A method and system for designing a wind turbine blade

Abstract

The application discloses a design method and system of a wind turbine blade, and belongs to the field of wind power generation, and comprises the following steps: constructing a wind turbine blade model; using a Latin hypercube design method to generate initial sample points of a design scheme in the design space of the wind turbine blade model; constructing a Kriging surrogate model according to the initial sample points; using an improved multi-objective mantis algorithm to iteratively solve the Kriging surrogate model to obtain a Pareto front solution set; and selecting an optimal solution as the design scheme of the wind turbine blade from the Pareto front solution set according to the constraint conditions of the wind turbine blade. In view of the low optimization efficiency of the wind turbine blade in the prior art, the application constructs a mathematical optimization model of the wind turbine blade, then constructs a Kriging surrogate model according to sampling points and optimizes the hyperparameters of the Kriging surrogate model, and on this basis, an improved multi-objective mantis optimization algorithm and a multi-dimensional point adding strategy are introduced to adaptively update and optimize the solution of the surrogate model, so that the optimization efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wind power generation, and more particularly, to a design method and system of a wind turbine blade. BACKGROUND

[0002] Wind turbines are gradually developing towards large-scale, and the optimization design of large-scale wind turbine blades is a systematic complex problem involving multiple disciplines such as aerodynamics, structural mechanics, and material mechanics. The calculation of these problems requires the calling of special software, the writing of functions, and high-dimensional numerical calculation. These software calling, running, and numerical calculation make the overall optimization process very expensive in terms of time cost.

[0003] In view of the difficult problem of expensive calculation of the objective function, the approximate function relationship between the input variables and the output response is often constructed to use the predicted value of the surrogate model to replace the expensive calculation of the objective function, and the predicted value of the surrogate model is used to replace the expensive calculation of the fitness function of the multi-objective optimization algorithm. According to the "no free lunch" theorem, there is no universal optimization algorithm that can perform best on any problem, so it is crucial to explore the possibility of new algorithms in engineering. In addition, the multi-objective mantis optimization algorithm has its own disadvantages, so the overall performance of the multi-objective mantis optimization algorithm is optimized. In addition, the construction of the surrogate model is very rich, and each has its own advantages and disadvantages. At present, the Kriging surrogate model is used in the multi-objective optimization process, and there is a lack of overall optimization system, so reasonable determination of the number of surrogate models and determination of the construction form of the model will play an important role in improving the precision and cost control. In the updating and iteration process combined with the optimization algorithm, the model accuracy is often not enough, so the multi-dimensional adding point idea is introduced to guide the independent surrogate model to add points, so as to improve the fitting accuracy of the model and improve the prediction ability. SUMMARY

[0004] 1. Technical problem to be solved

[0005] In view of the low optimization efficiency of the wind turbine blade design in the prior art, the present application provides a design method and system of a wind turbine blade, which constructs a mathematical optimization model of a wind turbine blade, then constructs a Kriging surrogate model according to the sampling points and optimizes the hyperparameters thereof, and on this basis, introduces an improved multi-objective mantis optimization algorithm and a multi-dimensional adding point strategy to adaptively update and optimize the surrogate model for solving, thereby improving the optimization efficiency.

[0006] 2. Technical scheme

[0007] The purpose of the present application is achieved by the following technical scheme.

[0008] One aspect of the present application provides a design method of a wind turbine blade, comprising: constructing a wind turbine blade model; generating initial sample points of a design scheme in a design space of the wind turbine blade model by using a Latin hypercube design method; constructing a Kriging surrogate model according to the initial sample points; iteratively solving the Kriging surrogate model by using an improved multi-objective mantis algorithm to obtain a Pareto front solution set; and selecting an optimal solution as the design scheme of the wind turbine blade from the Pareto front solution set according to a constraint condition of the wind turbine blade.

[0009] Further, the wind turbine blade model is constructed, comprising: selecting cross-sectional airfoils Foil1 to Foil n as design variables; setting a target function comprising annual power generation and blade mass; setting a constraint condition comprising a value range of the design variables, blade deflection and a first-order natural frequency of the wind turbine blade; selecting cross-sectional airfoils Foil1 to Foil n as design variables, the design variables comprising chord length and twist angle of the cross-sectional airfoils.

[0010] The target function expression is as follows: Wherein, F(x) represents a total target function or a matrix of the target function; x represents a decision variable or a design variable in an optimization problem, f1(x) to fm(x) represent targets to be calculated respectively.

[0011] The constraint condition is expressed as follows: upper and lower limit constraint conditions of the design variables X: -Rx i ≤Δx i ≤Rx i , i = 1, 2, 3,..., n; wind turbine blade deflection constraint: δ max ≤δ allowable ; wind turbine blade first-order natural frequency constraint: δ f -|g(x)-Bn f |≤0; wherein, R represents a proportional factor of the design variables, used to adjust a variation range of the design variables, δ max represents a maximum deflection of the blade generated in a running process, δ allowable is a maximum deflection allowed, δ f represents a minimum frequency difference allowed, g(x) represents a first-order natural frequency under the design variable x, B represents a number of blades, n f represents a rated rotating speed of the blade; Δx i represents a variation range of the design variables, which is determined on initial original parameters and determines a design space of the design variables; x i represents the initial original parameters of the wind turbine blade; and n represents a number of the original parameters.

[0012] Further, according to the initial sample points, the Kriging surrogate model is constructed, including: using the central maximum minimum criterion to adjust the sample of the Latin hypercube sampling; using the adjusted sample of the Latin hypercube sampling to extract initial sample points in the value range of the design variable, to obtain the sample value of the design variable; inputting the sample value of the design variable into the wind turbine blade model to obtain the annual power generation and the blade mass objective function value corresponding to each sample point; calculating the correlation between the annual power generation and the blade mass; setting the number of Kriging surrogate models according to the correlation; and training the Kriging surrogate model by using the initial sample points and the maximum likelihood estimation method.

