A threshold analysis method and system for development of industries in arid regions

Abstract

This invention discloses a method and system for analyzing industrial development thresholds in arid regions, belonging to the field of water resource carrying capacity assessment. The method includes: acquiring multi-source panel data to construct a three-dimensional time-series matrix and standardizing it; calculating global objective weights, injecting them into a self-organizing map network for asymmetric stretching, identifying regional differentiation, and extracting typical unit samples; constructing a system dynamic model containing the upper limit expansion of water resources, industrial consumption metabolism, and land ecological stress feedback loops, and calibrating parameters using a genetic algorithm; constructing a dual-scenario evolution mechanism within the spatiotemporal boundary of the model output based on a non-dominated sorting genetic algorithm, combining constraints and endogenous penalty functions to optimize and obtain a dynamic threshold interval composed of the safe operating lower limit of the ecological degradation critical point and the absolute collapse upper limit before irreversible mutation. This invention addresses the problems of static and singular calculation methods, lack of nonlinear feedback characterization, and isolated and static results in existing arid region industrial threshold calculations.

Description

Technical Field

[0001] This invention relates to the field of water resource carrying capacity assessment, and in particular to a method and system for threshold analysis of industrial development in arid regions. Background Technology

[0002] Arid regions are characterized by scarce water resources and fragile ecosystems, resulting in a complex coupling relationship between industrial development and water supply and land carrying capacity. Scientifically defining the scale threshold for industrial development in arid regions is crucial for ensuring regional ecological security, optimizing industrial layout, and achieving sustainable development. Currently, the mainstream methods for calculating industrial carrying capacity or water resource carrying capacity in arid regions are largely based on conventional static accounting methods for water resources. These methods construct single or linear weighted index systems and combine them with the analytic hierarchy process (AHP), fuzzy comprehensive evaluation, or conventional ecological footprint models to assess carrying capacity, providing a fundamental reference for regional water resource management.

[0003] Existing technologies have significant limitations in their accounting methods and assessment paradigms. Traditional methods generally treat the upper limit of water resource supply as a static constant determined by the amount of conventional water resources, neglecting the dynamic expansion effect of unconventional water resource development and utilization on total water supply capacity driven by capital investment and technological progress. This results in an underestimation of the absolute collapse limit of industrial carrying capacity before irreversible abrupt changes, failing to truly reflect the supply potential of "total water," including unconventional water. Existing assessment models are mostly static cross-sectional analyses or linear system simulations, which are insufficient to characterize the nonlinear feedback relationships prevalent in the water-production-land complex system. For example, when industrial water use excessively encroaches on ecological water use, it can induce ecological stress effects such as decreased oasis vegetation vitality and exacerbated desertification, which in turn inhibit the long-term potential of industrial development. This nonlinear steady-state transition risk cannot be effectively captured in traditional static models.

[0004] Existing technologies suffer from the following main shortcomings: a single accounting scope fails to incorporate the dynamic expansion effect of unconventional water resources into the core analytical framework, leading to a systematic underestimation of the absolute collapse limit of water resources on industrial carrying capacity; the assessment paradigm is outdated, lacking the ability to characterize the nonlinear feedback loops and abrupt change risks of complex water-production-land systems; and the measurement results present isolated static extreme values, lacking an elastic dynamic threshold range composed of both the lower limit of safe operation and the upper limit of absolute collapse. Therefore, a new method for industrial threshold analysis is needed that integrates dynamic accounting of all water resources, nonlinear system dynamics evolution, and multi-scenario collaborative optimization to overcome these technical deficiencies and provide more scientific and accurate decision support for differentiated industrial planning and ecological red line management in arid regions. Summary of the Invention

[0005] To address the problems of static and singular calculation methods, lack of nonlinear feedback characterization, and isolated and static results in existing industrial threshold calculations for arid regions, this invention provides a method and system for analyzing industrial development thresholds in arid regions.

[0006] The technical solution adopted by this invention to solve its technical problem is: a method and system for analyzing the threshold of industrial development in arid areas. Preferably, the steps are: S1, acquiring multi-source panel data of the water-production-land composite system in the arid area to be tested, introducing a time dimension to construct a three-dimensional time-series matrix and performing spatiotemporal standardization to obtain a normalized steady-state matrix; S2, calculating the global objective weights of various indicators and injecting them into a self-organizing map network to asymmetrically stretch the multi-dimensional feature space, identifying regional functional differentiation characteristics and extracting typical unit samples; S3, constructing a system dynamics model including the expansion of water resource upper limits, industrial demand expansion, and land ecological stress feedback loops, and using a standard continuous genetic algorithm for regional parameter calibration; S4, constructing a dual-scenario evolution mechanism within the spatiotemporal evolution boundary output by the system dynamics model based on a non-dominated sorting genetic algorithm, combining constraints and endogenous penalty functions to optimize and obtain the dynamic threshold interval for industrial development composed of the lower limit of safe operation and the upper limit of absolute collapse before irreversible mutation, and outputting it.

