Index and weight combined water resource bearing capacity evaluation robustness analysis method, system, equipment and medium

Abstract

The invention discloses an index and weight combined water resource bearing capacity evaluation robustness analysis method, system and equipment and a medium. The method comprises the following steps: establishing a multi-dimensional evaluation index system according to a support index subset and a pressure index subset; querying index data of the research area in multiple years to form samples in multiple years, and calculating index weights by respectively adopting four weight calculation methods; constructing a disturbance scene, and calculating an annual water resource bearing capacity index of each year; in a disturbance scene, considering a plurality of disturbance factors, and executing sensitivity analysis to identify disturbance factors and indexes which have obvious influence on the water resource bearing capacity index; and carrying out robustness evaluation according to the distribution stability degree of the water resource bearing capacity index, and selecting a most robust weight calculation method and a corresponding robust disturbance scene. According to the method, the related problems of high subjectivity of an index system, single weight setting, insufficient uncertainty propagation mechanism and lack of quantitative judgment of robustness in the prior art are solved.

Description

Technical Field

[0001] This invention relates to the field of water resources analysis technology, and in particular to a robustness analysis method, system, equipment and medium for evaluating water resources carrying capacity using a combination of indicators and weights. Background Technology

[0002] Existing water environment carrying capacity (WRCC) assessment methods mostly employ fixed indicator systems, such as those based on the "PS" model, the "PSR" model, or the "water resources-water environment-ecological environment" model. Different studies select indicator sets based on researchers' experience or specific regional conditions, resulting in significant differences in assessment systems. The selection of indicators lacks a unified scientific sampling or systematic verification mechanism. Once the indicator set is determined, it is treated as a fixed input, lacking a quantitative description of the uncertainties in indicator selection (such as indicator redundancy, correlation, and differences in representativeness). This leads to results that are highly sensitive to the combination of indicators and poor assessment stability.

[0003] Current WRCC (Walking Capacity Computation) assessments commonly use methods such as the Analytic Hierarchy Process (AHP), entropy weighting, coefficient of variation (COP) method, or principal component analysis (PCA) to determine weights. Each weighting method inherently contains assumptions and biases; for example, AHP relies heavily on expert judgment, entropy weighting is based solely on sample dispersion, and PCA ignores the physical meaning of indicators. In practical applications, most studies employ only a single weighting scheme, failing to consider the uncertainty propagation effect of weights. This results in assessment results for the same region or dataset being significantly influenced by the choice of weight calculation method. Therefore, existing deterministic weighting methods struggle to reveal the sensitivity of weight perturbations to WRCC results, leading to insufficient reliability and robustness in carrying capacity assessments.

[0004] While existing research has attempted to characterize WRCC uncertainty using methods such as Bayesian estimation, univariate sensitivity analysis, or Monte Carlo sampling, most studies focus only on a single dimension of the index or weights. They lack a joint framework that considers the entire "index-weight" process, failing to simultaneously identify the interaction between index sampling and weight perturbations in bearing capacity calculation. This makes it difficult for current uncertainty research to fully reveal the distribution characteristics of WRCC index results and their robustness differences, limiting the systematic evaluation of model credibility.

[0005] Traditional WRCC evaluations often rely on single-calculation results as the final criterion, failing to construct outcome distribution characteristics and robustness indicators across multiple scenarios. Existing research lacks a unified quantitative standard for robustness, making it impossible to identify the most stable weighting method under different perturbation conditions. Therefore, it fails to provide decision-makers with statistically significant optimal weighting choices under complex and uncertain conditions, limiting the widespread application and decision-making value of WRCC evaluations. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a robustness analysis method for evaluating water resource carrying capacity by combining indicators and weights, which solves the problems of strong subjectivity of the indicator system, single weight setting, insufficient uncertainty propagation mechanism, and lack of quantitative judgment of robustness in the existing technology.

[0007] The second objective of this invention is to provide a robustness analysis system for evaluating water resource carrying capacity by combining indicators and weights.

[0008] A third objective of this invention is to provide an electronic device.

[0009] A fourth objective of this invention is to provide a computer-readable storage medium.

[0010] Technical solution: To achieve the above objectives, the robustness analysis method for water resource carrying capacity assessment described in this invention includes the following steps: (1) A multidimensional evaluation index system is established based on the supporting index subset and the pressure index subset. The supporting index subset includes four supporting index groups: water resources and water environment index, ecological protection index, water supply index and pollution control index. The pressure index subset includes four pressure index groups: population index, economic index, water use index and pollution load index. Each supporting index group includes multiple supporting indicators, and each pressure index group includes multiple pressure indicators. (2) Query the indicator data of the study area for multiple years to form multiple year samples. Normalize each indicator data and then calculate the indicator weights using equal weight method, entropy weight method, grouped entropy weight method and principal component analysis respectively. (3) Constructing disturbance scenarios: First, the indicators are selected and disturbed to determine the supporting indicators and the pressure indicators, and obtain multiple indicator subset sizes. For each indicator subset size, multiple random samplings are performed from the multidimensional evaluation indicator system. After the indicator selection sampling is completed, block self-sampling is performed on the year index of the indicator data to obtain the year subsample sequence under the year disturbance scenario. The indicator weights are calculated using four weight calculation methods on the year subsample sequence to obtain four sets of baseline weights. The baseline weights are disturbed by setting the weight disturbance amplitude. For each weight disturbance amplitude, the number of weight disturbance samplings is set to generate the disturbed weight set. Finally, multiple disturbance scenarios are generated by random combination. (4) Using the index data and corresponding weights in the disturbance scenario, calculate the pressure aggregate value of all pressure indicators and the support aggregate value of all support indicators for each year, and then calculate the annual water resources carrying capacity index for each year, and summarize to form a water resources carrying capacity index distribution sample corresponding to the disturbance scenario. (5) Under the disturbance scenario, multiple disturbance factors are considered, including the weight calculation method, the combination of indicator subset size, the number of indicator sampling, the year self-help block, the weight disturbance amplitude and the number of weight disturbance sampling. Sensitivity analysis is performed to identify the disturbance factors and indicators that have a significant impact on the water resources carrying capacity index. (6) Under the disturbance scenario, the robustness assessment is carried out based on the distribution stability of the water resources carrying capacity index obtained by different weight calculation methods, and the most robust weight calculation method and the corresponding robust disturbance scenario are selected.

[0011] Optionally, the water resources and water environment indicators in step (1) include rainfall, water production modulus, per capita water resources and river section water quality index; ecological protection indicators include inland water area, forest area and green coverage rate of urban built-up area; water supply indicators include centralized water supply capacity and total annual tap water supply; pollution control indicators include urban sewage treatment capacity, COD removal and environmental pollution control investment; population indicators include year-end resident population and urbanization level; economic indicators include the proportion of primary industry GDP, the proportion of secondary industry GDP and per capita GDP; water use indicators include total water use, per capita comprehensive water use, total domestic water use, per capita daily water use of residents, water use per 10,000 yuan of GDP and water use per 10,000 yuan of industrial added value; and pollution load indicators include total wastewater discharge and COD discharge.

[0012] Optionally, step (2) specifically includes the following steps: (2.1) Query Indicator data for the study area in each year, Each indicator is assigned a corresponding code, and all indicator data for a year form a yearly sample, totaling [data missing]. Sample from each year; Let the original data matrix of the stress index be: , This refers to the number of indicators related to stress. For the number of years, For the first In the sample of the year, the first The value of the pressure indicator; Let the original data matrix of the supporting indicators be: , The number of indicators to support the indicators, For the first In the sample of the year, the first The value of each supporting indicator; (2.2) Perform min-max normalization on each indicator data to normalize the values ​​of different indicators to the [0,1] interval, and obtain the first... Standardized value of the stress index and the Standardized indicator values ​​of the supporting indicators ; (2.3) The weights of the indicators are calculated by equal weight method, entropy weight method, group entropy weight method and principal component analysis respectively. The weights of the indicators obtained by the four weight calculation methods all satisfy the constraint that they are non-negative and sum to 1.