[0013] Further, the correlation between the annual power generation and the blade mass is calculated by the following formula: wherein, The correlation coefficient is used to measure the correlation of the target, and the range is between-1 and 1, X i,k and X j,k represent the average value of the target X i and X j at the kth sample point, and represent the average value of the target X i and X j , which is used to centralize the data, wherein i and j represent positive integers;

[0014]

[0015] The Kriging surrogate model is trained by using the initial sample points and the maximum likelihood estimation method, including: the maximum likelihood estimation method solves the hyperparameters of the Kriging surrogate model by minimizing the following formula: wherein, m represents the number of sample points, σ 2 represents the process variance, C ii is the diagonal element of the CholeSky decomposition matrix of the correlation matrix R between samples.

[0016] Further, the improved multi-objective mantis algorithm is used to iteratively solve the Kriging surrogate model to obtain the Pareto front solution set, including: establishing a mapping relationship between the position of the mantis individual and the value of the design variable of the wind turbine blade, randomly generating an initial mantis population representing different design schemes of the wind turbine blade; using the Kriging surrogate model to predict the target function value corresponding to each individual in the initial mantis population; performing non-dominated sorting on the position of the individual in the initial mantis population and the predicted target function value, extracting non-dominated solutions to generate an initial Pareto solution set, and storing it in an external file; updating the position of the individual in the mantis population based on the levy flight strategy and setting an adaptive step size; using the Kriging surrogate model to predict the target function value corresponding to each individual in the mantis population after the position is updated; based on the random sampling method, selecting part of the mantis individuals in the mantis population after the position is updated, and calculating the determination coefficient R2 and the mean square error MSE of the prediction accuracy of the Kriging surrogate model according to the predicted target function value and the real target function value of the corresponding individual; when the determination coefficient R2 is less than a threshold value ε1 or the mean square error is greater than a threshold value ε2, updating the Kriging surrogate model; using the updated Kriging surrogate model to predict the target function value of the current mantis population; performing non-dominated sorting on the position of the current mantis population and the updated predicted target function value, extracting non-dominated solutions and merging them with the Pareto solution set in the external file to obtain an updated Pareto solution set; combining the archive individual diversity maintenance strategy to perform Gaussian disturbance on the Pareto solution set in the current external file; according to the Pareto solution set after Gaussian disturbance, it is judged whether the position data and the predicted target function value of the current mantis population meet the preset conditions, if yes, the Pareto solution set in the current external file is output, otherwise, the next round of iterative optimization is performed.

[0017] The adaptive step size is set by the following formula: In the above formula, A is a fixed proportional scaling factor introduced for levy flight, is an introduced exponential decay, λ is an exponential parameter that controls the shape of the distribution, which affects the tail shape of the levy flight; It represents the current iteration value; MaxIt represents the maximum iteration value set by the optimization algorithm.

[0018] The determination coefficient R2 and the mean square error MSE of the prediction accuracy of the Kriging surrogate model are calculated by the following formula: Where, y ij is the real target value of the jth sampling point, is the predicted value of the jth sampling point using the surrogate model, It is the average of the true values ​​of the objective function of the sampled points, where n is the number of sampled points. and α MSE These are the trigger conditions for adaptive updates.

[0019] Furthermore, when the determination coefficient R² is less than the threshold ε1, or the mean squared error is greater than the threshold ε2, the Kriging surrogate model is updated, including: perturbing each dimension of the features of each individual in the current population to obtain a perturbed individual set; generating a random individual set using a random sequence; merging the perturbed individual set and the random individual set to form a candidate set; and determining the maximum objective function f of each candidate point in the candidate set. max and minimum value f min The maximum and minimum expected improvement values ​​EI of the candidate points are calculated as evaluation indicators. The formula for calculating the EI value is: EI(x)=σ(x)·(Z·Φ(Z)+φ(Z))+β·σ(x), Where Z represents the standardized value of candidate point x to the potential improvement of the model, μ(x) represents the mean of the Kriging surrogate model prediction at position x, σ(x) represents the standard deviation of the prediction, σ represents the uncertainty of the prediction, Φ(Z) represents the cumulative distribution function with respect to Z, φ(Z) represents the probability density function with respect to Z, and β is an exploration factor that regulates the exploration and utilization capabilities. The K-means clustering algorithm is used to adaptively cluster the candidate set, resulting in K clusters. The cluster C is calculated. j The EI value of candidate points in the data is used as the fitness value. Based on the fitness value, the cluster C is determined by non-dominated ranking. j The Pareto fronts of each cluster are used as new sample points and added to the original training set to update the training set. The Kriging surrogate model is then trained using the updated training set.

[0020] Furthermore, the characteristics of each individual in the current population are perturbed using the following formula: Where, x i,j (new) The new individual generated by the perturbation, x i,j Represents an original individual in the current population. The numerical representation of the j-th feature, δ i,j ξ is a perturbation random variable whose value ranges from [-1, 1], ensuring the randomness of the entire perturbation. ξ is a perturbation factor used to determine the proportional range of the perturbation. This represents the maximum value of the j-th feature for this individual. The minimum value of the j-th feature; N represents the current population size.

[0021] Further, the K-means clustering algorithm is used to adaptively cluster the candidate set, and the number of clusters K is determined by the following formula:

[0022] In the above formula, K(It) represents the number of groups to be divided at present, K min is the determined minimum number of data division groups, K max is the determined maximum number of division groups, It represents that with the increase of the number of iterations, the adaptive iteration factor will gradually decrease, It is the current iteration number of the optimization algorithm, MaxIt is the maximum iteration number of the optimization algorithm, C j represents the region division of the jth candidate set, which contains similar data, K represents the adaptive clustering number, which is equivalent to K(It), represents the ith candidate set sample point, represents the center of each clustering cluster.

[0023] Further, in combination with the archive individual diversity maintenance strategy, the Pareto solution set in the current external archive is subjected to Gaussian disturbance, including: obtaining the repeated individuals in the Pareto solution set in the current external archive; for each repeated individual, setting a random parameter and calculating the distance between all individuals in the Pareto solution set in the current external archive using the random parameter and and the distance updating the position of the repeated individual: wherein, is the optimal individual of the current population, that is, the mutation guide individual; is the repeated individual to be mutated at present; is a random parameter for controlling the adjustment range of the position; This random parameter is mainly used to enhance the mutation diversity of the individual; the repeated position updating step is repeated until there is no repeated individual in the Pareto solution set or the preset iteration number is reached.