[0007] Preferably, S2 specifically includes: obtaining the global objective weights of each system indicator using the entropy weight method; using the global objective weights to asymmetrically stretch the multidimensional spatial coordinate axes of the multi-year average normalized steady-state matrix to construct a weighted feature matrix; inputting the weighted feature matrix into a self-organizing map network for competitive learning; and extracting the prefecture-level cities in each cluster that achieve the absolute minimum deviation value as the typical unit samples by calculating the weighted spatial feature deviation.

[0008] Preferably, the system dynamics model constructed in S3 includes the following feedback loops: a positive feedback loop for expanding the upper limit of water resources, whose evolution is dominated by the Logistic equation with technical saturation constraints; a negative feedback loop for industrial consumption metabolism, which is used to force the high water-consuming production capacity to withdraw through a surge in the marginal acquisition cost of water resources when the industrial water demand approaches the upper limit of the total water supply; and a negative feedback loop for land ecological stress, which is used to trigger a nonlinear decline in the vegetation index, which characterizes the vitality of the oasis, when the remaining water volume is lower than the minimum ecological baseflow.

[0009] Preferably, the method for regional parameter calibration in S3 is as follows: using the long sequence panel data of the typical unit sample as a benchmark, a historical fitting loss function based on minimizing the root mean square relative error is constructed; a continuous genetic algorithm with real number encoding is used to find the optimal value in the multidimensional parameter space through arithmetic crossover and non-uniform mutation operations to obtain the set of nonlinear response elastic parameters corresponding to each type of region.

[0010] Preferably, the dual-scenario evolution mechanism in S4 specifically includes: Scenario 1: Under the premise of removing unconventional water intervention, with the goal of maximizing the total system benefit, the lower limit of safe operation is obtained to ensure that the ecological degradation threshold is not exceeded; Scenario 2: Under the premise of enabling dynamic expansion of the full amount of water, an endogenous penalty function based on the risk of ecological collapse is embedded in the objective function to obtain the upper limit of absolute collapse before the system undergoes irreversible mutation.

[0011] Preferably, in Scenario 1, the calculation logic for the safe operating lower limit of the ecological degradation critical point is as follows: A physical boundary closure operation is performed in the system dynamics model to lock the upper limit of available water volume to a rigid conventional water quota; using the scale vector of the region's dominant industry as the decision variable and maximizing economic benefits as the objective function, under the hard constraint that the total water consumption does not exceed the difference between the rigid conventional water quota and the minimum ecological base flow, the maximum effective economic scale supported by conventional water is obtained through iterative solution using a non-dominated sorting genetic algorithm, which serves as the safe operating lower limit of the ecological degradation critical point; the hard constraint condition is expressed as: ; in The target value sought is the lower limit of safe operation for the first stage of ecological degradation critical point. This represents the total number of industry categories. For the first The scale of the industry The output value coefficient per unit physical scale. For the first Water quotas for similar industries For rigid, conventional water quotas, It is the minimum ecological base flow.

[0012] Preferably, in scenario two, the endogenous penalty function includes a water resource consumption penalty term and a land degradation penalty term. The water resource consumption penalty term represents the exponential surge in water resource acquisition costs when the actual total water consumption approaches the limit of safe operation of all water resources. The land degradation penalty term is used to trigger ecological collapse penalties when the vegetation index, which represents the vitality of the oasis, approaches the critical point of irreversible desertification, forcibly depriving the system of economic benefits. The algorithm, through the surge of the water resource consumption penalty term and the land degradation penalty term, forcibly clears the economic benefits of the system that has exceeded the limit, thereby finding the absolute collapse upper limit before the irreversible mutation.

[0013] In a preferred embodiment, the objective function formula for scenario two, including endogenous penalties, is as follows: ; in For the first The scale of the industry The output value coefficient per unit physical scale. For water consumption quotas, This represents the dynamic upper limit of the total water volume. As the minimum ecological base flow, The vegetation vitality index represents the critical point of irreversible desertification. This is a real-time vegetation vitality index. The coefficient representing the exponential constraint of soaring marginal costs. and These are the weighting coefficients.

[0014] On the other hand, a threshold analysis system for industrial development in arid regions is provided. This system is equipped with the aforementioned threshold analysis method for industrial development in arid regions. It is characterized by comprising: a data acquisition and preprocessing module for acquiring and constructing a three-dimensional time-series standardized matrix; a regional functional differentiation identification module for extracting typical unit samples using a weighted self-organizing map network; a composite system dynamic simulation module for constructing a system dynamic model and calibrating parameters using a genetic algorithm; and a dynamic threshold interval calculation module for outputting a dynamic threshold interval for industrial development composed of a safe operating lower limit and an absolute collapse upper limit before irreversible mutation using a dual-scenario optimization algorithm.

