Design method and system of wind turbine blade

Abstract

The invention discloses a design method and system for a wind turbine blade, and belongs to the field of wind power generation. Adopting a Latin hypercube design method to generate initial sample points of a design scheme in a design space of the wind turbine blade model; according to the initial sample points, constructing a Kriging agent model; an improved multi-target mantis algorithm is adopted to carry out iterative solution on the Kriging proxy model, and a Pareto leading edge solution set is obtained; and selecting an optimal solution as a design scheme of the wind turbine blade from the Pareto leading edge solution set according to constraint conditions of the wind turbine blade. Aiming at low wind turbine blade design optimization efficiency in the prior art, a wind turbine blade mathematical optimization model is constructed, then a Kriging proxy model is constructed according to sampling points, hyper-parameters of the Kriging proxy model are optimized, and on this basis, an improved multi-target mantis optimization algorithm and a multi-dimensional point adding strategy are introduced to carry out adaptive updating optimization solution and the like on the proxy model. And the optimization efficiency is improved.

Description

Technical Field

[0001] The present application relates to the field of wind power generation, and more specifically, to a design method and system for wind turbine blades. Background Art

[0002] Wind turbines are gradually developing towards larger sizes, and the optimal design of large wind turbine blades is a systematic and complex problem that integrates multiple disciplines, involving aerodynamics, structural mechanics, and material mechanics. The calculation of these problems requires the use of dedicated software, function writing, and high-dimensional numerical calculations. The software calls, operations, and numerical calculations make the overall optimization process very time-consuming and expensive.

[0003] In order to solve the thorny problem of expensive objective function calculation, the predicted value of the surrogate model is often used to replace the expensive calculation of the objective function by constructing an approximate functional relationship between the input variables and the output response, and the predicted value of the surrogate model is used to replace the expensive calculation of the fitness function of the multi-objective optimization by combining it with the multi-objective optimization algorithm. Regarding the optimization algorithm, according to the "no free lunch" theorem, no general optimization algorithm can show the best effect on any problem, so it is crucial to explore the possibility of new algorithms in engineering. Combined with the disadvantages of the multi-objective mantis optimization algorithm, the overall performance of the multi-objective mantis optimization algorithm is optimized. In addition, there are many ways to build surrogate models, and each has its own advantages and disadvantages. At present, the use of Kriging surrogate model in the multi-objective optimization process lacks an overall optimization system, so the reasonable determination of the number of surrogate models and the construction form of the model will play an important role in improving accuracy and cost control. In the process of updating and iterating in combination with the optimization algorithm, the problem of insufficient model accuracy often occurs. Therefore, an adaptive strategy is introduced to use the multi-dimensional point addition idea to guide the addition of points to the independent surrogate model, which can improve the fitting accuracy of the model in many aspects and improve the prediction ability. Summary of the invention

[0004] 1. Technical issues to be solved

[0005] In response to the problem of low efficiency in wind turbine blade design optimization in the prior art, the present application provides a design method and system for wind turbine blades, constructs a mathematical optimization model for wind turbine blades, then constructs a Kriging proxy model based on sampling points and optimizes its hyperparameters, and on this basis introduces an improved multi-objective Mantis optimization algorithm and a multi-dimensional point adding strategy to adaptively update and optimize the proxy model, thereby improving the optimization efficiency.

[0006] 2. Technical solution

[0007] The purpose of this application is achieved through the following technical solutions.

[0008] One aspect of the present application provides a design method for a wind turbine blade, comprising: constructing a wind turbine blade model; using a Latin hypercube design method to generate initial sample points of a design solution in the design space of the wind turbine blade model; constructing a Kriging proxy model based on the initial sample points; using an improved multi-objective mantis algorithm to iteratively solve the Kriging proxy model to obtain a Pareto frontier solution set; and selecting an optimal solution from the Pareto frontier solution set as a design solution for the wind turbine blade based on the constraints of the wind turbine blade.

[0009] Further, construct a wind turbine blade model, including: selecting cross-sectional airfoils Foil1 to Foil n as design variables; set the objective function including annual power generation and blade mass; set constraints, including the range of design variables, blade deflection and the first-order natural frequency of wind turbine blades; select cross-sectional airfoils Foil1 to Foil n As design variables, the design variables include the chord length and twist angle of the cross-sectional airfoil.

[0010] The objective function expression is as follows: Among them, F(x) represents the overall objective function, or the matrix of the objective function; x represents the decision variable or design variable in the optimization problem, and f1(x) to fm(x) represent the objectives to be calculated respectively.

[0011] Constraints, the expression is as follows: Upper and lower limit constraints of design variable X: -Rx i ≤Δx i ≤Rx i ,i=1,2,3......n; wind turbine blade deflection constraint: δ max ≤δ allowable ; The first-order natural frequency constraint of wind turbine blades: δ f -|g(x)-Bn f |≤0; where R represents the proportional factor of the design variable, which is used to adjust the range of the design variable, δ max Indicates the maximum deflection of 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 the design variable x, B represents the number of blades, n f Indicates the rated speed of the blade; Δx i It represents the range of variation of the design variable, which is determined based on the initial original parameters and determines the design space of the design variable; x i represents the original parameters of the wind turbine blade; n represents the number of original parameters.

[0012] Furthermore, a Kriging proxy model is constructed based on the initial sample points, including: using the centralized maximum and minimum criterion to adjust the samples of Latin hypercube sampling; using the Latin hypercube sampling after the adjusted samples to extract initial sample points within the value range of the design variables to obtain sample values ​​of the design variables; inputting the sample values ​​of the design variables into the wind turbine blade model to obtain the annual power generation and blade quality objective function values ​​corresponding to each sample point; calculating the correlation between the annual power generation and the blade quality; setting the number of Kriging proxy models based on the correlation; and using the initial sample points to train the Kriging proxy model using the maximum likelihood estimation method.

