CN113159405B - Wind power prediction method for optimizing LSSVR (least Square support vector regression) based on improved satin blue gardener algorithm - Google Patents

Abstract

The invention belongs to the technical field of wind power, and particularly relates to a wind power prediction method for optimizing LSSVR (least square support vector regression) based on an improved satin blue gardener algorithm. The invention provides an LSSVR wind power ultra-short-term prediction method based on secondary decomposition and ISBO optimization parameters, which considers the complexity of a model training process and prediction, constructs a secondary decomposition strategy based on secondary decomposition and t-mean test, and carries out decomposition, dynamic division and reconstruction processing on an original wind power sequence; in order to improve the population diversity and the algorithm convergence degree of the satin blue gardener algorithm in the iterative process, the standard satin blue gardener algorithm is improved, two parameters of a least square support vector regression model are optimized by utilizing the improved satin blue gardener algorithm, and a wind power LSSVR prediction model with excellent performance is established.

Description

Wind power prediction method for optimizing LSSVR (least Square support vector regression) based on improved satin blue gardener algorithm

Technical Field

The invention belongs to the technical field of wind power, and particularly relates to a wind power prediction method for optimizing LSSVR (least square support vector regression) based on an improved satin blue gardener algorithm.

Background

With the rapid development of the wind power market, the installed capacity of wind power and the generated energy of wind power are continuously increased. Due to the random fluctuation of the wind power, the safety, controllability and economy of the power system are seriously affected by large-scale wind power integration. By establishing a high-performance wind power prediction system, the wind power at the future moment is accurately predicted, and large-scale wind power can be effectively and stably accessed into a power network. The historical wind power data is considered to be a time sequence with fluctuation characteristics, a signal decomposition technology and machine learning are combined, the method is applied to wind power prediction, the generalization capability of a prediction model can be enhanced, and the accuracy of wind power prediction can be greatly improved.

Based on the time scale characteristics of the original signal sequence, the empirical mode decomposition EEMD is integrated to realize adaptive decomposition, so that the decomposition method is favorable for processing the nonlinear and non-stable wind power signal sequence. And aiming at the subsequences generated after EEMD decomposition, a prediction model is respectively established, so that wind power prediction can be easily realized. The highest frequency subsequence IMF1 produced by EEMD still fluctuates considerably. Therefore, it is considered in the literature that the high frequency sequence generated by the EEMD is decomposed twice, so that the prediction difficulty of the high frequency sequence can be effectively reduced.

The literature: liu Hui, Duan Zhu, Wu Haiping, et al, wind speed for estimating the model based on data decoding, feature selection and group method of data handling network [ J ]. measuring element, 2019,148:1-12. calculating EEMD by using sample entropy to generate entropy value of each wind speed subsequence, dividing the inherent mode function IMFs subsequence by the median value of each subsequence entropy, dividing each sequence before the corresponding median value into high frequency bands, dividing each sequence after the median value into low frequency bands, reconstructing the high frequency band subsequence into high frequency components by a superposition mode, and performing secondary decomposition on the high frequency components by wavelet packet decomposition to obtain a plurality of subcomponents with moderate fluctuation;

the literature: 697-720. Wind Power sub-sequences generated by EEMD are divided by using arrangement entropy, the random degree of each sequence is judged according to the arrangement entropy of adjacent sub-sequences, 12 sub-sequences generated by EEMD are divided into 4 parts, and then the 4 parts of sub-sequences are reconstructed by an overlapping mode to obtain 4 Wind Power sub-components for model training and reducing the complexity of Prediction;

the literature: zhang Xin Lei, Li Gen. short-term wind power multistep prediction method [ J ] electric measurement and instrument based on IEEMD and LS-SVM combination, 2020,57(6):52-60. through constructing the improved EEMD method, decompose the original wind power into a series of IMFs subsequence, Re component, adopt the run length decision method to carry on screening division to subsequence, reconstruct into high, middle, low frequency three kinds of frequency bands, and set up LSSVR prediction model to the component of different frequency bands, have reduced the complexity of model training and prediction;

the literature: the method comprises the following steps of (1) carrying out a self-adaptive weight-based satin blue gardener optimization algorithm [ J ] on the basis of a Luxiayi technology, Liu Sheng, Korea Fii, and the like, (J) carrying out an intelligent computer and application, 2018,8(6): 94-100), providing an adaptive weight-based improved satin blue gardener algorithm WSBO, and verifying the feasibility of the WSBO algorithm through a unimodal and multimodal test function;

the literature: research on LS-SVM wind speed prediction method based on PSO parameter optimization [ J ]. Chinese Motor engineering journal, 2016,36(23): 6337-;

the literature: the super-short-term wind power combination prediction [ J ] of the power grid technology based on the CEEMD-SBO-LSSVR, 2021,45(03):855-864. the SBO algorithm is adopted to optimize two parameters of the LSSVR, the CEEMD-SBO-LSSVR super-short-term wind power prediction method is provided, and the prediction accuracy is high;

the methods proposed by the above documents have disadvantages, the artificial subjectivity of the IMFs subsequence division is strong by using the sample entropy and the permutation entropy, and the run length judgment method divides the subsequence under a given threshold value; the SBO algorithm and the WSBO algorithm have low speed at the initial stage of searching parameters and poor global optimization capability; when the parameters of the LSSVR model are optimized by utilizing the particle swarm optimization, the LSSVR model is easy to fall into local optimization, so that the performance of the established wind speed prediction model is poor.

Disclosure of Invention

The invention aims to provide an LSSVR wind power ultra-short term prediction method based on secondary decomposition and ISBO optimization parameters, which can effectively solve the problems that parameters are difficult to determine when a wind power prediction model is established by using least square support vector regression, and model training and prediction complexity are high when a secondary decomposition method is used for deeply excavating wind power time sequence characteristics.

