Step-by-step clustering factorial analysis method based on input-output

Abstract

The invention discloses a step-by-step clustering factorial analysis method based on input-output, and the method comprises the steps: constructing a composite water-carbon input-output model based on the trade activity characteristics of each economic department; then forming a data set based on the composite water-carbon input-output model, processing the complexity of the water-carbon coupling risk by utilizing step-by-step clustering analysis, and identifying a key risk department in the data set; then analyzing an action mechanism of a supply side strategy and screening a water-carbon key department set; analyzing and clarifying a response mechanism of the multi-dimensional risk system to a multi-level strategy by utilizing factorial analysis; and finally, analyzing a multi-factor response mechanism, comprehensively evaluating a plurality of indexes under multiple scenes by using an entropy weight TOPSIS method, and screening out an effective water-carbon coupling cooperation scheme. According to the method, the whole-industry influence of the interactive supply side strategy is quantified, and a collaborative management scheme of coupling risks is disclosed.

Description

Technical Field

[0001] The present invention belongs to the technical field of methods specially suitable for administrative purposes, and specifically is a stepwise clustering factorial analysis method based on input-output. Background Art

[0002] Greenhouse gases, especially carbon dioxide, produced by human activities are the main cause of climate change. Urbanization is the core driving force of regional economic development. In order to achieve higher economic growth, energy demand continues to expand and carbon emissions continue to increase. The increase in carbon emissions will further aggravate future climate change. Climate change will form a new hydroclimatic regime, greatly affecting the availability of regional water resources, and then affecting industrial production and economic development. Therefore, the coordinated management of regional water-carbon coupling risks is an important cornerstone for achieving water conservation and carbon reduction goals and promoting social sustainable development.

[0003] The complex trade activities within the economic system have led to a high degree of interdependence and complex exchanges among various economic sectors. Demand and supply are the two main trade drivers in the economic system, which shape the multi-directional transmission of water consumption and carbon emissions in production activities. Previous studies have rarely paid attention to the impact of supply-side strategies on the implicit water-carbon flows in trade activities, lacking the analysis of the mechanism of action of supply-side strategies, and the analysis of the internal interactive representation of multidimensional risk systems under the interactive strategy framework. At the methodological level, traditional methods are limited to the evaluation of water-carbon flows from various accounting perspectives, lacking integrated statistical analysis for complex data sets, and failing to fully explore and explain the potential systemic risks and interactive information in input-output data. Therefore, it is urgent to integrate diversified methods and develop a water-carbon coupling risk collaborative management model with powerful data analysis capabilities to achieve sustainable social and economic development under the goals of water conservation and carbon reduction. Summary of the invention

[0004] In view of the problems existing in the background technology, the present invention provides a stepwise clustering factorial analysis method based on input-output, and the technical solution includes: step A: constructing a composite water-carbon input-output model based on the characteristics of trade activities of various economic sectors;

[0005] Step B: Based on the composite water-carbon input-output model, the data set is composed and stepwise cluster analysis is used to deal with the complexity of water-carbon coupling risks, capture the discrete and nonlinear relationship of multiple variables, and identify the key risk sectors in the data set;

[0006] Step C: Analyze the mechanism of supply-side strategies and screen out the key water-carbon sectors;

[0007] Step D: Use factorial analysis to clarify the response mechanism of the multi-dimensional risk system to multi-level strategies;

[0008] Step E: Based on the multi-factor response mechanism analyzed in step D, the entropy weight TOPSIS method is used to comprehensively evaluate multiple indicators under multiple scenarios, and effective water-carbon coupling synergy solutions are screened out with the goals of economic sustainability and water-carbon coupling risk mitigation.

