Topological optimization method for wind power blade with periodic structure under random field load effect

Abstract

The invention provides a topological optimization method for a wind power blade with a periodic structure under the action of a random field load, and belongs to the technical field of wind power generation. The K-L expansion method is adopted to discretize the random field problem, the random load field problem is converted into the random variable uncertainty problem, then the problem is solved through the displacement superposition principle, the orthogonal similarity transformation method and the Monte Carlo method, the calculation efficiency is high, and the method is easy to implement. The method can be effectively applied to topological optimization of the wind power blade with the periodic structure under the random field load effect.

Description

Technical Field

[0001] The present invention belongs to the technical field of wind power generation, and in particular relates to a topology optimization method for a wind turbine blade with a periodic structure under the action of a random field load. Background Art

[0002] As the core component of a wind turbine, the performance of wind turbine blades directly affects the power generation efficiency, power generation cost and service life. The design method of wind turbine blades is usually carried out by topology optimization. In the topology optimization of wind turbine blades, uncertainty is usually modeled by random variables or random fields. The former can be regarded as a component of the latter. When considering concentrated loads or uniformly distributed loads, the uncertain parameters of the load can be modeled as random variables. However, for physical quantities that vary throughout the space, such as material properties or randomly distributed loads, this type of uncertainty parameter with spatial dispersion problems needs to be processed by introducing a random field model. When describing a random field, in addition to considering the mean and standard deviation of the variable distribution, the correlation between random variables must also be considered. And as a periodic structure, wind turbine blades lack the periodic structure under the influence of Gaussian random field loads in the relevant technology. This application scheme. Summary of the Invention

[0003] The present invention provides a topology optimization method for a wind turbine blade with a periodic structure under the action of a random field load. The KL expansion method is used to discretize the random field problem, and the random load field problem is converted into a random variable uncertainty problem. The problem is then solved by the displacement superposition principle, the orthogonal similarity transformation method and the Monte Carlo method. The method has high computational efficiency and can effectively solve at least one technical problem involved in the background technology.

[0004] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0005] A topology optimization method for a wind turbine blade with a periodic structure under random field loads comprises the following steps:

[0006] Step S1, defining a design domain containing a periodic structure wind turbine blade and basic constraints, wherein the design domain is divided into a plurality of periodic array subdomains;

[0007] Step S2, using the density distribution of materials in the design domain as the design variable and minimizing the mean and standard deviation of the structural flexibility as the objective function, constructing a topology optimization model of a wind turbine blade with a periodic structure under random field loads;

[0008] Step S3: Define a random field load, discretize the random field load into multiple sub-loads using the KL expansion method, and superimpose the displacements of each sub-load based on the displacement superposition principle of elastic structures to obtain the total displacement of the wind turbine blade with a periodic structure, and calculate the overall structural flexibility of the wind turbine blade with a periodic structure.

[0009] Step S4: perform finite element analysis to calculate the sensitivity of the objective function to the design variables in each iteration process, and correct the sensitivity by the average value of the sensitivity at the current iteration number and the sensitivity in the historical iteration process;

[0010] In step S5, periodic constraints are imposed, with the same sensitivity of the units at the same position in all subdomains as the constraint, and the design variables are updated using the BESO method until the maximum number of iterations is reached or the convergence condition is met, completing the optimization process.

[0011] As a preferred improvement, the wind turbine blade with periodic structure is a two-dimensional periodic structure, which is formed by a periodic arrangement of several identical unit cell structures. The design domain is divided into M=M1×M2 subdomains, where M1 and M2 correspond to the number of subdomains in the y-axis and x-axis directions, respectively.