The technical scheme of the invention is as follows:

a wind power prediction method for optimizing LSSVR based on an improved satin blue gardener algorithm is characterized by comprising the following steps:

s1, wind power data of the prediction target are obtained, and the wind power data are converted into sub-components, intermediate-frequency components and low-frequency components after being processed, wherein the specific method comprises the following steps:

the wind power is decomposed once by decomposing EEMD by adopting an ensemble empirical mode, and the decomposition result of EEMD on the target s (t) is as follows:

wherein f is_i(t) is the ith IMF component, r_n(t) is the Re component, n represents the number of IMFs;

after primary decomposition is carried out on original wind power data through EEMD, IMFs and Re subsequences with the frequency from high to low are generated;

performing secondary decomposition on the IMF1 subsequence by adopting Wavelet Packet Decomposition (WPD), specifically performing 3-layer WPD on IMF1 to obtain W₁～W₈A total of 8 sub-components;

dynamically dividing IMF 2-IMFn and Re subsequences by using a t-mean value inspection method to obtain two subsequences of a middle frequency band and a low frequency band, and then respectively superposing the two subsequences in a superposition mode to respectively reconstruct an intermediate frequency component sequence and a low frequency component sequence;

s2, respectively carrying out normalization processing on the component sequences obtained in the step S1:

wherein x and x' respectively represent wind power sub-sequence data and normalized wind power sub-sequence data, and x_maxAnd x_minRespectively the maximum value and the minimum value in the selected sub-sequence data set;

selecting data from the normalized component sequences as a training set, and respectively constructing input and output matrixes of the components, specifically:

the method comprises the following steps of reconstructing a phase space of a wind power sequence at the continuous sampling moment of each component sequence, converting the phase space into an input matrix and an output matrix, setting a phase space embedding dimension m, and taking single-step prediction of the wind power as an example, constructing the input matrix and the output matrix of a training set as follows:

x, Y is the input and output matrix of a component sequence, M is the number of training set, X is the matrix of (M-M) X M, Y is the matrix of (M-M) X1, the input of the ith row in X is a matrix composed of X_i,x_i+1,x_i+2,…,x_i+m-1The output of the ith row in the corresponding Y is x_i+m；

S3, constructing respective Least Squares Support Vector Regression (LSSVR) models by using the input and output matrixes of the component sequences obtained in the step S2:

where γ is the regularization parameter, σ is the kernel width, x_iAnd

respectively the true value and the predicted value of the wind power output at the ith moment, gamma_min、γ_maxRespectively minimum and maximum values, sigma, of a set regularization parameter_min、σ_maxAre respectively setMinimum and maximum kernel function widths of (1);

s4, optimizing the regularization parameter gamma and the kernel function width sigma of the model constructed in the step S3 by adopting an improved satin blue gardener algorithm to obtain the optimized regularization parameter gamma and the optimized kernel function width sigma;

s5, substituting the optimized parameters obtained in the step S4 into the model established in the step S3 to obtain an LSSVR prediction model of each component sequence, and training the prediction model according to the training set obtained in the step S2 to obtain a trained prediction model;

s6, inputting the real-time data of the prediction target into the trained prediction model to obtain the wind power prediction values of the components, and respectively carrying out reverse normalization processing to obtain the prediction values of the components after reverse normalization:

x＝x′(x_max-x_min)+x_min

wherein x and x' respectively represent wind power sub-sequence data and normalized wind power sub-sequence data, and x_maxAnd x_minRespectively the maximum value and the minimum value in the selected sub-sequence data set;

and respectively superposing the predicted values of the components at corresponding moments to obtain the final predicted value of the ultra-short-term wind power at each moment.

Further, in step S4, an improved satin blue gardener algorithm is used for the optimization, and the specific method is as follows:

a) initializing relevant parameters of the SBO of the satin blue gardener algorithm, including the nest number N, the step length upper limit alpha, the variation probability p and the maximum iteration number t of the initialized SBO_maxProportional coefficient z, standard deviation s in individual variation, dimension of variable to be optimized and upper and lower limits V of variable to be optimized_MAX、V_MIN；

b) Randomly initializing chaotic vectors, introducing a chaotic sequence with ergodicity and randomness into the initialization of a satin blue gardener nest, and initializing the population of an SBO algorithm by adopting chaotic cube mapping, wherein the chaotic cube mapping formula is as follows:

y_n+1＝4y_n ³-3y_n

wherein-1. ltoreq. y_n≤1,n＝0,1,2…；

The method for realizing the population initialization of the satin blue gardener algorithm by introducing the chaotic sequence comprises the following steps:

(i) setting the maximum iteration times N-1 and the population size N;

(ii) randomly generating a D-dimensional initial vector Y₁＝(y₁₁,…,y_1j,…,y_1D) Wherein, y_1j∈[-1,1]J is not less than 1 and not more than D, and Y₁≠0；

(iii) Will Y₁Substituting into chaotic cubic mapping formula to iterate for N-1 times to obtain N chaotic vectors, Y_i＝(y_i1,y_i2,…,y_iD),i＝1,2,…,N；

(iv) The obtained chaos vector Y is obtained_iMapping to the search space by:

wherein, y_ijIs the j-th coordinate, x, of the i-th cell_ijAs a population position X_iJ-dimensional coordinate of middle ith nest, U_j、L_jAre j dimension population positions X respectively_iUpper and lower bounds of (1);

obtaining N population positions X_i＝(x_i1,x_i2,…,x_iD) 1,2, …, N as initial data of the improved satin blue gardener algorithm;

obtaining a chaotic vector through cubic mapping, and mapping the chaotic vector to a search space, thereby obtaining an initial population X of N nests ═ X₁,X₂,…,X_N}；

c) By a fitness function f (x)_i) Calculating the cost function value F of all the nest individuals_iProbability p of all nest individuals being selected_i：

In the formula, f (x)_i) The fitness function value of the ith nest is 1,2, …, N;

cost function value F for all nest individuals_iSorting from small to large, and taking the minimum value F_minCorresponding nest position X_minAs the current best nest position X_eliteAnd remain to the next generation;

d) defining an adaptive weight ω, wherein the weight ω changes in a linear decreasing form in the first half of the iteration period, and the weight ω changes in a convex function form in the second half of the iteration period:

in the formula, t_maxIs the maximum iteration number of the ISBO algorithm, t is the current iteration number, omega_max、ω_minThe maximum value and the minimum value of the weight are respectively;

in the improved SBO algorithm, the male bird updates the nest point position of the t round through continuous communication learning

The updated nest point position is obtained

The expression is as follows:

in the formula, x_kjCurrent random search for male satin blue gardenersTo the j-th element of the best nest, k is the probability of being selected from all individual nests, p_iA nest serial number obtained under a roulette selection mechanism; p is a radical of_kThe probability that the nest corresponding to the sequence number k is selected is shown, wherein k is 1, … and N; x is the number of_elite,jThe j-th element of the best nest in the whole population;

j is the jth dimension element of the current wheel nest position, wherein j is 1, … and D; lambda [ alpha ]_jStep size factor of j dimension element; omega is adaptive weight; alpha is the upper limit of the step length;

e) introducing mutation operators, and randomly mutating the nests in a probability distribution manner to obtain the positions of the mutated nests

The variant expression is as follows:

s＝z×(V_MAX-V_MIN)

wherein s is the standard deviation; z is a proportionality coefficient; n (0,1) is a random number of a standard normal distribution, V_MAX、V_MINThe upper and lower boundaries of the nest position respectively;

f) and (c) searching the optimal nest position in all the populations before and after the variation, returning to the step c to continue the iteration until the maximum iteration times is met, stopping the iteration, and taking the finally found optimal nest position as a parameter value to be optimized and selected.