[0013] Optionally, the weight perturbation of the baseline weights in step (3) specifically includes the following steps: Set the weight perturbation amplitude parameter There are several levels, corresponding to the amplitude of each weight perturbation, and the number of weight perturbation sampling times is set. ; For each set of baseline weights, record The baseline weight vector is determined based on a pre-defined perturbation amplitude. Adjusting the concentration parameters of the Dirichlet distribution ,conduct Second sampling, obtained The perturbated weight vector; the Dirichlet weight perturbation calculation process is as follows: , , , in This represents the perturbed weight vector. Represents the baseline weight vector. This represents the random perturbation weight vector in the Dirichlet model. Indicates the magnitude of the disturbance. Indicates concentration parameter, It is a positive minimum value to avoid a denominator of 0; the generated weight vector Each component is non-negative and the sum is 1.

[0014] Optionally, step (4) specifically includes the following steps: First, set the water resource carrying capacity index. As a comprehensive representative indicator, and with an annual time unit; for the first For each year's sample, calculate the weighted aggregate value of all supporting indicators for the entire year. The weighted aggregate value of all stress indicators Then calculate the first Annual water resources carrying capacity index for each year : , , , In the formula and Representing the year The next The first pressure indicator and the first Standardized values ​​of each supporting indicator; These are the corresponding indicator weights; Indicates the year The water resource carrying capacity index below; Using the index data and corresponding weights of the disturbance scenario, the aggregated pressure value for each year is calculated. and supporting aggregate value Then, the annual water resources carrying capacity index for each year is obtained. Sequence; the annual water resources carrying capacity index calculated for each year. The data are aggregated to form a water resource carrying capacity index corresponding to the disturbance scenarios. Distributed sample pool.

[0015] Optionally, step (5) specifically includes the following steps: (5.1) For the disturbance scenario, consider multiple disturbance factors, disturbance factors This includes the weighting calculation method, the combination of indicator subset sizes, the number of indicator samplings, the year bootstrap block, the magnitude of weight perturbation, and the number of weight perturbation samplings. A Type-II main effects model in ANOVA is used to calculate the sum of squares of the main effects of each perturbation factor. And the proportion of the total variance explained by the disturbance factor, in the effect size of ANOVA. As a statistic measuring the amount of variance explained by a factor, its calculation formula is: , , , In the formula Indicates the disturbance factor Type-II sum of squares, Indicates the disturbance factor degrees of freedom Indicates the mean square of the residuals. Represents the sum of squared residuals. Represents the residual degrees of freedom. Represents the total sum of squares. The effect size representing the residual contribution; (5.2) Based on the partial derivative relationship between the water resources carrying capacity index and the pressure index data and the supporting index data, calculate the effect of each index on the carrying capacity index. The marginal impact is used to obtain the sensitivity coefficient of the indicator, and the specific calculation formula is as follows: , , This is the sensitivity coefficient for the pressure index. To support the sensitivity coefficient of the indicator, the higher the sensitivity, the greater the impact of the indicator on the water resources carrying capacity index.

[0016] Optionally, step (6) specifically includes the following steps: (6.1) For each disturbance scenario, each weight calculation method, and each year under that disturbance scenario Calculate the corresponding water resource carrying capacity index The interquartile range (IQR) value under different weighting calculation methods is used as the annual distribution dispersion; IQR is defined as the difference between the upper quartile and the lower quartile of the data distribution, i.e. The upper quartile is the 75th percentile. The lower quartile is the 25th percentile. ; (6.2) Under the same disturbance scenario, the water resource carrying capacity index corresponding to different weighting calculation methods is calculated. The IQR values ​​are sorted in ascending order, assigned ranks, and converted to quantiles to obtain the IQR rank quantile value for each weighting method under this perturbation scenario. , , For perturbation scenarios Weight calculation method and year The IQR value below; (6.3) For the same disturbance scenario, the IQR rank quantile values ​​of each weight calculation method are averaged over the annual dimension to obtain the annual average robustness score of each weight calculation method in that disturbance scenario; for the disturbance scenario Weight calculation method in Calculate its value under the disturbance scenario. All years rank quantile The annual average is calculated using the following formula: , This represents the annual average robustness score for different weighting methods under different disturbance scenarios. For perturbation scenarios and weight calculation method All corresponding years; (6.4) After obtaining the annual average robustness score for each disturbance scenario, evaluate the robustness of each weight calculation method from the perspective of cross-disturbance scenarios. For each weight calculation method, evaluate the robustness based on its annual average robustness score set across all disturbance scenarios. , For the set of disturbance scenarios, calculate the annual average robustness score. The three statistical measures, namely the maximum value, 95th percentile, and mean, are calculated using the following formula: , , , This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The maximum value represents whether the weight calculation method is robust under the most unfavorable perturbation scenario; This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The 95th percentile represents the true robustness under most perturbation scenarios, avoiding the influence of extreme values; This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The average value; (6.5) Constructing a weight calculation method Comprehensive robustness indicators The calculation formula is: , Comprehensive robustness indicators A smaller value indicates a more robust weighting calculation method, which is reflected in the overall robustness index. As the primary criterion, select a comprehensive robustness indicator. The method for calculating the minimum weight is the optimal robust solution; when there are ties, compare them sequentially. , , Until the distinction is made, , , A smaller value indicates a more robust weighting method; when weights are still tied, priority is given to selecting all weights. The median of IQR is smaller than that of the IQR. (6.6) Output the optimal robust method and the corresponding comprehensive robustness index value. At the same time, provide the corresponding Statistical results of the annual distribution dispersion (IQR) values ​​for each disturbance scenario.

[0017] The robustness analysis system for water resource carrying capacity assessment of this invention includes: The indicator system construction module is used to establish a multi-dimensional evaluation indicator system based on the supporting indicator subset and the pressure indicator subset. The supporting indicator subset includes four supporting indicator groups: water resources and water environment indicators, ecological protection indicators, water supply indicators, and pollution control indicators. The pressure indicator subset includes four pressure indicator groups: population indicators, economic indicators, water use indicators, and pollution load indicators. Each supporting indicator group includes multiple supporting indicators, and each pressure indicator group includes multiple pressure indicators. The indicator weight calculation module queries indicator data for the study area for multiple years, forms multiple year samples, normalizes each indicator data, and then calculates the indicator weight using equal weight method, entropy weight method, grouped entropy weight method, and principal component analysis method respectively. The disturbance scenario construction module is used to construct disturbance scenarios. First, indicator selection and disturbance are performed to determine supporting and stress indicators, resulting in multiple indicator subset sizes. For each indicator subset size, multiple random samples are taken from the multidimensional evaluation indicator system. After the indicator selection and sampling is completed, block self-sampling is performed on the year index of the indicator data to obtain the year sub-sample sequence under the year disturbance scenario. Four weight calculation methods are used to calculate the indicator weights on the year sub-sample sequence to obtain four sets of baseline weights. The baseline weights are then perturbed, and the perturbation amplitude is set. For each perturbation amplitude, the number of weight perturbation sampling times is set to generate a perturbed weight set. Finally, multiple disturbance scenarios are generated through random combination. The carrying capacity index calculation module is used to calculate the pressure aggregate value of all pressure indicators and the support aggregate value of all support indicators for each year using the indicator data and corresponding weights in the disturbance scenario, and then calculate the annual water resources carrying capacity index for each year, and summarize them to form a water resources carrying capacity index distribution sample corresponding to the disturbance scenario. The sensitivity analysis module is used to perform sensitivity analysis under disturbance scenarios, considering multiple disturbance factors, including weight calculation methods, combination of indicator subset sizes, number of indicator samplings, year self-help blocks, weight disturbance amplitude, and number of weight disturbance samplings, to identify disturbance factors and indicators that have a significant impact on the water resources carrying capacity index. The robustness analysis module is used to conduct robustness assessments based on the distribution stability of the water resource carrying capacity index obtained by different weighting calculation methods under disturbance scenarios, and to select the most robust weighting calculation method and the corresponding robust disturbance scenario.

[0018] The electronic device of the present invention includes one or more processors, one or more memories, and one or more programs. The programs are stored in the memory and configured to be executed by the processor. When the programs are loaded onto the processor, they implement the steps of a robust analysis method for evaluating water resource carrying capacity using a combination of indicators and weights as described above.