[0015] Preferably, the model accuracy verification unit is used to verify the structural robustness of the simulated trajectory of the system dynamics model through the coefficient of determination, Nash efficiency coefficient and average relative error; the dual-scenario collaborative optimization unit is equipped with a non-dominated sorting genetic algorithm processor, used to perform the optimization of the lower limit of safe operation under conventional water hardness constraints, and the optimization of the upper limit of absolute collapse before irreversible mutation by enabling full water dynamic feedback and embedding the dual endogenous penalty function of water resource cost surge and ecological collapse; the threshold interval output unit is used to generate a closed dynamic threshold interval for industrial development.

[0016] The beneficial effects of this invention are as follows: It incorporates the dynamic expansion effects of both conventional and unconventional water resources driven by technological investment into the core feedback loop, overcoming the technical shortcomings of traditional methods that only consider static conventional water quotas, leading to a systematically low upper limit of the physical carrying capacity for industry. This makes the measurement results closer to the true physical supply limit of arid regions. Simultaneously, this invention constructs a system dynamics model including positive feedback for water resource upper limit expansion, negative feedback for industrial consumption and metabolism, and negative feedback for land ecological stress. By coupling the saturation equation using Logistic regression with a cubic steady-state transformation function based on vegetation indices, it achieves a dynamic characterization of the nonlinear evolution and ecological mutation risks in the water-production-land composite system, compensating for the shortcomings of existing static cross-sectional analyses in capturing system feedback mechanisms and mutation timing. Furthermore, this invention employs global objective weights to asymmetrically stretch the self-organizing mapping network, forcing the clustering process to prioritize responses to core water and soil constraint variables. Combined with inverse feature restoration and deviation minimization search to extract typical unit samples, it effectively improves the physical interpretability of regional functional differentiation identification and the sample confidence of parameter calibration. Attached Figure Description

[0017] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the optimal embodiment of the method and system for analyzing industrial development thresholds in arid regions according to the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] S1: Obtain multi-source panel data of the water-production-land composite system in the arid area to be tested, introduce the time dimension to construct a three-dimensional time series matrix and perform spatiotemporal standardization to obtain the normalized steady-state matrix; Acquire multi-source historical panel data of the water, production, and land composite system in the arid region to be tested. The water system indicators include total water resource system indicators, specifically subdivided into: conventional water resources, including surface water supply, groundwater supply, groundwater level, and external water transfer indicators; unconventional water resources, including reclaimed water utilization, mine drainage water output and utilization rate, brackish water utilization, rainwater harvesting, and flood engineering volume; hydrophysical parameters, including precipitation, evaporation, runoff, and groundwater storage change data based on GRACE satellite inversion; and ecological protection baselines, including minimum ecological base flow, groundwater extraction red line, and minimum water level of wetlands and lakes. The industrial system indicators include: macroeconomic indicators, including GDP, industrial added value, population size, and urbanization rate of prefecture-level cities by industry; industrial water efficiency indicators, including water consumption per 10,000 yuan of GDP, water consumption per 10,000 yuan of industrial added value, and irrigation quotas for different types of farmland; core industry output indicators, including coal production, thermal power generation, output value of major coal chemical products, and cotton and grain planting area; and technology and cost indicators, including marginal costs of reclaimed water and mine water treatment, investment quotas for water-saving irrigation facilities, and industrial water reuse rate. The land system indicators include: land use data, including oasis area, desert area, and the expansion rate of industrial and urban construction land; ecological vitality indices, including normalized difference vegetation index, net primary productivity, and leaf area index; and spatial conflict indicators, including data on changes in oasis-desert ecotones, soil salinization, and frequency of dust storms.

[0021] After obtaining the panel data mentioned above, a time dimension was introduced, treating each city in each year as an independent spatiotemporal slice sample to construct a three-dimensional time-series matrix. The three dimensions of this matrix are: the first dimension is the prefecture-level city administrative unit, the second dimension is the indicator item, and the third dimension is the year. Using ArcGIS spatial statistics tools, the raster-formatted remote sensing data was extracted according to administrative boundaries, achieving alignment of multi-source heterogeneous data in both spatial and temporal scales.

[0022] Global range standardization was performed. The global maximum and minimum values ​​for each indicator were found across all prefecture-level cities throughout the entire study period. For positive indicators, such as the Normalized Difference Vegetation Index (NDVI), a larger value indicates better system stability. The positive standardization formula was used: the standardized value equals the original value minus the global minimum divided by the difference between the global maximum and global minimum. For negative indicators, such as desert area, a larger value indicates stronger system stress. The negative standardization formula was used: the standardized value equals the global maximum minus the original value divided by the difference between the global maximum and global minimum. The standardized values ​​eliminated dimensions and preserved the longitudinal fluctuation characteristics of the indicators over time, with values ​​ranging from 0 to 1.