The invention has the beneficial effects that: the invention provides an LSSVR wind power ultra-short-term prediction method based on secondary decomposition and ISBO optimization parameters, which considers the complexity of a model training process and prediction, constructs a secondary decomposition strategy based on secondary decomposition and t-mean test, and carries out decomposition, dynamic division and reconstruction processing on an original wind power sequence; in order to improve the population diversity and the algorithm convergence degree of the satin blue gardener algorithm in the iterative process, the standard satin blue gardener algorithm is improved, two parameters of a least square support vector regression model are optimized by utilizing the improved satin blue gardener algorithm, and a wind power prediction model with excellent performance is established.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a flow chart of a regression model for ISBO optimization of LSSVR in accordance with the present invention;

FIG. 3 is a graph of the convergence of the ISBO and other comparative optimization algorithms of the present invention on a standard test function, where (a) is f₁Comparison of the function convergence curves, (b) is f₂Comparison of the function convergence curves, (c) is f₃Comparison of the function convergence curves, (d) is f₄Comparison of the function convergence curves, (e) is f₅Comparison of the function convergence curves, where (f) is f₆Comparison of the function convergence curves, (g) is f₇Comparison of the function convergence curves, (h) is f₈Comparing function convergence curves;

FIG. 4 is a WPD secondary decomposition validity verification result diagram of the IMF1 subsequence, (a) is a prediction result of an IMF1 subsequence test set under ISBO-LSSVR and WPD-ISBO-LSSVR models respectively, and (b) is a prediction error needle diagram of an IMF1 subsequence test set under ISBO-LSSVR and WPD-ISBO-LSSVR models;

FIG. 5 is a prediction result graph of the QDS-ISBO-LSSVR and other comparative models in the test set, (a) is prediction results (1 month) of the prediction models of the single model LSSVR and the same optimization algorithm in different decomposition modes, (b) is prediction results (1 month) of the prediction models of the different optimization algorithms in the QDS decomposition mode, (c) is prediction results (7 months) of the prediction models of the single model LSSVR and the same optimization algorithm in different decomposition modes, and (d) is prediction results (7 months) of the prediction models of the different optimization algorithms in the QDS decomposition mode.

Detailed Description

The invention is described in detail below with reference to the figures and examples.

As shown in FIG. 1, the invention relates to an LSSVR wind power ultra-short term prediction method based on secondary decomposition and ISBO optimization parameters, which specifically comprises the following steps:

step one, considering the random fluctuation of an original wind power sequence, constructing a secondary decomposition strategy QDS based on secondary decomposition and t-mean value detection, and comprising the following steps:

1) performing primary decomposition on the wind power by adopting Ensemble Empirical Mode Decomposition (EEMD); the ensemble empirical mode decomposition adds Gaussian white noise to the whole time-frequency space for multiple times aiming at the mode aliasing phenomenon existing in the empirical mode decomposition, can adaptively decompose a given complex signal s (t) into a series of IMFs with stable signal characteristics and a residual component Re, and the EEMD decomposition result is as follows:

wherein f is_i(t) is the ith IMF component, r_n(t) is the Re component, n represents the number of IMFs;

white noise with standard deviation of 0.2 and collection frequency of 100 is added into the EEMD, and the EEMD is adopted to carry out primary decomposition on an original wind power sequence to generate IMFs and Re subsequences with frequencies from high to low;

2) considering that the volatility of the highest-frequency subsequence IMF1 generated by EEMD is large, the wavelet packet decomposition WPD is adopted to carry out secondary decomposition on the IMF1 subsequence, and because the decomposition of each layer of the WPD is to decompose the signal of the previous layer into high-frequency components and low-frequency components, namely the number of the components generated by each layer is 2ⁱ(i is the number of decomposition layers), so the number of generated components increases as the number of decomposition layers increases; theoretically, when the WPD is decomposed into 3 layers, the wavelet packet can approach any nonlinear function, and engineering application is met; with the increase of the number of generated components, the modeling complexity during training of each component is increased, and meanwhile, the WPD decomposition fineness is considered, so that the 3-layer WPD decomposition is performed on the IMF1 to obtain W₁～W₈A total of 8 sub-components;

3) because each subsequence generated by EEMD has the characteristic that the mean value is approximately 0, and the frequency of each subsequence is sequentially reduced and mutually independent, the dynamic division is carried out on the IMF 2-IMFn and Re subsequences by utilizing a t-mean value inspection method to obtain two subsequences of a middle frequency band and a low frequency band, and then the two subsequences are respectively superposed in a superposition mode and are respectively reconstructed into a middle frequency component sequence and a low frequency component sequence;

the t test is a hypothesis test method, the probability p of sample difference occurrence is represented by a t distribution theory, and the p value is used for reflecting whether the sample difference has statistical significance and reflecting the degree of accepting the minimum significance level of the original hypothesis; therefore, using the t-test, it can be inferred whether there is a significant difference between the mean of a population of samples and the assumed test value; generally, when p is greater than 0.05, the difference is not significant, and the larger the value of p is, the more sufficient the reason for accepting the original hypothesis is;

the invention uses t test to carry out zero-mean hypothesis test on each IMF subsequence, and sets two-sided hypothesis: primitive hypothesis H₀: the mean value of the IMF components is 0; alternative hypothesis H₁: the mean value of IMF components is not equal to 0, and the significance level is 5%; that is, when the p value is greater than the set significance level, the original hypothesis H is accepted₀(ii) a Otherwise, accepting alternative hypothesis H₁；