[0009] The composite water-carbon input-output model constructed in step A is:

[0010] X=V(IB) -1

[0011] w=V(IB) -1 p

[0012] c=V(IB) -1 q

[0013] Among them, X represents the known total output of each department in the regional system; V represents the known initial input of each department (the total initial input of all departments is the regional gross domestic product (GDP); I represents the unit matrix; B represents the direct allocation coefficient; (IB) -1 represents the Ghosh inverse matrix; p represents the direct water resource use intensity of each department, p=PW / X; PW represents the known direct water resource use of each department; q represents the direct carbon emission intensity of each department, q=QC / X; QC represents the known direct carbon emissions of each department; w represents the water resource use of each department on the supply side, and c represents the carbon emissions of each department on the supply side.

[0014] The specific process of identifying the key risk sectors in the data set in step B is as follows: construct a data set containing water-carbon flow information of all sectors, the explanatory variables in the data set are composed of the known initial input V of each sector, the known direct water resource usage PW of each sector and the known direct carbon emissions QC of each sector; the response variables in the data set are composed of the water resource usage w of each sector on the supply side and the carbon emissions c of each sector on the supply side; α The class α of samples is split into subclasses e and f, n e +n f =n α ; According to the Wilks likelihood ratio criterion, if the split point is optimal, the Wilks value Λ reaches the minimum, and when the Λ value is very large, classes e and f can no longer be divided and are merged into class α; when no classes can be further cut or merged, clustering is completed, and the original departments are divided into different clusters; then, according to the water resource usage w of each department on the supply side and the carbon emissions c of each department on the supply side, the high-consumption clusters of water-carbon are found and screened as key risk departments, among which:

[0015]

[0016] The Wilks statistic Λ is defined as E represents the within-group sum of squares of the sample; H represents the between-group sum of squares; n e and n f Represents the number of samples in sets e and f respectively; e i and f j Represent the sample values ​​of sets e and f respectively; and The sample means of sets e and f respectively; n α represents the number of samples in set α; P represents the number of response variables; F represents the F test. When the Wilks statistic is the smallest, the sample mean is evaluated by the F test, μ e and μ f represent the overall mean of e and f, respectively, and H 0 Represents the null hypothesis μ e =μ f , H 1 represents the alternative hypothesis μ e ≠μ f , the significance level ρ is 0.05; if F ≥ F ρ , then reject H 0 , indicating that the two groups of samples are significantly different, and cutting is performed; on the contrary, if F < F ρ , then H 0 is true.

[0017] The specific process of analyzing the mechanism of action of the supply-side strategy in step C is to simulate the input- and allocation-oriented supply-side strategy for the identified key risk sectors; and finally screen out a set of water-carbon key sectors consisting of key sectors with greater impact on water use and key sectors with greater impact on carbon emissions;

[0018] In the input-oriented strategy, the initial input V of the key department is changed; in the allocation-oriented strategy, the direct allocation coefficient B of the key department is changed.

[0019] The key sectors with greater impact on water use are selected from the scenario where the water use value w of each sector on the supply side changes greatly;

[0020] The key sectors with greater impact on carbon emissions are selected from scenarios where the carbon emissions c values ​​of various sectors on the supply side change greatly.

[0021] The initial investment V for changing the key department is: reducing the initial investment V for changing the key department by 30%;

[0022] The changing of the direct allocation coefficient B of the key department is: reducing the direct allocation coefficient B of the key department by 30%.

[0023] The specific process of using factorial analysis in step D to clarify the response mechanism of the multidimensional risk system to the multi-level strategy is: the selected key sectors with a greater impact on water use and the key sectors with a greater impact on carbon emissions are set as factors, and the input-oriented strategy and the allocation-oriented strategy are respectively used as the low level and high level of the factor.

