A copula function-based optimization decision management method for urban water, energy and environmental systems

Abstract

The application discloses a kind of based on Copula function's urban water, energy and environmental system optimization decision management method, comprising: S1. the Copula joint distribution function of water environment capacity and available energy amount in urban water is constructed;S2. the resource optimization allocation and joint risk management model of urban water, energy and environmental system is established;S3. the resource optimization allocation and joint risk management model of urban water, energy and environmental system is solved;The method realizes the optimization allocation and joint risk management of urban water-energy-environment system water and energy under uncertain conditions.Provide urban water-energy-environment system resource optimization allocation scheme and long-term planning scheme of sewage treatment process under different risk scenario combinations on the basis of maximum economic benefit, and help decision makers better realize the trade-off between joint default risk and system benefit, to realize urban risk controllable and water-energy-environment collaborative development provides scientific method.

Description

Technical Field

[0001] The present invention relates to the technical field of water body management, and in particular to an optimization decision-making management method for urban water, energy and environmental systems based on Copula functions. Background Art

[0002] Currently, there are few planning models that comprehensively consider the joint risks of urban water-energy-environment systems and the inherent connections and laws between the linkages.

[0003] Most existing planning models consider only the optimization of pairwise relationships. Some researchers have explored the water-environment relationship, including basin-wide water quality management, combined water quality and water quantity allocation, and optimized water pollutant emission reduction in basins. Other experts have also studied the water-energy relationship and developed mathematical programming methods widely applied to the planning and management of integrated water-energy systems. However, due to a lack of clear theoretical support for the water-energy-environment nexus, decision-makers have often focused solely on the efficient use of urban water resources or improved water quality in actual policies and planning, rarely considering the three together. Within the urban water-energy-environment system, the acquisition, treatment, and distribution of water all involve energy consumption. Water source acquisition includes both direct water diversion from clean water bodies such as rivers, lakes, streams, and seas, as well as the comprehensive utilization of tailwater from sewage treatment plants and reclaimed water plants. Water treatment refers to the process of treating water sources into water suitable for comprehensive utilization. Water distribution refers to the process of transporting usable water sources to appropriate treatment plants, and then distributing it to black and odorous water bodies that need water replenishment and quality improvement. The "Guidelines for the Treatment of Urban Black and Odorous Water Bodies," issued in 2015, clearly state that the evaluation indicators for the classification of urban black and odorous water bodies include transparency, dissolved oxygen (DO), oxidation-reduction potential (ORP), and ammonia nitrogen (NH3-N). The energy consumption of different black and odorous water treatment processes for different black and odorous water quality indicators also varies, and this energy consumption issue is often overlooked. Considering the water, energy, and environmental subsystems in a separate and isolated manner cannot achieve the optimal configuration of the integrated system. Achieving the coordinated and sustainable development of urban water, energy, and environment is imperative.

[0004] Research on the integrated urban water-energy-environment system is not only urgent but also complex. On the one hand, the system is plagued by uncertainties in hydrological conditions, pollution sources, pollutant migration and transformation, and energy supply. These uncertainties, including water flow, water environmental capacity, rainfall, power generation, electricity markets, technological advances, and policy changes, contribute to the system's complexity. Risks arise from systemic uncertainties, such as water quality violations (the risk of black and odorous water bodies due to insufficient water purification capacity) and energy shortages caused by factors such as water pollution load thresholds (water environmental capacity), the randomness of energy availability, and extreme climate change. This can lead to economic losses such as reduced production for polluting enterprises. On the other hand, system planning models, as abstract mathematical generalizations of real-world problems, often differ from reality. The complex interactive relationship between water environmental capacity and energy presents complex nonlinearity, dynamics, and uncertainty. Furthermore, the mutual influence between the water environment and energy subsystems creates the risk of joint system shortages. For a long time, current models in practical policy and planning have primarily focused on analyzing risks arising from water quality violations or energy shortages. Few models have comprehensively considered the joint risks of the urban water-energy-environment system and the inherent connections and patterns within these systems. Clearly, achieving the synergistic goals of joint risk assessment and management of the urban water-energy-environment system and optimal allocation of pollution loads is a current frontier and hot topic in related research, both domestically and internationally. Summary of the Invention