[0019] The computer-readable storage medium of the present invention stores a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to perform the steps of a robust analysis method for evaluating water resource carrying capacity using a combination of indicators and weights as described above.

[0020] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) This invention overcomes the limitations of subjectivity and certainty in the construction of indicator system. By extracting and combining the indicator set in layers under the framework of "pressure indicators and support indicators", it systematically describes the uncertainty of indicator selection, avoids subjective bias caused by relying solely on a fixed indicator system, and improves the representativeness and universality of the indicator system. (2) This invention solves the problems of single and biased weight setting. By introducing multiple weight calculation methods and Dirichlet probability perturbation model, it realizes parallel simulation of multiple weight schemes and random perturbation, thereby quantifying the impact of different weight settings on WRCC evaluation results and overcoming the sensitivity and bias problems caused by traditional deterministic weighting. (3) This invention realizes the joint propagation analysis of the uncertainty of indicators and weights. In view of the limitation of existing studies that only consider the uncertainty of a single factor, this invention uses Monte Carlo stratified sampling and block bootstrapping to generate multi-level disturbance scenarios, comprehensively characterizes the coupling influence and propagation mechanism of the indicator system and weight changes on the bearing capacity results, and thus systematically reveals the statistical characteristics and dominant uncertainty sources of the WRCC result distribution. (4) This invention establishes a robustness quantification and method optimization mechanism for WRCC evaluation results. By introducing a robustness quantification index system based on annual interquartile range (IQR), the distribution of WRCC results under different scenarios and weighting methods is statistically analyzed. A method for calculating IQR rank quantile and robustness comprehensive index is proposed. Finally, the weight scheme that maintains the most stable performance under multiple disturbance scenarios is selected, realizing the quantitative robustness assessment of WRCC evaluation results and the selection of the optimal method, providing a reliable decision-making basis for regional water environment carrying capacity analysis. Attached Figure Description

[0021] Figure 1 This is a graph showing the cumulative distribution of R in different years in this invention; Figure 2 This is a diagram showing the distribution of R under perturbation in the weight calculation method of this invention; Figure 3 This is a diagram showing the distribution of R under the perturbation of the size combination of index subsets in this invention; Figure 4 This is a diagram showing the distribution of R under the weight perturbation amplitude perturbation in this invention; Figure 5 This is a diagram showing the distribution of R under the weight perturbation sampling number perturbation in this invention; Figure 6 This is a diagram showing the distribution of R under the perturbation of the number of index samplings in this invention; Figure 7 This is a diagram showing the distribution of R under the perturbation of the year-based self-service block in this invention; Figure 8 This is a diagram showing the dominant effects of perturbation factors in different years in this invention; Figure 9 This is a robustness analysis diagram of different weight calculation methods in this invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0023] Example 1: A robustness analysis method for evaluating water resource carrying capacity using a combination of indicators and weights according to the present invention includes the following steps: (1) A multidimensional evaluation index system is established based on the supporting index subset and the pressure index subset. The supporting index subset includes four supporting index groups: water resources and water environment index, ecological protection index, water supply index and pollution control index. The pressure index subset includes four pressure index groups: population index, economic index, water use index and pollution load index. Each supporting index group includes multiple supporting indicators, and each pressure index group includes multiple pressure indicators. Water resources and water environment indicators include rainfall, water yield modulus, per capita water resources, and river section water quality index; ecological protection indicators include inland water area, forest area, and urban built-up area green coverage rate; water supply indicators include centralized water supply capacity and total annual tap water supply; pollution control indicators include urban sewage treatment capacity, COD removal, and environmental pollution control investment; population indicators include year-end resident population and urbanization level; economic indicators include the proportion of primary industry GDP, the proportion of secondary industry GDP, and per capita GDP; water use indicators include total water consumption, per capita comprehensive water consumption, total domestic water consumption, per capita daily water consumption of residents, water consumption per 10,000 yuan of GDP, and water consumption per 10,000 yuan of industrial added value; pollution load indicators include total wastewater discharge and COD discharge. Among these, all supporting indicators and all pressure indicators are divided into negative and positive impact indicators according to their direction of influence on water resource carrying capacity. The river section water quality index is a negative impact indicator, and the rest are positive impact indicators. As shown in Table 1, a multi-dimensional evaluation indicator system based on the "pressure P-support S model" is established.

[0024] Table 1. Complete Set of WECC Evaluation Indicators

[0025] (2) Query the indicator data of the study area in multiple years to form multiple year samples. Normalize each indicator data and then use equal weight method, entropy weight method, group entropy weight method and principal component analysis to calculate the indicator weights and obtain multiple weight allocation schemes. Step (2) specifically includes the following steps: (2.1) All supporting indicators and all pressure indicators can be found in the Statistical Yearbook, Water Resources Bulletin, and Ecological Environment Quality Bulletin. Indicator data for the study area in each year, Each indicator is assigned a corresponding code, and all indicator data for a year form a yearly sample, totaling [data missing]. Sample from each year; Let the original data matrix of the stress index be: , This refers to the number of indicators related to stress. , For the number of years, ; For the first In the sample of the year, the first The value of the pressure indicator; Let the original data matrix of the supporting indicators be: , The number of indicators to support the indicators, , For the first In the sample of the year, the first The value of each supporting indicator; (2.2) Perform min-max normalization on each indicator data to normalize the values ​​of different indicators to the [0,1] interval, so that indicators of different dimensions are comparable, and obtain the first... Standardized value of the stress index and the Standardized indicator values ​​of the supporting indicators ; For positive impact indicators, min-max normalization is performed, and the specific calculation formula is as follows: , , For indicators with negative impact, a min-max normalization process is performed. The specific calculation formula is as follows: , , in, For the first In the sample of the year, the first The value of the pressure indicator. For the first In the sample of the year, the first The values ​​of the supporting indicators, For the first The standardized value of the stress indicator. For the first The standardized values ​​of the supporting indicators; Indicates the first The stress index is the highest value among all years in the sample. Indicates the first The maximum value of each supporting indicator across all year samples; Indicates the first The minimum value of the stress index across all years in the sample. Indicates the first The minimum value of the supporting indicator across all years of the sample; (2.3) The weights of the indicators were calculated by equal weight method, entropy weight method, group entropy weight method and principal component analysis (PCA). The weights obtained by the four methods all meet the constraint that they are non-negative and sum to 1. Multiple weight allocation schemes were obtained to provide a reference for subsequent robustness analysis. (2.3.1) The calculation of index weights using the equal weight method includes the following steps: Assume the evaluation indicators include Item pressure indicators and For each supporting indicator, the weight of the pressure indicator is... , For the supporting indicators, the weight of each supporting indicator is: , ; That is, regarding stress indicators: Regarding supporting indicators: ; (2.3.2) The entropy weight method is used to calculate the index weights, and the information entropy is used to determine the objective weights, reflecting the differences of the indicators in the sample data. The specific steps include the following: For the In the sample of the year, the first The pressure index and the first Standardized indicator values ​​of the supporting indicators and Calculate the first The pressure index and the first The supporting indicators in the first Proportion of samples in each year and : , , Calculate the first according to the information entropy formula. Item pressure indicators and Information entropy value of supporting indicators and ; , , in For example, a positive minimum value that is not zero. To avoid The situation; and They represent the first Item pressure indicators and The information entropy value of a supporting indicator reflects the degree of uncertainty of the indicator value across all sample distributions. and The larger the value, the more uniform the indicator is, and the less information it provides.

[0026] Calculate the first The pressure index and the first Coefficient of difference of supporting indicators and : , , The larger the difference coefficient, the greater the variation of the indicator among samples, and the higher its information utility.

[0027] Calculate the weights, normalize the difference coefficients of each indicator, and obtain the first... Item pressure indicators and Weight of each supporting indicator and : , , income For the entropy weight method Objective weighting of each stress indicator; results For the entropy weight method The objective weights of each supporting indicator The sum is 1, each The sum is 1.