Performing t-test on the mean difference of each IMF subsequence at the significance level of 5%, and when the p value of each subsequence starting from IMF2 is tested to be more than the significance level of 5%, the subsequences meet the 0-mean hypothesis; when a sequence has a first occurrence of a p-value with a significance level of less than 5%, the subsequence does not satisfy the 0-mean hypothesis, and is referred to as a critical sequence IMF_d(d is the sequence number of the subsequence) as the boundary point between the middle frequency band and the low frequency band of the IMFs subsequence, so that the IMFs 2-IMFs_d-1Dynamically dividing the subsequences into intermediate frequency bands, and performing IMF_dThe IMFn and Re subsequences are dynamically divided into low frequency bands;

overlapping the subsequences of the middle frequency band and the low frequency band obtained by the t-mean test division in a superposition mode, and reconstructing respectively to obtain 1 middle frequency component and 1 low frequency component;

in specific implementation, for example, wind power data of a certain wind power plant in 1 month is selected, and sampling time intervals are 1 hour;

step two, normalizing each component sequence obtained in the step one, as shown in formula (2):

wherein x and x' respectively represent wind power sub-sequence data and normalized wind power sub-sequence data, and x_maxAnd x_minRespectively the maximum value and the minimum value in the selected sub-sequence data set;

taking the data of the last two days of each normalized component sequence as a test set of the corresponding component, taking the residual data as a training set of the corresponding component, and respectively constructing an input matrix and an output matrix of each component as follows:

the method comprises the following steps of reconstructing a phase space of a wind power sequence at the continuous sampling moment of each component sequence, converting the phase space into an input matrix and an output matrix, setting a phase space embedding dimension m, and taking single-step prediction of the wind power as an example, constructing the input matrix and the output matrix of a training set as follows:

wherein X, Y is the input and output matrix of a component sequence, M is the number of training sets, X is the matrix of (M-M) X M, Y is the matrix of (M-M) X1, and the input of the ith row in X is a matrix composed of X_i,x_i+1,x_i+2,…,x_i+m-1The output of the ith row in the corresponding Y is x_i+mSet m to 6.

Thirdly, constructing respective Least Square Support Vector Regression (LSSVR) models by using the input and output matrixes of the component sequences obtained in the second step, wherein the LSSVR models are as follows:

LSSVR is an optimization problem with constraints:

in the formula, omega is a weight vector; e is an error variable; gamma is a regularization parameter.

The regression function established using LSSVR is:

in the formula, alpha_iIs Lagrange multiplier; b is a bias vector; k (x, x)_i) For the kernel function, the radial basis kernel function is chosen as follows:

wherein σ is the kernel function width;

establishing an LSSVR regression model of each component with regularization parameters gamma and kernel function width sigma as main parameters by using the input and output matrixes of each component sequence constructed in the step two and combining the formulas (4) to (6);

the fitness function of the LSSVR in the training learning process is given as follows:

in the formula, x_iAnd

respectively the true value and the predicted value of the wind power output at the ith moment, gamma_min、γ_maxRespectively minimum and maximum values, sigma, of a set regularization parameter_min、σ_maxRespectively the minimum value and the maximum value of the set kernel function width;

fourthly, aiming at the optimization problem of the regularization parameter gamma and the kernel function width sigma in the LSSVR model of each component sequence, constructing an improved satin blue gardener algorithm ISBO, as shown in FIG. 2, specifically as follows:

1) initializing relevant parameters of the SBO of the satin blue gardener algorithm, including the nest number N, the step length upper limit alpha, the variation probability p and the maximum iteration number t of the initialized SBO_maxProportional coefficient z, standard deviation s in individual variation, dimension of variable to be optimized and upper and lower limits V of variable to be optimized_MAX、V_MIN；

2) The chaotic vector is initialized randomly, and a chaotic sequence with ergodicity and randomness is introduced into the initialization of a satin blue garden bird nest to improve the diversity of the positions of the chaotic vector, the chaotic cube mapping is adopted to initialize the population of an SBO algorithm, and the chaotic cube mapping formula is as follows:

the method for realizing the population initialization of the satin blue gardener algorithm by introducing the chaotic sequence comprises the following steps:

(i) setting the maximum iteration times N-1 and the population size N;

(ii) randomly generating a D-dimensional initial vector Y₁＝(y₁₁,…,y_1j,…,y_1D) Wherein, y_1j∈[-1,1]J is not less than 1 and not more than D, and Y₁≠0；

(iii) Will Y₁The substitution formula (8) iterates for N-1 times to obtain N chaotic vectors Y_i＝(y_i1,y_i2,…,y_iD),i＝1,2,…,N；

(iv) The obtained chaos vector Y is obtained_iMapping to a search space by the formula (9) to obtain N population positions X_i＝(x_i1,x_i2,…,x_iD) 1,2, …, N as initial data of the improved satin blue gardener algorithm;

in the formula, y_ijIs the j-th coordinate, x, of the i-th cell_ijAs a population position X_iJ-dimensional coordinate of middle ith nest, U_j、L_jAre j dimension population positions X respectively_iUpper and lower bounds of (1);

obtaining a chaotic vector through cubic mapping of a formula (8), and mapping the chaotic vector to a search space by using a formula (9) to obtain an initial population X of N nests ═ X₁,X₂,…,X_N}；

3) By a fitness function f (x)_i) Calculating the cost function value F of all the nest individuals_iProbability p of all nest individuals being selected_iRespectively shown in formulas (10) and (11):

in the formula, f (x)_i) The fitness function value of the ith nest is 1,2, …, N;

cost function value F for all nest individuals_iSorting from small to large, and taking the minimum value F_minCorresponding nest position X_minAs the current best nest position X_eliteAnd remain to the next generation;

4) self-adaptive weight is introduced into the swarm intelligent optimization algorithm, so that the balance between global search and local search of the optimization algorithm can be realized; the self-adaptive weight omega is defined, and when the weight omega changes in a linear decreasing mode in the first half of the iteration period of the optimization algorithm, the optimization algorithm is ensured to have global search capability in the initial iteration stage when the weight omega is larger, and the speed of searching the global optimal solution by the algorithm is properly accelerated; when in the second half of the iteration period of the optimization algorithm, the weight ω changes in the form of a convex function to ensure the convergence speed of the optimization algorithm, as shown in equation (12):

in the formula, t_maxIs the maximum iteration number of the ISBO algorithm, t is the current iteration number, omega_max、ω_minThe maximum value and the minimum value of the weight are respectively;

in the improved SBO algorithm, the male bird updates the nest point position of the t-th round through continuous communication learning