[0005] The present invention aims to overcome the shortcomings of the existing technology by providing a Copula-based method for optimizing decision-making and management of urban water, energy, and environmental systems. This method employs Copula functions to stochastically simulate and quantify the combined changes in treatment capacity and electricity consumption within urban water treatment systems, providing support for collaborative decision-making and risk management of urban water, energy, and the environment. It also quantitatively analyzes and manages the potential risks of black and odorous water bodies and energy shortages caused by the random uncertainties of water quality and energy availability in the system. This method achieves the goals of urban water pollution control, efficient energy utilization, and risk avoidance, providing a foundation for the sustainable development of the urban water, energy, and environmental system.

[0006] A Copula function-based optimization decision-making management method for urban water, energy, and environmental systems includes the following steps:

[0007] S1. Construct the Copula joint distribution function of water environment capacity and available energy in urban water;

[0008] S11: Time series data statistics; identify and analyze water environment and energy conditions in urban water, and collect relevant water quality and electricity consumption data;

[0009] S12: Variable correlation measurement; measure the dependence between water environment and energy in urban water based on historical statistical data;

[0010] S13: Determine the univariate marginal distribution function; select the appropriate marginal probability distribution function line shape, use the maximum likelihood method to estimate the parameters of the marginal probability distribution function, and use the non-parametric Kolmogorov-Smimov goodness-of-fit test to select the most appropriate marginal probability distribution type for energy and water resources;

[0011] S14: Determine the multivariate copula joint distribution function; select the most appropriate copula function to describe the water environmental capacity-energy joint distribution function in the urban water system through distribution function assumptions, parameter estimation, and goodness of fit tests;

[0012] S2. Establish a resource optimization allocation and joint risk management model for urban water, energy, and environmental systems;

[0013] S21: Identifying and Resolving System Complexity; 1) To effectively address interval and random uncertainties in the system, expressed as interval numbers and probability densities, analyze pre-set scenarios related to decision-making, and make corrections after random events occur to minimize the system penalties caused by decision errors due to uncertain information in the first stage of decision-making, an interval two-stage stochastic programming approach is introduced; 2) To handle decision-making problems in which integer and continuous variables coexist in the planning model due to the selection of sewage treatment processes, a mixed integer programming approach is introduced;

[0014] S22: Risk Identification; Risks are caused by systemic uncertainties, such as the risk of black and odorous water and energy shortages caused by the threshold of water pollution load and the randomness of energy availability. Furthermore, the intricate interactive relationship between water environment capacity and energy in urban water systems is nonlinear, dynamic, and uncertain. The mutual influence of the water environment and energy subsystems creates the risk of joint system shortages.

[0015] S23: Risk Measurement; To effectively utilize and quantify the interactions between random processes of different random variables and the joint shortage risk of the system under uncertain conditions, we introduce chance-constrained programming and the Copula joint distribution function obtained above. Combining the Copula function with the CCP allows the CCP to represent the relationship between the individual default risk probability constraints of the water environment and energy subsystems and the joint default risk probability constraints of the water-energy-environment combined system.

[0016] S24: Risk Decision Making: Combining interval two-stage stochastic programming, mixed integer programming, random chance constrained programming, and Copula analysis, a Copula-based interval stochastic mixed integer programming model is established to achieve optimal allocation of water and energy and risk decision-making for urban water-energy-environment systems under uncertain conditions.