[0024] Another aspect of the present application also provides a wind turbine blade design system, comprising: a model building module, which builds a wind turbine blade model according to selected design variables, sets a target function containing annual energy production and blade mass, and sets constraint conditions of the design variables; the design variables include a cross-sectional airfoil; the constraint conditions include a value range of the design variables; a sample point module, which adjusts samples of a Latin hypercube sampling by using a central maximum minimum criterion, extracts initial sample points in the value range of the design variables by using the Latin hypercube sampling with the adjusted samples, and obtains sample values of the design variables; a surrogate module, which calculates a correlation between the annual energy production and the blade mass according to the sample values of the design variables and the wind turbine blade model, sets a number of Kriging surrogate models according to the correlation, and trains the Kriging surrogate models by using the initial sample points; and a processing module, which solves the Kriging surrogate models by using an improved multi-objective mantis algorithm to obtain a Pareto front solution set, and selects an optimal solution as a design scheme of the wind turbine blade according to constraint conditions of the wind turbine blade.

[0025] The processing module comprises: a solving unit, which establishes a mapping relationship between positions of mantis individuals and value ranges of the design variables of the wind turbine blade, randomly generates an initial mantis population representing different design schemes of the wind turbine blade, predicts target function values corresponding to each individual in the mantis population by using the Kriging surrogate model, and performs non-dominated sorting on the positions of the mantis population and the predicted target function values, extracts non-dominated solutions to generate a Pareto front solution set and store the Pareto front solution set in an external file; and an updating unit, which sets an adaptive step length based on a levy flight strategy, and updates the positions of the individuals in the mantis population.

[0026] The surrogate model updating unit updates the Kriging surrogate model, and the updating comprises: performing disturbance processing on each dimension feature of each individual in a current population to obtain a disturbed individual set; generating a random individual set by using a random sequence; merging the disturbed individual set and the random individual set to form a candidate set; calculating evaluation indexes of each candidate point in the candidate set; clustering the candidate set by using a K-means clustering algorithm according to the evaluation indexes to obtain K clustering clusters; calculating Pareto front points of each clustering cluster by non-dominated sorting; and updating the Kriging surrogate model by using the Pareto front points; and a diversity maintenance unit, which performs Gaussian disturbance on the Pareto front solution set in the external file.

[0027] 3. Beneficial effects

[0028] Compared with the prior art, the present application has the following advantages:

[0029] The Latin hypercube design method is used to efficiently sample in the blade design space, and representative initial sample points are obtained. A Kriging surrogate model is constructed based on the sample points to approximate the global design model of the blade. Since the complexity of the surrogate model is much lower than that of the original model, direct search optimization on the original complex model is avoided, which greatly reduces the computational cost and improves the design optimization efficiency. The Kriging model has good non-linear modeling capability and can accurately reflect the internal relationship between the objective function and the design variables, thereby effectively covering the design space with fewer sample points.

[0030] To overcome the slow convergence speed and the tendency to fall into local optimum of the standard multi-objective mantis algorithm, an adaptive step levy flight strategy is introduced to improve it. Through the random large step search generated by levy flight, the algorithm can jump out of the local optimal region and enhance the global exploration ability. At the same time, with the iteration, the step length decays exponentially, making the algorithm pay more attention to local fine search in the later stage. The adaptive step strategy effectively balances the exploration and exploitation ability of the algorithm, and speeds up the convergence speed of the algorithm.

[0031] During the optimization search process, a series of potential candidate points are selected in the design space through multi-dimensional feature disturbance and random sampling of the current population individuals. The maximum minimum expected improvement function is used to evaluate the information gain of the candidate points, i.e. to calculate the probability that the objective function value at the candidate point exceeds the current optimal value. Then, adaptive K-means clustering is performed on the candidate point set to obtain a reasonable number of clusters. The Pareto frontier points are extracted from each cluster as new sample points to update the Kriging model. By selecting the most representative and information gain points to dynamically correct the surrogate model, the prediction accuracy of the surrogate model can be significantly improved, ensuring the correctness of the optimization search direction.

[0032] To solve the problem of loss of diversity of Pareto solution set in the evolution process, an archive individual diversity maintenance strategy based on Gaussian disturbance is proposed. By performing Gaussian mutation on the Pareto non-dominated solutions in the external archive, the distribution and universality of the solution set in the target space are increased, effectively avoiding premature convergence to the local Pareto frontier.

[0033] The improved multi-objective mantis algorithm and the Kriging surrogate model are organically combined and embedded into the wind turbine blade design optimization system. Through the strategy of balancing global exploration and local development, the surrogate model is efficiently searched, and the surrogate model is updated adaptively during the optimization process to correct its prediction ability, finally obtaining accurate and reliable blade optimization design results. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1This is a schematic diagram of the wind turbine blade optimization process based on the adaptive multidimensional point-addition proxy model according to an embodiment of this application;

[0035] Figure 2 This is a flowchart illustrating the improved multi-objective mantis optimization algorithm according to an embodiment of this application. Detailed Implementation

[0036] The present application will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0037] like Figure 1 As shown, a wind turbine blade model is constructed; an improved Latin hypercube design method is used to generate initial sample points for the design scheme in the design space of the wind turbine blade model; based on the initial sample points, a Kriging surrogate model is constructed; an improved multi-objective mantis algorithm is used to iteratively solve the Kriging surrogate model to obtain the Pareto front solution set; from the Pareto front solution set, the optimal solution is selected as the design scheme of the wind turbine blade according to the constraints of the wind turbine blade.

