High-dimensional fan blade reliability optimization method based on sparse orthogonal lattice points

Abstract

The invention provides a high-dimensional fan blade reliability optimization method based on sparse orthogonal lattice points, and relates to the technical field of high-dimensional fan blades, and the method comprises the following steps: S1, building a finite element model; s2, generating sparse orthogonal lattice points; s3, evaluating the response quantity of each performance index, and judging whether a reliability requirement is met or not; s4, quantitative sensitivity analysis; and S5, modifying the dispersibility of the key material parameters to carry out reliability evaluation. The invention provides a new uncertainty quantification method for a high-dimensional problem, a sampling error of sampling simulation and an approximate error of an agent model are avoided by directly substituting a design sample into the model for calculation, quantification of the high-dimensional problem is realized through sparse orthogonal lattice points, information loss caused by dimension reduction processing of a sensitivity analysis method is avoided, and the method is suitable for large-scale popularization and application. And when a reliability evaluation result does not meet a design requirement, an intermediate calculation result can be fully utilized to carry out sensitivity analysis, and a specific solution is provided for reliability optimization design.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of high-dimensional fan blade, and particularly relates to a high-dimensional fan blade reliability optimization method based on sparse orthogonal grids. BACKGROUND

[0002] High-dimensional problems mainly refer to complex problems involving multiple independent variables, which are commonly seen in mathematics, physics and engineering fields, and are characterized by the explosive increase in computational complexity and the rise in problem complexity caused by the increase in dimension.

[0003] The uncertainty quantification problem of the super-long flexible blade is essentially a super-high-dimensional random problem, and its high-dimensional characteristics mainly come from the following aspects: first, a large number of uncertainty parameters exist in the material itself at the macro and micro scales, such as the anisotropic elastic modulus, elastic limit, fatigue performance parameters and curing degree of the resin matrix in the composite layer, and these constitutive model parameters themselves have extremely high dimension; second, the load environment has high complexity, including the aerodynamic and hydrodynamic loads from wind, waves and flow, which have significant time and space randomness, and a large number of uncertain frequency and amplitude components are included in the random process; third, additional uncertainties are caused by geometric and manufacturing tolerances, such as the small deviations of the layer thickness, skin thickness, web position and blade shape that occur in the manufacturing and installation process, which will affect the structural performance. The coupling of the above-mentioned factors causes the blade structure probability response to involve hundreds of random input variables, so that the traditional probability analysis method cannot be applied due to the dimension disaster, and an advanced uncertainty quantification method for high-dimensional problems must be developed.

[0004] The uncertainty quantification method for high-dimensional problems can be mainly divided into three categories: sampling simulation method, proxy model method and sensitivity analysis method.

[0005] The sampling simulation method takes the Monte Carlo method as the core, and derives improved methods such as Latin hypercube sampling and quasi-Monte Carlo sampling for more efficient exploration of high-dimensional space. Latin hypercube sampling performs stratified sampling in each dimension, and then randomly combines each dimension level to avoid aggregation or blank in the dimensions, but it is still affected by the dimension disaster, and may miss the key areas generated by the coupling of variables; quasi-Monte Carlo sampling uses a low-discrepancy sequence to replace the pseudo-random number to more uniformly and efficiently fill the high-dimensional space, but its convergence rate is closely related to the dimension, and in the case of extremely high dimension, a large sample is often needed to show better convergence performance than the standard Monte Carlo method.

[0006] Proxy modeling approaches approximate the original high-dimensional physical model by constructing a simplified model with low computational cost, using surrogate model simulations with extremely low single-run overhead to support the massive computations required for uncertainty quantification. Typical methods include multinomial chaotic expansion, Kriging, and neural networks. The first two types construct multinomial or Gaussian process models based on input-output samples, while neural networks are mostly implemented using deep learning frameworks. Although surrogate models significantly reduce computational costs, their accuracy is heavily dependent on the quality and scale of the training samples, and the sample size required to construct a high-precision surrogate model increases exponentially with the input dimension. Furthermore, surrogate models have low predictive reliability outside the scope of the training data, and methods such as neural networks still have black-box characteristics, requiring meticulous validation to ensure their reliability.