[0012] As a preferred improvement, the elastic modulus of each element in the design domain is defined based on the SIMP material interpolation technology, which is expressed as:

[0013]

[0014] Where, E s,t represents the elastic modulus of the element at the position (s, t) in the design domain; E0 represents the elastic modulus of the solid element; Represents the density of the unit at the position (s, t) in the design domain, where s and t represent the position of the subdomain in the design domain and the exact position of the unit in the subdomain. If a unit is a solid, its corresponding The value is 1; otherwise, if the cell is empty, the corresponding The value is the preset threshold x min , x min >0; p represents the penalty factor.

[0015] As a preferred improvement, the basic constraints include volume constraints of the entire structure, volume constraints of the subdomains, and volume constraints of the units in the subdomains.

[0016] As a preferred improvement, the topology optimization model of a wind turbine blade with a periodic structure under random field loads is expressed as:

[0017]

[0018] In the formula, J represents the optimization objective; μ(c) and σ(c) respectively represent the mean and standard deviation of the structural flexibility; β represents the weight factor, which is used to measure the importance of the standard deviation of the structural flexibility; f(x, ω) represents a random field load acting on the region D, x represents the spatial coordinate at any position on the region D, and ω represents a subset of all elements on the region D; KU = f(x, ω) is the finite element equilibrium equation of the structure, K represents the stiffness matrix; U represents the displacement matrix; ω ∈ Θ indicates the uncertainty of the random field load f(x, ω); V * represents the overall volume of the structure; V s represents the volume of the subdomain s; N e represents the number of elements; v s,t represents the volume of the element at the position (s, t); Ω represents the design domain; ρ 1,t = ρ 2,t = …ρ s,t … = ρ M,t means that the density of the elements at the same position in each cycle is the same.

[0019] As a preferred improvement, the K-L expansion form of the random field load f(x, ω) is as follows:

[0020]

[0021] In the formula, θ(x) represents the mean function of the random field load f(x, ω); L represents the truncation order under the accuracy condition. In this embodiment, L = 7; represents the orthogonal eigenfunction under the i-th order truncation; λ i represents the orthogonal eigenfunction corresponding eigenvalue; α i (ω) represents a random variable;

[0022] λ i and satisfy the characteristic equation:

[0023]

[0024] In the formula, C(x1, x2) represents the covariance function of the load magnitudes at positions x1 and x2, and is expressed as:

[0025]

[0026] In the formula, σ f represents the interval standard deviation; d represents the correlation length of the random field load f(x, ω), which is used to represent the correlation between the function values of each point in the random field load f(x, ω).

[0027] As a preferred improvement, the overall load vector f(ω) corresponding to the random field load f(x, ω) is expressed as:

[0028]

[0029] The structural displacement vectors corresponding to each load after discretization are u0, u1, u2…u L , and the overall displacement vector under the action of the structural load vector f(ω) can be expressed as:

[0030]

[0031] The structural flexibility c(ω) of the structure under the action of the random field load f(x, ω) can be expressed as:

[0032]

[0033] In the formula, c ij represents the inner product of the vector f i and the vector u j , c ij = f i T u j , and T represents the transpose matrix.

[0034] As a preferred improvement, the optimized objective function is expressed as:

[0035]

[0036] The sensitivity of the objective function to the design variables is expressed as:

[0037]

[0038] In the formula, U ie is the displacement vector of element e of the structure under the action of the load F i , and K e represents the stiffness matrix of element e when it is filled with material; E0 represents the elastic modulus of element e when it is filled with material; E min is the minimum value of the elastic modulus given to avoid singularity of the stiffness matrix, and take E min = 10 -3 .

[0039] As a preferred improvement, the corrected sensitivity is expressed as:

[0040]

[0041] In the formula, k is the current iteration number, and k > 2.