[0038] The initial mathematical optimization model for the wind turbine blade is constructed, including: selecting the main airfoils Foil_1 to Foil_n as the main optimized airfoils based on the original wind turbine blade. To better fit the length of the entire blade and provide better accuracy, as many airfoils as possible are selected as the basic airfoils. The number of design variables depends on the number of selected airfoil sections n, usually twice the number of sections, i.e., 2n design variables. For each airfoil section Foil_1 to Foil_n, the changes in chord length and twist angle, or other parameters, are taken as input variables X = {Δx1, Δx2, Δx3, ..., Δx} of the mathematical optimization model. n The input variables are determined based on the number of airfoil sections selected. The parameter variations selected for each section serve as design variables; therefore, the number of design variables is theoretically a multiple of the number of selected airfoil sections. Besides chord length and twist angle, other geometric parameters, such as relative airfoil thickness and camber, can be selected as design variables to further expand the design space. The objective function required for the optimal design of the wind turbine blade is determined as follows: Here, x is the design variable vector. Common optimization objectives include increasing annual power generation (AEP) and reducing blade mass (Mass). Taking AEP and Mass as an example, the objective function of the bi-objective optimization model can be expressed as: Y = {AEP, Mass}, where AEP is the annual power generation and Mass is the blade mass. The constraints of the mathematical model are determined as follows: the upper and lower bound constraints of the design variable X are -Rx. i ≤Δx i ≤Rx ii = 1, 2, 3...n; the range of design variables can be controlled by adjusting the scale factor R. Wind turbine blade deflection constraint: δ max ≤ δ allowable ; δ max is the maximum allowable deflection value. Wind turbine blade first order natural frequency constraint: δ f - |g(x) - Bn f | ≤ 0; where, represents the scale factor of design variables, used to adjust the range of design variables, δ max represents the maximum deflection generated by the blade during operation, δ allowable is the maximum allowable deflection, δ f represents the minimum allowable frequency difference, g(x) represents the first order natural frequency under design variables x, B represents the number of blades, n f represents the rated rotational speed of the blade.

[0039] The Latin Hypercube Design (LHD) is a space-filling experimental design method commonly used in the selection of initial sample points in computer simulation experiments. The basic idea is to divide the value range of each design variable into n subintervals, and then randomly select a sample point in each subinterval, so that the selected sample points are uniformly distributed in each dimension and fully cover the entire design space. Compared with traditional orthogonal experimental design, Latin Hypercube Design can better explore high-dimensional design space and obtain a representative set of sample points. Kriging Surrogate Model is an interpolation model based on spatial correlation, commonly used to establish an approximate substitute model for complex and high-cost simulation models. Kriging model assumes that the unknown function is a random process, consisting of a deterministic part (global trend) and a random part (local deviation). By maximizing the likelihood function to estimate the model hyperparameters, and using sample point data to train and build the Kriging model. Kriging model has good nonlinear fitting ability and statistical properties, can provide prediction value while giving confidence interval, quantifying the uncertainty of prediction. Therefore, Kriging model is widely used in surrogate model optimization, reliability analysis and other fields. The Centered Maximin Criterion is an improved strategy for classical Latin Hypercube sampling, aiming to further improve the space-filling and uniformity of sample points. Based on the original Latin Hypercube sampling, the sample points in each subinterval are fixed at the center of the interval, and then the distribution of sample points is optimized by maximizing the minimum distance between any two sample points. The optimization objective can be expressed as: maximize min(d(x i ,x j )), i≠j, where d(*) represents the distance measure between sample points, commonly using Euclidean distance. By solving this optimization problem, a set of sample points with better space-filling and more uniform distribution can be obtained, which helps to improve the accuracy and generalization ability of the surrogate model.

[0040] Specifically, use the Centered Maximin Criterion to improve the Latin Hypercube sampling to extract initial sample points within the upper and lower limits of design variables, or use other sampling methods to obtain initial sample points, i.e. design variables X = {Δx1, Δx2, Δx3,..., Δx nThe minimization criterion, based on the original Latin hypercube sampling, further fixes the sample points in each sub-interval at their center position and optimizes the minimum distance between sample points to maximize the spacing between them. The optimization objective of the minimization criterion is as follows: In the above formula: ||x i -x j || represents the sample points xi and x in the sampling. j The Euclidean distance between two points. This represents the minimum distance between all sample points.

[0041] Numerical computation is used to calculate the values ​​of the objective function, thus obtaining the corresponding response function: Y = {(f 11 ,f 12 ,f 13 ,......f 1m ),(f 21 ,f 22 ,f 23 ,......f 2m ),(f 31 ,f 32 ,f 33 ,......f 3m ),......(f n1 ,f n2 ,f n3 ,......f nm When the correlation is strong, a multi-output model can be built to share information. When the correlation is not strong, a model is built for each output to better capture the characteristics of each output. The Pearson coefficient can be used to measure the linear correlation of the objective function, and the Spearman correlation coefficient can be used to determine non-linear correlation. The Pearson correlation coefficient is detailed below: In the above formula, X represents the correlation coefficient, used to measure the relevance of a target, and its range is between -1 and 1. i,k and X j,k Represents target X i and X j The value at the k-th sample point, as well as Indicates target X i and X j The average value is used to center the data, where Spearman correlation coefficient: k is the number of sample points, dk is the difference in ranking of the kth sample on different objectives, d k = rank(X i,k ) - rank(X j,k ), if |p| is close to 1, it means strong correlation, if close to 0, it is weak correlation, then this threshold can be set to 0.6, because the multi-output surrogate model through my experiment, for small sample fitting precision is not high. If it is to be expanded to more outputs, the correlation coefficient can be calculated respectively, and the correlation matrix is obtained, Then more targets respectively see which target correlation is high, then use one, not high is to use multiple models.

[0042] The obtained data is used to train the surrogate model and the optimization algorithm is used to optimize the hyperparameters of the Kriging surrogate model. The selection of hyperparameters has an important role in the performance and quality of the model. Determining the hyperparameters depends on the size, complexity of the problem, computing resources and the requirement for the optimization accuracy of the hyperparameters. Generally speaking, in a simple scenario, manual selection and grid search are more suitable, however, in some complex scenarios, optimization algorithm is more suitable, therefore, genetic algorithm, particle swarm optimization algorithm and the like can be selected to globally optimize, and the optimal hyperparameters are found by using the optimization algorithm to minimize the negative log-likelihood function of the surrogate model. In the Kriging model, the negative log-likelihood function is as follows: In the above formula, m represents the number of sample points, σ 2 represents the process variance, C ii is the diagonal element of the CholeSky decomposition matrix of the correlation matrix R.