[0007] Sensitivity analysis aims to screen key variables for dimensionality reduction by assessing the contribution of each variable to the system response. Common methods include the Morris screening method and the Sobol index method. The former can qualitatively rank the importance of variables, while the latter can quantitatively calculate the contribution rate of each variable, but its standard implementation (such as the Saltelli algorithm) requires further processing. The simulation ( For sample size, Dimensionality reduction (often involving high dimensionality) is computationally expensive. To mitigate this, it is often combined with surrogate models to reduce the cost of a single simulation and dimensionality reduction techniques such as active subspaces are introduced to reduce the number of samples required. However, these methods typically treat dimensionality reduction as a necessary preprocessing step, potentially ignoring interactions or tail effects between the removed parameters, leading to biased reliability assessments. Furthermore, the dimensionality reduction process is disconnected from subsequent analysis, serving only a filtering function and inevitably resulting in irreversible information loss.

[0008] Therefore, current methods for uncertainty quantification of high-dimensional problems have limitations, such as sampling errors, high computational costs, approximation errors introduced by surrogate models, information loss, and low reliability. A new uncertainty quantification method is needed to achieve uncertainty quantification for high-dimensional problems. Summary of the Invention

[0009] To address the shortcomings of the prior art, the present invention aims to provide a high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points. This method solves the problems of approximate errors and difficulty in achieving high-precision reliability assessment with low computational cost in the uncertainty quantification methods for high-dimensional problems in the prior art. At the same time, since it does not involve dimensionality reduction operations, it avoids the information loss caused by the dimensionality reduction process of sensitivity analysis.

[0010] Specifically, it includes the following steps: S1. Establish the finite element model: Establish the finite element model based on the pre-bending coordinate system of the blade; S2. Generate sparse orthogonal grid points: Generate normally distributed random variables based on the elastic modulus, shear modulus and density of each blade layup material in each direction. Select input variables from these variables and input them into the finite element model to generate sparse orthogonal grid points. Calculate the finite element simulation results for each sample and extract strain data for different layup materials. Obtain response estimates for each performance index through post-processing. The performance indexes include stability response factor, inter-fiber failure factor and fatigue failure factor. Establish system response The parameters in each dimension follow a functional relationship. The system response estimate is obtained based on sparse orthogonal lattice points: ; Among them, It is the total number of material parameters. As a level factor, For sparse orthogonal lattice point set The weights; To be related to the level factor Relationship between functions Related estimation errors; One method for selecting input quantities from normally distributed random variables is to construct a sparse orthogonal lattice set. Based on meeting the grid configuration requirements Global orthogonal grid set The values ​​of each sample in the subset are used as input values; S3. Evaluate the response of each performance index to determine whether the reliability threshold is met: Based on the influence of the variability of material density, elastic modulus in each direction, and shear modulus on the system response, several uncertainty variables are introduced. The finite element model is treated as a linear system, and the sparse orthogonal lattice point set in step S2 is considered. Evaluate the mean of the system response and variance And calculate reliability Given reliability thresholds for each performance metric, determine the reliability of the performance metric. Is it greater than the reliability threshold? If the reliability... If the reliability threshold is ≥, then the reliability is satisfied, and the reliability is output. If reliability If the reliability threshold is not met, proceed to steps S4 and S5. S4. Quantitative Sensitivity Analysis: Compare the simulated results of each sparse point under each performance index with the mean of the evaluation. The response difference is calculated, and the absolute value is taken to obtain the maximum deviation result. The elastic modulus corresponding to the main direction perpendicular to the ply material is identified as the first key material parameter. S5. Reliability Assessment by Modifying the Dispersion of Key Material Parameters: Given a tolerance limit for the dispersion of the first key material parameter, reduce the tolerance limit at set intervals until it reaches the lowest threshold. Based on step S2, generate orthogonal grid points under the updated distribution of the first key material parameter. In the finite element model, only change the value of the first key material parameter to the newly generated orthogonal grid points. Perform two finite element simulations for stability and inter-fiber failure respectively to obtain a secondary reliability assessment. When the tolerance limit drops to the lowest threshold, control the dispersion of the first key material parameter within the lowest threshold. Based on step S4, identify the material parameter with the second largest impact on the response of the finite element model as the second key material parameter, modify the dispersion, and repeat the above process until reliability is achieved. It is greater than the reliability threshold in step S3.