[0028] (2.3.3) The weights of the indicators are calculated using the grouped entropy weight method, which includes the following steps: First, the indicators are grouped by category. The pressure indicator system is divided into 4 groups, namely P1–P4, and the support indicator system is divided into 4 groups, namely S1–S4. Within each group, the entropy weight method is used to calculate the weight of each indicator. Then, according to the preset equal weights of the groups, the entropy weights in each group are multiplied by the equal weights to obtain the final weight of each indicator. The grouped entropy weight method takes into account the importance of different categories of indicators, so that the contribution of different subsystems to the comprehensive index can be reflected in a predetermined proportion, which is a combination of equal weights and entropy weights. ,all The sum is 1; ,all The sum of is 1; ,all The sum is 1; ,all The sum of is 1; ,all The sum is 1; ,all The sum is 1; ,all The sum is 1; ,all The sum of is 1; in , , , These are the pressure indicators from groups 1, 2, 3, and 4, respectively. The coefficient of difference of the pressure indicators , , , These are the supporting indicators from groups 1, 2, 3, and 4, respectively. The coefficient of difference of the supporting indicators.

[0029] (2.3.4) Principal component analysis (PCA) is used to extract key feature information from the data and calculate the index weights. The specific steps include: Z-score standardization was performed on the data of each indicator to eliminate the influence of dimensions. That is, for the first indicator, the Z-score standardization was applied. In the sample of the year, the first Item pressure indicators and The value of each supporting indicator and Calculate the corresponding standardized value and The standardized matrix is ​​obtained. and : , , , , , , in For the sample of all years, the first The average value of each stress indicator. For the sample of all years, the first The average value of each supporting indicator. For the sample of all years, the first The standard deviation of the stress index. For the sample of all years, the first The standard deviation of each supporting indicator; Calculate the normalization matrix separately and Correlation matrix and Then, perform eigenvalue decomposition to obtain eigenvectors. , Load matrix , and the eigenvalues ​​corresponding to each principal component , , Principal components, the maximum number of principal components in the stress index. With pressure index quantity Equal, the largest principal component number supporting the indicator Respectively with the number of supporting indicators equal; , , Correlation matrix of stress indicators Perform eigenvalue decomposition to obtain eigenvectors. and eigenvalue diagonal matrix : , , , , in Indicates the first The eigenvalues ​​of the principal components It is the first Each principal component corresponds to an eigenvector. Indicates the first The contribution coefficient of the pressure index in the direction of the principal component; Correlation matrix of supporting indicators Perform eigenvalue decomposition to obtain eigenvectors. and eigenvalue diagonal matrix : , , , , in Indicates the first The eigenvalues ​​of the principal components It is the first Each principal component corresponds to an eigenvector. Indicator of stress The contribution coefficient in the direction of this principal component; First, calculate the cumulative variance contribution rate of the principal components, where the formula for calculating the contribution rate d of a single principal component is: , , in , For the first The eigenvalues ​​of the principal components , For the first The variance contribution rate of each principal component; the summation symbol Principal component number; for stress indicators, principal component number. For supporting indicators, principal component numbers ; Based on the principle of cumulative variance contribution rate, the top principal components whose cumulative variance contribution reaches 90% are retained. Assuming we select the top [number of principal components]... If there are principal components, then the cumulative principal component contribution rate is: , , according to Before retaining pressure indicators Principal components, according to Before retaining support indicators One principal component; Calculate the principal component loading matrix, the first... Item pressure indicators and The supporting indicators in the first The loadings on the principal components are respectively , ,but: ,form Load matrix ; ,form Load matrix ; Based on the retained principal components and their loadings, calculate the comprehensive score for each indicator; specifically, multiply the absolute loadings of the indicator on the retained principal components by the variance contribution rate of that principal component and sum them up; then the score for the [missing information] is calculated. Item pressure indicators and The overall score of each supporting indicator and The calculation formula is: , , The higher the overall score of an indicator, the greater its role in the main components.

[0030] The overall scores of the indicators are normalized, and the standardized scores yield the indicator weights: , , and This refers to the indicator weights calculated using Principal Component Analysis (PCA), which reflect the contribution of each indicator to the main information.

[0031] (3) Introduce random disturbances to characterize the uncertainty of indicator selection, year sample uncertainty, and weight calculation method uncertainty, and construct a disturbance scenario. The specific steps are as follows: (3.1) Perform perturbation on the indicator selection to determine the size of the indicator subset; for each combination of indicator subset sizes, perform random sampling; Set the size of the support indicator subset and the stress indicator subset to a pair of numerical values ​​( , ),in The number of pressure indicators selected. To determine the number of supporting indicators selected, various combinations of indicator subset sizes are formed. In perturbation scenarios, various combinations of indicator subset sizes can be considered, for example: To examine the impact of different indicator set sizes on the results, at least one indicator should be selected in each group within each indicator subset. Monte Carlo random sampling was performed from the multidimensional evaluation index system in step (1), and stratified sampling with equal probability was performed independently for the pressure index and the support index respectively, obtaining samples of a scale of [missing information]. and Each set contains a subset of pressure indicators and a subset of support indicators. Combined, repeated sampling process Next, get A set of candidate indicators; for example Three possible values.

[0032] (3.2) After the sampling of the index selection is completed, the year index of the time series index data is subjected to block self-sampling. The time series index data is subjected to a self-sampling bootstrap with a block size of 2 to obtain the year sub-sample sequence under the year perturbation scenario, thereby maintaining the autocorrelation structure in the time series. On the year sub-sample sequence, the index weights are calculated using the four weight calculation methods in step (2) respectively to obtain four sets of baseline weights. This process is equivalent to simulating the impact of year sample differences on weight assignment, providing a benchmark starting point for the next step of weight perturbation. Each set of baseline weights meets the requirement that the weight sum is 1.

[0033] (3.3) The baseline weights are perturbed using the Dirichlet model, introducing weight uncertainty; the perturbed weights are all non-negative and sum to 1; by adjusting the concentration parameter of the Dirichlet distribution, the intensity of the perturbation can be controlled, causing the weights to fluctuate at different amplitudes near the baseline value, generating the corresponding perturbed weight set, and obtaining a series of weight perturbation scenarios from slight perturbation to significant perturbation; specifically including the following steps: (3.3.1) Set the weight perturbation amplitude parameter Divided into several levels, For each type of weight perturbation amplitude, set the number of weight perturbation sampling times. That is, the number of times the Dirichlet distribution is sampled. That is, under each set of baseline weights, different perturbation amplitudes are applied. Secondary weighted perturbation sampling; (3.3.2) For each set of baseline weights obtained in step (3.2), let be... The baseline weight vector is determined based on a pre-defined perturbation amplitude. Adjusting the concentration parameters of the Dirichlet distribution ,conduct Second sampling, obtained The perturbated weight vector; the Dirichlet weight perturbation calculation process is as follows: , , , In the formula This represents the perturbed weight vector. Represents the baseline weight vector. This represents the random perturbation weight vector in the Dirichlet model. Indicates the magnitude of the disturbance. Indicates concentration parameter, It is a positive minimum value to avoid the denominator being 0; Dirichlet's probabilistic model guarantees the generation of weight vectors. Each component is non-negative and sums to 1, and the perturbation amplitude can be adjusted. The degree to which the control weights deviate from the baseline value; with the amplitude of the disturbance As the disturbance increases, the disturbance intensity gradually increases, and the disturbance amplitude... This indicates no disturbance, with weights equal to the baseline value; disturbance magnitude The larger the value, the more significant the fluctuation of the weight deviating from the baseline value.

[0034] For example, taking the range of baseline weights from 0.029 to 0.190 as an example, the disturbance amplitude under a baseline weight of 0.029... The expected standard deviation of the weights within the perturbation range is 0.024%–0.851%, corresponding to a 90% weight variation range of approximately 0.0286–0.0430, while the perturbation amplitude under a baseline weight of 0.190 is... The expected standard deviation of the weights within the disturbance range is 0.055%-0.851%, corresponding to a 90% weight change range of approximately 0.1891-0.2227, which can effectively cover the intensity range from minor to significant disturbances, as shown in Table 2.

[0035] When the baseline weight is small, such as 0.029, the absolute fluctuation of its weight value is small even with a large disturbance amplitude; conversely, when the baseline weight is large, such as 0.190, its fluctuation range is relatively widened under the same disturbance amplitude. This can be mitigated by setting different disturbance amplitudes. The scope can cover a variety of scenarios, from "minor perturbations" to "significant perturbations," providing ample experimental space for evaluating the robustness of the model.