[0013] Furthermore, the correlation between annual power generation and blade quality is calculated using the following formula: in, Represents the correlation coefficient, which is used to measure the relevance of the target. Its range is between -1 and 1. i,k and X j,k Indicates target X i and X j The value at the kth sample point, as well as Indicates target X i and X j The average value of is used to center the data, where i and j represent positive integers;

[0014]

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

[0016] Furthermore, an improved multi-objective mantis algorithm is used to iteratively solve the Kriging proxy model to obtain a Pareto frontier solution set, including: establishing a mapping relationship between the position of mantis individuals and the design variable values ​​of wind turbine blades, and randomly generating an initial mantis population representing different design schemes of wind turbine blades; using the Kriging proxy model to predict the objective function value corresponding to each individual in the initial mantis population; performing non-dominated sorting on the positions and predicted objective function values ​​of the individuals in the initial mantis population, extracting non-dominated solutions to generate an initial Pareto solution set, and storing it in an external archive; based on the levy flight strategy, setting an adaptive step size, and updating the positions of individuals in the mantis population; using the Kriging proxy model to predict the objective function value corresponding to each individual in the mantis population after the position is updated; for the mantis population after the position is updated, selecting some mantis individuals based on a random sampling method, and selecting the corresponding individuals according to the predicted objective function value and The true objective function value is used to calculate the determination coefficient R2 and mean square error MSE of the prediction accuracy of the Kriging proxy model; when the determination coefficient R2 is less than the threshold ε1, or the mean square error is greater than the threshold ε2, the Kriging proxy model is updated; the objective function value of the current mantis population is predicted using the updated Kriging proxy model; the position of the current mantis population and the updated predicted objective function value are non-dominated sorted, the non-dominated solutions are extracted and merged with the Pareto solution set in the external archive to obtain the updated Pareto solution set; combined with the archived individual diversity maintenance strategy, the Pareto solution set in the current external archive is Gaussian perturbed; based on the Pareto solution set after Gaussian perturbation, it is determined whether the position data of the current mantis population and the predicted objective function value meet the preset conditions. If so, the Pareto solution set in the current external archive is output, otherwise, the next round of iterative optimization is carried out.

[0017] Set the adaptive step size using the following formula: In the above formula, A is a fixed scaling factor introduced for levy flight, is the exponential decay introduced, λ is the exponential parameter that controls the distribution shape, which affects the tail shape of 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 mean square error MSE of the prediction accuracy of the Kriging proxy model are calculated using the following formula: Among them, y ij is the true target value of the jth sampling point, is the predicted value of the j-th sampling point using the surrogate model, is the average value of the true value of the objective function of some sample points extracted, n is the number of sample points extracted, and α MSEThey are respectively the triggering conditions for adaptive updating.

[0019] Furthermore, when the coefficient of determination R2 is less than the threshold ε1, or the mean square error is greater than the threshold ε2, the Kriging proxy model is updated, including: performing perturbation on the dimensional features of each individual in the current population to obtain a perturbed individual set; using a random sequence to generate a random individual set; merging the perturbed individual set and the random individual set to form a candidate set; and adjusting the maximum value of the objective function f of each candidate point in the candidate set according to the maximum value of the objective function f of each candidate point in the candidate set. max and the minimum value f min , calculate the maximum and minimum expected improvement values ​​EI of the candidate points as the evaluation index. The calculation formula of EI value is: EI(x)=σ(x)·(Z·Φ(Z)+φ(Z))+β·σ(x), Among them, Z represents the standardization of the potential improvement value of the candidate point x to the model, μ(x) represents the mean predicted by the Kriging surrogate model at position x, σ(x) represents the standard deviation of the prediction, indicating 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 capabilities; the K-means clustering algorithm is used to adaptively cluster the candidate set to obtain K clusters; the cluster C is calculated j The EI value of the candidate point in is used as the fitness value, and the cluster C is determined by non-dominated sorting according to the fitness value. j The Pareto frontier points of each cluster are taken as new sample points, added to the original training set, and the training set is updated; the Kriging proxy model is trained using the updated training set.

[0020] Furthermore, the dimensional features of each individual in the current population are disturbed by the following formula: Among them, x i,j (new) The new individuals generated by the perturbation, x i,j Represents an original individual in the current population The numerical representation of the jth feature, δ i,j is a disturbance random variable, and its value range is between [-1, 1], which ensures the individual randomness of the entire disturbance. ξ is a disturbance factor, which is used to determine the proportion range of the disturbance. represents the maximum value of the jth feature of this individual, The minimum value of the jth feature; N represents the number of individuals in the current population.

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

[0022] In the above formula, K(It) means the number of groups that need to be divided at present, K min is the minimum number of data partition groups, K max is the maximum number of partition groups that can be determined. It means that as the number of iterations increases, the adaptive iteration factor will gradually decrease. It is the current number of iterations of the optimization algorithm, MaxIt is the maximum number of iterations of the optimization algorithm, and C j It represents the region division of the j-th candidate set, which contains similar data. K represents the number of adaptive clusters, which is equivalent to K(It). represents the i-th candidate set sample point, Represents the center of each cluster.