[0024] The specific process of selecting the optimal solution for water-carbon coupling risk in step E is as follows: according to the low and high levels of the factors, the entropy weight TOPSIS method is used, with economic sustainability and water-carbon coupling risk mitigation as the goals, and the solutions are ranked by comprehensively considering multiple indicators to form the optimal water-carbon coupling synergistic solution:

[0025]

[0026] d j =1-ee j

[0027]

[0028] r ij =z ij ω j

[0029]

[0030] Where TX = [tx ij ] n×m Represents n scenarios (n = 2 4 =16, i.e., 2-level factorial scenario of 4 key sectors), a matrix consisting of m positive evaluation indicators (m=5, i.e., GDP, ws, ps, cs and qs); z ij Represents tx ij Standardization of pp ij represents probability; ee i represents information entropy; d j represents the information utility value; ω j represents the entropy weight of the indicator; r ij represents the elements in the weighting matrix; and Represent the positive and negative ideal points of the sample respectively; and Represents the distance between the sample and the positive and negative ideal points respectively; S i Represents the relative closeness of the sample to the ideal point; Representatives of S i Normalization of

[0031] The multiple indicators are: regional gross domestic product (GDP); total water use by sector (ws); water use intensity (ps), where ps = ws / GDP; total carbon emissions by sector (cs); carbon intensity (qs), where qs = cs / GDP

[0032] After step D, the sum of squares of the two factors and the sum of squares of the interaction of the two factors were calculated to quantify the interaction between the factors.

[0033] The beneficial effects of the present invention are: analyzing the response and interaction mechanism of the multidimensional risk system under the interactive supply-side strategy, and clarifying the collaborative management path of water-carbon coupling risks. The invention integrates input-output, step-by-step clustering, factor analysis and entropy weight TOPSIS methods, based on the perspective of economic-environmental sustainable development, focusing on the water-carbon composite multidimensional supply chain architecture, identifying the key sectors of water-carbon coupling risks, quantifying the industry-wide impact of interactive supply-side strategies, analyzing the multi-sector response mechanism under the multidimensional interactive framework, and revealing the collaborative management plan for coupling risks. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The figure is a flow chart of an embodiment of a stepwise clustering factorial analysis method based on input and output according to the present invention.

[0035] Figure 2 Schematic diagram of clustering of key risk departments in an embodiment of the present invention.

[0036] Figure 3 It is a schematic diagram of the impact of the supply-side strategy on water-carbon transfer in the entire industry in an embodiment of the present invention.

[0037] Figure 4 Schematic diagram of the water-carbon response mechanism under the interactive strategy in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The embodiments are described in detail below in conjunction with the accompanying drawings.

[0039] like Figure 1 As shown, the present invention proposes a stepwise clustering factorial analysis method based on input and output, comprising:

[0040] Step A: Based on the characteristics of trade activities of various economic sectors, the water resource use and carbon emission performance of economic activities are incorporated to construct a composite water-carbon input-output model to meet the quantitative supply-side water-carbon flow transmission; focus on the supply chain cascade model to quantify the implicit water-carbon flow on the supply side.

[0041] Step B: Based on the composite water-carbon input-output model, the data set is composed and stepwise cluster analysis is used to deal with the complexity of water-carbon coupling risks, capture the discrete and nonlinear relationships of multiple variables, and identify the key risk sectors in the data set.

[0042] Step C: Analyze the mechanism of action of the supply-side strategy for the key risk sectors identified in step B, that is, conduct scenario simulation for the key risk sectors. The designed scenario includes two different strategies: the input-oriented strategy represents the reduction of the initial investment of the key sectors, and the allocation-oriented strategy represents the reduction of the direct allocation coefficient of the key sectors; and screen out the water-carbon key sector set. Through supply-side scenario simulation from different angles, clarify the mechanism of action of each scenario plan on the multidimensional risk system, and quantify the impact of different strategies on the water-carbon transmission of the entire industry.

[0043] Step D: Based on the scenario simulated in Step C, use factorial analysis to clarify the response mechanism of the multi-dimensional risk system to the multi-level strategy.

[0044] Step E: Based on the multi-factor response mechanism analyzed in step D, the entropy weight TOPSIS method is used to comprehensively evaluate multiple indicators under multiple scenarios, and effective water-carbon coupling synergy solutions are screened out with the goals of economic sustainability and water-carbon coupling risk mitigation.

