Intelligent simulation method for water engineering dispatching runoff

Abstract

The invention discloses a water engineering scheduling runoff intelligent simulation method, which comprises the following steps: edge distribution function fitting: calculating a mean value, a discrete coefficient and a skewness coefficient by applying a moment method, and constructing a daily runoff frequency curve by adopting a P-III type curve; constructing a wisdom knowledge set: establishing the wisdom knowledge set of parameters in a mixed Copula set by using a time sequence model, and calibrating the parameters of the wisdom knowledge set by using a cooperative search algorithm and taking the minimum akaike information criterion of theoretical distribution and empirical distribution as a target; and daily runoff simulation: establishing a mixed condition Copula set based on a Bayesian rule, and generating long-sequence daily runoff by adopting Latin hypercube sampling. According to the method, the daily runoff simulation difficulty of the mixed Copula is reduced, the number of parameters is reduced, the fitting precision of the mixed Copula is improved, the construction speed of the mixed Copula set is increased, and a valuable technical tool is provided for drainage basin management.

Description

Technical Field

[0001] The invention belongs to the field of runoff simulation, and in particular relates to an intelligent simulation method for runoff in water project scheduling. Background Art

[0002] Runoff is an important research object in hydrology, which covers all aspects of the hydrological cycle, including precipitation, evaporation, surface runoff, groundwater runoff, etc. Influenced by its random process, stochastic simulation methods have been widely used in the field of hydrology. The development of efficient stochastic simulation methods is of great significance to the sustainable management of water resources, flood risk assessment and the formulation of water conservancy project operation strategies. By generating a large amount of data with similar statistical characteristics to the measured data, it is possible to more accurately evaluate the performance of water conservancy projects, formulate response strategies for extreme hydrological events, and optimize water resources allocation and utilization. In addition, long-term hydrological simulation data can be used to verify and improve hydrological models, improve the accuracy of model predictions, and provide a scientific basis for water resources planning and management.

[0003] In order to achieve efficient simulation of runoff, Copula is widely used due to its advantages such as no need for normalization and flexible modeling. Copula can effectively capture the complex interdependencies between data sets and enhance the robustness of the model by avoiding the uncertainty in the normalization transformation. When simulating hydrological variables with complex spatiotemporal interdependencies, a single Copula model cannot fully describe the complex dependency structure. Hybrid Copula enhances the model's ability to flexibly capture and express multiple dependency characteristics of hydrological variables by combining Copulas with different characteristics. However, the hybrid Copula model combines multiple single Copula models through weight coefficients. As the number of hybrid Copula types increases, the number of parameters increases significantly. In this case, the traditional parameter estimation method has low fitting efficiency when dealing with hybrid Copula models with a large number of parameters. How to consider improving the fitting accuracy of hybrid Copula, accelerating the calibration speed, and reducing the number of calibration parameters is a hot topic and difficulty in the field of runoff simulation, which has important significance and application value for water resources management and utilization. Summary of the invention

[0004] The present invention provides a method for intelligent simulation of runoff in water project scheduling to solve the problems of large number of parameters, long calibration time and low calibration accuracy in the current mixed copula for daily runoff simulation. The method simplifies the runoff simulation process and reduces the parameter complexity by integrating scene recognition and parameter optimization technology. In addition, the Crow Search Algorithm (CSA) is used to accurately estimate parameters and improve the calibration accuracy of the mixed copula.

[0005] To solve 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 moment method to determine the mean, skewness coefficient and coefficient of variation of the data, and use the P-Ⅲ curve to construct the daily runoff frequency curve;

[0007] S2. Based on the historical runoff data, a time series model is constructed, the Manhattan distance of runoff on different days is calculated as the driving variable, and the intelligent knowledge set of each parameter in the M-dimensional mixed Copula set is established;

[0008] S3. Use cooperative search algorithm to minimize the theoretical distribution and the empirical distribution Akaike information criterion, and calibrate the parameters of the wisdom knowledge set;

[0009] S4. Based on the Bayesian rule, a mixed conditional Copula set is established, Latin hypercube sampling is used to generate random numbers, and new runoff values ​​are simulated based on the previous M-1 runoff values.

[0010] Further optimization, the mixed Copula expression established in step S2 is as follows:

[0011] Where N is the number of Copulas; C mix (u1,u2,...,u n ) is a mixed Copula; C i (u1,u2,...,u n θ i ) is the i-th mixed copula type; is the i-th weight parameter; is the copula parameter of the i-th copula.

[0012] Further optimization, the intelligent knowledge set expression of the Copula parameters and weight parameters established in step S2 is as follows:

[0013] Where M is the number of samples; D is the Copula dimension; θ i,t is the Copula parameter of the i-th Copula at the j-th moment; ω i,t is the weight parameter of the i-th Copula at the j-th moment; Λ is the conversion function; u x,j is the cumulative distribution function value of the j-th sample at the x-th moment; the rest are constants.