[0023] Furthermore, combined with the archived individual diversity maintenance strategy, the Pareto solution set in the current external archive is subjected to Gaussian perturbation, including: obtaining repeated individuals in the Pareto solution set in the current external archive; for each repeated individual, setting random parameters and Calculate the distance between all individuals in the Pareto solution set in the current external archive Using random parameters and And distance Update the positions of duplicate individuals: in, is the optimal individual of the current population, that is, the mutation-guided individual; It is the duplicate individual that needs to be mutated at present; is a random parameter that controls the amplitude of position adjustment; This random parameter is mainly used to enhance the diversity of individual variation; the position update step is repeated until there are no duplicate individuals in the Pareto solution set or the preset number of iterations is reached.

[0024] Another aspect of the present application also provides a wind turbine blade design system, including: a model construction module, which sets an objective function including annual power generation and blade quality, and constraints of the design variables according to selected design variables to construct a wind turbine blade model; the design variables include cross-sectional airfoils; the constraints include the value range of the design variables; a sample point module, which uses a centralized maximum and minimum criterion to adjust the samples of Latin hypercube sampling, and uses the adjusted Latin hypercube sampling to extract initial sample points within the value range of the design variables to obtain sample values ​​of the design variables; an agent module, which calculates the correlation between annual power generation and blade quality according to the sample values ​​of the design variables and the wind turbine blade model, sets the number of Kriging agent models according to the correlation, and trains the Kriging agent model using the initial sample points; a processing module, which uses an improved multi-objective mantis algorithm to solve the Kriging agent model to obtain a Pareto frontier solution set; and selects the optimal solution as the design scheme of the wind turbine blade according to the constraints of the wind turbine blade.

[0025] The processing module includes: a solution unit, which establishes a mapping relationship between the position of a mantis individual and the design variable value of a wind turbine blade, and randomly generates an initial mantis population representing different design schemes of the wind turbine blade; uses a Kriging proxy model to predict the objective function value corresponding to each individual in the mantis population; performs non-dominated sorting on the position of the mantis population and the predicted objective function value, extracts non-dominated solutions to generate a Pareto frontier solution set and stores it in an external archive; sets an adaptive step size based on a levy flight strategy, and updates the position of individuals in the mantis population.

[0026] The proxy model updating unit updates the Kriging proxy model. The updating includes: perturbing the dimensional 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; calculating the evaluation index of each candidate point in the candidate set; clustering the candidate set using the K-means clustering algorithm according to the evaluation index to obtain K clusters; calculating the Pareto frontier points of each cluster through non-dominated sorting; and updating the Kriging proxy model using the Pareto frontier points. The diversity maintenance unit performs Gaussian perturbations on the Pareto frontier solution set in the external archive.

[0027] 3. Beneficial effects

[0028] Compared with the prior art, the advantages of this application are:

[0029] The Latin hypercube design method is used to efficiently sample the blade design space, obtain representative initial sample points, and build a Kriging proxy model based on the sample points to approximate the global design model of the blade. Since the complexity of the proxy model is much lower than the original model, it avoids searching and optimizing directly on the original complex model, greatly reducing the computational cost and improving the design optimization efficiency. The Kriging model has good nonlinear modeling capabilities and can more accurately reflect the intrinsic relationship between the objective function and the design variables, thereby achieving effective coverage of the design space with fewer sample points.

[0030] In view of the defects of the standard multi-objective mantis algorithm such as slow convergence speed and easy to fall into local optimality, this application introduces an adaptive step-size levy flight strategy to improve it. Through the random large-step search generated by levy flight, the algorithm can jump out of the local optimal area and enhance the global exploration ability. At the same time, as the iteration proceeds, the step size decays exponentially, making the algorithm pay more attention to local fine search in the later stage. The adaptive step-size strategy effectively balances the exploration and development capabilities of the algorithm and accelerates the convergence speed of the algorithm.

[0031] In the optimization search process, a series of potential candidate points are selected in the design space by perturbing the multidimensional features of the current population individuals and random sampling. The maximum and minimum expected improvement function is used to evaluate the information gain of the candidate points, that is, the probability that the objective function value at the candidate point exceeds the current optimal value is calculated. Then the candidate point set is adaptively clustered by K-means 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 points and information gain points to dynamically correct the proxy model, the prediction accuracy of the proxy model can be significantly improved, ensuring the correctness of the optimization search direction.

[0032] In order to solve the problem that the Pareto solution set is prone to lose diversity during the evolution process, this application proposes an archived individual diversity maintenance strategy based on Gaussian perturbation. By performing Gaussian mutation on the Pareto non-dominated solutions in the external archive, the distribution and extensiveness of the solution set in the target space are increased, effectively avoiding the algorithm from converging to the local Pareto frontier too early.

[0033] The improved multi-objective Mantis algorithm is organically combined with the Kriging proxy model and embedded in the wind turbine blade design optimization system. The proxy model is efficiently searched through a strategy that takes into account both global exploration and local development. At the same time, the proxy model is adaptively updated during the optimization process to correct its prediction ability, ultimately obtaining accurate and reliable blade optimization design results. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1A schematic diagram of a flow chart of wind turbine blade optimization based on an adaptive multi-dimensional point-adding agent model according to an embodiment of the present application;

[0035] Figure 2 A flow chart of the improved multi-objective mantis optimization algorithm according to an embodiment of the present application. DETAILED DESCRIPTION