[0043] Specifically, Cholesky decomposition is a method of decomposing a symmetric positive definite matrix into a lower triangular matrix and its transpose matrix product. Specifically, for a symmetric positive definite matrix A, there exists a unique lower triangular matrix L, such that A = LL^T holds, where L^T represents the transpose matrix of L. This lower triangular matrix L is called the Cholesky decomposition matrix or Cholesky factor of matrix A.

[0044] In the process of constructing the Kriging model, the inverse matrix and determinant of the correlation matrix R need to be calculated. Since the correlation matrix R is symmetric positive definite, it can be decomposed by Cholesky to obtain a lower triangular matrix L, such that R = LL^T. In the negative log-likelihood function of the Kriging model, the diagonal elements of the Cholesky decomposition matrix L are used to calculate the logarithmic value of the determinant of the correlation matrix: ln(det(R)) = 2∑ln(L_ii), where L_ii represents the ith diagonal element of the Cholesky decomposition matrix L. Using Cholesky decomposition to simplify the inverse matrix and determinant calculation of the correlation matrix can significantly improve the computational efficiency of Kriging model hyperparameter estimation and optimization.

[0045] In this embodiment, the improved multi-objective mantis optimization algorithm is used in the wind turbine blade design optimization Figure 2 The specific flowchart of the multi-objective mantis optimization algorithm is also given in the embodiment, including the following steps: initializing the population; randomly generating a certain number of mantis individuals, each individual representing a set of wind turbine blade design variables. The initial position of the individual is randomly generated within the value range of the design variable. The individuals of the initial population are input into the trained Kriging surrogate model to predict the corresponding objective function (annual power generation and blade mass) values, which are used as the fitness function values of the individuals.

[0046] The initial population is sorted according to non-dominated sorting and crowding distance, and the individuals with better performance are selected for archiving to form an external archive set. Non-dominated sorting is used to compare and distinguish the advantages and disadvantages of individuals in the population. In multi-objective optimization problems, there are usually multiple conflicting objective functions, making it difficult to directly compare the advantages and disadvantages of individuals. Non-dominated sorting is based on Pareto dominance, which divides the population into multiple non-dominated fronts. If all objective function values of individual A are not worse than individual B, and at least one objective function value is better than individual B, then individual A dominates individual B. Through non-dominated sorting, the advantages and disadvantages of individuals can be evaluated according to the non-dominated layer they belong to. Individuals in the front non-dominated layer are better than individuals in the back non-dominated layer. Non-dominated sorting can effectively handle the trade-off between multiple objective functions and provide a basis for the selection and evolution of multi-objective optimization algorithms. Crowding distance is an index used to measure the density of individuals in the population in multi-objective optimization, reflecting the spatial density around the individual. On the basis of non-dominated sorting, crowding distance is used to distinguish the advantages and disadvantages of individuals in the same non-dominated layer, maintaining the diversity of the population.

[0047] For each objective function, the individuals in the same non-dominated layer are sorted according to the objective function value. For the two boundary individuals (the minimum and maximum of the function value), their crowding distance is infinite. For the middle individual i, its crowding distance is the sum of the difference of the function value of the adjacent two individuals on this objective function: where f[i+1] and f[i-1] are the function value of the next and previous individual of individual i on this objective function, f max and f min are the maximum and minimum of this objective function in this non-dominated layer. The crowding distance of an individual is the sum of the crowding distance on all objective functions. The larger the crowding distance, the lower the spatial density of the region where the individual is located, the larger the interval between individuals, and the better the diversity. In the selection process, the individuals in the earlier non-dominated layer are preferred; for the individuals in the same non-dominated layer, the individuals with larger crowding distance are preferred. In this way, the population diversity can be considered while converging to the Pareto front, and premature convergence to local optimal solution can be avoided. In the embodiment of wind turbine blade optimization design, the non-dominated sorting is used to compare the performance of the blade design schemes on the two objectives of annual energy production and blade mass, and the population is divided into different non-dominated layers. The crowding distance is used to maintain the diversity of the blade design schemes in the same non-dominated layer, and the individuals with sparse distribution are preferentially retained. Through the non-dominated sorting and crowding distance calculation, the blade design schemes with better performance and uniform distribution can be selected in the iteration process, the external archive set is formed, and finally the Pareto front solution set of the wind turbine blade optimization design problem is obtained.

[0048] The position is updated based on the multi-objective mantis optimization algorithm. The original multi-objective mantis optimization algorithm uses levy flight to generate irregular random jumps and multi-scale step changes, improves the global search ability of the algorithm, introduces a fixed scaling factor and exponential decay in the levy flight, and improves the levy flight into an adaptive step size by exponential decay. The search process of the algorithm uses large steps to explore in the early stage, and the search process gradually changes to small steps in the later stage. The algorithm is locally searched by small steps, effectively balances the exploration and development process, and improves the performance and convergence effect of the algorithm. Levy flight is a random walk process, and its step length follows a heavy-tailed distribution (such as Levy distribution), which can generate irregular random jumps and multi-scale step changes. Compared with traditional Gaussian random walk, Levy flight has more large-step jumps and small-step local search. Irregular random jumps refer to the large-step jump behavior generated by Levy flight. Compared with traditional Gaussian random walk, its step length distribution has a heavier tail, resulting in more large-amplitude displacement. This irregular jump enables the optimization algorithm to explore a large range in the search space, escape from the current local area, and find new promising solution regions. Irregular random jumps increase the global search ability of the algorithm, which helps to avoid premature convergence and fall into local optimum. In this application, irregular random jumps can help the optimization algorithm to explore a large range in the blade design parameter space, generate significantly different blade design schemes, and explore new optimization directions to improve the globality and robustness of the optimization. Multi-scale step changes enable the optimization algorithm to search in different granularities in the blade design parameter space. Large step changes help the algorithm to explore globally in the design space and generate significantly different blade schemes. Small step changes fine-tune and optimize the blade scheme in the local area to improve the design accuracy and performance. The introduction of multi-scale step changes can balance the exploration and development capabilities of the algorithm, and improve the efficiency and quality of wind turbine blade optimization design.