[0017] S25: Risk control: Set risk scenario combinations with different joint risk probability levels and single resource risk probability levels to achieve system risk control;

[0018] S3. Solve the resource optimization allocation and joint risk management model of urban water, energy and environmental systems;

[0019] S31: Set the decision variable z j Introduce into the model, so that x ± =x - +Δx·z, where Δx=x + -x - , and z∈[0,1];

[0020] S32: Convert the joint probability constraint into a series of linear constraints, and require the joint probability distribution of the Copula function to satisfy the joint probability of the given conditions under the violation probability condition of each linear constraint; in order to obtain the probability of design violation constraint Assume there are m random variables, given the first m-1 designs, the probability of violating the constraint is Then we can solve Get the last constraint violation probability;

[0021] S33: Converting uncertain constraints into deterministic constraints

[0022] S34: For the optimization model that maximizes the objective function, first establish the upper bound sub-model and solve it; the optimization result of the upper bound sub-model can be obtained: and

[0023] S35: Based on the results of the upper bound model, substitute it into the lower bound sub-model to obtain the optimization results of the lower bound sub-model: and

[0024] S36: The result of merging the upper and lower bounds is the final result of the model; where:

[0025] Moreover, the statistical indicators commonly used in step S12 for measuring the correlation between multiple random variables mainly include Pearson linear correlation coefficient, Kendall rank correlation coefficient τn and Spearman rank correlation coefficient ρn. The correlation calculation is based on formulas (1) to (3):

[0026]

[0027] Where n is the sample length; and X i and Y i The mean of the series; and X i and Y i Variance of the series;

[0028]

[0029] In the formula, when (X i -X j )(Y i -Y j )>0, sgn=1, when (X i -X j )(Yi-Y j )<0, sgn=-1, when (X i -X j )(Y i -Y j )=0 when sgn=0;

[0030]

[0031] Where R i For X i In X1, X2, ..., X n rank; S i Y i In Y1, Y2, ..., Y n rank;

[0032] Furthermore, the likelihood function is calculated in step S13 according to equations (4) to (5), and then dlnL(θ) / d(θ)=0, and the maximum value of the likelihood function L(θ) is the maximum likelihood estimate of the population parameter θ.

[0033]

[0034]

[0035] Hypothesis testing problem: H0: The overall distribution of the sample comes from obeys a specific distribution; H1: The overall distribution of the sample does not obey a specific distribution; if F n (X) represents the cumulative frequency distribution of the sample, F t (X) represents the assumed theoretical distribution, then the test statistic is constructed:

[0036]

[0037] When D>D(n,a), H0 is rejected, otherwise H0 hypothesis is accepted; where D(n,a) is the rejection critical value obtained by looking up the table, a is the significance level, and n represents the sample size.

[0038] Furthermore, the log-likelihood function in step S14 is calculated according to equations (7) to (10), and then the function is solved to obtain the maximum likelihood estimates of θ1, θ2, and α.

[0039] H(x,y;θ1,θ2,α)=C(F(x;θ1),G(y;θ2);α) (7)

[0040]

[0041]

[0042]

[0043] The empirical Copula function and the squared Euclidean distance method are used to perform the goodness of fit test, and the empirical Copula of the sample is defined as follows:

[0044]

[0045] The smaller the squared Euclidean distance is, the better the selected Copula function fits the observed data; its expression is (12):

[0046]

[0047] Where C(U, V) is the selected Copula function and C0(U, V) is the empirical Copula function.

[0048] Moreover, the general formula of the interval random mixed integer programming model in step S24 is shown in formulas (13) to (19):

[0049] The objective function expression is:

[0050]

[0051] The constraint expression is:

[0052]

[0053] C(1-P1, 1-P2, ..., 1-p m )=1-p 联合 (15)

[0054]

[0055] δ ± =0 or 1 (17)

[0056] x ± ≥0 (18)

[0057]

[0058] The advantages and technical effects of the present invention are:

[0059] This paper presents a Copula-based optimization decision-making and management method for urban water, energy, and environmental systems. This method addresses the current situation where there is limited research on collaborative optimization decision-making and joint risk management models for water quantity, water quality, and electricity consumption within the context of the urban water-energy-environment nexus, hindering the coordinated and efficient development of urban water, energy, and the environment, as well as risk control and management. The paper proposes a Copula function to simulate and quantify the relationship between water environmental capacity and available energy in urban water systems. Based on this, a Copula-based interval stochastic mixed integer programming model (CISMIP) is established, combining this model with Interval Two-Stage Stochastic Programming (ITSP), Mixed Integer Programming (MILP), and Chance Constrained Programming (CCP) optimization methods. This model achieves optimal allocation of water quantity and energy and joint risk management for the urban water-energy-environment system under uncertain conditions. It also provides a long-term planning scheme for sewage treatment processes and optimized resource allocation for the urban water-energy-environment system based on economic benefit maximization under different risk scenarios. It also helps decision makers better balance joint default risk with system benefits, providing a scientific approach for achieving controllable urban risks and coordinated development of the water-energy-environment system. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is an overall flow chart for constructing the water quantity, water quality and electricity optimization configuration and joint risk management model for the urban water-energy-environment system of the present invention;

[0061] Figure 2 This is a diagram of the framework for constructing and solving the Copula-based Interval Stochastic Mixed Integer Programming model (CISMIP) of the present invention. DETAILED DESCRIPTION

[0062] In order to further understand the content, features and effects of the present invention, the following embodiments are given as examples and described in detail with reference to the accompanying drawings. It should be noted that the present embodiments are illustrative and not restrictive, and the scope of protection of the present invention cannot be limited thereby.

[0063] A Copula function-based optimization decision-making management method for urban water, energy, and environmental systems includes the following steps:

[0064] S1. Construct the Copula joint distribution function of water environment capacity and available energy in urban water;

[0065] S11: Time series data statistics; identify and analyze water environment and energy conditions in urban water, and collect relevant water quality and electricity consumption data;

[0066] S12: Variable correlation measurement; measure the dependence between water environment and energy in urban water based on historical statistical data;

[0067] S13: Determine the univariate marginal distribution function; select the appropriate marginal probability distribution function line shape, use the maximum likelihood method to estimate the parameters of the marginal probability distribution function, and use the non-parametric Kolmogorov-Smimov goodness-of-fit test to select the most appropriate marginal probability distribution type for energy and water resources;

[0068] S14: Determine the multivariate copula joint distribution function; select the most appropriate copula function to describe the water environmental capacity-energy joint distribution function in the urban water system through distribution function assumptions, parameter estimation, and goodness of fit tests;

[0069] S2. Establish a resource optimization allocation and joint risk management model for urban water, energy, and environmental systems;

[0070] S21: Identifying and Resolving System Complexity; 1) To effectively address interval and random uncertainties in the system, expressed as interval numbers and probability densities, analyze pre-set scenarios related to decision-making, and make corrections after random events occur to minimize the system penalties caused by decision errors due to uncertain information in the first stage of decision-making, an interval two-stage stochastic programming approach is introduced; 2) To handle decision-making problems in which integer and continuous variables coexist in the planning model due to the selection of sewage treatment processes, a mixed integer programming approach is introduced;

[0071] S22: Risk Identification; Risks are caused by systemic uncertainties, such as the risk of black and odorous water and energy shortages caused by the threshold of water pollution load and the randomness of energy availability. Furthermore, the intricate interactive relationship between water environment capacity and energy in urban water systems is nonlinear, dynamic, and uncertain. The mutual influence of the water environment and energy subsystems creates the risk of joint system shortages.

[0072] S23: Risk Measurement; To effectively utilize and quantify the interactions between random processes of different random variables and the joint shortage risk of the system under uncertain conditions, we introduce chance-constrained programming and the Copula joint distribution function obtained above. Combining the Copula function with the CCP allows the CCP to represent the relationship between the individual default risk probability constraints of the water environment and energy subsystems and the joint default risk probability constraints of the water-energy-environment combined system.