[0042] As a preferred improvement, the applied periodic constraint condition is expressed as:

[0043]

[0044] The beneficial effects of the present invention are:

[0045] The KL expansion method is used to discretize the random field problem, and the random load field problem is converted into a random variable uncertainty problem, which is then solved through the displacement superposition principle, orthogonal similarity transformation method and Monte Carlo method. It has high computational efficiency and can be effectively applied to the topology optimization of wind turbine blades with periodic structures under random field loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0047] Figure 1 represents the design domain of the wind turbine blade with periodic structure in Example 1;

[0048] Figure 2 A comparison diagram of the structural configuration after topology optimization of the present application and the prior art under different cycle numbers;

[0049] Figure 3 It represents the structural configuration diagram obtained by the topology optimization method of the present application under different correlation length conditions;

[0050] Figure 4 It represents the structural configuration diagram obtained by the topology optimization method of this application under different weight coefficient conditions. DETAILED DESCRIPTION

[0051] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0052] This embodiment provides a topology optimization method for a wind turbine blade with a periodic structure under random field loads, comprising the following steps:

[0053] Step S1 : defining a design domain of a wind turbine blade having a periodic structure and basic constraints, wherein the design domain is divided into a plurality of subdomains of periodic arrays.

[0054] The wind turbine blade with a periodic structure is a two-dimensional periodic structure, which is formed by periodically arranging a number of identical unit cell structures. In order to fully consider the periodic characteristics of the wind turbine blade, the design domain is divided into a number of completely identical sub-domains. As Figure 1 shown, in this embodiment, the wind turbine blade is a two-dimensional periodic structure, and the design domain is divided into M = M1×M2 sub-domains, where M1 and M2 respectively correspond to the number of sub-domains in the y-axis and x-axis directions.

[0055] The basic constraint conditions include the volume constraint of the overall structure, the volume constraint of the sub-domains, and the volume constraint of the elements in the sub-domains.

[0056] Step S2: Using the density distribution of the material in the design domain as the design variable, and minimizing the mean and standard deviation of the structural compliance as the objective function, a topology optimization model of the wind turbine blade with a periodic structure under the action of a random field load is constructed.

[0057] Taking the density of the element at the position (s, t) in the design domain as the design variable, where s and t respectively represent the position of the sub-domain in the design domain and the exact position of the element in the sub-domain to which it belongs; p represents the penalty factor. If an element is a solid, the corresponding value is taken as 1; conversely, if the element is an empty element, the corresponding value is taken as a preset threshold x min , x min > 0, to avoid the problem of singularity of the structural stiffness matrix during the optimization process.

[0058] Based on the SIMP material interpolation technique, the elastic modulus of each element in the design domain is defined as:

[0059]

[0060] In the formula, E s,t represents the elastic modulus of the element at the position (s, t) in the design domain; E0 represents the elastic modulus of the solid element.

[0061] The topology optimization model of the wind turbine blade with a periodic structure under the action of a random field load is expressed as:

[0062]

[0063] Where J represents the optimization objective; μ(c) and σ(c) represent the mean and standard deviation of the structural flexibility, respectively; β represents the weight factor, which is used to measure the importance of the standard deviation of the structural flexibility; f(x, ω) represents a random field load acting on region D, x represents the spatial coordinates of any position on region D, and ω represents a subset of all units on region D; KU = f(x, ω) is the finite element equilibrium equation of the structure, K represents the stiffness matrix; U represents the displacement matrix; ω∈Θ indicates that the random field load f(x, ω) is uncertain; V * Represents the overall volume of the structure; V s represents the volume of subdomain s; N e Indicates the number of units; v s,t represents the volume of the unit at the position (s, t); Ω represents the design domain; ρ 1,t =ρ 2,t =…ρ s,t …=ρ M,t This means that the density of cells at the same position in each period is the same.

[0064] In step S3, a random field load is defined and discretized into multiple sub-loads using the KL expansion method. Based on the displacement superposition principle of elastic structures, the displacements under each sub-load are superimposed to obtain the total displacement of the wind turbine blade with a periodic structure, and the overall structural flexibility of the wind turbine blade with a periodic structure is calculated.