[0036] The present application is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0037] like Figure 1 As shown in the figure, a wind turbine blade model is constructed; an improved Latin hypercube design method is used to generate initial sample points of the design scheme in the design space of the wind turbine blade model; a Kriging proxy model is constructed based on the initial sample points; an improved multi-objective mantis algorithm is used to iteratively solve the Kriging proxy model to obtain a Pareto frontier solution set; from the Pareto frontier 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] Constructing an initialized mathematical optimization model for wind turbine blades, including: selecting the main cross-sectional airfoils Foil_1~Foil_n based on the original wind turbine blade as the main optimized airfoils of the wind turbine blade, and selecting as many cross-sections as possible as the basic airfoils in order to better fit the length of the entire blade and provide better accuracy. The number of design variables depends on the number of selected airfoil sections n, which is usually twice the number of sections, that is, 2n design variables. In each section Foil_1~Foil_n, the chord length and twist angle of the airfoil or the change in more parameters are taken as the input variables X={Δx1,Δx2,Δx3,......,Δx n}, the input variables are determined according to the number of selected airfoil sections. The parameter variation of each section is used as the design variable. Therefore, the number of design variables is theoretically a multiple of the selected airfoil section. In addition to chord length and twist angle, other geometric parameters can also be selected as design variables, such as the relative thickness and curvature of the airfoil, to further expand the design space. Determine the objective function required for the optimization design of wind turbine blades, namely: Among them, x is the design variable vector. Common optimization objectives include increasing annual energy production (AEP) and reducing blade mass (Mass). Taking AEP and Mass as examples, the objective function of the dual-objective optimization model can be expressed as: Y = {AEP, Mass}, where AEP is the annual energy production and MaSS is the mass of the blade. Determine the constraints of the mathematical model: The upper and lower limit constraints of the design variable X: -Rx i ≤Δx i ≤Rx i,i=1,2,3......n; The range of design variables can be controlled by adjusting the proportional factor R. Wind turbine blade deflection constraint: δ max ≤δ allowable ; δ max The maximum allowable deflection value. The first-order natural frequency constraint of the wind turbine blade is: f -|g(x)-Bn f |≤0; where Represents the proportional factor of the design variable, which is used to adjust the range of the design variable, δ max Indicates the maximum deflection of 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 the design variable x, B represents the number of blades, n f Indicates the rated speed of the blade.

[0039] The Latin Hypercube Design method is used to generate the initial sample points of the design scheme in the design space of the wind turbine blade model; based on the initial sample points, the Kriging surrogate model is constructed. The Latin Hypercube Design (LHD) method is a space-filling experimental design method, which is often used to select 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 evenly distributed in each dimension and fully cover the entire design space. Compared with the traditional orthogonal experimental design, the Latin Hypercube Design can better explore the high-dimensional design space and obtain a representative set of sample points. The Kriging Surrogate Model is an interpolation model based on spatial correlation, which is often used to establish an approximate alternative model for complex and high-cost simulation models. The Kriging model assumes that the unknown function is a random process consisting of a deterministic part (global trend) and a random part (local deviation). The model hyperparameters are estimated by maximizing the likelihood function, and the Kriging model is constructed using sample point data training. The Kriging model has good nonlinear fitting ability and statistical characteristics. It can provide prediction values ​​while giving confidence intervals to quantify prediction uncertainty. Therefore, the Kriging model is widely used in surrogate model optimization, reliability analysis and other fields. The Centered Maximin Criterion is an improved strategy for the classic Latin hypercube sampling, which aims to further improve the spatial filling and uniformity of sample points. Based on the original Latin hypercube sampling, this criterion fixes the sample points of each subinterval at the center of the interval, and then optimizes the distribution of sample points 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, and Euclidean distance is often used. 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 proxy model.

[0040] Specifically, the centralized maximum and minimum criteria are used to improve the Latin hypercube sampling to extract the initial sample points at the upper and lower limits of the design variables, or other sampling methods are used to obtain the initial sample points, that is, the design variables X = {Δx1, Δx2, Δx3, ..., Δx n}. The maximum minimization criterion is to further fix the sample points of each subinterval at its center position on the basis of the original Latin hypercube sampling, and make the sample points as far apart as possible by optimizing the minimum distance between the sample points. The optimization objective of the maximum minimization criterion is as follows: In the above formula: ||x i -x j || represents the sample points xi and x j The Euclidean distance between two points, It represents the minimum distance of all sample points.

[0041] Use numerical calculation to calculate the value of the objective function, that is, to obtain 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 for each output can be built 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 the nonlinear correlation. The details of the Pearson correlation coefficient are as follows: In the above formula, Represents the correlation coefficient, which is used to measure the relevance of the target. Its range is between -1 and 1. i,k and X j,k Indicates target X i and X j The value at the kth sample point, as well as Indicates target X i and X j The average value of is used to center the data, where Spearman correlation coefficient: k is the number of sample points, dk is the ranking difference of the kth sample in different targets, and d k =rank(X i,k )-rank(X j,k), if |ρ is close to 1, it means strong correlation, if it is close to 0, it means weak correlation, then this threshold can be set to 0.6, because the multi-output proxy model has not been fitted accurately for a small number of samples after my experiments. If you want to expand to more outputs, you can calculate the correlation coefficients separately and obtain the correlation matrix. Then, for more targets, see which ones have high correlation and use one, and if not, use multiple models.

[0042] Use the obtained data to train the proxy model and use the optimization algorithm to optimize the hyperparameters of the Kriging proxy model. The selection of hyperparameters plays an important role in the performance and quality of the model. The determination of hyperparameters depends on the scale, complexity, computing resources and requirements for the optimization accuracy of hyperparameters. Generally speaking, manual selection and grid search are more appropriate in simple scenarios. However, in some complex scenarios, optimization algorithms are more suitable. Therefore, genetic algorithms, particle swarm algorithms, etc. can be selected for global optimization. The optimal hyperparameters are found by minimizing the negative log-likelihood function of the proxy model using the optimization algorithm. 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 are the diagonal elements of the CholeSky decomposition matrix of the correlation matrix R.