[0014] Further optimization, the optimization target of the cooperative search algorithm in step S3 is as follows:

[0015] Where 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 sample empirical joint distribution; C(g) is the sample theoretical joint distribution; n m,g,...,k To satisfy X≤x i1 ,X≤x i2 ,...,X≤x iM The number of samples.

[0016] Further optimization, the steps of the cooperative search algorithm in step S3 are as follows:

[0017] S3.1: Generate the initial employees according to the following formula. After evaluating the objective functions of all schemes, M∈[1,I] leaders will be selected from the initial population to form an external elite set.

[0018] Where I is the number of solutions in the current population; is the jth position of the ith individual in the kth iteration; φ(L,U) is a function that generates uniformly distributed random numbers in [L,U].

[0019] S3.2: Considering that every employee can obtain new information by exchanging information with the chairman, the board of directors, and the leaders of the board of supervisors, the team communication process consists of three parts: the chairman's knowledge A, the collective knowledge of the board of directors B, and the collective knowledge of the board of supervisors C. The chairman is randomly selected from the board of directors to simulate a rotation mechanism, while all members of the board of directors and the board of supervisors are assigned the same position when calculating B and C.

[0020] In the formula, is the jth value of the i-th individual in the k+1th iteration; is the jth value of the optimal solution of the i-th individual in the k-th generation; The jth value of the indth global optimal solution from the beginning to the kth generation, where ind is a randomly selected index from the set {1,2,...,M}; represents the knowledge gained by randomly selecting a chair from an external elite set; and are the average knowledge of the M global optimal solutions and I individual optimal solutions found so far; α and β are the adjustment and The learning coefficient of the influence degree.

[0021] S3.3: In addition to learning from leaders, employees also need to summarize their own experiences in the opposite direction to acquire new knowledge, as shown below:

[0022] In the formula, The jth value of the i-th reflected solution in the k+1th iteration.

[0023] S3.4: The team gradually improves its market competitiveness by ensuring that all high-performing employees are protected, as follows:

[0024] Where F(x) is the fitness of the solution.

[0025] Further optimization, the Copula expression of the conditions required for daily runoff simulation in step S4 is as follows:

[0026] Where ε is the random number obtained by Latin hypercube sampling; C cond (u j |u j-1 ,...,u j-t ) is given by u j-1 ,...,u j-t In this case, j According to the marginal distribution obtained in step S1, calculate u j Inverse function X j =F -1 (u j ) to obtain the required simulated runoff value.

[0027] Compared with the prior art, the beneficial technical effects of the above technical solutions adopted in the present invention are as follows: ① In order to solve the problem of too many mixed Copula parameter sets, a dimensionality reduction method based on a smart 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 the samples in each two-dimensional variable space as the driving variable, the smart knowledge set of each parameter of the mixed 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 In view of the low efficiency and low precision of traditional mixed Copula parameter estimation, the present invention adopts the CSA algorithm for parameter estimation, avoids the construction of a complex maximum likelihood equation group, improves the parameter calibration accuracy, and reduces the parameter calibration time. ③ The runoff simulation method proposed in the present invention combines the smart knowledge set with CSA, and obtains the runoff simulation result by conditional distribution sampling. Compared with the traditional method, this method has faster calculation speed and higher fitting accuracy, and significantly improves the efficiency and accuracy of runoff simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 The present invention is a flow chart of the intelligent simulation method for water project runoff scheduling.

[0029] Figure 2The figure shows the fitting effect and QQ graph of single Copula and Copula of the present invention.

[0030] Figure 3 It is the parameter error strip diagram and QQ diagram of the Copula simulation results of the present invention. DETAILED DESCRIPTION

[0031] In order to better understand the technical content of the present invention, specific embodiments are given and described as follows in conjunction with the accompanying drawings.

[0032] In the present invention, various aspects of the present invention are described with reference to the accompanying drawings. The embodiments of the present invention are not limited to those described in the accompanying drawings. It should be understood that the present invention is implemented by any of the various concepts and embodiments introduced above, as well as the concepts and implementations described in detail below, because the concepts and embodiments disclosed in the present invention are not limited to any implementation. In addition, some aspects disclosed in the present invention can be used alone or in any appropriate combination with other aspects disclosed in the present invention.

[0033] refer to Figure 1 The present invention provides a method for intelligent simulation of water project runoff scheduling, comprising the following steps:

[0034] S1. Based on historical runoff data, data features were extracted, the mean, skewness coefficient and coefficient of variation of the data were determined using the moment method, and the daily runoff frequency curve was constructed using the P-Ⅲ curve.