[0049] The specific step is improved as follows: In the above formula, A is a fixed scaling factor introduced for levy flight, is an introduced exponential decay, and λ is an exponential parameter that controls the shape of the distribution and affects the tail shape of the levy flight. The updated population individuals are input into the Kriging surrogate model to predict the fitness function value. In order to balance the calculation efficiency and optimization accuracy, part of the individuals are extracted to calculate the true target function value, and the model accuracy is determined. The true value of part of the individuals in this generation population is calculated using the corresponding proportion of the current population, and the coefficient of determination R 2 and mean square error MSE are used as the basis for judgment. When one of them is lower than the threshold, adaptive sampling update will be performed, that is: MSEi ≥α MSE wherein, is the determination coefficient, is the mean square error, y ij is the true target value of the jth sampling point, is the predicted value of the jth sampling point using the proxy model, is the average value of the true value of the objective function of the extracted partial sample points, and n is the number of sample points, and α MSE are the trigger conditions of adaptive update, respectively.

[0050] According to the model accuracy, it is determined whether to perform adaptive multi-dimensional point addition, and the trained proxy model is updated. An adaptive multi-dimensional point addition strategy is proposed to improve the prediction accuracy of the proxy model, and the specific steps are as follows: the maximum and minimum values of the characteristics of each individual in the population are used as the threshold of random disturbance, the population of this generation is disturbed, and the disturbed population and the population generated by the random sequence are used to form the candidate set population, and the specific formula is as follows: In the above formula, x i,j (new) The new individual generated by the formula is x i,j , which represents an original individual in the current population , and δ i,j is a disturbance random variable, whose value range is between [-1, 1], which guarantees the randomness of the entire disturbed individual, and ξ is a disturbance factor used to determine the proportion range of disturbance, , which represents the maximum value of the jth characteristic of this individual, , which represents the minimum value of the jth characteristic.

[0051] The maximum and minimum expected improvement (EI) strategy is introduced, and the EI value of the candidate point is calculated as an index to measure the value of the candidate point. The larger the EI value, the higher the improvement potential of the candidate point, which is more conducive to improving the performance of the Kriging proxy model, and the specific formula is as follows: EI(x)=σ(x)·(Z·Φ(Z)+φ(Z))+β·σ(x), in the above formula, Z represents the standardization of the potential improvement value of the model of the candidate point x, μ(x) represents the mean value predicted by the Kriging proxy model at position x, σ(x) represents the standard deviation of the prediction, represents the uncertainty of the prediction, Φ(Z) represents the cumulative distribution function about Z, φ(Z) represents the probability density function about Z, and β is the exploration factor, which adjusts the exploration and utilization ability.

[0052] The points in the candidate set are adaptively clustered using a clustering method. The clustering method is selected not only because it can divide the candidate set into different groups, but also because it can divide the candidate set more reasonably and more specifically. In view of the complexity of calculation, the data points are divided using adaptive K-means clustering. The adaptive clustering means that the number of clusters will be adaptively changed with the increase of the iteration number, and the adaptive iteration factor will gradually decrease with the increase of the iteration number. It is the current iteration number of the optimization algorithm, and MaxIt is the maximum iteration number of the optimization algorithm. C

[0053] In the above formula, K(It) represents the number of groups that need to be divided at present, K min is the minimum number of data division groups determined, max is the maximum number of division groups determined, It is the current iteration number of the optimization algorithm, and MaxIt is the maximum iteration number of the optimization algorithm. C j represents the region division of the jth candidate set, which contains similar data, and K represents the adaptive cluster number, which is equivalent to K(It), represents the ith candidate set sample point, represents the center of each cluster.

[0054] The idea of non-dominated sorting and crowded distance is used. The expected improvement value of each cluster is taken as the reference of non-dominated sorting, and the sample points in the Pareto front of each cluster are selected as new points for adding to the training set. Therefore, by distinguishing different data in the clustering method and enriching the data by improving the expected value, a multi-dimensional adding strategy is provided. For each cluster of candidate points, the expected improvement is taken as the fitness function: EI(x i )=[EI1(x i ),EI2(x i ),…,EI K (x i )], where K is the number of objective functions, x i is the candidate point, and EI is a kind of expected improvement strategy. This value is used as the fitness function and as the basis for generating the Pareto front. In this application, each candidate solution (blade design scheme) corresponds to multiple objective function values (such as annual power generation and blade mass). Through non-dominated sorting, non-dominated solutions in the candidate solution set can be found to form the Pareto front. The solutions on the Pareto front represent the blade design schemes that achieve the optimal balance between the objective functions, providing a set of optimized choices for decision makers.

[0055] For each candidate point in each cluster, its expected improvement value is used as the fitness function for non-dominated sorting. The candidate points on the Pareto front are selected as new points to be added to the training set of the Kriging surrogate model. These Pareto front points have excellent performance on the expected improvement values of various objective functions, and can provide high-quality new samples for the surrogate model to improve the prediction accuracy of the surrogate model. By selecting the Pareto front points in each cluster as new points, the most valuable candidate points in different regions can be selected, and the improvement potential of multiple objective functions can be considered. The clustering method helps to distinguish different types of candidate points, and the concept of Pareto front ensures that the selected new points have advantages in multiple objective functions. This multi-dimensional point adding strategy considers the diversity and superiority of candidate points, which helps to improve the performance of the surrogate model and the optimization effect.

[0056] The proxy model is used to predict the real function value; the archive is updated and the diversity is maintained. The original multi-objective mantis optimization algorithm gradually converges during the iteration process, which will cause the individuals of part of the population to tend to the same or similar individual positions, and then the individual repetition phenomenon occurs. A guided diversity maintenance strategy is proposed to effectively improve this problem. The repetition individuals are guided to the current optimal individual based on the introduction of the hunting behavior of the whale, so that they move along the direction of the optimal individual and maintain a certain randomness to avoid falling into a local optimal solution. When detecting the existence of repeated individuals in the population, the hunting behavior of the whale can be used to process these individuals. First, the optimal individual in the current population is determined as the hunting target. Then, for each repeated individual, the process of surrounding the prey is simulated, and the repeated individual is moved and updated around the optimal individual. Through the simulation of the hunting behavior of the whale, the repeated individual can be updated under the guidance of the optimal individual to obtain a new position and solution. In this way, the diversity of the population can be maintained while the convergence speed of the population is accelerated, and the optimization performance of the algorithm is improved. In this application, the hunting behavior of the whale is used to process repeated individuals, which can effectively maintain the diversity of the population. When repeated blade design schemes appear during the optimization process, the repeated schemes can be guided to the current optimal blade design scheme through the movement and update in the surrounding and attacking stages, while a random factor is introduced to avoid completely copying the optimal scheme. In this way, new design schemes can be explored while the information of the current optimal scheme is fully utilized to accelerate the convergence speed of the optimization.

