evaluation indicators. This shows that by introducing urban economic aggregate constraints, dynamic expansion mechanism of hierarchical system and annual spatial allocation strategy at the sub-regional scale, the application example method can more effectively characterize the spatiotemporal evolution characteristics of urban economic level within the province and improve the stability and accuracy of spatial simulation results.

[0280] Table 1 Evaluation Indicators for Two Methods

[0281]

[0282] Figure 2 The error distribution maps for the two methods are shown. The error distribution indicates that the model has higher prediction accuracy in the northern and western mountainous regions, while the errors are relatively higher in the coastal and mountain-sea transition zones. The terrain in this region is predominantly mountainous and hilly, with significant topographic relief and relatively limited transportation in the northwest. The overall economic development level is lower, and the spatial pattern is more stable, making it easier for the model to characterize its changing features. In contrast, the coastal region has more plains, some cities have highly concentrated economic activities, and economic development changes rapidly, resulting in a more complex spatial pattern and increasing the simulation difficulty. Compared to the RF-CA method, the method in this application example significantly reduces the number of erroneous pixels in these complex areas, indicating that it can better characterize the impact of topographic constraints and regional economic differences on the spatial evolution of urban economics, thus improving the overall accuracy of GDP spatial simulation.

[0283] This application also provides an electronic device, including: a processor, and a memory coupled to the processor, the memory being used to store a computer program; the processor being used to execute the computer program stored in the memory, so that the electronic device performs the method as described in any of the above embodiments.

[0284] Electronic devices can be computing devices such as desktop computers, laptops, handheld computers, and cloud servers. These electronic devices may include, but are not limited to, processors and memory.

[0285] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the electronic device, connecting various parts of the device via various interfaces and lines.

[0286] The memory can be used to store the computer program, and the processor implements various functions of the electronic device by running or executing the computer program stored in the memory and calling the data stored in the memory.

[0287] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function, etc.; the data storage area may store data created based on the use of the mobile phone, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0288] This application also provides a storage medium, which is a computer-readable storage medium. The computer program is stored in the computer-readable storage medium, and when executed by a processor, the computer program can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0289] This application also provides a computer program product, including: a computer program or instructions that, when the computer program or instructions are run on a computer, cause the computer to perform any of the above possible implementation methods.

[0290] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A method for simulating urban economic level space, characterized by, include: The city obtains multi-source driving factor data and economic level statistics of each spatial unit in time series. Several spatial units constitute a sub-region, and all sub-regions constitute the city as a whole. The driving factor data includes: natural environmental conditions, land use characteristics, population and economic activity intensity, and transportation accessibility. The driving factor feature vector is obtained by standardizing the driving factor data, and the economic level level is obtained by the economic level statistics. Based on the aforementioned economic level statistics, a time series prediction model for the total economic level is constructed at both the sub-regional and overall regional scales to characterize the evolution of the total economic level. Based on the economic level, a spatial unit economic level development probability model is constructed to characterize the probability of changes in the economic level of a spatial unit within a given time period. Based on the constructed multi-scale collaborative cellular automaton model, the spatial distribution of economic level grades of each spatial unit is obtained. The cellular automaton model uses the total economic level as a constraint and the probability of change in economic level grades as the input to the spatial unit state transition probability. Based on the spatial distribution of economic level levels of each spatial unit, the economic level of each spatial unit is converted into a continuous economic level value. The simulated total urban economic level is then obtained from the continuous economic level values ​​of each spatial unit. Based on the constructed multi-scale cooperative cellular automata model, the spatial distribution results of the economic level of each spatial unit are obtained, specifically including: Based on the aforementioned time-series forecasting model for total economic level, the upper bound of the highest level in the economic level classification system is dynamically expanded. Under the premise of satisfying the total economic level constraint, spatial units within the sub-region are ranked according to the comprehensive development probability of spatial units. The comprehensive development probability is defined by the economic level development probability of the spatial unit, the neighborhood effect factor, and the development inhibition factor. Spatial units are selected sequentially from high to low based on the comprehensive development probability for iterative updates of economic level. Based on the aforementioned time-series forecasting model for total economic level, the upper bound of the highest level in the economic level classification system is dynamically expanded, specifically including: The economic level hierarchy is updated at predetermined time intervals wherein denotes the time span between two successive level extension operations; at a time node the economic level hierarchy within each sub-region consists of a finite number of discrete levels, the economic level of a spatial unit ranges from: wherein, denotes a time node a corresponding highest rank number; at each preset time interval At the end, a dynamic expansion operation is performed on the economic level hierarchy, with the The time node corresponding to the second level expansion moment is: Let the highest rank upper bound corresponding to the last rank expansion time be Then the highest rank upper bound corresponding to the current rank expansion time is Update as follows: wherein, is the total growth rate of the urban economic level in the time interval , which is specifically expressed as: wherein, represents the time node corresponding target economic level total amount, represents the time node corresponding target economic level total amount; When satisfied At that time, at the highest level of the existing economic level hierarchy. Add a new highest level based on the existing level The value range corresponding to this newly added level is defined as follows: , Spatial units are selected sequentially from high to low probability of comprehensive development for iterative updates of economic level, specifically including: For the selected spatial unit Not exceeding the highest level of the current year Under the constraints, its economic level was changed from Complete a level update; After each spatial unit is selected and updated, the total economic level within the current sub-region is calculated in real time based on the updated spatial unit level results. Let the current year's economic level be _____. ,grade The corresponding upper and lower thresholds are respectively and Then its grade representative value is defined as: Record the time node within the current sub-region. Belongs to the level The number of spatial units is: The total economic level of this sub-region in the current year is then expressed as: The current economic level of the sub-region With the time series forecasting model of total economic level at time nodes The target economic level of the corresponding sub-region The comparison is made, and the error is defined as: When error Less than the preset tolerance threshold If the sub-region is determined to have met the total economic level constraint in the current year, the spatial unit level update within the sub-region is stopped; otherwise, the next spatial unit is selected from the sorting sequence and the above process is repeated.