[0035] S2. Based on the historical runoff data, the Manhattan distance of runoff on different days is calculated as the driving variable, a time series model is constructed, and the intelligent knowledge set of each parameter in the M-dimensional hybrid Copula set is established. The expressions of the hybrid Copula model and the intelligent knowledge set of each parameter are as follows:

[0036] Where N is the number of Copulas; M is the number of samples; D is the Copula dimension; C mix (u1,u2,...,u n ) is a mixed Copula; C i (u1,u2,...,u n θ i ) is the i-th mixed Copula type; θ i,t is the Copula parameter of the i-th Copula at the j-th moment; ω i,t is the weight parameter of the i-th Copula at the j-th moment; Λ is the conversion function; u x,j is the cumulative distribution function value of the j-th sample at the x-th moment; the rest are constants.

[0037] S3. To determine the parameters of the wisdom knowledge set, the present invention uses CSA to optimize the parameters of the wisdom knowledge set, and the optimization objective function is to minimize the Akaike information criterion, which is expressed as follows:

[0038] Where 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 sample empirical joint distribution; C(g) is the sample theoretical joint distribution; n m,g,...,k To satisfy X≤x i1 ,X≤x i2 ,...,X≤x iM The number of samples.

[0039] The steps for CSA parameter optimization are as follows:

[0040] S3.1: Generate the initial employees according to the following formula. After evaluating the objective functions of all schemes, M∈[1,I] leaders will be selected from the initial population to form an external elite set.

[0041] Where I is the number of solutions in the current population; is the jth position of the ith individual in the kth iteration; φ(L,U) is a function that generates uniformly distributed random numbers in [L,U].

[0042] S3.2: Considering that every employee can obtain new information by exchanging information with the chairman, the board of directors, and the leaders of the board of supervisors, the team communication process consists of three parts: the chairman's knowledge A, the collective knowledge of the board of directors B, and the collective knowledge of the board of supervisors C. The chairman is randomly selected from the board of directors to simulate a rotation mechanism, while all members of the board of directors and the board of supervisors are assigned the same position when calculating B and C.

[0043] In the formula, is the jth value of the i-th individual in the k+1th iteration; is the jth value of the optimal solution of the i-th individual in the k-th generation; is the jth value of the indth global optimal solution from the beginning to the kth generation, where ind is an index randomly selected from the set {1, 2, ..., M}; represents the knowledge gained by randomly selecting a chair from an external elite set; and are the average knowledge of the M global optimal solutions and I individual optimal solutions found so far; α and β are the adjustment and The learning coefficient of the influence degree.

[0044] S3.3: In addition to learning from leaders, employees also need to summarize their own experiences in the opposite direction to acquire new knowledge, as shown below:

[0045] In the formula, The jth value of the i-th reflected solution in the k+1th iteration.

[0046] S3.4: The team gradually improves its market competitiveness by ensuring that all high-performing employees are protected, as follows:

[0047] Where F(x) is the fitness of the solution.

[0048] Based on the Bayesian rule, a mixed conditional Copula set is established, Latin hypercube sampling is used to generate random numbers, and new runoff values ​​are simulated based on the previous M-1 runoff values. The conditional Copula calculation formula is as follows:

[0049] Where ε is the random number obtained by Latin hypercube sampling; C cond (u j |u j-1 ,...,u j-t ) is given by u j-1 ,...,u j-t In this case, j According to the marginal distribution obtained in step S1, calculate u j Inverse function X j =F -1 (u j ) to obtain the required simulated runoff value.

[0050] A hydrological station was taken as the research object, and the three-dimensional Copula was used as an example to test the performance of the method. The runoff simulation method proposed in the present invention, the traditional single Copula and the traditional mixed Copula runoff simulation method were used to perform runoff simulation, and the model construction and simulation results were compared. Table 1 is a comparison of the single three-dimensional Clayton Copula, Gumbel Copula, traditional mixed Copula and the method proposed in the present invention (mixed CSA_Copula) in model construction. The first three types of traditional Copula models use the maximum likelihood method for parameter calibration. Among them, RMSE represents the root mean square error, and AIC represents the Akaike information criterion. Figure 2The three types of Copula and the empirical joint distribution QQ graph and the mixed Copula density graph are displayed. Compared with the traditional method, the method of the present invention effectively reduces the number of parameters and improves the joint distribution fitting accuracy, as shown in Table 1. Compared with the traditional maximum likelihood estimation method, this method constructs an intelligent knowledge base for each parameter in the three-dimensional mixed Copula set, and uses the CSA algorithm to calibrate the parameters to avoid solving complex maximum likelihood equations. The mixed Copula construction method proposed in the present invention simplifies parameter estimation and improves the accuracy of Copula model construction.

[0051] Table 1 Fitting accuracy, number of parameters and calibration time of different types of Copula

[0052] Table 2 shows the differences between the daily runoff statistical parameters simulated by different types of Copula and the measured runoff statistical parameters. Figure 3 The prediction strip chart and QQ chart of various statistical indicators are displayed. Overall, the indicators obtained by the method proposed in the present invention are better than those of the traditional Copula, indicating that the daily runoff simulated by the method of the present invention can retain the characteristics of the measured data and show high reliability.