[0045] The composite water-carbon input-output model constructed in step A is:

[0046] X=V(IB) -1

[0047] w=V(IB) -1 p

[0048] c=V(IB) -1 q

[0049] Among them, X represents the known total output of each department in the regional system; V represents the known initial input of each department (the total initial input of all departments is the regional gross domestic product (GDP); I represents the unit matrix; B represents the direct allocation coefficient; (IB) -1 represents the Ghosh inverse matrix; p represents the direct water resource use intensity of each department, p=PW / X; PW represents the known direct water resource use of each department; q represents the direct carbon emission intensity of each department, q=QC / X; QC represents the known direct carbon emissions of each department; w represents the water resource use of each department on the supply side, and c represents the carbon emissions of each department on the supply side.

[0050] The specific process of identifying the key risk sectors in the data set in step B is: constructing a data set containing water-carbon flow information of all sectors (the number of samples in the data set is n α That is, the total number of departments, n α=15), the explanatory variables in the data set consist of the known initial input V of each department, the known direct water resource usage PW of each department, and the known direct carbon emissions QC of each department; the response variables in the data set consist of the water resource usage w of each department on the supply side and the carbon emissions c of each department on the supply side. α The class α of the samples is divided into subclasses e and f(n e +n f =n α ), according to the Wilks likelihood ratio criterion, if the split point is optimal, the Wilks value Λ reaches the minimum, and when the Λ value is very large, classes e and f can no longer be divided and are merged into class α; by segmenting and merging the sample set, the discrete and nonlinear relationship of multiple variables is captured, the natural classification of economic sectors is achieved, and the key risk sectors with significant water-carbon flows are screened out, specifically:

[0051]

[0052] The Wilks statistic Λ is defined as E represents the within-group sum of squares of the sample; H represents the between-group sum of squares; n e and n f Represents the number of samples in sets e and f respectively; e i and f j Represent the sample values ​​of sets e and f respectively; and The sample means of sets e and f respectively; n α represents the number of samples in set α; P represents the number of response variables; F represents the F test. When the Wilks statistic is the smallest, the sample mean is evaluated by the F test, μ e and μ f represent the overall mean of e and f, respectively, and H 0 Represents the null hypothesis μ e =μ f , H 1 represents the alternative hypothesis μ e ≠μ f , the significance level ρ is 0.05. If F ≥ F ρ , then reject H 0 , indicating that the two groups of samples are significantly different, and cutting is performed; on the contrary, if F < F ρ , then H 0 If it is true, it means that there is no significant difference between the two groups of samples, and the two groups are merged. After a series of cutting and merging processes, when no class can be further cut or merged, the clustering is completed, and the original departments are divided into different clusters. Then, according to the size of the response variable (i.e., the water resource usage w of each department on the supply side and the carbon emissions c of each department on the supply side), the high water-carbon consumption clusters are found, and finally 8 departments are screened as key risk departments.

[0053] The specific process of analyzing the mechanism of action of the supply-side strategy in step C is to simulate the input- and allocation-oriented supply-side strategy for the 8 identified key risk sectors. In the input-oriented strategy, the initial input V of the key sector is reduced by 30%; in the allocation-oriented strategy, the direct allocation coefficient B of the key sector is reduced by 30%. According to the formula of step A, after the initial input V or the direct allocation coefficient B changes, a new water-carbon flow (i.e., the water resource usage w of each sector on the supply side and the carbon emissions c of each sector on the supply side) will be obtained. Under different scenarios, the new water-carbon flow will be used as the basis for further screening of sectors, and finally a set of water-carbon key sectors will be screened out; specifically: in the scenario where the w value changes greatly, the 4 key sectors with a greater impact on water use; in the scenario where the c value changes greatly, the 4 key sectors with a greater impact on carbon emissions will be screened out.