[0011] Further: In step S1, after establishing the finite element model, it is verified, including: assigning all material parameters in the finite element model to their pre-set design values, performing modal analysis using finite element analysis software, calculating the first few natural frequencies, comparing the calculation results with the corresponding first few natural frequencies of the simulation software with the same parameter settings, and outputting qualified finite element model parameters if the error is within the specified range.

[0012] Further: In step S2, the method for generating sparse orthogonal grid points and calculating the finite element simulation results for each sample is as follows: given the number of orthogonal grid points to be generated. The weight function generated by the Schmidt orthogonalization process is a distribution function of certain material parameters. orthogonal polynomials When the material parameters follow a normal distribution, the orthogonal polynomial corresponding to the standard normal distribution is obtained. for ; by Solve the system of linear equations with algebraic precision and use the inverse division operator to obtain the weights corresponding to each orthogonal lattice point.

[0013] Further: In step S3, the mean of the system response is evaluated. and variance And calculate reliability The method is: to adopt The sparse orthogonal lattice points are used to quantify various performance indicators of the blade. Let the sparse orthogonal lattice point set be... The corresponding weight is The system response and the parameters of each dimension follow a functional relationship. Evaluate the mean of the system response ,variance and reliability for: (1); (2); (3); reliability This represents the probability that the response factor falls within the reliability range.

[0014] Furthermore: when performing stability analysis, If the value is greater than the given first threshold, the stability analysis changes the values ​​of each material parameter in the finite element model to the sparse orthogonal lattice point set generated in step S2, and performs buckling analysis. The first eigenvalue of buckling that is not concentrated at the blade tip is extracted as the response factor. If the response factor is less than or equal to the stability threshold, it is considered a failure.

[0015] Furthermore: when performing inter-fiber failure analysis, When the strain is less than a given second threshold, the inter-fiber failure analysis first extracts the strain of each node from the finite element simulation results. Based on the rotation axis matrix Decompose it into fiber directions, based on the two-dimensional stiffness matrix. The stress along the fiber direction was calculated. ; The stress along the fiber direction was calculated using the PUCK criterion and based on the finite element simulation results. Then, the inter-fiber failure factor was calculated. for ; ; in, It is the calculated stress perpendicular to the fiber direction. Tensile strength perpendicular to the fiber direction. The compressive strength is perpendicular to the fiber direction. In-plane shear strength For stretching PUCK parameters, To compress the PUCK parameter, the threshold is 1. If the evaluation result is greater than 1, it is considered a failure.