[0053] Table 2 Daily runoff statistical parameters obtained from different types of Copula simulations

[0054] Although the present invention has been described above with preferred embodiments, it is not intended to limit the present invention. A person skilled in the art of the present invention may make various modifications and improvements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the definition of the claims.

Claims

1. A method for intelligent simulation of runoff in water project scheduling, characterized in that: The steps include: S1. Based on historical runoff data, extract data features, use the moment method to determine the mean, skewness coefficient and coefficient of variation of the data, and use the P-Ⅲ curve to construct the daily runoff frequency curve; S2. Based on the historical runoff data, a time series model is constructed, the Manhattan distance of runoff on different days is calculated as the driving variable, and the intelligent knowledge set of each parameter in the M-dimensional mixed Copula set is established; S3. Use cooperative search algorithm to minimize the theoretical distribution and the empirical distribution Akaike information criterion, and calibrate the parameters of the wisdom knowledge set; S4. Based on the Bayesian rule, a mixed conditional Copula set is established, Latin hypercube sampling is used to generate random numbers, and new runoff values ​​are simulated based on the previous M-1 runoff values.

2. According to claim 1, a water project scheduling runoff intelligent simulation method is characterized in that: The mixed Copula expression established in step S2 is as follows: Where N is the number of Copulas; C mix (u1,u2,...,u n ) is a mixed Copula; C i (u1,u2,...,u n θ i ) is the i-th mixed Copula type; ω i is the i-th weight parameter; θ i is the Copula parameter of the ith Copula.

3. The method for intelligent simulation of runoff in water project scheduling according to claim 2 is characterized in that: The smart knowledge set expressions of the Copula parameters and weight parameters established in step S2 are as follows: Where M is the number of samples; D is the Copula dimension; θ i,t is the Copula parameter of the i-th Copula at the j-th moment; ω i,t is the weight parameter of the i-th Copula at the j-th moment; Λ is the conversion function; u x,j is the cumulative distribution function value of the j-th sample at the x-th moment; the rest are constants.

4. The method for intelligent simulation of runoff in water project scheduling according to claim 3 is characterized in that: The optimization goal of the cooperative search algorithm in step S3 is as follows: Where 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 sample empirical joint distribution; C(g) is the sample theoretical joint distribution; n m,g,...,k To satisfy X≤x i1 ,X≤x i2 ,...,X≤x iM The number of samples.

5. The method for intelligent simulation of runoff in water project scheduling according to claim 4 is characterized in that: The steps of the cooperative search algorithm in step S3 are as follows: S3.1: Generate the initial employees according to the following formula. After evaluating the objective functions of all schemes, M∈[1,I] leaders will be selected from the initial population to form an external elite set; Where I is the number of solutions in the current population; is the jth position of the ith individual in the kth iteration; φ(L,U) is a function that generates random numbers that conform to uniform distribution in [L,U]; S3.2: Considering that every employee can obtain new information by exchanging information with the chairman, the board of directors, and the leaders of the board of supervisors; the team communication process consists of three parts: the chairman's knowledge A, the board of directors' collective knowledge B, and the board of supervisors' collective knowledge C; the chairman is randomly selected from the board of directors to simulate a rotation mechanism, while all members of the board of directors and the board of supervisors are assigned the same position when calculating B and C; In the formula, is the jth value of the ith individual in the k+1th iteration; is the jth value of the optimal solution of the i-th individual in the k-th generation; is the jth value of the indth global optimal solution from the beginning to the kth generation, where ind is an index randomly selected from the set {1, 2, ..., M}; represents the knowledge gained by randomly selecting a chair from the external elite set; and are the average knowledge of the M global optimal solutions and I individual optimal solutions found so far; α and β are the adjustment and The learning coefficient of the impact degree; S3.3: In addition to learning from leaders, employees also need to summarize their own experiences in the opposite direction to acquire new knowledge, as shown below: In the formula, The jth value of the i-th reflected solution in the k+1th iteration; S3.4: The team gradually improves its market competitiveness by ensuring that all high-performing employees are protected, as follows: Where F(x) is the fitness of the solution.

6. The method for intelligent simulation of runoff in water project scheduling according to claim 5 is characterized in that: The Copula expression of the conditions required for daily runoff simulation in step S4 is as follows: Where ε is the random number obtained by Latin hypercube sampling; C cond (u j |u j-1 ,...,u j-t ) is given by u j-1 ,...,u j-t In this case, j The conditional probability of u is calculated according to the marginal distribution obtained in step S1. j Inverse function X j =F -1 (u j ) to obtain the required simulated runoff value.

Images