[0043] Specifically, Cholesky decomposition is a method for decomposing a symmetric positive definite matrix into the product of a lower triangular matrix and its transposed matrix. 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 transposed 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, it is necessary to calculate the inverse matrix and determinant of the correlation matrix R. Since the correlation matrix R is symmetric and positive definite, it can be decomposed by Cholesky to obtain the lower triangular matrix L, so 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 i-th diagonal element of the Cholesky decomposition matrix L. Using Cholesky decomposition to simplify the calculation of the inverse matrix and determinant 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 Figure 2 The specific flowchart of the multi-objective mantis optimization algorithm is also given in the paper, which includes the following steps: initializing the population; randomly generating a certain number of mantis individuals, each of which represents a set of wind turbine blade design variables. The initial position of the individual is randomly generated within the range of the design variable. The individuals of the initial population are input into the trained Kriging agent model, and the corresponding objective function (annual power generation and blade quality) values ​​are predicted as the fitness function values ​​of the individuals.

[0046] According to the non-dominated sorting and crowding calculation, the first-generation population is archived with individuals with better performance to form an external archive set. Non-dominated sorting is used to compare and distinguish the pros and cons of individuals in the population. In multi-objective optimization problems, there are usually multiple conflicting objective functions, which makes it difficult to directly compare the pros and cons of individuals. Non-dominated sorting is based on the Pareto dominance relationship and divides the population into multiple non-dominated fronts. If all the objective function values ​​of individual A are not inferior to those of individual B, and at least one objective function value is better than that of individual B, then individual A is said to dominate individual B. Through non-dominated sorting, the pros and cons of individuals can be evaluated according to the non-dominated layer in which they are located. Individuals in the front non-dominated layer are better than those 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 indicator used to measure the density of individuals in the population in multi-objective optimization, reflecting the spatial density around individuals. On the basis of non-dominated sorting, crowding degree is used to distinguish the advantages and disadvantages of individuals in the same non-dominated layer and maintain 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 (with the smallest and largest function values) after sorting, their crowding degree is infinite. For the middle individual i, its crowding degree is the sum of the function value differences of the two adjacent individuals on the objective function: Among them, f[i+1] and f[i-1] are the function values ​​of the next and previous individuals of individual i on the objective function, respectively. max and f minis the maximum and minimum value of the objective function in the non-dominated layer. The crowding degree of all objective functions is summed to obtain the crowding degree of the individual. The larger the crowding degree, the lower the spatial density of the area where the individual is located, the larger the interval between individuals, and the better the diversity. In the selection process, individuals at the front of the non-dominated layer are preferred; for individuals in the same non-dominated layer, individuals with larger crowding degree are preferred. In this way, while converging to the Pareto front, the diversity of the population can be taken into account to avoid premature convergence to the local optimal solution. In the embodiment of the optimization design of wind turbine blades, non-dominated sorting is used to compare the advantages and disadvantages of blade design schemes in terms of annual power generation and blade quality, and the population is divided into different non-dominated layers. Crowding degree is used to maintain the diversity of blade design schemes in the same non-dominated layer, and individuals with sparse distribution are preferentially retained. Through non-dominated sorting and crowding degree calculation, blade design schemes with better performance and uniform distribution can be selected in the iterative process to form an external archive set, and finally the Pareto front solution set of the wind turbine blade optimization design problem is obtained.

[0048] Based on the multi-objective mantis optimization algorithm, the position is updated. The original multi-objective mantis optimization algorithm uses levy flight to generate irregular random jumps and multi-scale step changes to improve the global search ability of the algorithm. Fixed scaling factors and exponential decay are introduced in levy flight. Levy flight is improved into an adaptive step by exponential decay, so that the search process of the algorithm uses large step exploration in the early stage, and the later search process gradually becomes a small step search for the algorithm locally, effectively balancing the exploration and development process to improve the performance and convergence effect of the algorithm. Levy flight is a random walk process whose step obeys a heavy-tailed distribution (such as Levy distribution) and can generate irregular random jumps and multi-scale step changes. Compared with the traditional Gaussian random walk, Levy flight has more large step jumps and small step local searches. Irregular random jumps refer to the large step jump behavior generated by Levy flight. Compared with the traditional Gaussian random walk, its step distribution has a heavier tail and produces more large displacements. This irregular jump enables the optimization algorithm to conduct a large-scale exploration in the search space, jump out of the current local area, and discover new promising solution areas. Irregular random jumps increase the global search capability of the algorithm, which helps to avoid premature convergence and falling into local optimality. In the present application, irregular random jumps can help the optimization algorithm to conduct a large-scale exploration in the blade design parameter space, generate blade design schemes with large differences, explore new optimization directions, and improve the globality and robustness of the optimization. Multi-scale step size changes enable the optimization algorithm to search at different granularities in the blade design parameter space. Large step size changes help the algorithm to conduct a global exploration in the design space and generate blade schemes with large differences; small step size changes fine-tune and optimize the blade schemes in the local area to improve the sophistication and performance of the design. The introduction of multi-scale step size changes can balance the exploration and development capabilities of the algorithm and improve the efficiency and quality of the wind turbine blade optimization design.