[0023] To prevent the logarithmic function from becoming meaningless due to zero values ​​in subsequent information entropy calculations, a slight shift correction is applied to the standardized values: the final normalized steady-state eigenvalue equals the standardized value plus a very small positive number, typically 0.000001. This yields the normalized steady-state matrix, where each element is between 0.000001 and 1.000001.

[0024] S2: Calculate the global objective weights of each indicator and inject them into the self-organizing map network to perform asymmetric stretching of the multidimensional feature space, identify regional functional differentiation characteristics and extract typical unit samples. The global objective weights of each system indicator are obtained using the entropy weight method. The entropy weight method is an objective weighting method that determines weights based on the magnitude of the information entropy of an indicator. Its basic logic is: if the values ​​of an indicator differ significantly across spatial units and time points, it indicates that the indicator contains a large amount of information and should be assigned a higher weight; conversely, if the values ​​are very similar, the information content is small and a lower weight should be assigned. Specifically, in this invention, the calculation of entropy weights is based on a normalized steady-state matrix. Since the normalized steady-state matrix has eliminated dimensions, it can be directly used for entropy weight calculation. For each indicator, the entropy value of its values ​​at all time points in all spatial units is calculated, and then the weight is determined based on the entropy value. Finally, the global objective weight of each system indicator is obtained, and the sum of the weights is 1.

[0025] After obtaining the global objective weights, these weights are used to asymmetricly stretch the multidimensional coordinate axes of the multi-year average normalized steady-state matrix to construct a weighted feature matrix. The multi-year average normalized steady-state matrix is ​​an M×N two-dimensional matrix obtained by averaging the normalized steady-state matrix along the time dimension, where each row represents a spatial unit and each column represents an indicator. Asymmetric stretching refers to multiplying the value of each coordinate axis, i.e., each indicator, by the corresponding global objective weight. Because different indicators have different weights, the degree of stretching is asymmetric. Indicators with larger weights have their coordinate axes stretched in space, while indicators with smaller weights are compressed. After asymmetric stretching, the weighted feature matrix is ​​obtained, where each row vector represents the coordinates of a spatial unit in the weighted feature space.

[0026] The weighted feature matrix is ​​then input into a self-organizing map network (SOM) for competitive learning. SOM is an unsupervised artificial neural network capable of mapping high-dimensional input data onto a low-dimensional grid while preserving the topological structure. In this invention, the number of nodes in the input layer of the SOM is equal to the number of columns in the weighted feature matrix, and the output layer is a two-dimensional neural network. The network learns through competition: each time a weighted feature vector of a spatial unit is input, the distance between this vector and the weight vectors of all output layer neurons is calculated, and the neuron with the closest distance wins and updates its weight vector and the weight vectors of its neighboring neurons. After multiple iterations, the network converges, and each spatial unit is mapped to an optimally matched neuron on the two-dimensional grid. During the competitive learning process, the weighted spatial feature deviation needs to be calculated. The weighted spatial feature deviation refers to the weighted Euclidean distance between the weighted feature vector of each spatial unit and the centroid of its cluster. The sum of the deviations of all spatial units reflects the cohesion of the clustering results. By calculating the weighted spatial feature deviation, prefecture-level cities that achieve the absolute minimum deviation value in each cluster are extracted as typical unit samples. In other words, in each cluster, the spatial unit with the smallest deviation best represents the typical characteristics of that cluster and is therefore selected as the typical unit sample.

[0027] S3: Construct a system dynamics model that includes the expansion of water resource ceiling, the expansion of industrial demand, and the feedback loop of land ecological stress, and use a standard continuous genetic algorithm for regional parameter calibration; A system dynamics model is a simulation model used to model the time-varying behavior of complex systems. The system dynamics model constructed in this invention includes the following three core feedback loops: The feedback loop is a positive feedback loop for expanding the upper limit of water resources. The evolution of this loop is dominated by the Logistic equation with technological saturation constraints. The upper limit of water resources is not constant but dynamically increases with unconventional water investment and technological progress. The Logistic equation describes a limit to the growth process, namely the maximum exploitable water resources under technological saturation constraints. Its form is: the growth rate of the total available water resources is proportional to the current available water resources and also proportional to the remaining potential. When the available water resources approach the theoretical limit, the growth rate approaches zero.