The updated nest point position is obtained

The expression is as follows:

in the formula, x_kjThe j-th dimension element of the best nest randomly searched currently for the male satin blue gardener, k is the probability p of being selected from all nest individuals_iA nest serial number obtained under a roulette selection mechanism; p is a radical of_kThe probability that the nest corresponding to the sequence number k is selected is shown, wherein k is 1, … and N; x is the number of_elite,jThe j-th element of the best nest in the whole population;

j is the jth dimension element of the current wheel nest position, wherein j is 1, … and D; lambda [ alpha ]_jStep size factor of j dimension element; omega is adaptive weight; alpha is the upper limit of the step length;

5) usually, strong males rob decorations of other male bird nests, variation operators are introduced into an optimization algorithm, the diversity of populations at the later stage of iteration can be enhanced, the nests can be randomly varied in a probability distribution mode, and varied nest point positions are obtained

The method considers the Gaussian variation of the standard SBO algorithm to have less ideal variation effect on individuals, improves a variation formula, and the improved variation expression is as follows:

s＝z×(V_MAX-V_MIN) (17)

wherein s is the standard deviation; z is a proportionality coefficient; n (0,1) is a random number of a standard normal distribution, V_MAX、V_MINThe upper and lower boundaries of the nest position respectively;

6) finally, searching the optimal nest position in all the populations before and after the variation, returning to the process 3) to continue the iteration until the maximum iteration times is met, and stopping the iteration; and taking the finally found optimal nest position as a parameter value to be optimally selected.

Optimizing regularization parameters gamma and kernel function width sigma in the LSSVR model of each component sequence by using an ISBO algorithm under the fitness function given in the step three according to the input and output matrix of each component sequence in the step two to obtain two LSSVR parameters after the ISBO algorithm is optimized, and establishing an LSSVR prediction model of each component sequence;

step six, sending the test set of each component sequence into the trained LSSVR prediction model of each component sequence to obtain the wind power prediction value of each component, respectively carrying out reverse normalization processing on the components by using an equation (18) to obtain each component prediction value after reverse normalization, and respectively superposing the prediction values of each component at corresponding moments to obtain the final ultra-short-term wind power prediction value of each moment;

x＝x′(x_max-x_min)+x_min (18)

wherein x and x' respectively represent wind power sub-sequence dataAnd normalized wind power sub-sequence data, x_maxAnd x_minThe maximum value and the minimum value in the selected sub-sequence data set are respectively.

And verifying the excellent degree of the established prediction model by adopting the evaluation indexes of root mean square error RMSE, mean absolute error MAE and mean absolute percentage error MAPE, wherein the formula of each evaluation index is as follows:

wherein N represents the number of test samples; y is_iAnd

the real value and the predicted value of the output power of the ith sample are respectively.

Examples

Wind power data of 2016, 1 month and 7 months of a certain wind power plant of an Elia power grid in Belgium are selected, the sampling time interval is 1h, 744 sampling points are arranged in each month, and a prediction model is established by respectively utilizing actual measurement data of the wind power in each month. The method uses SPSS software to perform t-mean test of the wind power subsequence, wherein the significance level is set to be 5% (namely the confidence level percentage is 95%), and the test value is 0. On an MATLAB simulation platform, a least square support vector regression LSSVR is used as a basic learning model of a wind power subsequence, an improved satin blue gardener algorithm ISBO is adopted to optimize regularization parameters and kernel function width of the LSSVR, and an ultra-short-term wind power prediction model based on QDS-ISBO-LSSVR is established.

According to the invention, 8 standard test functions are adopted to respectively carry out comparison test on a standard satin blue gardener algorithm SBO, a standard particle swarm algorithm PSO, a self-adaptive weight satin blue gardener algorithm WSBO and an improved satin blue gardener algorithm ISBO in an MATLAB.

To verify the search capability of the improved SBO algorithm, 8 standard test functions and their parameters were chosen as shown in table 1.

TABLE 1 parameters of the Standard test function

And (3) considering the randomness of the global optimal value search results of the SBO, PSO, WSBO and ISBO algorithms on 8 test functions, respectively operating each test function for 30 times by utilizing each optimization algorithm, and setting the optimization iteration times of each optimization algorithm to be 300.

And calculating the optimal value, the worst value, the average value and the standard deviation of each test function under 30-time operation, and taking the optimal value, the worst value, the average value and the standard deviation as evaluation indexes of each optimization algorithm for searching the optimal value of the test function, wherein the average value reflects the searching accuracy of the optimization algorithm on the optimal value of the test function, and the standard deviation reflects the robustness of the optimization algorithm on the searching of the test function.

The evaluation index values of each test function under 4 optimization algorithms are shown in table 2, and the ISB values in table 2 are the optimization results of the improved SBO algorithm provided by the invention.

Table 24 algorithm optimization result comparison

Observing each optimization algorithm search function f in table 2₁～f₈4 evaluation indexes, finding a WSBO and ISBO algorithm pair function f₂、f₆The final search results of the optimal values are consistent, 4 index values of the optimal values are superior to those of PSO and SBO algorithms, and the WSBO and ISBO algorithms can search the function f₆Global optimum value of 0; in addition, 4 optimization algorithms were applied to other test functions (f)₁、f₃～f₅、f₇～f₈) In the search result of the optimal value, the evaluation indexes of the optimization algorithms have difference in order of magnitude, and the optimization precision and robustness of the improved SBO algorithm provided by the invention are optimal.

In order to show the improved optimization performance of the SBO algorithm in the present invention, fig. 3 shows that each optimization algorithm searches for f₁～f₈And when the standard test function has the optimal value, the convergence curve increases along with the iteration times.

In FIG. 3, in the search function f₁～f₃、f₇～f₈In the process, the convergence degree of the PSO algorithm is almost not changed greatly, which shows that the traditional PSO algorithm is difficult to jump out of local optimum in the iteration process. In the search function f₁～f₈When the optimal value is obtained, the standard SBO algorithm has a convergence effect in the whole iteration process, but the convergence change is weak; the WSBO algorithm and the ISBO algorithm provided by the invention can show rapid convergence capability, but the ISBO algorithm has stronger convergence capability. Therefore, compared with PSO, SBO and WSBO algorithms, the ISBO algorithm provided by the invention has the advantages of fastest convergence speed, minimum target fitness value of final search and optimal optimization performance.

The quadratic decomposition strategy QDS constructed by the invention comprises the following steps: performing primary decomposition on an original wind power sequence by using an EEMD (electric energy mechanical decomposition), performing secondary decomposition on an IMF1 subsequence generated by the EEMD by using a WPD (wavelet decomposition device), dynamically dividing the IMF 2-IMFn subsequence generated by the EEMD by using t-mean inspection, performing superposition reconstruction on each divided frequency band sequence by using a superposition mode, and selecting wind power data of 1 month and 7 months in 2016 for experiments respectively in order to explain the specific implementation process of QDS;

1) the secondary decomposition strategy QDS constructed by the method is utilized to process the original wind power sequence of 2016, 1 and 1 months.