[0073] S24: Risk Decision Making: Combining interval two-stage stochastic programming, mixed integer programming, random chance constrained programming, and Copula analysis, a Copula-based interval stochastic mixed integer programming model is established to achieve optimal allocation of water and energy and risk decision-making for urban water-energy-environment systems under uncertain conditions.

[0074] S25: Risk control: Set risk scenario combinations with different joint risk probability levels and single resource risk probability levels to achieve system risk control;

[0075] S3. Solve the resource optimization allocation and joint risk management model of urban water, energy and environmental systems;

[0076] S31: Set the decision variable z j Introduce into the model, so that x ± =x - +Δx·z, where Δx=x + -x - , and z∈[0,1];

[0077] S32: Convert the joint probability constraint into a series of linear constraints, and require the joint probability distribution of the Copula function to satisfy the joint probability of the given conditions under the violation probability condition of each linear constraint; in order to obtain the probability of design violation constraint Assume there are m random variables, given the first m-1 designs, the probability of violating the constraint is Then we can solve Get the last constraint violation probability;

[0078] S33: Converting uncertain constraints into deterministic constraints

[0079] S34: For the optimization model that maximizes the objective function, first establish the upper bound sub-model and solve it; the optimization result of the upper bound sub-model can be obtained:

[0080] S35: Based on the results of the upper bound model, substitute it into the lower bound sub-model to obtain the optimization results of the lower bound sub-model: and

[0081] S36: The result of merging the upper and lower bounds is the final result of the model; where:

[0082] Moreover, the statistical indicators commonly used in step S12 for measuring the correlation between multiple random variables are mainly Pearson linear correlation coefficient, Kendall rank correlation coefficient τ n and Spearman rank correlation coefficient ρ n , related calculations are as follows:

[0083]

[0084] Where n is the sample length; and X i and Y i The mean of the series; and X i and Y i Variance of the series;

[0085]

[0086] In the formula, when (X i -X j )(Y i -Y j )>0, sgn=1, when (X i -X j )(Y i -Y j )<0, sgn=-1, when (X i -X j )(Y i -Y j )=0 when sgn=0;

[0087]

[0088] Where R i For X i In X1, X2, ..., X n rank; S i Y i In Y1, Y2, ..., Y n rank;

[0089] Furthermore, the likelihood function is calculated in step S13 according to equations (4) to (5), and then dlnL(θ) / d(θ)=0, and the maximum value of the likelihood function L(θ) is the maximum likelihood estimate of the population parameter θ.

[0090]

[0091]

[0092] Hypothesis testing problem: H0: The overall distribution of the sample comes from obeys a specific distribution; H1: The overall distribution of the sample does not obey a specific distribution; if F n (X) represents the cumulative frequency distribution of the sample, F t (X) represents the assumed theoretical distribution, then the test statistic is constructed:

[0093]

[0094] When D>D(n,a), H0 is rejected, otherwise H0 hypothesis is accepted; where D(n,a) is the rejection critical value obtained by looking up the table, a is the significance level, and n represents the sample size.

[0095] Furthermore, the log-likelihood function in step S14 is calculated according to equations (7) to (10), and then the function is solved to obtain the maximum likelihood estimates of θ1, θ2, and α.

[0096] H(x,y;θ1,θ2,α)=C(F(x;θ1),G(y;θ2);α) (7)

[0097]

[0098]

[0099]

[0100] The empirical Copula function and the squared Euclidean distance method are used to perform the goodness of fit test, and the empirical Copula of the sample is defined as follows:

[0101]

[0102] The smaller the squared Euclidean distance is, the better the selected Copula function fits the observed data; its expression is (12):

[0103]

[0104] Where C(U, V) is the selected Copula function and C0(U, V) is the empirical Copula function.