[0057] Specifically, the improved multi-objective mantis optimization algorithm includes the following steps: checking repeated individuals based on the merged population archive; introducing a random parameter and So that the repeated individuals can have a certain randomness in the process of moving towards the optimal individual, avoiding coinciding with the original individual. The distance between each individual is calculated for position updating. Use Individual position updating is performed to develop the individual towards the optimal direction, and the specific implementation principle is as follows: In the above formula, is the optimal individual of the current population, that is, the mutation guiding individual; is the repeated individual that needs to be mutated at present; is a random parameter for controlling the position adjustment range; This random parameter is mainly used to enhance the mutation diversity of the individual. In this embodiment, there are still other ways for the strategy of algorithm improvement, such as introducing the crossover mutation of the genetic algorithm and other strategies. The iteration termination condition is checked, and if it is satisfied, the Pareto front solution set is output, otherwise the iteration is returned to continue updating, and the iteration termination condition is satisfied;

[0058] From the output Pareto front solution set, according to the design constraints and preferences of the wind turbine blade, the optimal blade design scheme is selected as the final optimization result. The weight of each objective function, the feasibility of the design and other factors can be considered to select the solution that meets the requirements from the Pareto front solution set as the optimal design scheme.

[0059] To sum up, the wind turbine blade optimization system based on the adaptive multi-dimensional point adding Kriging surrogate model provided in the application improves the multi-objective mantis optimization algorithm through multiple strategies, improves the balance ability between global search and local search of the algorithm, and improves the distribution quality of the Pareto front. The prediction accuracy of the Kriging surrogate model is significantly improved through the adaptive multi-dimensional point adding strategy. The improved multi-objective mantis optimization algorithm is combined with the prediction model to optimize the wind turbine blade as a whole, which can greatly reduce the calculation cost of the objective function and improve the overall optimization efficiency. The application is conducive to quickly and accurately designing a wind turbine blade with high wind energy utilization rate, while optimizing the mass and structure of the blade, reducing the production cost of wind power generation. The application solves the problem that there is no overall optimization system in the multi-objective optimization process using the Kriging surrogate model, and proposes to use a disturbed population to generate a candidate set and combine clustering to divide the data points. In each clustering cluster, the non-dominated sorting is used to find more potential points, the model accuracy is adaptively updated, and the problem of lack of algorithm diversity in the multi-objective mantis optimization algorithm is improved.

[0060] The above description of the application and its embodiments is illustrative, and not restrictive. Many variations of the application will become apparent to those of ordinary skill in the art upon review of the above description. The scope of the application should, therefore, be determined not with reference to the above description, but instead should be given with reference to the pending claims along with their full scope or equivalents. It is therefore contemplated to cover by the present application any and all modifications that fall within the scope of the present application. It is intended that changes in form and detail not be regarded as departure from the spirit, nature, or scope of the application unless such change would result in departure from the scope of the appended claims. It is also contemplated that the use of the terms "including", "comprising", "having" and variations thereof herein do not limit the scope of the application to the features or steps so described. It is intended that the description of the embodiments are an enabling and best mode for carrying out the application, and that such description is sufficient to enable one skilled in the art to make and use the application.

Claims

1. A method for designing wind turbine blades, characterized in that, include: Construct a model of a wind turbine blade; The Latin hypercube design method is used to generate initial sample points for design schemes in the design space of the wind turbine blade model; Based on the initial sample points, construct the Kriging proxy model; An improved multi-objective mantis algorithm is used to iteratively solve the Kriging surrogate model to obtain the Pareto solution set; From the Pareto solution set, the optimal solution is selected as the design scheme for the wind turbine blade based on the constraints of the wind turbine blade. An improved multi-objective mantis algorithm is used to iteratively solve the Kriging surrogate model, including: Establish a mapping relationship between the location of individual mantises and the design variable values ​​of wind turbine blades, and randomly generate an initial mantis population representing different design schemes of wind turbine blades; The Kriging surrogate model was used to predict the objective function value for each individual in the initial mantis population. The positions of individuals in the initial mantis population and the predicted objective function values ​​are non-dominated and sorted. Non-dominated solutions are extracted to generate an initial Pareto solution set, which is then stored in an external archive. Based on the Levy flight strategy, an adaptive step size is set to update the position of individuals in the mantis population; The Kriging surrogate model was used to predict the objective function value of each individual in the mantis population after the position update. For the mantis population after location update, some mantis individuals are selected based on random sampling. The coefficient of determination R2 and mean square error MSE of the Kriging surrogate model are calculated based on the predicted objective function value and the actual objective function value of the corresponding individuals. When the coefficient of determination R² is less than the threshold Or the mean square error is greater than the threshold. When necessary, update the Kriging proxy model; Predict the objective function value of the current mantis population using the updated Kriging surrogate model; The current mantis population position and the updated predicted objective function value are sorted non-dominatedly, the non-dominated solutions are extracted and merged with the Pareto solution set in the external archive to obtain the updated Pareto solution set; In conjunction with the strategy of maintaining the diversity of archived individuals, Gaussian perturbation is applied to the Pareto solution set in the current external archive; Based on the Pareto solution set after Gaussian perturbation, determine whether the current mantis population's location data and the predicted objective function value meet the preset conditions. If yes, output the Pareto solution set in the current external file; otherwise, proceed to the next round of iterative optimization. Update the Kriging proxy model, including: The characteristics of each individual in the current population are perturbed to obtain a set of perturbed individuals; A random set of individuals is generated using a random sequence; Merge the set of perturbed individuals and the set of random individuals to form a candidate set; Based on the maximum objective function value of each candidate point in the candidate set and minimum value Calculate the maximum and minimum expected improvement values ​​EI for candidate points as evaluation indicators. The formula for calculating the EI value is: ； ； Where Z represents Standardization of candidate points to the potential improvement value of the model Indicates the location The mean value predicted by the Kriging surrogate model at that location. The standard deviation of the forecast represents the uncertainty of the forecast. Let Z represent the cumulative distribution function. Let Z represent the probability density function. It is an exploration factor that regulates the ability to explore and utilize. The K-means clustering algorithm is used to adaptively cluster the candidate set, resulting in K clusters. Calculate clusters The EI value of candidate points in the data is used as the fitness value, and clusters are determined based on the fitness value through non-dominated ranking. Pareto frontier; The Pareto fronts of each cluster are added as new sample points to the original training set to update the training set; The Kriging proxy model is trained using the updated training set.