[0049] The specific step size improvements are as follows: In the above formula, A is a fixed scaling factor introduced for levy flight, is the exponential decay introduced, and λ is the exponential parameter that controls the distribution shape, which affects the tail shape of the levy flight. The updated population individuals are input into the Kriging proxy model to predict their fitness function values. In order to balance the computational efficiency and optimization accuracy, some individuals are extracted to calculate the true objective function value, determine the model accuracy, and use the corresponding proportion of the current population to calculate the true value of some individuals in this generation of population. The coefficient of determination R 2 And the mean square error MSE is used as the judgment basis. When one of the targets is lower than the threshold, adaptive sampling update will be performed, that is: MSE i ≥α MSE,in, is the coefficient of determination, is the mean square error, y ij is the true target value of the jth sampling point, is the predicted value of the j-th sampling point using the surrogate model, is the average value of the true value of the objective function of some sample points extracted, n is the number of sample points extracted, and α MSE They are respectively the triggering conditions for adaptive updating.

[0050] According to the model accuracy, it is determined whether to perform adaptive multi-dimensional addition of points, re-update the training agent model, and propose an adaptive multi-dimensional addition of points strategy to improve the prediction accuracy of the agent model. The specific steps are as follows: Use the maximum and minimum values ​​of each individual feature in the population as the threshold of random disturbance, perturb this generation of population, and form the candidate set population through the perturbed population and the population generated by the random sequence. The specific formula is as follows: In the above formula, x i,j (new) The new individuals generated by the perturbation, x i,j Represents an original individual in the current population The numerical representation of the jth feature, δ i,j is a disturbance random variable, and its value range is between [-1,1], which ensures the individual randomness of the entire disturbance. ξ is a disturbance factor, which is used to determine the proportion range of the disturbance. represents the maximum value of the jth feature of this individual, The minimum value of the j-th feature.

[0051] The maximum and minimum expected improvement (EI) strategy is introduced to calculate the EI value of the candidate point as an indicator 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. The specific formula is as follows: EI(x)=σ(x)·(Z·Φ(Z)+φ(Z))+β·σ(x), where Z represents the standardized value of the potential improvement of the model by the candidate point x, μ(x) represents the mean predicted by the Kriging surrogate model at position x, σ(x) represents the standard deviation of the prediction, and 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 regulates the exploration and utilization capabilities.

[0052] The clustering method is used to divide the candidate set points into adaptive clusters. The clustering method is chosen not only because clustering can divide the candidate set into different groups, but also to divide the candidate set more reasonably and more targeted. Considering the complexity of calculation, adaptive K-means clustering is used to divide the data points. Clustering adaptation means that as the number of iterations increases, the number of clusters will change adaptively, as follows:

[0053] In the above formula, K(It) means the number of groups that need to be divided at present, K min is the minimum number of data partition groups, K max is the maximum number of partition groups that can be determined. It means that as the number of iterations increases, the adaptive iteration factor will gradually decrease. It is the current number of iterations of the optimization algorithm, MaxIt is the maximum number of iterations of the optimization algorithm, and C j It represents the region division of the j-th candidate set, which contains similar data. K represents the number of adaptive clusters, which is equivalent to K(It). represents the i-th candidate set sample point, Represents the center of each cluster.

[0054] Using the idea of ​​non-dominated sorting and crowding distance, the expected improvement value of each cluster is used as a reference for non-dominated sorting, and the sample points on the Pareto frontier in each cluster are selected as new points to be added to the training set. Therefore, by distinguishing different data in the clustering method and enriching the data with the improvement expectation, a multi-dimensional point addition strategy is provided. For each candidate point of the cluster group, its expected improvement is used 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 It is a candidate point, and EI uses an expected improvement strategy, using this value as the fitness function as the basis for generating the Pareto frontier. In this application, each candidate solution (blade design scheme) corresponds to multiple objective function values ​​(such as annual power generation, blade quality, etc.). Through non-dominated sorting, non-dominated solutions in the candidate solution set can be found to form a Pareto frontier. The solution on the Pareto frontier represents the blade design scheme that achieves the optimal balance between the various objective functions, providing decision makers with a set of optimized options.

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

[0056] Use a proxy model to predict the true function value; archive update and diversity maintenance. The original multi-objective mantis optimization algorithm will gradually converge during the iteration process, which will cause individuals in some populations to tend to the same or similar individual positions, and then individual repetition will occur. A guided diversity maintenance strategy is proposed to effectively improve this problem. Based on the introduction of whale hunting behavior to handle repeated individuals, the repeated individuals are guided to the current optimal individual, so that they move in the direction of the optimal individual, and a certain randomness is maintained to avoid falling into the local optimal solution. Among them, when repeated individuals are detected in the population, these individuals can be processed using whale hunting behavior. First, the optimal individual in the current population is determined as the hunting target. Then, for each repeated individual, the process of whales encircling prey is simulated, and the repeated individuals are moved and updated around the optimal individual. Through the simulation of this whale hunting behavior, the repeated individuals can be updated under the guidance of the optimal individual to obtain a new position and solution. In this way, the convergence speed of the population can be accelerated while maintaining the diversity of the population, and the optimization performance of the algorithm can be improved. In this application, the use of whale hunting behavior to handle repeated individuals can effectively maintain the diversity of the population. When repeated blade design solutions appear during the optimization process, these repeated solutions can be guided to the current optimal blade design solution through mobile updates in the roundup and attack phases, while introducing random factors to avoid completely copying the optimal solution. In this way, while exploring new design solutions, the information of the current optimal solution can be fully utilized to accelerate the convergence speed of optimization.