[0054] The specific process of quantifying the main effects and their interactions of the departmental response process in step D is to set the four key departments with greater impact on water use and the four key departments with greater impact on carbon emissions as factors, and the input-oriented strategy and the allocation-oriented strategy as the low level and high level of the factor respectively.

[0055] The specific process of selecting the optimal solution for water-carbon coupling risk in step E is as follows: according to the low and high levels of the factors, the entropy weight TOPSIS method is used, with the goal of economic sustainability and water-carbon coupling risk mitigation, and multiple indicators (i.e., regional gross domestic product (GDP); total water use by sectors (ws); water use intensity (ps), where ps = ws / GDP; total carbon emissions by sectors (cs); carbon intensity (qs), where qs = cs / GDP) are comprehensively considered to rank the solutions and form the optimal water-carbon coupling synergistic solution, the formula is:

[0056]

[0057] d j =1-ee j

[0058]

[0059] r ij =z ij ω j

[0060]

[0061] Where TX = [tx ij ] n×m Represents n scenarios (n = 2 4=16, i.e., 2-level factorial scenario of 4 key sectors), a matrix consisting of m positive evaluation indicators (m=5, i.e., GDP, ws, ps, cs and qs); z ij Represents tx ij Standardization of pp ij represents probability; ee i represents information entropy; d j represents the information utility value; ω j represents the entropy weight of the indicator; r ij represents the elements in the weighting matrix; and Represent the positive and negative ideal points of the sample respectively; and Represents the distance between the sample and the positive and negative ideal points respectively; S i Represents the relative closeness of the sample to the ideal point; Representatives of S i Normalization of .

[0062] After step D, we can also calculate the sum of squares of the two factors and the sum of squares of their interaction to quantify the interaction between the factors:

[0063] The water consumption on the supply side (the sum of w of each department in the regional system ws) and the carbon emissions on the supply side (the sum of c of each department in the regional system cs) are used as response variables, and the quantitative factor effects are calculated using factorial analysis. Taking the factorial analysis of 2 factors and 2 levels as an example, the scenario result y ij Represents the simulated value when factor A is at level i and factor B is at level j, i = 1, ..., a; a = 2 represents the value of factor A includes two levels, low and high. Similarly, j = 1, K, b; b = 2 represents the value level of factor B. The main formula is as follows:

[0064] y ij =μ+α i +β j +(αβ) ij

[0065]

[0066] SS AB =SS T -SS A -SS B

[0067] Among them, y ij represents the simulated value when factor A is at level i and factor B is at level j; μ represents the overall average effect; α i represents the effect of factor A at level i; β j Represents the effect of factor B at level j; (αβ)ij represents the interaction between factors A and B; y.. represents the sum of all y ij ;y i. =y i1 +y i2 ;y .j =y 1j +y 2j SS T Stands for Total Squares; SS A , SS B and SS AB They represent the sum of squares of factor A, factor B, and their interaction.

[0068] Figure 2 It is a cluster of key risk sectors based on stepwise clustering. As can be seen from the figure, water conservation on the supply side should focus on agriculture, carbon emission reduction should focus on energy and water supply and metallurgy, and other services, chemicals, machinery manufacturing and catering industries have significant water-carbon coupling risk pressure.

[0069] Figure 3 This is the change in water-carbon transfer flow in the entire industry under the supply-side strategy. As can be seen from the figure, the reduction of initial input or output allocation in agriculture, and the reduction of output allocation in the chemical, service, and food industries can achieve better water-saving effects; the reduction of initial input or output allocation in the energy and water supply industry, and the reduction of output allocation in other services, machinery manufacturing, and metallurgy can achieve better carbon emission reduction effects.

[0070] Figure 4 It is a water-carbon response mechanism under the interactive strategy. As can be seen from the figure, agriculture and food industry, agriculture and chemical industry, chemical industry and service industry are interrelated and compete with each other in terms of water resource utilization; there is a complex interactive relationship between machinery manufacturing industry and energy and water supply industry, machinery manufacturing industry and service industry, energy and water supply industry and service industry in terms of carbon emissions; the initial input reduction of agriculture and the output allocation reduction of food, chemical industry and other service industries are the best water-carbon coupling synergy solutions.