[0028] The feedback loop is a negative feedback loop of industrial consumption metabolism. This loop is used to force the exit of water-intensive industries when their water demand approaches the upper limit of total water supply, due to a surge in the marginal cost of acquiring water resources. Industrial consumption metabolism refers to the phenomenon where industrial activities consume water resources and generate economic output, but when total water consumption approaches the upper limit of supply, the cost of acquiring additional water resources rises exponentially, leading to a sharp decline in the economic benefits of water-intensive industries, thereby forcing these industries to downsize or exit the market. This negative feedback mechanism prevents the unlimited expansion of industries from causing water resource depletion.

[0029] The feedback loop is a negative feedback loop of land ecological stress. This loop triggers a nonlinear decline in vegetation indices, which characterize oasis vitality, when the remaining water volume falls below the minimum ecological baseflow. The minimum ecological baseflow refers to the amount of water that must be retained to maintain the basic ecological functions of rivers and the stability of oases. When human activities consume too much water, causing the remaining water volume to fall below the minimum ecological baseflow, the vegetation index will decline rapidly and nonlinearly, i.e., an ecological stress effect will occur. This decline further reduces the region's ecological service functions and water conservation capacity, which in turn exacerbates water shortages and land degradation, forming a negative feedback loop.

[0030] After constructing the system dynamics model, regional parameter calibration is required using a standard continuous genetic algorithm. The purpose of parameter calibration is to ensure that the historical trajectory output by the model matches the actual observed data. Specifically, the method involves using long-sequence panel data of typical unit samples extracted by S2 as a benchmark to construct a historical fitting loss function based on minimizing the root mean square relative error. Long-sequence panel data refers to the observed values ​​of various system variables for typical unit samples over multiple consecutive years. The loss function is defined as the square root of the mean of the sum of squared relative errors between the model's simulated values ​​and the observed values. The genetic algorithm is a global optimization algorithm that simulates a natural evolutionary process. The standard continuous genetic algorithm uses real-number encoding, meaning each parameter to be calibrated is directly represented by a real number. In this invention, the parameters to be calibrated include the saturation limit value in the Logistic equation, the growth rate constant, the threshold for surges in industry costs, and the sensitivity coefficient for nonlinear decline in the vegetation index. The genetic algorithm operates as follows: randomly generating an initial population, with each individual representing a parameter vector; calculating the fitness of each individual, where fitness is the reciprocal or negative of the loss function; selecting individuals with high fitness for arithmetic crossover, where the corresponding parameters of two parent individuals are linearly combined according to certain weights to produce offspring; and performing a non-uniform mutation operation, which adds a random perturbation to the parameters with a certain probability, gradually decreasing with each generation. Through multiple generations of evolution, the parameter set that minimizes the loss function is finally obtained, which is the nonlinear response elasticity parameter set corresponding to that type of region. For different regional functional zones, the above parameter calibration process is performed separately to obtain the parameter sets corresponding to each type of region.

[0031] S4: Based on the non-dominated sorting genetic algorithm, a dual-scenario evolution mechanism is constructed within the spatiotemporal evolution boundary output by the system dynamics model. Combining the constraints and the endogenous penalty function, the dynamic threshold interval of industrial development, consisting of the lower limit of safe operation and the upper limit of absolute collapse before irreversible mutation, is obtained and output.

[0032] Non-dominated sorting genetic algorithms are multi-objective optimization algorithms capable of handling problems with multiple conflicting objectives. In this invention, the algorithm searches within the spatiotemporal evolution boundary output by the system dynamics model. The spatiotemporal evolution boundary refers to the state space range defined by the system dynamics model, such as the total water resources not being negative, the industry scale not exceeding the market capacity, and the vegetation index not being lower than 0.

[0033] The dual-scenario evolution mechanism specifically includes Scenario 1 and Scenario 2.

[0034] Scenario 1: Under the premise of eliminating unconventional water intervention, the objective function is to maximize the total system benefit, optimizing to find the safe operating lower limit that ensures the ecological degradation threshold is not exceeded. The safe operating lower limit of the ecological degradation threshold refers to the maximum safe scale that industries can achieve relying solely on conventional water resources without utilizing unconventional water expansion; exceeding this scale will trigger irreversible ecological degradation. The specific calculation logic is as follows: A physical boundary closure operation is performed in the system dynamics model, locking the upper limit of available water volume to a rigid conventional water quota. The rigid conventional water quota refers to the multi-year average amount of conventional surface water and exploitable groundwater resources, without considering unconventional water replenishment. The scale vector of the region's leading industries is used as decision variables, such as cotton planting area, coal chemical production capacity, and agricultural product processing volume. The objective function is to maximize economic benefit, i.e., maximizing the sum of the output value of each industry minus costs. Simultaneously, the hard constraint that the total water consumption does not exceed the difference between the rigid conventional water quota and the minimum ecological baseflow must be met. This hard constraint ensures that water used for industrial development will not crowd out the water needed to maintain basic ecological functions and residents' lives. Under this constraint, the maximum effective economic scale under conventional water support is obtained through iterative solution using a non-dominated sorting genetic algorithm, which serves as the safe operating lower limit for the ecological degradation threshold.