[0016] Furthermore: when performing fatigue strength analysis, Fatigue strength analysis was performed at the blade tip. shaft and A unit load of 1 Nm was applied along the axial direction, and the strain of each component under the unit force was extracted to obtain the relationship between the unit bending moment and the stress in the fiber direction. The fatigue failure factor was calculated based on the Markov distribution. ; ; in, , These are the characteristic values ​​of the tensile and compressive strength of the material; ; It is the average value of fiber stress cycles. It is the stress cycle amplitude. is the number of cycles under different mean and amplitude values ​​in the Markov distribution, and m is the fatigue strength index.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention provides a novel method for quantifying uncertainty in high-dimensional problems. By directly substituting designed samples into the model for calculation, it avoids the sampling error of sampling simulation and the approximation error of surrogate models. It achieves the quantification of high-dimensional problems through sparse orthogonal grid points without involving dimensionality reduction operations, thus avoiding the information loss caused by the dimensionality reduction process of sensitivity analysis. Furthermore, when the reliability assessment results do not meet the design requirements, the intermediate calculation results can be fully utilized to carry out sensitivity analysis, providing guidance for reliability optimization design. 2. This invention effectively avoids the approximation error introduced by the proxy model by constructing a high-fidelity finite element model of the blade, and has good extrapolation ability; 3. This invention uses sparse orthogonal grid points in a scientifically designed parameter space as samples, which significantly suppresses sampling errors while achieving high-precision reliability assessment at a low computational cost. 4. This invention proposes a strategy to improve system reliability by adjusting the dispersion of key material parameters. When adjusting the parameter dispersion, only a very small number of grid simulation results under the new parameter configuration need to be obtained and weighted and fused with some calculation results of the original grid set, so as to quickly update the reliability assessment and significantly reduce the computational overhead. Attached Figure Description

[0018] Figure 1 This is a flowchart of the reliability quantization and dispersion optimization based on sparse orthogonal grid points in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the finite element model in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram showing the comparison of natural frequencies in modal analysis according to Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the results of the five components with the lowest reliability in the inter-fiber failure analysis in Embodiment 1 of the present invention. The horizontal axis represents the reliability of the Mx condition and the My condition, respectively. Figure 5 This is a schematic diagram of the mean and variance results of fatigue strength analysis in Embodiment 1 of the present invention; Figure 6This is a schematic diagram showing the maximum deviation between the sparse orthogonal grid points and the mean in Embodiment 1 of the present invention; Figure 7 This is a reliability comparison analysis chart under different dispersion conditions in Embodiment 1 of the present invention. The horizontal axis represents the tolerance limit, the vertical axis represents the reliability, the horizontal axis represents the period, and the vertical axis represents the absolute deviation. Detailed Implementation

[0019] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0020] Example 1: Taking a 126-meter-long commercial wind turbine blade as the research object, this study examines the impact of material uncertainty on its structural reliability, specifically covering the analysis and evaluation of three performance indicators: stability, inter-fiber failure, and fatigue strength.

[0021] The specific process is as follows: Figure 1 As shown, a high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points is proposed. First, a finite element model of the blade is constructed and verified by modal analysis. Second, sparse orthogonal grid points are generated and the finite element simulation results of each sample are calculated. The strain data of the simulation results are extracted, and the response estimates of each performance index are obtained through post-processing. These estimates are then compared with the given standard performance indexes to determine whether the reliability requirements are met. If they are met, the reliability assessment is completed. If not, a quantitative sensitivity analysis is performed on the simulation results of the index. The dispersion of key material parameters is identified and modified, new simulation grid points are designed, and the reliability assessment is quickly updated by weighting the simulation results with those of the original samples to obtain the optimal dispersion design scheme.

[0022] The reliability requirement of this embodiment is: given a reliability threshold, the blade's reliability with respect to this performance index should be greater than 99.75%. The response estimates for all performance indices in this embodiment meet the safety factor requirements. Therefore, the reliability results obtained in this embodiment essentially reflect the level of residual risk caused by the inherent dispersion of material properties, based on compliance with industry safety standards. Higher reliability means lower residual risk. Thus, setting the reliability threshold to 99.75% is sufficiently conservative and safe.

[0023] The following are the specific steps of the high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points applied in this embodiment: S1. Establishment and Verification of the Finite Element Model like Figure 2As shown, in the simulation environment, the finite element model of the blade is established based on the pre-bending coordinate system. The pre-bending coordinate system is a local coordinate system, with its origin at the intersection of the local chord length and the pre-bending axis, moving along the blade's pre-bending, pre-cone angle, and sweep angle. It moves along the blade deformation direction as the rotor rotates and the local pitch angle is adjusted. The total blade length is 126 meters, and the 300 mm tip is ignored during modeling, resulting in an effective model length of 125.7 meters.