[0065] The KL expansion form of the random field load f(x,ω) is as follows:

[0066]

[0067] Wherein, θ(x) represents the mean function of the random field load f(x, ω); L represents the truncation order that meets the accuracy condition, and in this embodiment, L=7; represents the orthogonal characteristic function under the i-th order truncation; λ i represents the orthogonal characteristic function The corresponding eigenvalue; α i (ω) represents a random variable;

[0068] λ i and Satisfies the characteristic equation:

[0069]

[0070] Where C(x1,x2) represents the covariance function of the load magnitude at positions x1 and x2, which is expressed as:

[0071]

[0072] In the formula, σ frepresents the standard deviation of the interval; d represents the correlation length of the random field load f(x, ω), which is used to express the correlation between the function values at each point in the random field load f(x, ω). Given the correlation length d, the correlation coefficient of the load between any two points depends only on the distance between the two points and is not affected by their specific spatial locations. Given the correlation length d, the correlation coefficient of the load magnitude at any two points is related only to the distance between the two points and is not affected by their specific locations.

[0073] In a Gaussian random field, the random variable α i (ω) is an orthogonal random variable with mean 0 and variance 1, which satisfies the following equation:

[0074] H[α i ]=0;

[0075] H[α i α j ]=δ i,j ;

[0076] Where H represents the expectation; δ i,j Represents the Kronecker delta symbol. When i=j, δ i,j Take 1, otherwise δ i,j Take 0; j represents the variable number.

[0077] Then the random variable α i (ω) is defined as follows:

[0078]

[0079] The random field load f(x,ω) can be represented by a linear combination of orthogonal functions. Based on the linear superposition principle, let: f0 = θ(x); Then the overall load vector f(ω) corresponding to the random field load f(x,ω) is expressed as:

[0080]

[0081] After discretization, the structural displacement vector corresponding to each load is u0, u1, u2…u L , the overall displacement vector under the action of the structural load vector f(ω) can be expressed as:

[0082]

[0083] The structural flexibility c(ω) of the structure under the action of random field load f(x,ω) can be expressed as:

[0084]

[0085] Where c ij Represents vector fi The inner product with vector u j , c ij = f i T u j , where T represents the transpose matrix.

[0086] Based on the orthogonality between random variables α i , the mean value of the structural flexibility can be expressed as:

[0087]

[0088] In the formula, c ii represents the inner product of vector f i and vector u i , c ij = f i T u i ;

[0089] The variance of the structural flexibility c is calculated by the following formula:

[0090]

[0091] In the formula, α i , α j , α k , α l represent different variables respectively, δ ij , δ kl represent the Kronecker symbol, c ij , c kl represent the structural flexibility values; α ijkl represents the fourth-order central moment of α i , α ijkl = E(α i α j α k α l ), i, j, k, l = 0, 1…L;

[0092] Since the load field is a normal random field, therefore, α i are independent of each other and follow the distribution α i ~ N(0, 12), and the Monte Carlo method can be used to calculate α ijkl .

[0093] Then the optimization objective function is expressed as:

[0094]

[0095] Step S4: perform finite element analysis to calculate the sensitivity of the objective function to the design variables in each iteration process, and correct the sensitivity by the average value of the sensitivity at the current iteration number and the sensitivity in the historical iteration process.

[0096] The mean μ(c) and variance σ(c) of the structural flexibility c are related to the unit design variables. The derivatives of are expressed as:

[0097]

[0098] Objective function J versus design variables The derivative of can be expressed as:

[0099]

[0100] Define the variable w ij for:

[0101]

[0102] Then the derivative of the objective function with respect to the design variable can be simplified as:

[0103]

[0104] In order to improve the computational efficiency, the orthogonal similarity transformation method is used to reduce w ij The computational cost of the matrix w is composed of elements w ij is a real symmetric matrix of order (L+1)×(L+1), then there are L+1 real numbers λ0,λ1,…,λ L And an orthogonal matrix Q such that:

[0105] Q T WQ=diag{λ0,λ1,…,λ L};

