An intelligent simulation method for water engineering dispatch runoff

Abstract

The application discloses a water engineering scheduling runoff intelligent simulation method, comprising: edge distribution function fitting: using the matrix method to calculate the mean, dispersion coefficient and skewness coefficient, and adopting a P-III type curve to construct a daily runoff frequency curve; wisdom knowledge set construction: using a time series model to establish wisdom knowledge sets of each parameter in a mixed Copula set, using a cooperative search algorithm, taking the minimum of the Akaike information criterion of the theoretical distribution and the empirical distribution as the target, and calibrating the wisdom knowledge set parameters; daily runoff simulation: based on the Bayesian rule, a mixed conditional Copula set is established, and Latin hypercube sampling is used to generate a long sequence of daily runoff. The method reduces the difficulty of daily runoff simulation by the mixed Copula, reduces the number of parameters, improves the fitting precision of the mixed Copula, speeds up the construction speed of the mixed Copula set, and provides a valuable technical tool for basin management.

Description

Technical Field

[0001] This invention belongs to the field of runoff simulation, specifically relating to an intelligent simulation method for water project scheduling runoff. Background Technology

[0002] Runoff is a crucial subject of study in hydrology, encompassing all aspects of the hydrological cycle, including precipitation, evaporation, surface runoff, and groundwater runoff. Due to its stochastic nature, stochastic simulation methods are widely used in hydrology. Developing efficient stochastic simulation methods is of great significance for sustainable water resource management, flood risk assessment, and the formulation of operational strategies for water conservancy projects. By generating large amounts of data with statistical characteristics similar to measured data, the performance of water conservancy projects can be more accurately assessed, response strategies for extreme hydrological events can be formulated, and water resource allocation and utilization can be optimized. Furthermore, long-term hydrological simulation data can be used to validate and improve hydrological models, enhance model prediction accuracy, and provide a scientific basis for water resource planning and management.

[0003] To achieve efficient runoff simulation, Copula models are widely used due to their advantages such as no need for normalization and flexible modeling. Copula can effectively capture complex interdependencies between datasets and enhance model robustness by avoiding uncertainties in normalization transformation. When simulating hydrological variables with complex spatiotemporal dependencies, a single Copula model cannot fully describe the complex dependency structure. Hybrid Copula models enhance the model's ability to flexibly capture and express multiple dependency features of hydrological variables by combining Copula models with different features. However, hybrid Copula models combine multiple single Copula models through weighting coefficients, and the number of parameters increases significantly with the increase of hybrid Copula types. In this case, traditional parameter estimation methods have low fitting efficiency when dealing with hybrid Copula models with a large number of parameters. How to improve the fitting accuracy of hybrid Copula models, accelerate the calibration speed, and reduce the number of calibration parameters is a hot and difficult research topic in the field of runoff simulation, and has important significance and application value for water resource management and utilization. Summary of the Invention

[0004] This invention addresses the problems of numerous parameters, long calibration times, and low calibration accuracy in current hybrid Copula daily runoff simulations by providing an intelligent runoff simulation method for water engineering scheduling. This method simplifies the runoff simulation process and reduces parameter complexity by integrating scene recognition and parameter optimization techniques. Furthermore, it employs the Crow Search Algorithm (CSA) for accurate parameter estimation, improving the calibration accuracy of hybrid Copula.

[0005] To address the above problems, the specific implementation scheme of the present invention is as follows:

[0006] S1. Based on historical runoff data, extract data features, use the method of moments to determine the mean, skewness coefficient and coefficient of variation of the data, and construct the daily runoff frequency curve using the P-III type curve;

[0007] S2. Based on historical runoff data, construct a time series model, calculate the Manhattan distance of different daily runoffs as the driving variable, and establish a set of intelligent knowledge for each parameter in an M-dimensional hybrid Copula ensemble;

[0008] S3. Using a cooperative search algorithm, with the goal of minimizing the Akaike information criterion between the theoretical distribution and the empirical distribution, the parameters of the intelligent knowledge set are calibrated.