2. The spatial simulation method for urban economic level as described in claim 1, characterized in that, The economic level level is derived from the aforementioned economic statistical data, specifically including: Let the economic level corresponding to space unit i at time t be G i (t), let the sequence of hierarchical threshold values obtained by discretization in its belonging sub-region be: Discretized economic level Represented as: Among them, the hierarchical threshold sequence contains a total of Each threshold corresponds to a set of values. A range of economic levels.

3. The spatial simulation method for urban economic level as described in claim 1, characterized in that, The time-series forecasting model for the total economic level is an S-shaped curve model: in, Indicates time The corresponding total economic level; This is an upper bound parameter used to characterize the evolution trend of the total economic level; its value is obtained by fitting historical statistical data. and It is a curve shape control parameter used to adjust the growth direction and growth rate of the total economic level over time.

4. The spatial simulation method for urban economic level as described in claim 1, characterized in that, The probability model for the development level of the spatial unit's economic level is a random forest model. in, spatial unit In time The corresponding driving factor feature vector; d is the number of driving factors; This is the current forecast time point; The probability of development of the economic level of a spatial unit; The number of base learners; Indicates the first The classification output of each base learner; This is an indicator function. It takes the value 1 when the base learner determines that the economic level of the spatial unit has changed, and takes the value 0 otherwise.

5. The spatial simulation method for urban economic level as described in claim 1, characterized in that, Based on the spatial distribution of economic level grades of each spatial unit, the economic level grades of the spatial units are converted into continuous economic level values ​​for each spatial unit. The simulated total urban economic level is then obtained from the continuous economic level values ​​of each spatial unit, specifically including: Let the first Each sub-region at a time node The economic level threshold sequence is as follows: in, The threshold number is the number of spatial units. Belongs to the Each sub-region, at a specific time point The city's economic level is categorized as follows: The continuous economic level value corresponding to this spatial unit is defined as: in, Representing spatial units At the time point Continuous values ​​of economic level; By summing up the continuous economic level values ​​of all spatial units, the simulated total economic level of the city is calculated: in, The total number of spatial units within the study area; Calculate the ratio between the simulated total urban economic level and the target total urban economic level: in, To be at the time node The target total amount of urban economic development; when At that time, the continuous economic level values ​​of all spatial units are adjusted proportionally in a uniform manner: in, This represents a continuous value of the economic level of a spatial unit after proportional adjustment. By adjusting the above proportions, the simulated total urban economic level is made to meet the overall scale target constraints, namely: Where M represents the number of spatial units within the study area.

6. An electronic device, characterized in that, The electronic device includes: a processor, and a memory coupled to the processor. The memory is used to store computer programs; The processor is configured to execute the computer program stored in the memory, so that the electronic device performs the urban economic level spatial simulation method as described in any one of claims 1-5.

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