[0106] Introduce the following matrix:

[0107] f=[f0,f1,…,f L ];

[0108] u=[u0,u1,…,u L ];

[0109] F=[F0,F1,…,F L ] = fQ;

[0110] U=[U0,U1,…,U L ]=uQ;

[0111] Construct the following function:

[0112]

[0113] For any design variable, the following equation holds:

[0114]

[0115] Then, we can obtain:

[0116]

[0117] In the formula, U ie is the displacement vector of element e of the structure under the action of load F i , and K e represents the stiffness matrix of element e when it is filled with material; E0 represents the elastic modulus of the element when it is filled with material; E min is the minimum value of the elastic modulus given to avoid singularity of the stiffness matrix. Take E min = 10 -3 .

[0118] To ensure the convergence of the optimization, the current sensitivity value is usually averaged with the historical information to correct the element sensitivity value. The corrected sensitivity is expressed as:

[0119]

[0120] In the formula, k is the current iteration number, and k > 2.

[0121] Step S5: Apply periodic constraint conditions. With the sensitivity of elements at the same position in all subdomains being the same as the constraint, use the BESO method to update the design variables until the maximum iteration number is reached or the convergence condition is satisfied, thus completing the optimization process.

[0122] To meet the periodic requirements of the structure and ensure the same situation of element deletion or addition, the sensitivity of elements at the same position in each subdomain should be kept consistent. The sensitivity of the element at the (s, t) position in the design domain is represented by ε s,t , and can be calculated as the average value of the sensitivities of elements at the same position in all subdomains, which is expressed as:

[0123]

[0124] After obtaining the objective function and constraint function, calculate the relevant sensitivity values, and then update the design variables through the BESO method.

[0125] Example 1

[0126] This example provides a topology optimization method for a wind turbine blade with a periodic structure under random field loads. The design domain targeted is as shown in Figure 1As shown, the size is 6m×3m, which is divided into 600×300 units. The Young's modulus E of the wind turbine blade material is 1000Pa, the Poisson's ratio μ is 0.3, the penalty factor p is 3, the weight coefficient β is 1, and the filtering radius r min = 3.

[0127] Both ends of the bottom of the design domain structure are completely fixed. The random field load (wind load) is evenly distributed on the upper surface of the blade, and the load magnitude at each point in the field follows a normal distribution f~N(1,0.12).

[0128] In the optimization process, the BESO method is used to update the design variables, the iteration rate is 0.02, and the maximum number of iterations is 200.

[0129] The design domain is divided into three types with the number of periods M = 1×1, M = 1×2, and M = 1×3. The correlation length d is taken as 0.15m, the material volume fraction is set to 0.4, and the topology optimization methods provided by the present application and the prior art are respectively used for optimization to obtain the topology configurations as Figure 2 shown. The specific numerical results obtained in the optimization process are shown in Table 1.

[0130] Table 1 Optimization results of the present application and the prior art under different numbers of periods

[0131]

[0132] Combined with Table 1 and Figure 2 it can be seen that:

[0133] (1) The topology configurations obtained by the present application and the prior art are different. The results obtained by the prior art contain more fine struts and holes, indicating that the uncertainty of the random load field has a certain impact on the topology optimization of periodic structures;

[0134] (2) The design results obtained by the prior art and the present application are both symmetric because the design domain and boundary conditions are symmetric in the optimization;

[0135] (3) The results of the present application and the prior art both have clear boundaries and obvious periodicity, proving the effectiveness of the method proposed in this paper;

[0136] (4) At each number of periods, the objective function values obtained by the present application are always lower than those obtained by the prior art, indicating that the design results obtained by the present application have better mechanical performance.