[0035] In the system dynamics model, a physical boundary closure operation is performed to lock the upper limit of available water volume to a rigid conventional water quota. Using the scale vector of the region's dominant industries as decision variables and maximizing economic benefits as the objective function, under the hard constraint that total water consumption does not exceed the difference between the rigid conventional water quota and the minimum ecological baseflow, a non-dominated sorting genetic algorithm is used iteratively to obtain the maximum effective economic scale supported by pure conventional water, which serves as the safe lower limit for the ecological degradation threshold. This hard constraint is expressed by the following equation: ; in The target value sought is the lower limit of safe operation for the first stage of ecological degradation critical point. This represents the total number of industry categories. For the first The scale of the industry The output value coefficient per unit physical scale. For the first Water quotas for similar industries For rigid, conventional water quotas, It is the minimum ecological base flow.

[0036] Scenario 2: Under the premise of enabling dynamic expansion of the total water supply, an endogenous penalty function based on ecological collapse risk is embedded in the objective function to optimize and obtain the absolute upper limit of system collapse before irreversible mutation. Dynamic expansion of the total water supply refers to incorporating unconventional water resources such as reclaimed water and mine drainage water into the supply system, and the upper limit of the total water supply will dynamically increase over time with investment and technological progress. The endogenous penalty function includes a water resource consumption penalty term and a land degradation penalty term. The water resource consumption penalty term is used to characterize the exponential surge in water resource acquisition costs when the actual total water consumption approaches the safe operating limit of the total water supply. The land degradation penalty term is used to trigger ecological collapse penalty when the vegetation index, which characterizes oasis vitality, approaches the irreversible desertification threshold, forcibly depriving the system of economic benefits. The algorithm, through the surge of the water resource consumption penalty term and the land degradation penalty term, forcibly clears the economic benefits of the system that exceeds the limit, thereby optimizing and obtaining the absolute upper limit of system collapse before irreversible mutation. The absolute collapse limit before irreversible mutation refers to the maximum industrial scale that the system can withstand. Once this scale is exceeded, the system will undergo irreversible mutation, such as the complete desertification of the oasis or the collapse of the industrial system.

[0037] Under the premise of enabling dynamic expansion of the full water supply, an endogenous penalty function based on ecological collapse risk is embedded in the objective function. This endogenous penalty function includes a water resource consumption penalty term and a land degradation penalty term: the former characterizes the exponential surge in water resource acquisition costs when the actual total water consumption approaches the safe operating limit of the full water supply; the latter is used to trigger ecological collapse penalties when the vegetation index, representing oasis vitality, approaches the irreversible desertification threshold, forcibly stripping the system of economic benefits. The algorithm optimizes the absolute collapse ceiling before irreversible mutation by forcibly clearing the economic benefits of the system that has exceeded the limits through the surge of these two penalty factors. The corresponding objective function with endogenous penalties is: ; in For the first The scale of the industry The output value coefficient per unit physical scale. For water consumption quotas, This represents the dynamic upper limit of the total water volume. As the minimum ecological base flow, The vegetation vitality index represents the critical point of irreversible desertification. This is a real-time vegetation vitality index. The coefficient representing the exponential constraint of soaring marginal costs. and These are the weighting coefficients.

[0038] After completing the dual-scenario optimization, a closed dynamic threshold range for industrial development is finally output. The lower limit of this range is the safe operating limit at the ecological degradation critical point, and the upper limit is the absolute collapse limit before irreversible mutation. The actual scale of industrial development should be controlled within this range and as close as possible to the lower limit to ensure ecological security.

[0039] Example 2 This embodiment provides a system for implementing the above method. The system incorporates the aforementioned method for analyzing industrial development thresholds in arid regions, including a data acquisition and preprocessing module, a regional functional differentiation identification module, a composite system dynamic simulation module, and a dynamic threshold interval calculation module.

[0040] The data acquisition and preprocessing module is used to acquire and construct a three-dimensional time-series standardized matrix. This module specifically includes a multi-source data integration unit, a three-dimensional time-series matrix construction unit, and a global range standardization unit. The multi-source data integration unit connects to multi-dimensional indicator databases such as full-volume water resources, industrial economy, land use, and ecological vitality, enabling unified access to heterogeneous data. The three-dimensional time-series matrix construction unit introduces a time dimension, recombining spatial units and indicator items to construct a three-dimensional time-series matrix that preserves the longitudinal evolution characteristics of the indicators. The global range standardization unit performs indicator normalization across the entire spatiotemporal sample domain, eliminating dimensional influences through global extreme value comparison and performing zero-shift prevention processing to generate a normalized steady-state matrix.