[0057] Specifically, the improvement of the multi-objective mantis optimization algorithm includes the following steps: checking duplicate individuals based on the merged population archive; introducing random parameters and This allows repeated individuals to have a certain degree of randomness in the process of moving towards the optimal individual, avoiding overlap with the original individual. Calculate the distance between each individual Used for location updates. Update individual positions to allow individuals to develop in the optimal direction. The specific implementation principle is as follows: In the above formula: is the optimal individual of the current population, that is, the mutation-guided individual; It is the duplicate individual that needs to be mutated at present; is a random parameter that controls the amplitude of position adjustment; This random parameter is mainly used to enhance the diversity of individual mutations. In this embodiment, there are still other ways to improve the algorithm, such as introducing other strategies such as crossover mutation of genetic algorithms. Check the iterative termination condition. If it is met, output the Pareto frontier solution set. Otherwise, return to continue updating the iteration to guide the iterative termination condition to be met;

[0058] From the output Pareto frontier solution set, according to the design constraints and preferences of the wind turbine blades, the optimal blade design scheme is selected as the final optimization result. The weights of various objective functions, the feasibility of the design and other factors can be comprehensively considered, and the solution that best meets the requirements can be selected from the Pareto frontier solution set as the optimal design scheme.

[0059] In summary, the wind turbine blade optimization system based on the adaptive multi-dimensional point-adding Kriging proxy model provided by the present application improves the multi-objective mantis optimization algorithm through multiple strategies, improves the algorithm's ability to balance between global search and local search, and improves the distribution quality of the Pareto frontier. The prediction accuracy of the Kriging proxy 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 blades as a whole, which will greatly reduce the calculation cost of the objective function and improve the overall optimization efficiency. The present application is conducive to quickly and accurately designing wind turbine blades with high wind energy utilization, while optimizing the quality and structure of the blades, reducing the production cost of wind power generation. It solves the problem of lack of an overall optimization system in the multi-objective optimization process using the Kriging proxy model, and proposes to use a perturbed population to generate a candidate set and combine clustering to divide data points in a targeted manner, and use non-dominated sorting in each cluster cluster to find more potential points, adaptively update the model accuracy, and improve the thorny problem of the lack of algorithm diversity in the multi-objective mantis optimization algorithm in the process of obtaining the belt.

[0060] The invention of the present application and its implementation methods are described schematically above. The description is not restrictive. Without departing from the spirit or basic features of the present application, the present application can be implemented in other specific forms. What is shown in the accompanying drawings is only one of the implementation methods of the invention of the present application. The actual structure is not limited to this. Any figure mark in the claims should not limit the claims involved. Therefore, if a person of ordinary skill in the art is inspired by it, without departing from the purpose of the present invention, a structural method and an embodiment similar to the technical solution are designed without creativity, which should all fall within the scope of protection of this patent. In addition, the word "including" does not exclude other elements or steps, and the word "one" before the element does not exclude the inclusion of "multiple" elements. The multiple elements stated in the product claim can also be implemented by one element through software or hardware. The words first, second, etc. are used to indicate names, and do not indicate any specific order.

Claims

1. A method for designing a wind turbine blade, characterized in that: include: Build a wind turbine blade model; The Latin hypercube design method is used to generate initial sample points of the design scheme in the design space of the wind turbine blade model; Based on the initial sample points, a Kriging proxy model is constructed; The improved multi-objective mantis algorithm is used to iteratively solve the Kriging proxy model and obtain the Pareto frontier solution set. From the Pareto frontier 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.

2. The method for designing a wind turbine blade according to claim 1, characterized in that: Build a wind turbine blade model, including: Select the section airfoil Foil1 to Foil n As the design variable; where n represents a positive integer; Set up an objective function that includes annual energy production and blade quality; Set constraints, which include the range of design variables, blade deflection, and the first-order natural frequency of the wind turbine blade.

3. The method for designing a wind turbine blade according to claim 1, characterized in that: Construct a Kriging surrogate model, including: Adjust the sample of Latin hypercube sampling using the centered max-min criterion; The Latin hypercube sampling after sample adjustment is used to extract the initial sample points within the value range of the design variable to obtain the sample value 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 quality objective function values ​​corresponding to each sample point; Calculate the correlation between annual energy production and blade mass; According to the correlation, set the number of Kriging proxy models; Using the initial sample points, the Kriging surrogate model is trained using the maximum likelihood estimation method.

4. The method for designing a wind turbine blade according to any one of claims 1 to 3, characterized in that: The improved multi-objective mantis algorithm is used to iteratively solve the Kriging proxy model, including: Establish a mapping relationship between the position of mantis individuals and the design variable values ​​of wind turbine blades, and randomly generate initial mantis populations representing different design schemes of wind turbine blades; Use the Kriging surrogate model to predict the objective function value corresponding to each individual in the initial mantis population; Perform non-dominated sorting on the positions of individuals in the initial mantis population and the predicted objective function values, extract non-dominated solutions to generate an initial Pareto solution set, and store it in an external archive; Based on the Levy flight strategy, set the adaptive step size and update the position of individuals in the mantis population; Use the Kriging surrogate model to predict the objective function value corresponding to each individual in the mantis population after the position is updated; For the mantis population after the position update, some mantis individuals are selected based on the random sampling method, and the determination coefficient R2 and mean square error MSE of the prediction accuracy of the Kriging proxy model are calculated according to the predicted objective function value and the true objective function value of the corresponding individuals; When the determination coefficient R2 is less than the threshold ε1, or the mean square error is greater than the threshold ε2, the Kriging proxy model is updated; Use the updated Kriging surrogate model to predict the objective function value of the current mantis population; Perform non-dominated sorting on the current position of the mantis population and the updated predicted objective function value, extract the non-dominated solutions and merge them with the Pareto solution set in the external archive to obtain the updated Pareto solution set; Combined with the archived individual diversity maintenance strategy, Gaussian perturbation is performed on the Pareto solution set in the current external archives; According to the Pareto solution set after Gaussian perturbation, determine whether the current mantis population position data and the predicted objective function value meet the preset conditions. If so, output the Pareto solution set in the current external archive. Otherwise, proceed to the next round of iterative optimization.