[0137] In order to further study the influence of the correlation length of random field load on the optimization process, only the correlation length of random field is changed, while other optimization parameters remain unchanged. The correlation length d is set to 0.15, 0.3, 0.45, and 0.6 respectively, and the optimization process is carried out on the periodic structures of M = 1 × 1 and M = 1 × 3. The configuration obtained in this application is as follows Figure 3 As shown; the correlation length d is set to 0.15, 0.3, 0.45, and 0.6 respectively, and the periodic structures of M = 1×1 and M = 1×3 are optimized using the topology optimization methods of this application and the prior art. The optimization results are shown in Table 2:

[0138] Table 2 Optimization results of the present application and the prior art under different correlation length conditions

[0139]

[0140]

[0141] from Figure 3 As can be seen from Table 2, different values of the random field correlation length d yield different optimization results, indicating that the value of the correlation length d has a certain impact on the design results. Furthermore, under different correlation length conditions, the topological configurations obtained by the present application and the prior art are both symmetrical. When the correlation length is taken at different values, the numerical results obtained by the present application are all smaller than those obtained by the prior art. This further confirms that the structure designed by the present application has superior mechanical performance, thus reaffirming the effectiveness of the method proposed in the present application.

[0142] In order to study the influence of the weight coefficient β on the optimization results, keeping other conditions unchanged, taking the correlation length d = 0.15, and only changing the size of β, the topology optimization method of this application is used to optimize the structure with a period number of M = 1 × 1 under the conditions of β = 2, 3, 4, and 5. The obtained configuration is as follows Figure 4 The results of the present application and the prior art are shown in Table 3.

[0143] Table 3 Optimization results of the present application and the prior art under different weight coefficients

[0144]

[0145] Combined with Table 3 and Figure 4 It can be seen that when the weight coefficient β changes, the topological configuration of the periodic structure also changes accordingly, indicating that the size of the weight coefficient has a certain influence on the optimization results of the periodic structure. Regardless of the value of β, the objective function value obtained by the processing of this application is lower than the objective function value obtained by the existing technology method, further confirming the effectiveness of the optimization method provided by this application in improving the mechanical properties of the structure.

[0146] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit of the present invention and the scope protected by the claims, and all of them fall within the protection scope of the present invention.

Claims

1. A topology optimization method for a wind turbine blade with a periodic structure under random field loads, characterized in that, It includes the following steps: Step S1, define the design domain and basic constraint conditions of the wind turbine blade with periodic structures. The design domain is divided into several sub-domains of periodic arrays; Step S2, taking the density distribution of materials in the design domain as the design variable and minimizing the mean and standard deviation of the structural flexibility as the objective function, construct a topology optimization model of the wind turbine blade with periodic structures under the action of random field loads; Step S3, define the random field load, discretize the random field load into multiple sub-loads by using the K-L expansion method, and according to the displacement superposition principle of elastic structures, superimpose the displacement amounts under each sub-load to obtain the total displacement of the wind turbine blade with periodic structures, and calculate the overall structural flexibility of the wind turbine blade with periodic structures; Step S4, perform finite element analysis, calculate the sensitivity of the objective function to the design variable in each iteration process, and correct the sensitivity with the average value of the sensitivity in the current iteration and the sensitivity in the historical iteration process; Step S5, apply periodic constraint conditions, take the same sensitivity of the elements at the same position in all sub-domains as the constraint, and use the BESO method to update the design variable until the maximum iteration number is reached or the convergence condition is satisfied, and complete the optimization process.

2. The topology optimization method of a wind turbine blade with a periodic structure under random field loads according to claim 1, characterized in that The wind turbine blade with periodic structures is a two-dimensional periodic structure, formed by periodic arrangement of several identical unit cell structures. The design domain is divided into M = M1×M2 sub-domains, where M1 and M2 respectively correspond to the number of sub-domains in the y-axis and x-axis directions.