[0036] Table 2

[0037] (3.4) By randomly sampling and arranging indicators, years, and weight perturbations in the combination space, multiple perturbation scenarios are generated through random combinations, i.e., generating... The disturbance scenarios are the four sampling combinations of indicators. Sampling times for the three indicators Two sampling scenarios for different years, one with no year disturbance and one with disturbance, and four weighted disturbance magnitudes. Number of perturbations for 4 types of weights A total of 1,536 scenario results were generated by combining 384 disturbance scenarios with four weighting calculation methods. The generation of a large number of scenarios provided sufficient data support for subsequent sensitivity analysis and robustness assessment.

[0038] This invention introduces a stratified random sampling mechanism, automatically generating multiple representative subsets of indicators from the complete set of indicators, thus systematically characterizing the uncertainty in the indicator selection process. Compared with traditional fixed indicator systems, this invention generates 384 scenarios within a sampling range of 100–400 times, significantly enhancing the coverage and representativeness of the indicator system. In applications at the watershed or regional level, random combination analysis can identify highly sensitive indicators (such as rainfall, total water consumption, and COD emissions), providing quantitative basis for subsequent indicator simplification and key monitoring, and improving the interpretability and practicality of the model.

[0039] This invention combines four weight calculation methods—equal weighting, entropy weighting, grouped entropy weighting, and principal component analysis (PCA)—and employs a Dirichlet probability model for perturbation simulation. This invention simultaneously maintains the non-negativity constraint and normalization characteristics of the weights. The weight perturbation amplitude is set to 0.1-0.6, systematically covering scenarios from "light perturbation" to "significant perturbation," allowing for a quantifiable description of the variability of the WRCC index under different weight configurations. Parallel weighting and perturbation simulation across multiple schemes enable systematic control of weight uncertainty propagation, fundamentally overcoming the shortcomings of traditional single-weighting models that are susceptible to subjective bias.

[0040] This invention establishes a three-dimensional joint perturbation framework of "indicator sampling—weight perturbation—year self-sampling," which can simultaneously quantify the uncertainty propagation effect of indicators, weights, and time dimensions; it employs... ANOVA and the overall The method identifies key perturbation factors, and the results show that the weighting calculation method and the size of the index are the dominant factors affecting WRCC fluctuations. This comprehensive sensitivity analysis mechanism enables the model to effectively distinguish the contribution sources of different methods to the variation of results, providing a scientific basis for subsequent model selection and management decisions.

[0041] (4) Using the index data and corresponding weights in the disturbance scenario, calculate the pressure aggregate value of all pressure indicators and the support aggregate value of all support indicators for each year, and then calculate the annual water resources carrying capacity index for each year, and summarize to form a water resources carrying capacity index distribution sample corresponding to the disturbance scenario. Step (4) specifically includes the following steps: First, set the water resource carrying capacity index. As a comprehensive representative indicator, and with an annual time unit; for the first For each year's sample, calculate the weighted aggregate value of all supporting indicators for the entire year. The weighted aggregate value of all stress indicators Then calculate the first Annual carrying capacity index for each year : , , , In the formula and Representing the year The next The first pressure indicator and the first Standardized values ​​of each supporting indicator; These are the corresponding indicator weights; R t Indicates the year The water environment carrying capacity index is as follows: the higher the index, the greater the pressure is than the supporting capacity, and there is a risk of WRCC overload; the lower the index, the greater the supporting capacity is than the pressure, and the lower the risk of overload. According to the water resources carrying capacity index The defined formula, using indicator data and corresponding weights of the disturbance scenario, calculates the aggregated pressure value for each year. and supporting aggregate value Then, the annual water resources carrying capacity index for each year is obtained. Sequence; on a fixed perturbation matrix, where the fixed perturbation matrix refers to the set of all perturbed weighted samples generated under this perturbation scenario, the annual water resources carrying capacity index calculated for each year. The data are aggregated to form a water resource carrying capacity index corresponding to the disturbance scenarios. Distributed sample pool; in other words, a perturbation scenario generates several annual water resource carrying capacity indices. value, The combined values ​​reflect the possible range and distribution of the water resources carrying capacity index under this disturbance scenario.

[0042] (5) For the disturbance scenario constructed in step (3), consider multiple disturbance factors, including the weight calculation method and the combination of indicator subset sizes. Number of times the indicator is sampled Year self-service block Weighted disturbance amplitude and the number of sampling times for weight perturbation Sensitivity analysis was performed to identify the impact of the water resource carrying capacity index. The significant disturbance factors include the following steps: (5.1) For the disturbance scenario constructed in step (3), consider multiple disturbance factors, disturbance factors This includes the weight calculation method and the combination of indicator subset sizes. Weighted disturbance amplitude Year self-service block Weighted perturbation sampling times and the number of times the indicators are sampled Using ANOVA Main effects model, calculate the sum of squares of the main effects of each disturbance factor. And the proportion of the total variance explained by the disturbance factor, in the effect size of ANOVA. As a statistic measuring the amount of variance explained by a factor, its calculation formula is as follows: , , , In the formula Indicates the disturbance factor of sum of squares, Indicates the disturbance factor degrees of freedom Indicates the mean square of the residuals. Represents the sum of squared residuals. Represents the residual degrees of freedom. Represents the total sum of squares. The effect size represents the contribution of the residuals; effect size The larger the value, the greater the impact of the disturbance factor on the water resources carrying capacity index; (5.2) Based on the partial derivative relationship between the water resources carrying capacity index and the pressure index data and the supporting index data, calculate the effect of each index on the water resources carrying capacity index. The marginal impact is used to obtain the sensitivity coefficient of the indicator. Specifically, for each input indicator data, keeping other conditions constant, we analyze the impact of small changes in its value on the output water resources carrying capacity index, i.e., the partial derivative, to quantify the importance of the indicator. To eliminate the influence of extreme years, we take the median of the sensitivity coefficient of each indicator over multiple years as its representative value, thus obtaining the final indicator sensitivity. and Sensitivity analysis results can help identify which indicators have the greatest impact on carrying capacity assessment results, providing a basis for system regulation. , , This is the sensitivity coefficient for the pressure index. To support the sensitivity coefficient of the indicator, the higher the sensitivity, the greater the impact of the indicator on the water resources carrying capacity index; sensitivity analysis and robustness evaluation are independent of each other, sensitivity analysis identifies key factors and indicators, and robustness evaluation identifies robust disturbance scenarios.

[0043] (6) Under the constructed disturbance scenario, the water resource carrying capacity index obtained by different weighting methods Based on the stability of the distribution, a robustness assessment is conducted to select the most robust weight calculation method and the robust perturbation scenario under the robust weight calculation method. Specifically, the steps include the following: (6.1) For each disturbance scenario, each weight calculation method, and each year under that disturbance scenario Calculate the corresponding water resource carrying capacity index Interquartile range under different weighting calculation methods The value serves as the annual distribution dispersion. Defined as the difference between the upper and lower quartiles of the data distribution, i.e. The upper quartile is the 75th percentile. The lower quartile is the 25th percentile. ; In this step, the scenario and year are fixed, and the results obtained by different weighting calculation methods are compared. Value, calculate its distribution , The larger the value, the better the performance under different methods. The greater the difference, the more sensitive the assessment results for that year are to the weighting calculation method; The smaller the value, the more different the results obtained by different methods. The results are quite close, and the assessment results for that year are more robust to changes in the weighting calculation method.