Firstly, after the original wind power sequence of 1 month is decomposed in the EEMD, 8 IMF subsequences IMF 1-IMF 8 and 1 Re subsequence are generated.

Then, in the SPSS software, a mean value test is performed on the IMFs sequences generated by the EEMD using a t test, and a critical value for dividing the middle frequency band and the low frequency band is obtained (in the t test, when a mean value difference of the first IMF sequence has a significant meaning, a p value corresponding to the IMF sequence is used as the critical value). the results of the t-means test are shown in table 3.

T-mean test result of IMFs after EEMD decomposition of wind power of 1 month in 32016 years

As can be seen from table 3, the t-test significance p-value of IMF5 was 0.000<0.05, and therefore accepting an alternative hypothesis that the mean difference of IMF5 is significant, indicating that IMF5 is the first significantly varying subsequence of IMFs, and that the bold value of 0.000 in table 3 is the partition threshold, and therefore, the component IMF 2-IMFn that does not satisfy the mean assumption of 0 for the first time is considered to be the IMF_dAs the IMF5 is used as the boundary point between the middle band and the low band of the wind electronic sequence, the sequences IMF2 to IMF4 may be dynamically divided into the middle band, and the sequences IMF5 to IMF8, Re are dynamically divided into the low band. Then, the sequences IMF 2-IMF 4 are reconstructed into 1 intermediate frequency component sequence, and the sequences IMF 5-IMF 8 and Re are reconstructed into 1 low frequency component sequence by a superposition mode.

Finally, considering that the fluctuation of the highest-frequency subsequence IMF1 generated by EEMD is large, decomposing the highest-frequency subsequence IMF1 by using WPD to obtain W₁～W₈For a total of 8 sub-components.

2) The secondary decomposition strategy QDS constructed by the method is utilized to process the original wind power sequence of 2016, 7 months.

Firstly, after the original wind power sequence of 7 months is decomposed in the EEMD, 8 IMF subsequences IMF 1-IMF 8 and 1 Re subsequence are generated.

Then, in the SPSS software, a mean value test is performed on the IMFs sequences generated by the EEMD using a t test, and a critical value for dividing the mid-band component and the low-band component is obtained (in the t test, when a mean value difference of the first IMF sequence has a significant meaning, a p value corresponding to the IMF sequence is taken as a critical value). the results of the t-means test are shown in table 4.

T-mean test result of IMFs (intrinsic mode functions) of wind power in 7 months in 42016 years after EEMD (ensemble empirical mode decomposition)

As can be seen from table 4, the t-test significance p-value of IMF4 was 0.000<0.05, and therefore accepting an alternative hypothesis that the mean difference of IMF4 is significant, indicating that IMF4 is the first significantly varying subsequence of IMFs, and that the bold value of 0.014 in table 4 is the dividing threshold, so that the component IMF 2-IMFn that first fails to satisfy the mean 0 hypothesis is considered the IMF_dAs the IMF4 is used as the boundary point between the middle band and the low band of the wind electronic sequence, the sequences IMF2 to IMF3 may be dynamically divided into the middle band, and the sequences IMF4 to IMF8, Re are dynamically divided into the low band. Then, the sequences IMF 2-IMF 3 are reconstructed into 1 intermediate frequency component sequence, and the sequences IMF 4-IMF 8 and Re are reconstructed into 1 low frequency component sequence by a superposition mode.

Finally, considering that the fluctuation of the highest-frequency subsequence IMF1 generated by EEMD is large, decomposing the highest-frequency subsequence IMF1 by using WPD to obtain W₁～W₈For a total of 8 sub-components.

In summary, for the wind power data of 1 month and 7 months, the EEMD decomposition, the t hypothesis test, and the WPD decomposition are sequentially performed, so that the secondary decomposition, the dynamic division, and the reconstruction processing of the QDS can be realized, and finally 8W wind power data are obtained₁～W₈1 mid frequency component and 1 low frequency component, there being 10 sub-component sequences for each month. Wherein the sub-components W obtained in each month₁～W₈Compared with IMF1, the method has the characteristic of more moderate fluctuation, and can reduce the prediction difficulty; compared with the IMF 2-IMFn and Re subsequences, the obtained 1 intermediate frequency component and 1 low frequency component greatly reduce the training and prediction during model training and prediction respectivelyThe complexity of the process.

Aiming at the problem of large fluctuation of the highest-frequency subsequence IMF1 generated by EEMD, WPD is used for carrying out secondary decomposition on IMF1 to obtain W with mild fluctuation₁～W₈A subcomponent. In order to verify the WPD secondary decomposition effectiveness of the IMF1 subsequence, two comparison models are established, wherein firstly, the IMF1 subsequence is directly used as modeling data, and an ISBO-LSSVR prediction model is established to obtain a prediction value of the IMF1 subsequence; the other is that after the IMF1 subsequence is subjected to WPD decomposition, W with mild fluctuation is generated₁～W₈The subcomponents are respectively used as modeling data to establish a WPD-ISBO-LSSVR prediction model to obtain W₁～W₈And (4) superposing the predicted values of the sub-components to obtain the predicted value of the IMF1 sub-sequence.

Wind power actual measurement data of 744 sampling points in 2016, 1 month and are selected for experiments, firstly, EEMD is adopted to decompose wind power, and a series of IMFs subsequences and Re components are obtained. And performing modeling prediction by using the highest-frequency subsequence IMF1 in the IMFs subsequences. Wherein, the last 48 sampling points of the subsequence are used as a test set, and the rest data are used as a training set. The prediction models of ISBO-LSSVR and WPD-ISBO-LSSVR were established, respectively, and the prediction results thereof are shown in fig. 4 (a), and the prediction errors are shown in fig. 4 (b).

When (a) of FIG. 4 is observed, the prediction accuracy of the ISBO-LSSVR model is lower than that of the WPD-ISBO-LSSVR model, and the W obtained by decomposing the subsequence IMF1 again with WPD₁～W₈And a prediction model is established for the sub-components, so that the prediction precision is improved more easily, and the prediction difficulty of the high-frequency sub-sequence IMF1 is effectively reduced. From (b) of fig. 4, by comparing the error between the actual value of the IMF1 subsequence and the predicted value of the two prediction models, it can be seen that the prediction error amplitude of the WPD-ISBO-LSSVR model at each sampling point is smaller than that of the ISBO-LSSVR model, which indicates that the prediction error of the IMF1 subsequence under WPD quadratic decomposition is smaller than that of the IMF1 direct prediction.