3. The topology optimization method of a wind turbine blade with periodic structures under random field loads according to claim 1, wherein Define the elastic modulus of each unit in the design domain based on the SIMP material interpolation technology, expressed as: In the formula, E s,t represents the elastic modulus of the element at the position (s, t) in the design domain; E0 represents the elastic modulus of the solid element; Represents the density of the unit at the position (s, t) in the design domain, where s and t represent the position of the subdomain in the design domain and the exact position of the unit in the subdomain. If a unit is a solid, its corresponding The value is 1; Conversely, if the unit is an empty unit, then the corresponding value takes a preset threshold value x min , x min > 0; p represents a penalty factor.

4. The topology optimization method of a wind turbine blade with periodic structures under random field loads according to claim 3, wherein The basic constraint conditions include the volume constraint of the overall structure, the volume constraint of the sub-domains, and the volume constraint of the elements in the sub-domains.

5. The topology optimization method for a wind turbine blade with a periodic structure under a random field load according to claim 4, wherein The topology optimization model of the wind turbine blade with periodic structures under the action of random field loads is expressed as: In the formula, J represents the optimization objective; μ(c) and σ(c) respectively represent the mean and standard deviation of the structural flexibility; β represents the weight factor, which is used to measure the importance of the standard deviation of the structural flexibility; f(x, ω) represents a random field load acting on the region D, x represents the spatial coordinate at any position on the region D, and ω represents a subset of all elements on the region D; KU = f(x, ω) is the finite element equilibrium equation of the structure, K represents the stiffness matrix; U represents the displacement matrix; ω ∈ Θ indicates the uncertainty of the random field load f(x, ω); V * represents the overall volume of the structure; V s represents the volume of the subdomain s; N e represents the number of elements; v s,t represents the volume of the element at the position (s, t); Ω represents the design domain; ρ 1,t = ρ 2,t = …ρ s,t … = ρ M,t indicates that the density of the elements at the same position in each period is the same.

6. The topology optimization method for a wind turbine blade with a periodic structure under a random field load according to claim 5, characterized in that The K-L expansion form of the random field load f(x,ω) is as follows: Wherein, θ(x) represents the mean function of the random field load f(x, ω); L represents the truncation order under the accuracy condition, and in this embodiment, L = 7; represents the orthogonal eigenfunction under the i-th order truncation; λ i represents the orthogonal characteristic function The corresponding eigenvalue; α i (ω) represents a random variable; λ i and Satisfies the characteristic equation: In the formula, C(x1,x2) represents the covariance function of the load magnitudes at positions x1 and x2, expressed as: where σ f represents the interval standard deviation; d represents the correlation length of the random field load f(x, ω), which is used to represent the correlation between the function values of each point in the random field load f(x, ω).

7. The topology optimization method of a wind turbine blade with a periodic structure under a random field load according to claim 6, wherein The overall load vector f(ω) corresponding to the random field load f(x,ω) is expressed as: The structural displacement vectors corresponding to each load after discretization are u0, u1, u2…u L , and the overall displacement vector under the action of the structural load vector f(ω) can be expressed as: The structural flexibility c(ω) of the structure under the action of the random field load f(x,ω) can be expressed as: where c ij denotes the inner product of vector f i and vector u j , c ij = f i T u j , and T represents the transpose matrix.

8. The method for topology optimization of a wind turbine blade with a periodic structure under random field loads according to claim 7, characterized in that: The optimized objective function is expressed as: The sensitivity of the objective function to the design variable is expressed as: where U ie is the displacement vector of element e under the action of load F i , and K e represents the stiffness matrix of element e when it is filled with material; E0 represents the elastic modulus of the element when it is filled with material; E min is the minimum value of the elastic modulus given to avoid singularity of the stiffness matrix, and take E min = 10 -3 .

9. The method for topology optimization of a wind turbine blade with a periodic structure under random field loads according to claim 8, characterized in that: The corrected sensitivity is expressed as: In the formula, k is the current iteration number, and k>2.

10. The topology optimization method for a wind turbine blade with periodic structures under the action of a random field load according to claim 9, characterized in that, The applied periodic constraint conditions are expressed as:

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