[0024] In the mesh generation, a combination of 4-node surface elements, 3-node surface elements, and 8-node hexahedral elements were used for discretization, with the element size controlled within 100 mm. No mesh errors occurred during model checking. The layer thickness was assigned based on the equivalent thickness of each region.

[0025] The model includes 37 materials, of which 2 are isotropic and 35 are anisotropic. Each material is assessed for its elastic modulus, shear modulus, and density in three directions (X, Y, and Z). All material parameters in the model are assigned pre-defined design values. Modal analysis was performed using ANSYS software to calculate the first ten natural frequencies, and the results were compared with those calculated using the commercially available Bladed software with the same parameter settings.

[0026] like Figure 3 As shown, the errors of the first four natural frequencies are within 3%, and the errors of the fifth to tenth natural frequencies are within 10%, indicating that the finite element model successfully captures the general dynamic characteristics of the structure in terms of overall stiffness and mass distribution. It can be used for subsequent simulation analysis and output qualified finite element model parameters.

[0027] S2. Generate sparse orthogonal lattice points Given the number of orthogonal grid points to be generated The weight function generated by the Schmidt orthogonalization process is a distribution function of certain material parameters. orthogonal polynomials In particular, when the material parameters follow a normal distribution, the orthogonal polynomial corresponding to the standard normal distribution, i.e., the Hermite polynomial, can be directly obtained. for ; Using the binary search method Start calculation Solution: when hour, The solution at this time is ; when When, define a larger positive value Based on the bisection method in the interval Find the solution by taking the midpoint. ,like Then the solution ;like The solution lies in the interval. ;like The solution lies in the interval. Repeat this process, taking the midpoint of the interval where a solution exists, until the midpoint of some iteration is reached. satisfy The length of the interval where the solution exists is less than or equal to a certain preset value. At this point, the midpoint of the interval is... Due to the symmetry of the standard normal distribution, another solution... ; when When the standard normal distribution is symmetric, there must exist a solution. ; the definition is much larger than positive value Based on the bisection method in the interval Search for solutions Based on symmetry, another solution is ; And so on, to find Solution In the above process, express The first time One solution. .

[0028] That is Then, find the orthogonal lattice points and solve the following system of equations. ; in, This system of equations is a linear system, and its solution can be obtained directly using Matlab's inverse division operator. , which is the weight corresponding to each orthogonal grid point.

[0029] According to material production specifications, the permissible deviation, or tolerance limit, of material parameters is typically ±5% of the design value. Based on the 3σ criterion, it is assumed that the material parameters follow a normal distribution with a mean of the design value and a standard deviation of 1.67% of the design value. Assume that the design value of a certain material parameter is... Then its standard deviation is The orthogonal lattice points of this material parameter for ; in, These are standard orthogonal lattice points.

[0030] For each material parameter, namely the elastic modulus, shear modulus, and density in the X, Y, and Z directions of each blade layup material, an orthogonal lattice point set is generated. ,in It is the total number of material parameters. It is the first The number of orthogonal lattice points for each material parameter. Global orthogonal lattice point set. It can be obtained from the tensor product of various material parameters. ; remember The grid configuration is as follows , The number of orthogonal grid points used in each dimension is recorded. The global orthogonal grid point set is then sparsed according to the grid point configuration, and the level factor is defined as... This value reflects the accuracy level of sparse orthogonal grid points. Since each dimension has at least one orthogonal grid point, the grid point configuration... The minimum norm is Its upper bound is defined as Then the sparse orthogonal lattice point set Based on meeting the grid configuration requirements Some globally orthogonal lattice points, i.e. It consists of subsets. Its weights for ; in It is the product of the weights corresponding to the orthogonal grid points in each dimension.