[0009] S4. Based on Bayes' theorem, establish a mixed-condition Copula set, use Latin hypercube sampling to generate random numbers, and simulate new runoff values ​​based on the previous M-1 runoff values.

[0010] Further optimization is achieved by establishing the hybrid Copula expression in step S2 as follows:

[0011]

[0012] In the formula, N is the number of Copulas; C mix (u1,u2,...,u n ) is a mixture of Copula; C i (u1,u2,...,u n ;θ i ) represents the i-th hybrid Copula type; represents the i-th weight parameter; represents the Copula parameter of the i-th Copula.

[0013] Further optimization is achieved by establishing the intelligent knowledge set expression for the Copula parameters and weight parameters in step S2, as shown below:

[0014]

[0015] In the formula, M is the number of samples; D is the Copula dimension; θ i,t ω represents the Copula parameter at time j for the i-th Copula; i,t Let be the weight parameters of the i-th Copula at time j; Λ be the transformation function; u x,j Let x be the cumulative distribution function value of the j-th sample at time x; the rest are constants.

[0016] Further optimization is needed; the optimization objective for the cooperative search algorithm in step S3 is as follows:

[0017]

[0018] In the formula, M is the number of samples; N is the number of Copulas in the Copula set; k is the number of parameters of the Copula function; F p (g) is the empirical joint distribution of the samples; C(g) is the theoretical joint distribution of the samples; n m,g,...,k To satisfy X≤x i1 ,X≤x i2 ,...,X≤x iM The number of samples.

[0019] Further optimization is achieved by the following steps in the cooperative search algorithm of step S3:

[0020] S3.1: Generate the initial workforce according to the following formula. After evaluating the objective function of all options, select M ∈ [1, I] leaders from the initial population to form the external elite set.

[0021]

[0022] In the formula, I represents the number of solutions in the current population; Let φ(L,U) be the j-th position of the i-th individual in the k-th iteration; φ(L,U) is a function that generates a uniformly distributed random number in [L,U].

[0023] S3.2: Considering that every employee can obtain new information by communicating with the Chairman, the Board of Directors, and the Supervisory Board, the team communication process consists of three parts: the Chairman's knowledge A, the Board's collective knowledge B, and the Supervisory Board's collective knowledge C. The Chairman is randomly selected from the Board of Directors, simulating a rotation mechanism, while all members of the Board of Directors and the Supervisory Board are assigned the same position when calculating B and C.

[0024]

[0025] In the formula, This represents the j-th value of the ith individual in the (k+1)-th iteration. Let be the j-th value of the optimal solution for the i-th individual in the k-th generation; be From the beginning to the j-th value of the ind-th global optimal solution in generation k, where ind is an index randomly selected from the set {1,2,...,M}; This refers to the knowledge obtained by randomly selecting a chairperson from a pool of external elites; and These represent the average knowledge from the M global optimal solutions and I individual optimal solutions discovered so far; α and β are the adjustment... and The learning coefficient that influences the degree of influence.

[0026] S3.3: In addition to learning from leaders, employees also need to summarize their experiences in the opposite direction to gain new knowledge, as shown below:

[0027]

[0028] In the formula, The j-th value of the i-th reflective solution in the (k+1)-th iteration.

[0029] S3.4: The team enhances its market competitiveness by ensuring that all high-performing employees are protected, as specifically stated below:

[0030]

[0031] In the formula, F(x) represents the fitness of the solution.

[0032] Further optimization is achieved by expressing the Copula required for daily runoff simulation in step S4 as follows:

[0033]

[0034] In the formula, ε is a random number obtained through Latin hypercube sampling; C cond (u j |u j-1 ,...,u j-t ) is for a given u j-1 ,...,u j-t In this case, u j The conditional probability is calculated based on the marginal distribution obtained in step S1. j inverse function X j =F -1 (u j The desired simulated runoff value is obtained.