[0105] Moreover, the general formula of the interval random mixed integer programming model in step S24 is shown in formulas (13) to (19):

[0106] The objective function expression is:

[0107]

[0108] The constraint expression is:

[0109]

[0110] C(1P1,1-P2,…,1-p m )=1-p 联合 (15)

[0111]

[0112] δ ± =0 or 1 (17)

[0113] x ± ≥0 (18)

[0114]

[0115] In order to more clearly illustrate the specific embodiment of the present invention, an embodiment is provided below:

[0116] S1. Establish a water-energy joint distribution function for the water environment capacity and available electricity of a city's urban water system. Based on the Copula function, quantitatively analyze the joint change law of water environment capacity and available electricity in urban water, and provide a basic guarantee for the water environment-energy joint risk assessment and management in urban water systems.

[0117] S11: Collect and analyze the statistical results of water environment capacity and available electricity in a certain city from 2000 to 2020.

[0118] S12: Using Pearson linear correlation coefficient (r n ), Kendall rank correlation coefficient (τn) and Spearman rank correlation coefficient (ρn) measure the correlation between a city's water environment capacity and available electricity.

[0119] S13: Three common distribution types (normal, lognormal, and Weibull) were selected to fit the marginal distribution functions of the water environment capacity and available electricity in a city's urban water. After estimating the unknown parameters of the three distribution functions, a goodness-of-fit test was performed to select the most appropriate marginal distribution function. Parameter estimates were obtained using the maximum likelihood method, and the KS test was then used to test the goodness-of-fit of the marginal distribution functions.

[0120] S14: Common Copula types were selected: normal Copula function, t-Copula function, and Gumbel, Clayton, and Frank Copula functions among the Archimedean Copula functions. The maximum likelihood method was used for parameter estimation to obtain the parameters of the five Copula types. Finally, the empirical Copula function was used for goodness of fit test. The Copula function type with the smallest squared Euclidean distance was selected as the optimal joint distribution function to construct a water environment-energy joint distribution function for a city's water environment capacity and available electricity.

[0121] S2: Constructing a model for optimizing resource allocation and joint risk management of urban water-energy-environmental systems under uncertain conditions:

[0122] This model allocates water quantity, quality, and limited electricity to pollutant dischargers within a watershed while maximizing overall system benefits. Water environmental capacity is a random variable that varies with the natural conditions of the water body and the migration and transformation of pollutants. Available energy also exhibits random uncertainty. The first-stage decision variables are the water volume and pollution load promised by the manager to the pollutant discharger before the random variables occur. This is represented by the water volume multiplied by the pollution load generation rate. Because the target water volume and pollution load for each pollutant discharger are predetermined, meeting these energy-water and environmental requirements will generate corresponding benefits for the enterprise. Otherwise, the polluter will need to resort to more expensive pollution control measures, and rising electricity prices and the expansion of wastewater treatment capacity will impose "penalties" on the system's economic performance. Therefore, the second-stage decision-making process implements error correction after the random event occurs, aiming to minimize the system penalties caused by decision errors caused by uncertain information in the first-stage decision.

[0123] Taking into account the energy consumption for sewage treatment, energy supply, water quality emission standards, and urban sewage treatment capacity, a joint risk management model for the urban water-energy-environment system is established from the perspective of linkage. Scenario combinations with different joint risk levels and individual risk levels are set, and an interval randomized mixed integer programming model based on Copula analysis is applied to rationally arrange and configure the pollution loads generated by different water sources and sewage treatment processes under different joint risk levels, thereby achieving the maximum economic benefit. This model provides a decision-making plan for optimizing the configuration of water volume, water quality, and electricity consumption under different risk scenario combinations in the next 15 years, and selecting the sewage treatment process to achieve the maximum benefit for the urban water-energy-environment system. The specific expression of the model is as follows:

[0124] Objective function:

[0125]

[0126] (1) Net system benefit b when pollutant-discharging enterprises meet emission standards ± :

[0127]

[0128] (2) Pipeline transportation cost for water collection and utilization c t1 ± :

[0129]

[0130] (3) Pipeline transportation cost of sewage treatment c t2 ± :

[0131]