[0031] If the system responds The parameters in each dimension follow a functional relationship. Then, the system response estimate can be obtained based on sparse orthogonal lattice points. ; in, This represents a specific lattice point in the sparse orthogonal lattice set, corresponding to each of the input material parameters. This indicates the weight corresponding to a specific grid point; To be related to the level factor Relationship between functions The relevant estimation error, when Can be When the polynomial of order X is precisely estimated, i.e., the functional relationship... When the nonlinear relationship is ≤ 2L+1 order polynomial, At this point, the estimation error is within the set error threshold.

[0032] S3. Evaluate the response of each performance indicator. Considering the influence of the variability of material density, elastic modulus in each direction, and shear modulus on the system response, a total of 249 uncertainties were introduced. The mean of each variable is a pre-set design value, the standard deviation is 1.67% of the design value, and all variables follow a normal distribution. The finite element model is treated as a linear system, and... The sparse orthogonal grid points are used to quantitatively analyze various performance indicators of the blade. The design load in this embodiment is obtained through smoothing based on user feedback and is applied to the nodes in the main beam region.

[0033] Let the sparse orthogonal lattice point set be The corresponding weight is The system response and the parameters of each dimension follow a functional relationship. Then evaluate the mean of the system response. ,variance and reliability for (1); (2); (3); According to standard GL2010, the first threshold for stability analysis is 2.04. When performing inter-fiber failure and fatigue strength analysis, the second threshold is 1. .

[0034] Stability analysis was performed by changing the values ​​of each material parameter in the finite element model to the sparse orthogonal lattice point set generated in step S2, and buckling analysis was conducted using ANSYS software. The first eigenvalue of buckling not concentrated at the blade tip was extracted as the response factor, with a first threshold of 2.04. If the response factor is less than this value, it is considered a failure. The stability results for the two working conditions were calculated according to formulas (1) to (3), as shown in Table 1. It can be seen that the current parameter design meets the reliability requirements of the My condition, but does not meet the reliability requirements of the Mx condition. The Mx condition represents the case where the blade reaches its maximum flapping moment, and the My condition represents the case where the blade reaches its maximum oscillation moment.

[0035] The table below shows the stability assessment results under various operating conditions. Mean Variance Reliability Mx 2.1053 0.0009 98.63% My 2.1361 0.0009 99.94% Inter-fiber failure analysis first extracts the strain of each node from the finite element simulation results. Based on the rotation axis matrix Decompose it into fiber directions, based on the two-dimensional stiffness matrix. The stress along the fiber direction was calculated. .

[0036] in, ; ; The stress along the fiber direction was calculated using the PUCK criterion and based on the finite element simulation results. Then, the inter-fiber failure factor was calculated. for ; ; in, It is the calculated stress perpendicular to the fiber direction. Tensile strength perpendicular to the fiber direction. The compressive strength is perpendicular to the fiber direction. In-plane shear strength , , Theoretical shear strength, This refers to the transverse tensile strength.

[0037] The threshold is 1; if the evaluation result is greater than 1, it is considered a failure. Based on formulas (1) to (3), the reliability of each component of the blade under the two operating conditions is calculated, and the reliability results of the five components with the lowest reliability are listed. For example... Figure 4 As shown, from Figure 4 As can be seen, the current parameter design meets the reliability requirements of the My condition, but does not meet the reliability requirements of the Mx condition.

[0038] Fatigue strength analysis is performed at the blade tip. shaft and A unit load of 1 Nm was applied along the axial direction, and the strain of each component under the unit force was extracted to obtain the relationship between the unit bending moment and the stress in the fiber direction. The fatigue failure factor was calculated based on the Markov distribution. in, , These are the characteristic values ​​of the tensile and compressive strength of the material; ; It is the average value of fiber stress cycles. It is the stress cycle amplitude. In a Markov distribution, this represents the number of cycles under different means and amplitudes, where m is the fatigue strength exponent. When the material is glass fiber... When the material is carbon fiber, The threshold for the fatigue failure factor is 1; if it exceeds 1, it is considered a failure. The response results are calculated according to formulas (1) to (3).Figure 5 As shown, from Figure 5 As can be seen, the fatigue failure factors of each component at each location are all within the threshold, and the reliability is 1, which meets the reliability requirements, and the reliability is output. If the reliability requirements are not met, proceed to steps S4 and S5.