[0035] Compared with existing technologies, the beneficial technical effects of the above technical solutions adopted in this invention are as follows: ① To solve the problem of too many parameters in the hybrid Copula set, a dimensionality reduction method based on a knowledge set is proposed. By using a time series model to discretize the multidimensional variable space into multiple two-dimensional variables, and selecting the Manhattan distance of samples in each two-dimensional variable space as the driving variable, a knowledge set of each parameter of the hybrid Copula set is constructed. This method reduces the number of parameter estimates from M·(2N-1) to 3·(2N-1) (where M>>3), effectively reducing the difficulty of parameter calibration. ② To address the low efficiency and low accuracy of traditional hybrid Copula parameter estimation, this invention uses the CSA algorithm for parameter estimation, avoiding the construction of complex maximum likelihood equations, improving parameter calibration accuracy, and reducing parameter calibration time. ③ The runoff simulation method proposed in this invention combines the knowledge set with CSA, and obtains runoff simulation results through conditional distribution sampling. Compared with traditional methods, this method has a faster calculation speed, higher fitting accuracy, and significantly improves the efficiency and accuracy of runoff simulation. Attached Figure Description

[0036] Figure 1 This is a flowchart of the intelligent simulation method for water project scheduling runoff of the present invention.

[0037] Figure 2 The fitting effect of a single Copula with the Copula of this invention is shown in the QQ graph.

[0038] Figure 3 The figures show the parameter error bands and QQ plots of the Copula simulation results of this invention. Detailed Implementation

[0039] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0040] In this invention, various aspects of the invention are described with reference to the accompanying drawings. Embodiments of the invention are not limited to those described in the drawings. It should be understood that the invention is implemented through any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed in this invention are not limited to any particular implementation. Furthermore, some aspects of the invention disclosed can be used alone or in any suitable combination with other aspects of the invention disclosed.

[0041] refer to Figure 1 This invention provides an intelligent simulation method for water project scheduling runoff, comprising the following steps:

[0042] S1. Based on historical runoff data, extract data features, use the method of moments to determine the mean, skewness coefficient and variation coefficient of the data, and construct the daily runoff frequency curve using the P-III type curve.

[0043] S2. Based on historical runoff data, calculate the Manhattan distance of runoff for different days as the driving variable, construct a time series model, and establish a knowledge set of each parameter in an M-dimensional hybrid Copula ensemble. The expressions for the hybrid Copula model and the knowledge set of each parameter are shown below:

[0044]

[0045] In the formula, N is the number of Copulas; M is the number of samples; D is the dimension of the Copula; C mix (u1,u2,...,u n ) is a mixture of Copula; C i (u1,u2,...,u n ;θ i ) represents the i-th hybrid Copula type; θ i,t ω represents the Copula parameter at time j for the i-th Copula; i,t Let be the weight parameters of the i-th Copula at time j; Λ be the transformation function; u x,j Let x be the cumulative distribution function value of the j-th sample at time x; the rest are constants.

[0046] S3. To determine the parameters of the intelligent knowledge set, this invention uses CSA to optimize the parameters of the intelligent knowledge set. The optimization objective function is to minimize the Akaike Information Criterion, expressed as follows:

[0047]

[0048] In the formula, M is the number of samples; N is the number of Copulas in the Copula set; k is the number of parameters of the Copula function; F p (g) is the empirical joint distribution of the samples; C(g) is the theoretical joint distribution of the samples; n m,g,...,k To satisfy X≤x i1 ,X≤x i2 ,...,X≤x iM The number of samples.

[0049] The steps for optimizing CSA parameters are as follows:

[0050] S3.1: Generate the initial workforce according to the following formula. After evaluating the objective function of all options, select M ∈ [1, I] leaders from the initial population to form the external elite set.

[0051]

[0052] In the formula, I represents the number of solutions in the current population; Let φ(L,U) be the j-th position of the i-th individual in the k-th iteration; φ(L,U) is a function that generates a uniformly distributed random number in [L,U].