The predicted evaluation index values of the IMF1 sequences in the ISBO-LSSVR and WPD-ISBO-LSSVR models are shown in Table 5.

Table 5 prediction evaluation indexes of test set of IMF1 sequences under ISBO-LSSVR and QPD-ISBO-LSSVR models

As can be seen from Table 5, the WPD-ISBO-LSSVR model after WPD secondary decomposition of IMF1 has a prediction error X, which is compared with the ISBO-LSSVR model trained by directly using IMF1 sequence_RMSEReduced by 30.27% and X_MAEThe reduction by 23.53% shows that the WPD is adopted to carry out secondary decomposition on the IMF1, so that the implicit characteristics in the wind power sequence can be better excavated, a better prediction model is established, and the prediction precision is improved.

In order to verify the effectiveness of the ultra-short-term wind power prediction model based on the QDS-ISBO-LSSVR, the wind power data of 2016 (1 month) and 7 months are used for training and predicting the model respectively, wherein the data of the last two days are used for each month in the test set, and the residual data of each month are used as the training set of the corresponding month. The validity of QDS is verified by carrying out comparison experiments through LSSVR, ISBO-LSSVR, EEMD-ISBO-LSSVR and QDS-ISBO-LSSVR models, as shown in (a) and (c) of FIG. 5; comparative experiments are carried out through QDS-PSO-LSSVR, QDS-SBO-LSSVR and QDS-ISBO-LSSVR models, and the optimization capability of different optimization algorithms on each model parameter under QDS is verified, as shown in (b) and (d) of FIG. 5.

As can be seen from (a) and (c) of fig. 5, the model fitting capability corresponding to the quadratic decomposition strategy QDS is stronger under different decomposition modes of the same optimization algorithm; by comparing (b) and (d) of fig. 5, it can be seen that the prediction performance is the best when the prediction model of LSSVR is optimized by using the ISBO algorithm provided in the present invention.

In order to better reflect the prediction accuracy of each prediction model, the evaluation index values of each prediction model in 1 month and 7 months were calculated, as shown in table 6.

Prediction evaluation index of wind power in model of 1 month and 7 months in 62016

As can be seen from Table 6, in two months, the prediction precision of comparing LSSVR, ISBO-LSSVR, EEMD-ISBO-LSSVR and QDS-ISBO-LSSVR models and EEMD-ISBO-LSSVR and QDS-ISBO-LSSVR models is greatly improved, and the prediction precision of the QDS-ISBO-LSSVR model is the highest, which shows that the QDS decomposition technology can actually reduce the volatility of wind power sequences, effectively mine the local characteristic information of signals and improve the prediction performance; compared with QDS-PSO-LSSVR, QDS-SBO-LSSVR and QDS-ISBO-LSSVR models, the prediction errors of the three models are different due to the fact that the LSSVR parameters are different in optimizing capacity of PSO, SBO and ISBO optimization algorithms, and the prediction error of the QDS-ISBO-LSSVR model is the minimum. Through the analysis, the QDS-ISBO-LSSVR prediction model provided by the invention is verified to have higher prediction precision and stronger generalization capability.

Under the prediction model provided by the invention and other comparison models, the evaluation indexes of the wind power prediction results of two months are averaged, as shown in table 7.

Table 7 shows the average value of the evaluation indexes of the prediction models in 2016 for two months

As can be seen from Table 7, the RMSE, MAE and MAPE of the ISBO-LSSVR, EEMD-ISBO-LSSVR and QDS-ISBO-LSSVR models are compared to be the lowest, namely the prediction precision is the highest, which shows that the wind power sequence is decomposed into the sub-components with the moderate fluctuation for establishing the prediction model, which is beneficial to improving the prediction performance of the model and further verifies the effectiveness of the quadratic decomposition strategy QDS provided by the invention. On the other hand, the prediction precision of the LSSVR model (ISBO-LSSVR) optimized by the ISBO algorithm is higher than that of a single LSSVR model, which shows that the LSSVR prediction performance is greatly influenced by optimizing the parameters of the LSSVR model by the bionic optimization algorithm. According to the error evaluation index comparison results of the QDS-PSO-LSSVR, QDS-SBO-LSSVR and QDS-ISBO-LSSVR models, three models can be seenThe prediction error of the model is reduced in sequence, wherein the error X of the optimal model QDS-ISBO-LSSVR is less than that of the next optimal model QDS-SBO-LSSVR_RMSE、X_MAE、X_MAPERespectively reducing 8.06%, 23.36% and 25.94%, and further verifying that the improved satin blue gardener algorithm ISBO provided by the invention has stronger self-adaptive capability for improving model parameters. In conclusion, the QDS-ISBO-LSSVR-based ultra-short-term wind power prediction model provided by the invention has stronger robustness and applicability.

Claims (2)

1. A wind power prediction method for optimizing LSSVR based on an improved satin blue gardener algorithm is characterized by comprising the following steps:

s1, wind power data of the prediction target are obtained, and the wind power data are converted into a plurality of sub-components, intermediate frequency components and low frequency components after being processed, wherein the specific method comprises the following steps:

the wind power is decomposed once by decomposing EEMD by adopting an ensemble empirical mode, and the decomposition result of EEMD on a target signal s (t) is as follows:

wherein f is_i(t) is the ith IMF component, r_n(t) is the Re component, n represents the number of IMFs;

after primary decomposition is carried out on original wind power data through EEMD, IMF and Re subsequences with the frequency from high to low are generated;

performing secondary decomposition on the IMF1 subsequence by adopting Wavelet Packet Decomposition (WPD), specifically performing 3-layer WPD on IMF1 to obtain W₁～W₈A total of 8 sub-components;

dynamically dividing IMF 2-IMFn and Re subsequences by using a t-mean value inspection method to obtain two subsequences of a middle frequency band and a low frequency band, and then respectively superposing the two subsequences in a superposition mode to respectively reconstruct an intermediate frequency component sequence and a low frequency component sequence;

s2, respectively carrying out normalization processing on the component sequences obtained in the step S1:

wherein x and x' respectively represent wind power sub-sequence data and normalized wind power sub-sequence data, and x_maxAnd x_minRespectively the maximum value and the minimum value in the selected sub-sequence data set;

selecting data from the normalized component sequences as a training set, and respectively constructing input and output matrixes of the components, specifically:

the method comprises the following steps of reconstructing a phase space of a wind power sequence at the continuous sampling moment of each component sequence, converting the phase space into an input matrix and an output matrix, setting a phase space embedding dimension m, and taking single-step prediction of the wind power as an example, constructing the input matrix and the output matrix of a training set as follows:

x, Y is the input and output matrix of a component sequence, M is the number of training set, X is the matrix of (M-M) X M, Y is the matrix of (M-M) X1, the input of the ith row in X is a matrix composed of X_i,x_i+1,x_i+2,…,x_i+m-1The output of the ith row in the corresponding Y is x_i+m；