2. The design method for wind turbine blades according to claim 1, characterized in that: Constructing a wind turbine blade model includes: Select the airfoil section to As a design variable; where n represents a positive integer; Set an objective function that includes annual power generation and blade mass; Set constraints, including the range of design variables, blade deflection, and the first natural frequency of the wind turbine blade.

3. The design method for wind turbine blades according to claim 1, characterized in that: Constructing the Kriging proxy model includes: The Latin hypercube sampling sample is adjusted using the centralized maxima-min criterion; The initial sample points are drawn within the range of the design variable using the adjusted sample Latin hypercube sampling method to obtain the sample values ​​of the design variable; Input the sample values ​​of the design variables into the wind turbine blade model to obtain the annual power generation and blade mass objective function values ​​corresponding to each sample point; Calculate the correlation between annual power generation and blade mass; Set the number of Kriging proxy models based on relevance; Using the initial sample points, the Kriging surrogate model is trained using the maximum likelihood estimation method.

4. The design method for wind turbine blades according to claim 1, characterized in that: The adaptive step size is set using the following formula: In the above formula, A is a fixed scaling factor introduced for levy flight. It is the introduced exponential decay. It is an exponential parameter that controls the shape of the distribution and affects the tail shape of the levy flight; It represents the current iteration value; MaxIt represents the maximum iteration value set by the optimization algorithm.

5. The design method for wind turbine blades according to claim 1, characterized in that: The characteristics of each individual in the current population are perturbed using the following formula: in, The formula generates new individuals through perturbation. Represents an original individual in the current population. In the Numerical representation of each feature It is a perturbation random variable, and its value range is between [-1, 1], ensuring the randomness of the entire perturbation. It is a disturbance factor used to determine the proportional range of the disturbance. This indicates that the individual is in the first... The maximum value of each feature, No. The minimum value of each feature; N represents the current population size.

6. The design method for wind turbine blades according to claim 1, characterized in that: The number of clusters K in adaptive clustering is determined by the following formula: In the above formula, This indicates the number of groups that need to be divided. It is the minimum number of data groups that can be defined. It is the maximum number of definite partitions. This indicates that as the number of iterations increases, the adaptive iteration factor will gradually decrease. The region partitioning of the j-th candidate set represents a type of similar data, and K represents the adaptive number of clusters, equivalent to... , This represents the sample point of the i-th candidate set. This represents the center of each cluster.

7. The design method for wind turbine blades according to claim 1, characterized in that: Apply Gaussian perturbations to the Pareto solution set in the current external archive, including: Retrieve duplicate individuals from the Pareto solution set in the current external archive; For each duplicate individual, set a random parameter. and ; Calculate the distance between all individuals in the Pareto solution set of the current external archive. ; Using random parameters and and distance Update the position of duplicate individuals: in, It is the best individual in the current population, that is, the mutation-leading individual; It is a duplicate individual that currently needs to be mutated; It is a random parameter that controls the magnitude of position adjustment; This random parameter is primarily used to enhance the variation diversity of individuals; Repeat the position update step until there are no duplicate individuals in the Pareto solution set or the preset number of iterations is reached.

8. A wind turbine blade design system for implementing the method described in any one of claims 1-7, characterized in that, include: The model building module sets an objective function that includes annual power generation and blade mass, as well as constraints on the design variables, based on the selected design variables, and builds a wind turbine blade model. The design variables include the airfoil section; the constraints include the range of values ​​for the design variables. The sample point module uses the centralized maxima-minus criterion to adjust the Latin hypercube sampling sample. The adjusted Latin hypercube sampling is then used to extract initial sample points within the range of the design variable values ​​to obtain the sample values ​​of the design variable. The surrogate module calculates the correlation between annual power generation and blade mass based on the sample values ​​of design variables and the wind turbine blade model. It sets the number of Kriging surrogate models based on the correlation and trains the Kriging surrogate models using the initial sample points. The processing module uses an improved multi-objective mantis algorithm to solve the Kriging surrogate model and obtain the Pareto front solution set; The optimal solution is selected as the design scheme for the wind turbine blade based on the constraints of the wind turbine blade. The processing module includes: The solution unit establishes a mapping relationship between the position of individual mantises and the design variable values ​​of wind turbine blades, and randomly generates an initial mantis population representing different design schemes of wind turbine blades; Predict the objective function value for each individual in a mantis population using the Kriging surrogate model; The location of the mantis population and the predicted objective function value are non-dominated sorted, and the non-dominated solutions are extracted to generate a Pareto front solution set and stored in an external archive. Based on the Levy flight strategy, an adaptive step size is set to update the position of individuals in the mantis population; The proxy model update unit updates the Kriging proxy model, including: The characteristics of each individual in the current population are perturbed to obtain a set of perturbed individuals; A random set of individuals is generated using a random sequence; Merge the set of perturbed individuals and the set of random individuals to form a candidate set; Calculate the evaluation index for each candidate point in the candidate set; Based on the evaluation metrics, the K-means clustering algorithm was used to cluster the candidate set, resulting in K clusters. The Pareto fronts of each cluster were calculated using non-dominated sorting. Update the Kriging agent model using Pareto fronts; The diversity maintenance unit applies a Gaussian perturbation to the Pareto solution set in the external archive.

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