[0041] The regional functional differentiation identification module is used to extract typical unit samples using a weighted self-organizing map network. This module includes a global weight measurement unit, an asymmetric feature stretching unit, and a typical unit extraction unit. The global weight measurement unit, based on a normalized steady-state matrix, uses the entropy weight method to calculate the global objective weights of each system indicator on regional differentiation. The asymmetric feature stretching unit uses weight vectors to perform asymmetric physical stretching on the multi-dimensional feature space, constructing a weighted feature matrix that enforces the core soil and water constraints. The typical unit extraction unit runs the self-organizing map network for competitive learning, and extracts administrative units with minimal spatial feature deviation as typical unit samples by calculating the inverse reconstruction analytical values ​​of the cluster centers after training.

[0042] The composite system dynamic simulation module is used to construct the system dynamics model and calibrate parameters using a genetic algorithm. This module includes a dynamics model calculation engine and a latent parameter calibration unit. The dynamics model calculation engine runs a system of ordinary differential equations that includes a water resource ceiling expansion loop, an industrial consumption metabolism negative feedback loop, and a land ecological stress feedback loop. The latent parameter calibration unit is equipped with a standard continuous genetic algorithm optimizer, used to lock in latent feedback elasticity parameters reflecting specific regional characteristics by minimizing the fitting loss function, based on long-sequence historical data of typical units.

[0043] The dynamic threshold interval calculation module utilizes a dual-scenario optimization algorithm to output a dynamic threshold interval for industrial development, consisting of a safe operating lower limit at the ecological degradation critical point and an absolute collapse upper limit before irreversible mutation. This module further includes a model accuracy verification unit, a dual-scenario collaborative optimization unit, and a threshold interval output unit. The model accuracy verification unit verifies the structural robustness of the simulated trajectory of the system dynamics model using the coefficient of determination, Nash efficiency coefficient, and average relative error. The dual-scenario collaborative optimization unit is equipped with a non-dominated sorting genetic algorithm processor, used to perform optimization of the safe operating lower limit at the ecological degradation critical point under conventional water hardness constraints, and optimization of the absolute collapse upper limit before irreversible mutation with full water dynamic feedback and embedded endogenous penalty functions of surging water resource costs and ecological collapse. The threshold interval output unit generates a closed dynamic threshold interval for industrial development and provides overload risk warnings based on the current industrial stock's ranking.

[0044] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. The above descriptions are only preferred embodiments of this application. It should be noted that due to the limitations of written expression, while there are objectively infinite specific structures, those skilled in the art can make several improvements, modifications, or changes without departing from the principles of this application, and can also combine the above technical features in an appropriate manner. These improvements, modifications, changes, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of this application.

Claims

1. A method for threshold analysis of industrial development in arid regions, characterized in that, include: S1. Obtain multi-source panel data of the water-production-land composite system in the arid area to be tested, introduce the time dimension to construct a three-dimensional time series matrix and perform spatiotemporal standardization to obtain the normalized steady-state matrix. S2. Calculate the global objective weights of each indicator and inject them into the self-organizing map network to perform asymmetric stretching of the multidimensional feature space, identify regional functional differentiation characteristics and extract typical unit samples. S3. Construct a system dynamics model that includes the expansion of water resource ceiling, the expansion of industrial demand, and the feedback loop of land ecological stress, and use a standard continuous genetic algorithm to calibrate regional parameters. S4. Based on the non-dominated sorting genetic algorithm, a dual-scenario evolution mechanism is constructed within the spatiotemporal evolution boundary output by the system dynamics model. Combining the constraints and endogenous penalty function, the dynamic threshold range of industrial development, consisting of the safe operation lower limit of the ecological degradation critical point and the absolute collapse upper limit before irreversible mutation, is obtained and output.

2. The method for threshold analysis of industrial development in arid regions according to claim 1, characterized in that, S2 specifically includes: The global objective weights of each system index are obtained using the entropy weight method; The multidimensional spatial coordinate axes of the multi-year average normalized steady-state matrix are asymmetrically stretched using the global objective weights to construct a weighted feature matrix. The weighted feature matrix is ​​input into a self-organizing map network for competitive learning. By calculating the weighted spatial feature deviation, the prefecture-level cities in each cluster that achieve the absolute minimum deviation are extracted as the typical unit samples.

3. The method for threshold analysis of industrial development in arid regions according to claim 1, characterized in that, The system dynamics model constructed in S3 includes the following feedback loops: The evolution of the positive feedback loop of water resource ceiling expansion is dominated by the Logistic equation with technical saturation constraints. The negative feedback loop of industrial consumption metabolism is used to force the high water-consuming production capacity to be compressed and withdrawn when the industrial water demand approaches the upper limit of the total water supply through the surge in the marginal cost of water resource acquisition. A negative feedback loop of land ecological stress is used to trigger a nonlinear decline in vegetation indices characterizing oasis vitality when the remaining water volume falls below the minimum ecological baseflow.