[0071] The integrated water-carbon coupling risk analysis method in the implementation mode of the present invention is different from the existing technology. The input-output-centered method in the existing technology is limited to analyzing the supply chain characteristics of water-carbon transmission, socio-economic driving factors, and indirect responsibility allocation for water conservation and carbon reduction. However, the existing technology fails to provide a quantitative analysis of the mechanism of action of the supply-side strategy on water conservation and carbon reduction, the effect of the interactive strategy on the coordinated management of multi-dimensional risks, and the interactive response between departments in a multi-component composite system. The implementation method of the present invention identifies the key sectors of water-carbon coupling risks, quantifies the effect of the supply-side strategy on the coordinated management of multi-dimensional risks, and analyzes the multi-factor interactive response mechanism under the interactive multi-dimensional architecture, providing scientific guidance for the sustainable development of the region.

[0072] In the implementation mode of the present invention, the focus is on trade activities from the supply-side perspective, and based on a variety of integrated technologies, multi-dimensional risk relationships in the data set are extracted to identify key risk sectors, clarify the mechanism of action of interactive strategies, quantify the responses and interactions of multiple sectors, and obtain the best coupling and coordination solution.

[0073] This embodiment is only a preferred specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A stepwise clustering factorial analysis method based on input-output, characterized in that: include: Step A: A composite water-carbon input-output model is constructed based on the characteristics of trade activities in various economic sectors; Step B: Based on the composite water-carbon input-output model, the data set is composed and stepwise cluster analysis is used to deal with the complexity of water-carbon coupling risks, capture the discrete and nonlinear relationship of multiple variables, and identify the key risk sectors in the data set; Step C: Analyze the mechanism of supply-side strategies and screen out the key water-carbon sectors; Step D: Use factorial analysis to clarify the response mechanism of the multi-dimensional risk system to multi-level strategies; Step E: Based on the multi-factor response mechanism analyzed in step D, the entropy weight TOPSIS method is used to comprehensively evaluate multiple indicators under multiple scenarios, and effective water-carbon coupling synergy solutions are screened out with the goals of economic sustainability and water-carbon coupling risk mitigation.

2. The stepwise clustering factorial analysis method based on input-output according to claim 1 is characterized in that: The composite water-carbon input-output model constructed in step A is: X=V(I-B) -1 w=V(I-B) -1 p c=V(I-B) -1 q Among them, X represents the known total output of each department in the regional system; V represents the known initial input of each department (the total initial input of all departments is the regional gross domestic product (GDP); I represents the unit matrix; B represents the direct allocation coefficient; (IB) -1 represents the Ghosh inverse matrix; p represents the direct water resource use intensity of each department, p=PW / X; PW represents the known direct water resource use of each department; q represents the direct carbon emission intensity of each department, q=QC / X; QC represents the known direct carbon emissions of each department; w represents the water resource use of each department on the supply side, and c represents the carbon emissions of each department on the supply side.