S3, constructing respective Least Squares Support Vector Regression (LSSVR) models by using the input and output matrixes of the component sequences obtained in the step S2:

where γ is the regularization parameter, σ is the kernel width, x_iAnd

respectively the true value and the predicted value of the wind power output at the ith moment, gamma_min、γ_maxRespectively minimum and maximum values, sigma, of a set regularization parameter_min、σ_maxRespectively the minimum value and the maximum value of the set kernel function width;

s4, optimizing the regularization parameter gamma and the kernel function width sigma of the model constructed in the step S3 by adopting an improved satin blue gardener algorithm to obtain the optimized regularization parameter gamma and the optimized kernel function width sigma;

s5, substituting the optimized regularization parameter gamma and kernel function width sigma obtained in the step S4 into the model established in the step S3 to obtain an LSSVR prediction model of each component sequence, and training the prediction model according to the training set obtained in the step S2 to obtain a trained prediction model;

s6, inputting the real-time data of the prediction target into the trained prediction model to obtain the prediction values of the components, and respectively carrying out reverse normalization processing to obtain the prediction values of the components after reverse normalization:

x＝x′(x_max-x_min)+x_min

wherein x and x' respectively represent wind power sub-sequence data and normalized wind power sub-sequence data, and x_maxAnd x_minRespectively the maximum value and the minimum value in the selected sub-sequence data set;

and respectively superposing the predicted values of the components at corresponding moments to obtain the final predicted value of the ultra-short-term wind power at each moment.

2. The method for predicting wind power based on the improved satin blue gardener algorithm to optimize the LSSVR according to claim 1, wherein in step S4, the improved satin blue gardener algorithm is used for optimization, and the specific method is as follows:

a) initializing relevant parameters of the satin blue gardener algorithm SBO, including initializationThe number of nests N, the upper limit of step length alpha, the variation probability p and the maximum iteration number t of the SBO_maxProportional coefficient z, standard deviation s in individual variation, dimension of variable to be optimized and upper and lower limits V of variable to be optimized_MAX、V_MIN；

b) Randomly initializing chaotic vectors, introducing a chaotic sequence with ergodicity and randomness into the initialization of a satin blue gardener nest, and initializing the population of an SBO algorithm by adopting chaotic cube mapping, wherein the chaotic cube mapping formula is as follows:

y_n+1＝4y_n ³-3y_n

wherein-1. ltoreq. y_n≤1,n＝0,1,2…；

The method for realizing the population initialization of the satin blue gardener algorithm by introducing the chaotic sequence comprises the following steps:

(i) setting the maximum iteration times N-1 and the population size N;

(ii) randomly generating a D-dimensional initial vector Y₁＝(y₁₁,…,y_1j,…,y_1D) Wherein, y_1j∈[-1,1]J is not less than 1 and not more than D, and Y₁≠0；

(iii) Will Y₁Substituting into chaotic cubic mapping formula to iterate for N-1 times to obtain N chaotic vectors Y_i＝(y_i1,y_i2,…,y_iD),i＝1,2,…,N,；

(iv) The obtained chaos vector Y is obtained_iMapping to the search space by:

wherein, y_ijIs the j-th coordinate, x, of the i-th cell_ijAs a population position X_iJ-dimensional coordinate of middle ith nest, U_j、L_jAre j dimension population positions X respectively_iUpper and lower bounds of (1);

obtaining N population positions X_i＝(x_i1,x_i2,…,x_iD) 1,2, …, N as initial data of the improved satin blue gardener algorithm;

obtaining a chaotic vector through cubic mapping, and mapping the chaotic vector to a search space, thereby obtaining an initial population X of N nests ═ X₁,X₂,…,X_N}；

c) By a fitness function f (x)_i) Calculating the cost function value F of all the nest individuals_iProbability p of all nest individuals being selected_i：

In the formula, f (x)_i) The fitness function value of the ith nest is 1,2, …, N;

cost function value F for all nest individuals_iSorting from small to large, and taking the minimum value F_minCorresponding nest position X_minAs the current best nest position X_eliteAnd remain to the next generation;

d) defining an adaptive weight ω, wherein the weight ω changes in a linear decreasing form in the first half of the iteration period, and the weight ω changes in a convex function form in the second half of the iteration period:

in the formula, t_maxIs the maximum iteration number of the ISBO algorithm, t is the current iteration number, omega_max、ω_minThe maximum value and the minimum value of the weight are respectively;

in the improved SBO algorithm, the male bird updates the nest point position of the t round through continuous communication learning

Is updatedPosition of the nest

The expression is as follows:

in the formula, x_kjThe j-th dimension element of the best nest randomly searched currently for the male satin blue gardener, k is the probability p of being selected from all nest individuals_iA nest serial number obtained under a roulette selection mechanism; p is a radical of_kThe probability that the nest corresponding to the sequence number k is selected is shown, wherein k is 1, … and N; x is the number of_elite,jThe j-th element of the best nest in the whole population;

j is the jth dimension element of the current t-th nest position, wherein j is 1, … and D; lambda [ alpha ]_jStep size factor of j dimension element; omega is adaptive weight; alpha is the upper limit of the step length;

e) introducing mutation operator, and randomly mutating the nest in a probability distribution mode to obtain the position of the mutated nest

The variant expression is as follows:

s＝z×(V_MAX-V_MIN)

wherein s is the standard deviation; z is a proportionality coefficient; n (0,1) is a random number of a standard normal distribution, V_MAX、V_MINThe upper and lower boundaries of the nest position respectively;

f) and (c) searching the optimal nest position in all the populations before and after the variation, returning to the step c to continue the iteration until the maximum iteration times is met, stopping the iteration, and taking the finally found optimal nest position as a parameter value to be optimized and selected.

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