[0044] (6.2) Under the same disturbance scenario, the water resource carrying capacity index corresponding to different weighting calculation methods is calculated. of The values ​​are sorted in ascending order, assigned ranks, and converted to quantiles to obtain the weight calculation method for each weight under this perturbation scenario. rank percentile , , For perturbation scenarios Weight calculation method and year Below The rank quantile value is between 0 and 1. The smaller the value, the higher the robustness of the weight calculation method compared with other weight calculation methods. After rank quantile standardization, the robustness indicators under different disturbance scenarios are comparable. (6.3) For each weight calculation method under the same disturbance scenario The rank quantiles are then averaged over the annual dimension to obtain the annual average robustness score of each weight calculation method in this perturbation scenario; specifically, for the perturbation scenario... Weight calculation method in Calculate its value under the disturbance scenario. All years rank quantile The annual average is calculated using the following formula: , The annual average robustness score representing different weighting methods under the same disturbance scenario can be considered as the weighting method. In the disturbance scenario The robustness index over the entire evaluation period is such that the smaller the value, the more robust the weighting method is under the perturbation scenario. For perturbation scenarios and weight calculation method All corresponding years.

[0045] (6.4) After obtaining the annual average robustness score for each disturbance scenario, evaluate the robustness of each weight calculation method from the perspective of cross-disturbance scenarios. For each weight calculation method, evaluate the robustness based on its annual average robustness score set across all disturbance scenarios. , Given a set of disturbance scenarios; calculate the annual average robustness score. The three statistical measures, namely the maximum value, 95th percentile, and mean, are calculated using the following formula: , , , This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The maximum value represents whether the weight calculation method is robust under the most unfavorable perturbation scenario; This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The 95th percentile represents the true robustness under most perturbation scenarios, avoiding the influence of extreme values; This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The average value; (6.5) Constructing a weight calculation method Comprehensive robustness indicators The calculation formula is: , Comprehensive robustness indicators A smaller value indicates a more robust weighting calculation method, which is reflected in the overall robustness index. As the primary criterion, select a comprehensive robustness indicator. The method for calculating the minimum weight is the optimal robust solution; when there are ties, compare them sequentially. , , Until the distinction is made, , , A smaller value indicates a more robust weighting method; when weights are still tied, priority is given to selecting all weights. median and of Smaller; (6.6) Output the optimal robust method and the corresponding comprehensive robustness index value. At the same time, provide the corresponding Dispersion of annual distribution under various disturbance scenarios The statistical results can be presented in tables or graphs, serving as a basis for decision-makers to evaluate the reliability of solutions and verify the effectiveness of models. These outputs will provide strong support for subsequent management decisions and solution comparisons.

[0046] This invention constructs based on This invention establishes a quantitative robustness assessment system by using the distribution robustness index of (annual interquartile range) and combining it with the rank quantile, maximum value, 95th percentile, and mean value to calculate a comprehensive robustness index. This represents a significant breakthrough in achieving a balance between result stability and interpretability at the technical level. The robustness assessment framework established in this invention can be widely applied to research on water environment carrying capacity and resource allocation at the watershed, city, and regional levels, significantly improving the scientific nature of decision-making.

[0047] In order to characterize The overall distribution, such as Figure 1 As shown, different years are displayed. The cumulative distribution shows that the CDF curve from 2010 to 2013 was significantly to the right and rose slowly. The distribution is skewed and highly dispersed. The distribution ranges from 1.82 to 7.52, and the quartiles are... It ranged between 0.98 and 1.46. The period from 2014 to 2015 was a transitional one. The value ranges from 1.11 to 2.87. It decreased to 0.52. After 2016, the CDF curve shifted significantly to the left and became steeper. The overall size decreases and the fluctuations converge. The value ranges from 0.32 to 1.46. It dropped below 0.19. The vast majority of samples after 2016 fell below this level. Near or below, compared to 2010-2013, "most samples were in" Compared to the previous situation, the probability of overload risk has decreased. Overall, the regional WRCC situation reached an inflection point around 2016 and then entered a stable phase.

[0048] Figures 2-7 As shown, the weight calculation method and the combination of indicator subset sizes are illustrated respectively. Weighted disturbance amplitude Weighted perturbation sampling times Number of times the indicator is sampled Year self-service block Under disturbance The distribution shows that the differences are most significant under different weight calculation methods and indicator perturbation scenarios, while the differences are not significant under fixed structure, weight perturbation, and year self-sampling scenarios. Figure 2 Representing different weight calculation methods Value distribution; corresponding to the left figure The annual box plot of the values ​​shows the annual distribution of the groups grouped by the four weighting calculation methods. The boxes represent... (P25-P75), the median is the midline, which must be extended from P05 to P95; the right figure corresponds to four weighting methods. The ridgeline density plot (year-crossing merging) shows the median value indicated by the gray dashed line and numerical values. The curves are equidistant vertically, with the vertical height used only for visualization. Amplitudes can be compared within the same panel, but their values ​​are affected by the bin width. Values ​​within the 1-99th percentile range are clipped, histogram bin number N=1400, and normalized with per-bin probability; factor color schemes are consistent in both left and right graphs. Figures 3-7 Represent the combination of indicator subset sizes Number of times the indicator is sampled Weighted disturbance amplitude Weighted perturbation sampling times Year self-service block perturbation scenario Value distribution.

[0049] like Figure 8 As shown, this illustrates the dominant effect of perturbation factors in different years, expressing... The main sources of distribution uncertainty show that the dominant factors differ across years. In 2011-2017 and 2021-2022, the weighting calculation method mainly dominates, while in 2010 and 2018-2020, the sampling indicators mainly dominate. There are also 10.9%-29.3% of the uncertainty sources, residuals, which are major factors other than the indicator structure and weights. These may be unexplained interannual random fluctuations and data noise. The differences in years are driven by external disturbances such as hydrological year type, population and economic development, and pollution control policies.

[0050] Figure 9 As shown, this paper presents a robustness analysis of different weighting calculation methods. The left figure represents the robustness evaluation results. This indicates that the same weight calculation method is used under all perturbation scenarios. The maximum value, This indicates that the same weight calculation method is used under all perturbation scenarios. The P95 quantile represents the true robustness in most scenarios, avoiding the influence of extreme values; This represents the average value of the same weighting method across all perturbation scenarios. The value represents the average of the three factors; the smaller the value, the more robust the method. The right figure shows the R-distribution for robust and inrottle scenarios under the equal-weighted method. , , , , Dynamic Scene The distribution range is relatively large. The upper boundary represents the 95th quantile, the lower boundary represents the 05th quantile, and the broken line represents the median. , , , , In the scenario of perturbation of block 2 in the year, due to the small difference between the upper and lower boundaries, a broken line is displayed, which in fact also has upper and lower boundaries. The left figure shows the robustness evaluation results of different weight calculation methods. Under 384 scenarios, the comprehensive average score J of the equal weight method, PCA method, grouped entropy weight method, and entropy weight method are 0.49, 0.50, 0.89, and 0.96, respectively. The equal weight method is the most robust weighting method, and the entropy weight method is the least robust weighting method. Compared with the entropy weight method, the robustness of the equal weight method is improved by about 49%. For the robust scenarios of the equal weight method , , , , Year Self-Help Block 2 and the Least Robust Scenario , , , , Undisturbed by year A comparative analysis of the distribution was conducted, and it can be seen from the figure on the right that... , Complete set of indicators Stable distribution The variation ranged from 0.01 to 0.10, basically coinciding with the baseline under this scenario; while... , Minimum index sampling with replacement scenario The distribution was extremely unstable, especially in 2010, 2011, 2012, and 2013 when the IQR values ​​reached 11.78, 8.45, 5.36, and 5.16 respectively. It gradually stabilized after 2016. The range of variation is 0.21-0.27. The reason for this result is... , , , , The perturbation scenario for Year Self-Service Block 2 only involves a 10% weight perturbation and year sampling under a fixed method, while , , , , The perturbation scenario with no year change includes both index resampling perturbations and year resampling perturbations, which, combined with a 60% weighted perturbation, exacerbate the problem. The uncertainty lies in the weighting method, which further confirms that the overall uncertainty across years stems from the weighting approach, while the stability within a year is controlled by the selection of indicators.

[0051] The above figures illustrate the process and results of obtaining the weight allocation scheme, sensitivity analysis results, and robustness evaluation indicators by applying the method of this invention in Fuling District, Chongqing.