[0053] S3.2: Considering that every employee can obtain new information by communicating with the Chairman, the Board of Directors, and the Supervisory Board, the team communication process consists of three parts: the Chairman's knowledge A, the Board's collective knowledge B, and the Supervisory Board's collective knowledge C. The Chairman is randomly selected from the Board of Directors, simulating a rotation mechanism, while all members of the Board of Directors and the Supervisory Board are assigned the same position when calculating B and C.

[0054]

[0055] In the formula, This represents the j-th value of the ith individual in the (k+1)-th iteration. It is the j-th value of the optimal solution for the i-th individual in the k-th generation; Let j be the j-th value of the ind-th global optimal solution from the beginning to the k-th generation, where ind is the index randomly selected from the set {1, 2, ..., M}; This refers to the knowledge obtained by randomly selecting a chairperson from a pool of external elites; and These represent the average knowledge from the M global optimal solutions and I individual optimal solutions discovered so far; α and β are the adjustment... and The learning coefficient that influences the degree of influence.

[0056] S3.3: In addition to learning from leaders, employees also need to summarize their experiences in the opposite direction to gain new knowledge, as shown below:

[0057]

[0058] In the formula, The j-th value of the i-th reflective solution in the (k+1)-th iteration.

[0059] S3.4: The team enhances its market competitiveness by ensuring that all high-performing employees are protected, as specifically stated below:

[0060]

[0061] In the formula, F(x) represents the fitness of the solution.

[0062] Based on Bayes' theorem, a mixed-condition Copula set is established. Random numbers are generated using Latin hypercube sampling, and new runoff values ​​are simulated based on the previous M-1 runoff values. The formula for calculating the conditional Copula is shown below:

[0063]

[0064] In the formula, ε is a random number obtained through Latin hypercube sampling; Ccond (u j |u j-1 ,...,u j-t ) is for a given u j-1 ,...,u j-t In this case, u j The conditional probability is calculated based on the marginal distribution obtained in step S1. j inverse function X j =F -1 (u j The desired simulated runoff value is obtained.

[0065] Taking a hydrological station as the research object, and using the three-dimensional Copula as an example, the performance of the method was tested. Runoff simulation was performed using the runoff simulation method proposed in this invention, the traditional single Copula, and the traditional hybrid Copula. Model construction and simulation results were compared. Table 1 compares the model construction of the single three-dimensional Clayton Copula, Gumbel Copula, traditional hybrid Copula, and the proposed method (hybrid CSA_Copula). The first three types of traditional Copula models were calibrated using the maximum likelihood method. RMSE represents the root mean square error, and AIC represents the Akaike Information Criterion. Figure 2 This paper presents the QQ plots of the joint distribution of three types of Copulas with empirical data, as well as the density plot of the mixed Copulas. Compared with traditional methods, the method of this invention effectively reduces the number of parameters while improving the fitting accuracy of the joint distribution (see Table 1 for details). Compared with the traditional maximum likelihood estimation method, this method constructs a smart knowledge base for each parameter in the three-dimensional mixed Copula set and uses the CSA algorithm to calibrate the parameters, avoiding the need to solve complex maximum likelihood equations. The mixed Copula construction method proposed in this invention simplifies parameter estimation and improves the accuracy of Copula model construction.

[0066] Table 1. Fitting accuracy, number of parameters, and calibration time for different types of Copula.

[0067]

[0068] Table 2 shows the differences between the daily runoff statistics obtained from different types of Copula simulations and the measured runoff statistics. Figure 3 The proposed method presents predicted band plots and QQ plots for various statistical indicators. Overall, the indicators obtained by the proposed method are superior to those obtained by the traditional Copula method, indicating that the daily runoff simulated by the proposed method can retain the characteristics of measured data and demonstrates high reliability.

[0069] Table 2. Statistical parameters of daily runoff obtained from different types of Copula simulations.