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

6. The method for designing a wind turbine blade according to claim 4, characterized in that: Updates to the Kriging surrogate model include: Perform perturbation on the dimensional features of each individual in the current population to obtain a set of perturbed individuals; A random sequence is used to generate a set of random individuals; Merge the perturbed individual set and the random individual set to form a candidate set; According to the maximum value of the objective function of each candidate point in the candidate set f max and the minimum value f min , calculate the maximum and minimum expected improvement values ​​EI of the candidate points as the evaluation index. The calculation formula of the EI value is: EI(x)=σ(x)·(Z·Φ(Z)+φ(Z))+β·σ(x) Among them, Z represents the standardized value of the potential improvement of the model by the candidate point x, μ(x) represents the mean predicted by the Kriging surrogate model at position x, σ(x) represents the standard deviation of the prediction, and 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 exploitation capabilities. The K-means clustering algorithm is used to adaptively cluster the candidate set to obtain K clusters; Calculate the cluster C j The EI value of the candidate point in is used as the fitness value, and the cluster C is determined by non-dominated sorting according to the fitness value. j The Pareto frontier point; The Pareto frontier points of each cluster are used as new sample points, added to the original training set, and the training set is updated; Use the updated training set to train the Kriging surrogate model.

7. The method for designing a wind turbine blade according to claim 4, characterized in that: The dimensional features of each individual in the current population are disturbed by the following formula: Among them, x i,j (new) The new individual generated by the perturbation is represented by xi,j, which represents an original individual in the current population. The numerical representation of the jth feature, δ i,j is a disturbance random variable, and its value range is between [-1, 1], which ensures the individual randomness of the entire disturbance. ξ is a disturbance factor, which is used to determine the proportion range of the disturbance. represents the maximum value of the jth feature of this individual, The minimum value of the jth feature; N represents the number of individuals in the current population.

8. The method for designing a wind turbine blade according to claim 4, characterized in that: The number of clusters K for adaptive clustering is determined by the following formula: In the above formula, K(It) means the number of groups that need to be divided at present, K min is the minimum number of data partition groups, K max is the maximum number of partition groups that can be determined. It means that as the number of iterations increases, the adaptive iteration factor will gradually decrease. It is the current number of iterations of the optimization algorithm, MaxIt is the maximum number of iterations of the optimization algorithm, and C j It represents the region division of the j-th candidate set, which contains similar data. K represents the number of adaptive clusters, which is equivalent to K(It). represents the i-th candidate set sample point, Represents the center of each cluster.

9. The method for designing a wind turbine blade according to claim 4, characterized in that: Perform Gaussian perturbation on the Pareto solution set in the current external archive, including: Get the repeated individuals in the Pareto solution set in the current external archive; For each replicate, set the random parameters and Calculate the distance between all individuals in the Pareto solution set in the current external archive Using random parameters and And distance Update the positions of duplicate individuals: in, is the optimal individual of the current population, that is, the mutation-guided individual; It is the duplicate individual that needs to be mutated at present; is a random parameter that controls the amplitude of position adjustment; This random parameter is mainly 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.

10. A wind turbine blade design system, characterized in that: include: A model building module, which sets an objective function including annual power generation and blade mass, as well as constraints of design variables, based on the selected design variables, to build a wind turbine blade model; The design variables include the cross-sectional airfoil; the constraints include the value range of the design variables; The sample point module uses the centralized maximum and minimum criteria to adjust the sample of Latin hypercube sampling, and uses the Latin hypercube sampling after the adjustment to extract the initial sample points within the value range of the design variable to obtain the sample value of the design variable; The proxy module calculates the correlation between annual power generation and blade mass based on the sample values ​​of the design variables and the wind turbine blade model, sets the number of Kriging proxy models based on the correlation, and trains the Kriging proxy models using the initial sample points; In the processing module, the improved multi-objective mantis algorithm is used to solve the Kriging proxy model and obtain the Pareto frontier solution set; And according to the constraints of the wind turbine blades, the optimal solution is selected as the design scheme of the wind turbine blades; Processing modules, including: Solving the unit, establishing a mapping relationship between the position of the mantis individual and the design variable values ​​of the wind turbine blade, and randomly generating an initial mantis population representing different design schemes of the wind turbine blade; Use the Kriging surrogate model to predict the objective function value corresponding to each individual in the mantis population; Perform non-dominated sorting on the positions of the mantis population and the predicted objective function values, extract non-dominated solutions to generate a Pareto frontier solution set and store it in an external archive; Set adaptive step length based on levy flight strategy and update the position of individuals in the mantis population The proxy model update unit updates the Kriging proxy model. The update includes: Perform perturbation on the dimensional features of each individual in the current population to obtain a set of perturbed individuals; A random sequence is used to generate a set of random individuals; Merge the perturbed individual set and the random individual set to form a candidate set; Calculate the evaluation index of each candidate point in the candidate set; According to the evaluation index, the K-means clustering algorithm is used to cluster the candidate set to obtain K clusters; Calculate the Pareto frontier points of each cluster through non-dominated sorting; Use Pareto frontier points to update the Kriging proxy model; The diversity maintenance unit performs Gaussian perturbations on the Pareto frontier solution set in the external archive.

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