[0052] Example 2: The robust system for evaluating water resource carrying capacity in this invention includes: The indicator system construction module is used to establish a multi-dimensional evaluation indicator system based on the supporting indicator subset and the pressure indicator subset. The supporting indicator subset includes four supporting indicator groups: water resources and water environment indicators, ecological protection indicators, water supply indicators, and pollution control indicators. The pressure indicator subset includes four pressure indicator groups: population indicators, economic indicators, water use indicators, and pollution load indicators. Each supporting indicator group includes multiple supporting indicators, and each pressure indicator group includes multiple pressure indicators. The specific execution steps of the indicator system construction module are as shown in step (1) of Example 1.

[0053] The indicator weight calculation module queries indicator data of the study area for multiple years to form multiple year samples, normalizes each indicator data, and then calculates the indicator weight using equal weight method, entropy weight method, grouped entropy weight method and principal component analysis method respectively; the specific execution steps of the indicator weight calculation module are as shown in step (2) of Example 1.

[0054] The disturbance scenario construction module is used to construct disturbance scenarios. First, the indicator selection disturbance is performed to determine the supporting indicators and pressure indicators, and obtain multiple indicator subset sizes. For each indicator subset size, multiple random samplings are performed from the multidimensional evaluation indicator system. After the indicator selection sampling is completed, block self-sampling is performed on the year index of the indicator data to obtain the year sub-sample sequence under the year disturbance scenario. The indicator weights are calculated on the year sub-sample sequence using four weight calculation methods to obtain four sets of baseline weights. The baseline weights are perturbed, the weight perturbation amplitude is set, and the number of weight perturbation samplings is set for each weight perturbation amplitude to generate the perturbed weight set. Finally, multiple disturbance scenarios are generated by random combination. The specific execution steps of the disturbance scenario construction module are as shown in step (3) of Example 1.

[0055] The carrying capacity index calculation module is used to calculate the pressure aggregate value of all pressure indicators and the support aggregate value of all support indicators for each year using the indicator data and corresponding weights in the disturbance scenario, and then calculate the annual water resources carrying capacity index for each year, and summarize to form a water resources carrying capacity index distribution sample corresponding to the disturbance scenario; the specific execution steps of the carrying capacity index calculation module are as shown in step (4) in Example 1.

[0056] The sensitivity analysis module is used to consider multiple disturbance factors under disturbance scenarios. These disturbance factors include weight calculation methods, index subset size combinations, index sampling times, year self-help blocks, weight disturbance amplitude, and weight disturbance sampling times. Sensitivity analysis is performed to identify disturbance factors and indicators that have a significant impact on the water resources carrying capacity index. The specific execution steps of the sensitivity analysis module are as shown in step (5) of Example 1.

[0057] The robustness analysis module is used to conduct a robustness assessment under disturbance scenarios based on the distribution stability of the water resource carrying capacity index obtained by different weighting calculation methods, and to select the most robust weighting calculation method and the corresponding robust disturbance scenario. The specific execution steps of the robustness analysis module are as shown in step (6) of Example 1.

[0058] Example 3: An electronic device disclosed in this invention includes one or more processors, one or more memories, and one or more programs. The programs are stored in the memory and configured to be executed by the processor. When the programs are loaded onto the processor, they implement the steps of the robustness analysis method for water resource carrying capacity evaluation based on the combination of indicators and weights in Example 1.

[0059] Example 4: The present invention discloses a computer-readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to perform the steps of a robust analysis method for evaluating water resource carrying capacity using a combination of indicators and weights as described in Example 1.

Claims

1. A robustness analysis method for evaluating water resource carrying capacity using a combination of indicators and weights, characterized in that, Includes the following steps: (1) A multidimensional evaluation index system is established based on the supporting index subset and the pressure index subset. The supporting index subset includes four supporting index groups: water resources and water environment index, ecological protection index, water supply index and pollution control index. The pressure index subset includes four pressure index groups: population index, economic index, water use index and pollution load index. Each supporting index group includes multiple supporting indicators, and each pressure index group includes multiple pressure indicators. (2) Query the indicator data of the study area for multiple years to form multiple year samples. Normalize each indicator data and then calculate the indicator weights using equal weight method, entropy weight method, grouped entropy weight method and principal component analysis respectively. (3) Constructing a disturbance scenario: First, the indicator selection disturbance is carried out to determine the supporting indicators and the pressure indicators, and obtain multiple indicator subset sizes. For each indicator subset size, multiple random samplings are carried out from the multidimensional evaluation indicator system. After the indicator selection sampling is completed, block self-sampling is carried out on the year index of the indicator data to obtain the year subsample sequence under the year disturbance scenario. Four weight calculation methods are used to calculate the indicator weights on the year subsample sequence to obtain four sets of baseline weights. The baseline weights are perturbed, the perturbation amplitude is set, the number of sampling times for each perturbation amplitude is set, the perturbed weight set is generated, and finally, multiple perturbation scenarios are generated by random combination. (4) Using the index data and corresponding weights in the disturbance scenario, calculate the pressure aggregate value of all pressure indicators and the support aggregate value of all support indicators for each year, and then calculate the annual water resources carrying capacity index for each year, and summarize to form a water resources carrying capacity index distribution sample corresponding to the disturbance scenario. (5) Under the disturbance scenario, multiple disturbance factors are considered, including the weight calculation method, the combination of indicator subset size, the number of indicator sampling, the year self-help block, the weight disturbance amplitude and the number of weight disturbance sampling. Sensitivity analysis is performed to identify the disturbance factors and indicators that have a significant impact on the water resources carrying capacity index. (6) Under the disturbance scenario, the robustness assessment is carried out based on the distribution stability of the water resources carrying capacity index obtained by different weight calculation methods, and the most robust weight calculation method and the corresponding robust disturbance scenario are selected.

2. The robustness analysis method for evaluating water resource carrying capacity based on a combination of indicators and weights according to claim 1, characterized in that, The water resources and water environment indicators in step (1) include rainfall, water production modulus, per capita water resources and river section water quality index; the ecological protection indicators include inland water area, forest area and green coverage rate of urban built-up area; the water supply indicators include centralized water supply capacity and total annual tap water supply; the pollution control indicators include urban sewage treatment capacity, COD removal and environmental pollution control investment; the population indicators include year-end resident population and urbanization level; the economic indicators include the proportion of primary industry GDP, the proportion of secondary industry GDP and per capita GDP; the water use indicators include total water use, per capita comprehensive water use, total domestic water use, per capita daily water use of residents, water use per 10,000 yuan of GDP and water use per 10,000 yuan of industrial added value; and the pollution load indicators include total wastewater discharge and COD discharge.

3. The robustness analysis method for evaluating water resource carrying capacity based on a combination of indicators and weights according to claim 1, characterized in that, Step (2) specifically includes the following steps: (2.1) Query Indicator data for the study area in each year, Each indicator is assigned a corresponding code, and all indicator data for a year form a yearly sample, totaling [data missing]. Sample from each year; Let the original data matrix of the stress index be: ， This refers to the number of indicators related to stress. For the number of years, For the first In the sample of the year, the first The value of the pressure indicator; Let the original data matrix of the supporting indicators be: ， The number of indicators to support the indicators, For the first In the sample of the year, the first The value of each supporting indicator; (2.2) Perform min-max normalization on each indicator data to normalize the values ​​of different indicators to the [0,1] interval, and obtain the first... Standardized value of the stress index and the Standardized indicator values ​​of the supporting indicators ; (2.3) The weights of the indicators are calculated by equal weight method, entropy weight method, group entropy weight method and principal component analysis respectively. The weights of the indicators obtained by the four weight calculation methods all satisfy the constraint that they are non-negative and sum to 1.

4. The robustness analysis method for evaluating water resource carrying capacity based on a combination of indicators and weights according to claim 1, characterized in that, The specific steps for perturbing the baseline weights in step (3) include the following: Set the weight perturbation amplitude parameter There are several levels, corresponding to the amplitude of each weight perturbation, and the number of weight perturbation sampling times is set. ; For each set of baseline weights, record The baseline weight vector is determined based on a pre-defined perturbation amplitude. Adjusting the concentration parameters of the Dirichlet distribution ,conduct Second sampling, obtained The perturbated weight vector; the Dirichlet weight perturbation calculation process is as follows: ， ， ， in This represents the perturbed weight vector. Represents the baseline weight vector. This represents the random perturbation weight vector in the Dirichlet model. Indicates the magnitude of the disturbance. Indicates concentration parameter, It is a positive minimum value to avoid a denominator of 0; the generated weight vector Each component is non-negative and the sum is 1.