[0070]

[0071] While the present invention has been described above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for intelligent simulation of runoff in water engineering scheduling, characterized in that, Includes the following steps: S1. Based on historical runoff data, extract data features, use the method of moments to determine the mean, skewness coefficient and coefficient of variation of the data, and construct the daily runoff frequency curve using the P-III type curve; S2. Based on historical runoff data, construct a time series model, calculate the Manhattan distance of different daily runoffs as the driving variable, and establish a set of intelligent knowledge for each parameter in an M-dimensional hybrid Copula ensemble; S3. Using a cooperative search algorithm, with the goal of minimizing the Akaike information criterion between the theoretical distribution and the empirical distribution, the parameters of the intelligent knowledge set are calibrated. S4. Based on Bayes' theorem, establish a mixed-condition Copula set, use Latin hypercube sampling to generate random numbers, and simulate new runoff values ​​based on the previous M-1 runoff values; The hybrid Copula expression established in step S2 is shown below: In the formula, N is the number of Copulas; C mix (u1,u2,...,u n ) is a mixture of Copula; C i (u1,u2,...,u n ;θ i ) represents the i-th hybrid Copula type; ω i Let θ be the i-th weight parameter; i Let be the Copula parameter of the i-th Copula; The expressions for the intelligent knowledge set of Copula parameters and weight parameters established in step S2 are as follows: In the formula, M is the number of samples; D is the Copula dimension; θ i,t ω represents the Copula parameter at time j for the i-th Copula; i,t Let be the weight parameters of the i-th Copula at time j; Λ be the transformation function; u x,j Let x be the cumulative distribution function value of the j-th sample at time x; the rest are constants. The optimization objective of the cooperative search algorithm in step S3 is as follows: In the formula, M is the number of samples; N is the number of Copulas in the Copula set; k is the number of parameters of the Copula function; F p (g) is the empirical joint distribution of the samples; C(g) is the theoretical joint distribution of the samples; n m,g,...,k To satisfy X≤x i1 ,X≤x i2 ,...,X≤x iM The number of samples.

2. The intelligent simulation method for water project scheduling runoff according to claim 1, characterized in that, The steps of the cooperative search algorithm in step S3 are as follows: S3.1: Generate the initial staff according to the following formula. After evaluating the objective function of all schemes, select M ∈ [1, I] leaders from the initial population to form an external elite set; In the formula, I represents the number of solutions in the current population; This represents the j-th position of the i-th individual in the k-th iteration. φ(L,U) is a function that generates uniformly distributed random numbers within the range [L,U]. S3.2: Considering that every employee can obtain new information by exchanging information with the leaders of the Chairman, the Board of Directors and the Supervisory Board; the team communication process includes three parts: the Chairman's knowledge A, the collective knowledge of the Board of Directors B and the collective knowledge of the Supervisory Board C; the Chairman is randomly selected from the Board of Directors, simulating a rotation mechanism, while all members of the Board of Directors and the Supervisory Board are assigned the same position when calculating B and C; In the formula, This represents the j-th value of the ith individual in the (k+1)-th iteration. It is the j-th value of the optimal solution for the i-th individual in the k-th generation; Let j be the j-th value of the ind-th global optimal solution from the beginning to the k-th generation, where ind is the index randomly selected from the set {1, 2, ..., M}; This refers to the knowledge obtained by randomly selecting a chairperson from a pool of external elites; and These represent the average knowledge from the M global optimal solutions and I individual optimal solutions discovered so far; α and β are the adjustment... and The learning coefficient that influences the degree of influence; S3.3: In addition to learning from leaders, employees also need to summarize their experiences in the opposite direction to gain new knowledge, as shown below: In the formula, The j-th value of the i-th reflective solution in the (k+1)-th iteration; S3.4: The team enhances its market competitiveness by ensuring that all high-performing employees are protected, as specifically stated below: In the formula, F(x) represents the fitness of the solution.

3. The intelligent simulation method for water project scheduling runoff according to claim 2, characterized in that, The conditions required for daily runoff simulation in step S4 are expressed in Copula as follows: In the formula, ε is a random number obtained through Latin hypercube sampling; C cond (u j |u j-1 ,...,u j-t ) is for a given u j-1 ,...,u j-t In this case, u j The conditional probability; based on the marginal distribution obtained in step S1, calculate u. j inverse function X j =F -1 (u j The desired simulated runoff value is obtained.

Images