3. The stepwise clustering factorial analysis method based on input-output according to claim 1 is characterized in that: The specific process of identifying the key risk sectors in the data set in step B is as follows: construct a data set containing water-carbon flow information of all sectors, the explanatory variables in the data set are composed of the known initial input V of each sector, the known direct water resource usage PW of each sector and the known direct carbon emissions QC of each sector; the response variables in the data set are composed of the water resource usage w of each sector on the supply side and the carbon emissions c of each sector on the supply side; α The class α of samples is split into subclasses e and f, n e +n f =n α ; According to the Wilks likelihood ratio criterion, if the split point is optimal, the Wilks value Λ reaches the minimum, and when the Λ value is very large, classes e and f can no longer be divided and are merged into class α; when no classes can be further cut or merged, clustering is completed, and the original departments are divided into different clusters; then, according to the water resource usage w of each department on the supply side and the carbon emissions c of each department on the supply side, the high-consumption clusters of water-carbon are found and screened as key risk departments, among which: The Wilks statistic Λ is defined as E represents the within-group sum of squares of the sample; H represents the between-group sum of squares; n e and n f Represents the number of samples in sets e and f respectively; e i and f j Represent the sample values ​​of sets e and f respectively; and The sample means of sets e and f respectively; n α represents the number of samples in set α; P represents the number of response variables; F represents the F test; when the Wilks statistic is the smallest, the sample mean is evaluated by the F test, μ e and μ f represent the population means of e and f respectively, and H0 represents the null hypothesis μ e =μ f , H1 represents the alternative hypothesis μ e ≠μ f , the significance level ρ is 0.05; if F ≥ F ρ , then H0 is rejected, indicating that the two groups of samples are significantly different and cutting is implemented; on the contrary, if F<F ρ , then H0 is true.

4. The stepwise clustering factorial analysis method based on input-output according to claim 1 is characterized in that: The specific process of analyzing the mechanism of action of the supply-side strategy in step C is to simulate the input- and allocation-oriented supply-side strategy for the identified key risk sectors; and finally screen out a set of water-carbon key sectors consisting of key sectors with greater impact on water use and key sectors with greater impact on carbon emissions; In the input-oriented strategy, the initial input V of the key department is changed; in the allocation-oriented strategy, the direct allocation coefficient B of the key department is changed.

5. The stepwise clustering factorial analysis method based on input-output according to claim 4 is characterized in that: The key sectors with greater impact on water use are selected from the scenario where the water use value w of each sector on the supply side changes greatly; The key sectors with greater impact on carbon emissions are selected from the scenarios where the carbon emissions c values ​​of various sectors on the supply side change greatly; The initial investment V for changing the key department is: reducing the initial investment V for changing the key department by 30%; The changing of the direct allocation coefficient B of the key department is: reducing the direct allocation coefficient B of the key department by 30%.

6. The stepwise clustering factorial analysis method based on input-output according to claim 1 is characterized in that: The specific process of clarifying the response mechanism of the multidimensional risk system to the multi-level strategy in the step D is: the selected key sectors with greater impact on water use and the key sectors with greater impact on carbon emissions are set as factors, and the input-oriented strategy and the allocation-oriented strategy are respectively used as the low level and high level of the factor.

7. The stepwise clustering factorial analysis method based on input-output according to claim 1 is characterized in that: The specific process of selecting the optimal solution for water-carbon coupling risk in step E is as follows: according to the low and high levels of the factors, the entropy weight TOPSIS method is used, with economic sustainability and water-carbon coupling risk mitigation as the goals, and the solutions are ranked by comprehensively considering multiple indicators to form the optimal water-carbon coupling synergistic solution: d j =1-ee j r ij =z ij ω j Where TX = [tx ij ] n×m Represents n scenarios (n = 2 4 =16, i.e., 2-level factorial scenario of 4 key sectors), a matrix consisting of m positive evaluation indicators (m=5, i.e., GDP, ws, ps, cs and qs); z ij Represents tx ij Standardization of pp ij represents probability; ee i represents information entropy; d j represents the information utility value; ω j represents the entropy weight of the indicator; r ij represents the elements in the weighting matrix; and Represent the positive and negative ideal points of the sample respectively; and Represents the distance between the sample and the positive and negative ideal points respectively; S i Represents the relative closeness of the sample to the ideal point; Representatives of S i Normalization of The multiple indicators are: regional gross domestic product (GDP); total water use by sector (ws); water use intensity (ps), where ps=ws / GDP; total carbon emissions by sector (cs); and carbon intensity (qs), where qs=cs / GDP.

8. The stepwise clustering factorial analysis method based on input-output according to claim 1 or 7, characterized in that: After step D, the sum of squares of the two factors and the sum of squares of the interaction of the two factors were calculated to quantify the interaction between the factors.

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