5. The robustness analysis method for evaluating water resource carrying capacity based on a combination of indicators and weights according to claim 1, characterized in that, Step (4) specifically includes the following steps: First, set the water resource carrying capacity index. As a comprehensive representative indicator, and with an annual time unit; for the first For each year's sample, calculate the weighted aggregate value of all supporting indicators for the entire year. The weighted aggregate value of all stress indicators Then calculate the first Annual water resources carrying capacity index for each year : ， ， ， In the formula and Representing the year The next The first pressure indicator and the first Standardized values ​​of each supporting indicator; These are the corresponding indicator weights; Indicates the year The water resource carrying capacity index below; Using the index data and corresponding weights of the disturbance scenario, the aggregated pressure value for each year is calculated. and supporting aggregate value Then, the annual water resources carrying capacity index for each year is obtained. Sequence; the annual water resources carrying capacity index calculated for each year. The data are aggregated to form a water resource carrying capacity index corresponding to the disturbance scenarios. Distributed sample pool.

6. The robustness analysis method for evaluating water resource carrying capacity based on a combination of indicators and weights according to claim 5, characterized in that, Step (5) specifically includes the following steps: (5.1) For the disturbance scenario, consider multiple disturbance factors, disturbance factors This includes the weighting calculation method, the combination of indicator subset sizes, the number of indicator samplings, the year bootstrap block, the magnitude of weight perturbation, and the number of weight perturbation samplings. A Type-II main effects model in ANOVA is used to calculate the sum of squares of the main effects of each perturbation factor. And the proportion of the total variance explained by the disturbance factor, in the effect size of ANOVA. As a statistic measuring the amount of variance explained by a factor, its calculation formula is: ， ， ， In the formula Indicates the disturbance factor Type-II sum of squares, Indicates the disturbance factor degrees of freedom Indicates the mean square of the residuals. Represents the sum of squared residuals. Represents the residual degrees of freedom. Represents the total sum of squares. The effect size representing the residual contribution; (5.2) Based on the partial derivative relationship between the water resources carrying capacity index and the pressure index data and the supporting index data, calculate the effect of each index on the carrying capacity index. The marginal impact is used to obtain the sensitivity coefficient of the indicator, and the specific calculation formula is as follows: ， ， This is the sensitivity coefficient for the pressure index. To support the sensitivity coefficient of the indicator, the higher the sensitivity, the greater the impact of the indicator on the water resources carrying capacity index.

7. The robustness analysis method for evaluating water resource carrying capacity based on a combination of indicators and weights according to claim 1, characterized in that, Step (6) specifically includes the following steps: (6.1) For each disturbance scenario, each weight calculation method, and each year under that disturbance scenario Calculate the corresponding water resource carrying capacity index The interquartile range (IQR) value under different weighting calculation methods is used as the annual distribution dispersion; IQR is defined as the difference between the upper quartile and the lower quartile of the data distribution, i.e. The upper quartile is the 75th percentile. The lower quartile is the 25th percentile. ; (6.2) Under the same disturbance scenario, the water resource carrying capacity index corresponding to different weighting calculation methods is calculated. The IQR values ​​are sorted in ascending order, assigned ranks, and converted to quantiles to obtain the IQR rank quantile value for each weighting method under this perturbation scenario. , , For perturbation scenarios Weight calculation method and year The IQR value below; (6.3) For the same disturbance scenario, the IQR rank quantile values ​​of each weight calculation method are averaged over the annual dimension to obtain the annual average robustness score of each weight calculation method in that disturbance scenario; for the disturbance scenario Weight calculation method in Calculate its value under the disturbance scenario. All years rank quantile The annual average is calculated using the following formula: ， This represents the annual average robustness score for different weighting methods under different disturbance scenarios. For perturbation scenarios and weight calculation method All corresponding years; (6.4) After obtaining the annual average robustness score for each disturbance scenario, evaluate the robustness of each weight calculation method from the perspective of cross-disturbance scenarios. For each weight calculation method, evaluate the robustness based on its annual average robustness score set across all disturbance scenarios. , For the set of disturbance scenarios, calculate the annual average robustness score. The three statistical measures, namely the maximum value, 95th percentile, and mean, are calculated using the following formula: ， ， ， This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The maximum value represents whether the weight calculation method is robust under the most unfavorable perturbation scenario; This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The 95th percentile represents the true robustness under most perturbation scenarios, avoiding the influence of extreme values; This represents the annual average robustness score under all disturbance scenarios using the same weighting method. The average value; (6.5) Constructing a weight calculation method Comprehensive robustness indicators The calculation formula is: ， Comprehensive robustness indicators A smaller value indicates a more robust weighting calculation method, which is reflected in the overall robustness index. As the primary criterion, select a comprehensive robustness indicator. The method for calculating the minimum weight is the optimal robust solution; when there are ties, compare them sequentially. , , Until the distinction is made, , , A smaller value indicates a more robust weighting method; when weights are still tied, priority is given to selecting all weights. The median of IQR is smaller than that of the IQR. (6.6) Output the optimal robust method and the corresponding comprehensive robustness index value. At the same time, provide the corresponding Statistical results of the annual distribution dispersion (IQR) values ​​for each disturbance scenario.

8. A robustness analysis system for evaluating water resource carrying capacity using a combination of indicators and weights, characterized in that, include: The indicator system construction module is used to establish a multi-dimensional evaluation indicator system based on the supporting indicator subset and the pressure indicator subset. The supporting indicator subset includes four supporting indicator groups: water resources and water environment indicators, ecological protection indicators, water supply indicators, and pollution control indicators. The pressure indicator subset includes four pressure indicator groups: population indicators, economic indicators, water use indicators, and pollution load indicators. Each supporting indicator group includes multiple supporting indicators, and each pressure indicator group includes multiple pressure indicators. The indicator weight calculation module queries indicator data for the study area for multiple years, forms multiple year samples, normalizes each indicator data, and then calculates the indicator weight using equal weight method, entropy weight method, grouped entropy weight method, and principal component analysis method respectively. The disturbance scenario construction module is used to construct disturbance scenarios. First, the indicator selection disturbance is performed to determine the supporting indicators and the pressure indicators, resulting in multiple indicator subset sizes. For each indicator subset size, multiple random samplings are performed from the multidimensional evaluation indicator system. After the indicator selection sampling is completed, block self-sampling is performed on the year index of the indicator data to obtain the year subsample sequence under the year disturbance scenario. Four weight calculation methods are used to calculate the indicator weights on the year subsample sequence to obtain four sets of baseline weights. The baseline weights are perturbed, the perturbation amplitude is set, the number of sampling times for each perturbation amplitude is set, the perturbed weight set is generated, and finally, multiple perturbation scenarios are generated by random combination. The carrying capacity index calculation module is used to calculate the pressure aggregate value of all pressure indicators and the support aggregate value of all support indicators for each year using the indicator data and corresponding weights in the disturbance scenario, and then calculate the annual water resources carrying capacity index for each year, and summarize them to form a water resources carrying capacity index distribution sample corresponding to the disturbance scenario. The sensitivity analysis module is used to perform sensitivity analysis under disturbance scenarios, considering multiple disturbance factors, including weight calculation methods, combination of indicator subset sizes, number of indicator samplings, year self-help blocks, weight disturbance amplitude, and number of weight disturbance samplings, to identify disturbance factors and indicators that have a significant impact on the water resources carrying capacity index. The robustness analysis module is used to conduct robustness assessments based on the distribution stability of the water resource carrying capacity index obtained by different weighting calculation methods under disturbance scenarios, and to select the most robust weighting calculation method and the corresponding robust disturbance scenario.

9. An electronic device, characterized in that: It includes one or more processors, one or more memories, and one or more programs, said programs being stored in the memory and configured to be executed by the processor, said programs being loaded onto the processor to implement the steps of a robust analysis method for evaluating water resource carrying capacity according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to perform the steps of a robust analysis method for evaluating water resource carrying capacity according to any one of claims 1 to 7.

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