[0132] (4) Investment cost of sewage treatment equipment c t3 ± :

[0133]

[0134] (5) Sewage treatment safety cost c t4 ± :

[0135]

[0136] (6) Land cost of sewage treatment c t5 ± :

[0137]

[0138] (7) Electricity consumption cost of water collection and utilization c t6 ± :

[0139]

[0140] (8) Electricity consumption cost of sewage treatment c t7 ± :

[0141]

[0142] (9) Sewage treatment scale expansion cost c t8 ± :

[0143]

[0144] Constraints:

[0145] (1) Constraints on pipeline transportation capacity for water collection and utilization:

[0146]

[0147] (2) Constraints on pipeline transportation capacity of sewage treatment:

[0148]

[0149] (3) Constraints on the maximum water environment capacity of sewage:

[0150]

[0151] (4) Water collection and utilization and sewage treatment power supply capacity:

[0152]

[0153] (5) Water environment-energy joint risk constraints in urban water systems:

[0154] C{1-p m , 1-p n}=1-p 联合 (34)

[0155] (6) Constraints on sewage treatment scale expansion:

[0156]

[0157] (7) Non-negative constraints:

[0158]

[0159] The meanings of the parameters and variables in the above formula are shown in Table 1.

[0160] Table 1 Explanation of the meaning of each parameter in the model

[0161]

[0162]

[0163]

[0164] S3, solving the urban water-energy-environment system resource optimization allocation and joint risk management model according to steps S31-36.

[0165] Finally, all the parts not described in the present invention adopt mature products and mature technical means in the existing technology.

[0166] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all such improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A Copula function-based optimization decision-making management method for urban water, energy and environmental systems, characterized by: The following steps are involved: S1. Construct the Copula joint distribution function of water environment capacity and available energy in urban water; S11: Time series data statistics; identify and analyze water environment and energy conditions in urban water, and collect relevant water quality and electricity consumption data; S12: Variable correlation measurement; measure the dependence between water environment and energy in urban water based on historical statistical data; S13: Determine the marginal distribution function of a single variable; select the appropriate marginal probability distribution function line shape, estimate the parameters of the marginal probability distribution function using the maximum likelihood method, and use the non-parametric Kolmogorov-Smimov goodness-of-fit test to select the most appropriate marginal probability distribution type for energy and water resources; S14: Determine the multivariate copula joint distribution function; select the most appropriate copula function to describe the water environmental capacity-energy joint distribution function in the urban water system through distribution function assumptions, parameter estimation, and goodness of fit tests; S2. Establish a resource optimization allocation and joint risk management model for urban water, energy, and environmental systems; S21: Identifying and Resolving System Complexity; 1) To effectively address interval and random uncertainties in the system, expressed as interval numbers and probability densities, analyze pre-set scenarios related to decision-making, and make corrections after random events occur to minimize the system penalties caused by decision errors due to uncertain information in the first stage of decision-making, an interval two-stage stochastic programming approach is introduced; 2) To handle decision-making problems in which integer and continuous variables coexist in the planning model due to the selection of sewage treatment processes, a mixed integer programming approach is introduced; S22: Risk identification; Risks are caused by systemic uncertainty. Furthermore, there is a complex interactive relationship between water environment capacity and energy in urban water systems, which is nonlinear, dynamic, and uncertain. The mutual influence of the water environment and energy subsystems creates a joint systemic shortage risk. S23: Risk Measurement; To effectively utilize and quantify the interactions between random processes of different random variables and the joint shortage risk of the system under uncertain conditions, we introduce chance-constrained programming and the Copula joint distribution function obtained above. Combining the Copula function with the CCP allows the CCP to represent the relationship between the individual default risk probability constraints of the water environment and energy subsystems and the joint default risk probability constraints of the water-energy-environment combined system. S24: Risk Decision Making: Combining interval two-stage stochastic programming, mixed integer programming, random chance constrained programming, and Copula analysis, a Copula-based interval stochastic mixed integer programming model is established to achieve optimal allocation of water and energy and risk decision-making for urban water-energy-environment systems under uncertain conditions. S25: Risk control: Set risk scenario combinations with different joint risk probability levels and single resource risk probability levels to achieve system risk control; S3. Solve the resource optimization allocation and joint risk management model of urban water, energy and environmental systems; S31: Set the decision variable z j Introduce into the model, so that x ± =x - +Δx·z, where Δx=x + -x - , and z∈[0,1]; S32: Convert the joint probability constraint into a series of linear constraints, and require the joint probability distribution of the Copula function to satisfy the joint probability of the given conditions under the violation probability condition of each linear constraint; in order to obtain the probability of design violation constraint Assume there are m random variables, given the first m-1 designs, the probability of violating the constraint is Then we can solve Get the last constraint violation probability; S33: Converting uncertain constraints into deterministic constraints S34: For the optimization model that maximizes the objective function, first establish the upper bound sub-model and solve it; The upper limit sub-model optimization results can be obtained: and S35: Based on the results of the upper bound model, substitute it into the lower bound sub-model to obtain the optimization results of the lower bound sub-model: and S36: The result of combining the upper and lower bounds is the final result of the model; where:

2. The method for optimizing decision-making and management of urban water, energy, and environmental systems based on Copula functions according to claim 1, characterized in that: The statistical indicators commonly used in step S12 for measuring the correlation between multiple random variables are mainly Pearson linear correlation coefficient, Kendall rank correlation coefficient τ n and Spearman rank correlation coefficient ρ n , related calculations are as follows: Where n is the sample length; and X i and Y i The mean of the series; and X i and Y i Variance of the series; In the formula, when (X i -X j )(Y i -Y j )>0, sgn=1, when (X i -X j )(Y i -Y j )<0, sgn=-1, when (X i -X j )(Y i -Y j )=0 when sgn=0; Where R i For X i In X1, X2, …, X n rank; S i Y i In Y1, Y2,…, Y n rank; 3. The method for optimizing decision-making and management of urban water, energy, and environmental systems based on Copula functions according to claim 1, characterized in that: The likelihood function in step S13 is calculated according to formulas (4) to (5), and then dlnL(θ) / d(θ)=0. The maximum value of the likelihood function L(θ) is the maximum likelihood estimate of the population parameter θ. Hypothesis testing problem: H0: The overall distribution of the sample comes from obeys a specific distribution; H1: The overall distribution of the sample does not obey a specific distribution; if F n (X) represents the cumulative frequency distribution of the sample, F t (X) represents the assumed theoretical distribution, then the test statistic is constructed: When D>D(n,a), H0 is rejected, otherwise the H0 hypothesis is accepted; where D(n,a) is the rejection critical value obtained by looking up the table, a is the significance level, and n represents the sample size.

4. The method for optimizing decision-making and management of urban water, energy, and environmental systems based on Copula functions according to claim 1, characterized in that: The calculation of the log-likelihood function in step S14 is performed according to equations (7) to (10), and then the function is solved to obtain the maximum likelihood estimates of θ1, θ2 and α. H(x,y;θ1,θ2,α)=C(F(x;θ1),G(y;θ2);α) (7) The empirical Copula function and the squared Euclidean distance method are used to perform the goodness of fit test, and the empirical Copula of the sample is defined as follows: The smaller the squared Euclidean distance is, the better the selected Copula function fits the observed data; its expression is (12): Where C(U,V) is the selected Copula function and C0(U,V) is the empirical Copula function.

5. The method for optimizing decision-making and management of urban water, energy and environmental systems based on Copula functions according to claim 1 is characterized by: The general formula of the interval random mixed integer programming model in step S24 is shown in formulas (13) to (19): The objective function expression is: The constraint expression is: C(1-p1,1-p2,...,1-p m )=1-p 联合 (15) δ ± =0 or 1 (17) x ± ≥0 (18)

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