4. The method for threshold analysis of industrial development in arid regions according to claim 1, characterized in that, The method for performing regional parameter calibration in S3 is as follows: Using the long-sequence panel data of the typical unit samples as a benchmark, a historical fitting loss function based on minimizing the root mean square relative error is constructed. A continuous genetic algorithm with real-number encoding is used to find the optimal value in the multidimensional parameter space through arithmetic crossover and non-uniform mutation operations, thereby obtaining the set of nonlinear response elastic parameters corresponding to each type of region.

5. The method for threshold analysis of industrial development in arid regions according to claim 1, characterized in that, The dual-scenario evolution mechanism in S4 specifically includes: Scenario 1: Under the premise of removing unconventional water interventions, with the objective function of maximizing the total system benefit, find the safe operating lower limit that ensures that the ecological degradation threshold is not exceeded. Scenario 2: Under the premise of enabling dynamic expansion of the full water volume, an endogenous penalty function based on the risk of ecological collapse is embedded in the objective function to find the absolute upper limit of system collapse before irreversible mutation occurs.

6. The method for threshold analysis of industrial development in arid regions according to claim 5, characterized in that, In Scenario 1, the calculation logic for the safe operating lower limit of the ecological degradation critical point is as follows: In the system dynamics model, a physical boundary closure operation is performed to lock the upper limit of available water volume to a rigid conventional water quota; Using the scale vector of the region's leading industries as decision variables and maximizing economic benefits as the objective function, under the hard constraint that the total water consumption does not exceed the difference between the rigid conventional water quota and the minimum ecological base flow, the maximum effective economic scale under conventional water support is obtained through iterative solution using a non-dominated sorting genetic algorithm, which serves as the safe operating lower limit for the ecological degradation threshold. The hard constraint condition is expressed as follows: ； in The target value sought is the lower limit of safe operation for the first stage of ecological degradation critical point. This represents the total number of industry categories. For the first The scale of the industry The output value coefficient per unit physical scale. For the first Water quotas for similar industries For rigid, conventional water quotas, It is the minimum ecological base flow.

7. The method for threshold analysis of industrial development in arid regions according to claim 5, characterized in that, In scenario two, the endogenous penalty function includes a water resource consumption penalty term and a land degradation penalty term; The water consumption penalty term represents the exponential surge in water acquisition costs when the actual total water consumption approaches the limit of safe operation of all water resources. The land degradation penalty is used to trigger an ecological collapse penalty when the vegetation index, which represents the vitality of an oasis, approaches the irreversible desertification threshold, thereby forcibly depriving the system of economic benefits. The algorithm forces the economic benefits of the out-of-bounds system to zero by surging the water resource consumption penalty and land degradation penalty, thereby finding the absolute collapse limit before the irreversible mutation.

8. The method for threshold analysis of industrial development in arid regions according to claim 5, characterized in that, In scenario two, the objective function formula including endogenous penalties is: ； in For the first The scale of the industry The output value coefficient per unit physical scale. For water consumption quotas, This represents the dynamic upper limit of the total water volume. As the minimum ecological base flow, The vegetation vitality index represents the critical point of irreversible desertification. This is a real-time vegetation vitality index. The coefficient representing the exponential constraint of soaring marginal costs. and These are the weighting coefficients.

9. A threshold analysis system for industrial development in arid regions, equipped with the threshold analysis method for industrial development in arid regions as described in any one of claims 1-8, characterized in that, include: The data acquisition and preprocessing module is used to acquire and construct a three-dimensional time-series normalization matrix; The regional functional differentiation identification module is used to extract typical unit samples using a weighted self-organizing map network; The composite system dynamic simulation module is used to construct system dynamic models and calibrate parameters using genetic algorithms; The dynamic threshold interval calculation module is used to output the dynamic threshold interval for industrial development, which consists of the lower limit of safe operation and the upper limit of absolute collapse before irreversible mutation, using a dual-scenario optimization algorithm.

10. The threshold analysis system for industrial development in arid regions according to claim 9, characterized in that, The dynamic threshold interval calculation module further includes: The model accuracy verification unit is used to verify the structural robustness of the simulated trajectory of the system dynamics model by using the coefficient of determination, Nash efficiency coefficient and mean relative error. The dual-scenario collaborative optimization unit is equipped with a non-dominated sorting genetic algorithm processor, which is used to perform the lower bound optimization of safe operation under conventional water hard constraints, and the upper bound optimization of absolute collapse before irreversible mutation by enabling full water dynamic feedback and embedding the dual endogenous penalty function of water resource cost surge and ecological collapse. Threshold interval output unit, used to generate closed dynamic threshold intervals for industrial development.

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