[0039] S4. Quantitative Sensitivity Analysis Based on the calculation results of step S3, sensitivity analysis of stability and inter-fiber failure under the Mx condition is required. The simulation results for each sparse orthogonal lattice point under each performance index are subtracted from the mean response obtained from the evaluation. The absolute value is then used to obtain the maximum deviation between the sparse orthogonal lattice point and the mean. The corresponding material EY is identified as the first critical material parameter, where EY represents the elastic modulus perpendicular to the principal direction of the ply material. The results are as follows: Figure 6 As shown, Figure 6 In the diagram, the horizontal axis represents the sparse orthogonal grid point numbers, with the upper axis representing stability and the lower axis representing inter-fiber failure analysis. From... Figure 6 As can be seen, groups 444 and 445 of sparse orthogonal lattice points have the greatest impact on the stability results; groups 374 and 375 have the greatest impact on the inter-fiber failure results. Groups 444 and 445 of the sparse orthogonal lattice points correspond to a decrease / increase of one standard deviation in EY for material 6, respectively, while groups 374 and 375 correspond to a decrease / increase of one standard deviation in EY for material 11. The effects of the decrease / increase of other variables on the response can be seen in... Figure 6 It was observed that EY represents the elastic modulus perpendicular to the principal direction of the material.

[0040] S5. Modify material parameter dispersion to achieve reliability assessment Based on step S4, the first critical material parameters identified are EY for materials 6 and 11, and their dispersion is determined according to the requirements of the production process. In this embodiment, the tolerance limit is gradually reduced in 1% increments. When the tolerance limit is... At that time, according to 3 The principle is that the standard deviation of the first key material parameter is equal to the design value. Based on S2, orthogonal grid points with a sample size of 2 are generated under the new distribution of the material parameters. In the finite element model, only the values ​​of the key material parameters are changed to the newly generated orthogonal grid points. Two finite element simulations are performed on stability and inter-fiber failure, respectively. The new results are used to replace the previous simulation results of groups 444 and 445, and groups 374 and 375, respectively. Substitute them into formulas (1) to (3) to obtain a new reliability assessment. If the tolerance limit is reduced to the minimum threshold of 1%, then based on the first key material parameter dispersion being controlled within the minimum threshold of 1%, the material parameter with the second largest influence on the model response is identified as the second key material parameter based on step S4. Its dispersion is gradually modified, and so on, until the reliability is achieved. The value is greater than the reliability threshold in step S3. The dispersion modification result is as follows: Figure 7 As shown, from Figure 7 As can be seen, controlling the dispersion of materials No. 6 and No. 11 within 3% is sufficient to meet the reliability requirements. Since this process does not change the specific values ​​of the material parameters, but only reduces the allowable tolerance limits during production, it will not affect the other performance indicators that have already met the reliability requirements, and there is no need to repeat the verification of them.

[0041] The following uses materials No. 6 and No. 11 as examples. The parameters of the two materials are as follows: Based on step S5, which gradually reduces the tolerance limit from 5% in 1% increments, the first and second critical material parameters of material EY are shown in the table below: The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal lattice points, characterized in that: It includes the following steps: S1. Establish the finite element model: Establish the finite element model based on the pre-bending coordinate system of the blade; S2. Generate sparse orthogonal grid points: Generate normally distributed random variables based on the elastic modulus, shear modulus and density of each blade layup material in each direction. Select input variables from these variables and input them into the finite element model to generate sparse orthogonal grid points. Calculate the finite element simulation results for each sample and extract strain data for different layup materials. Obtain response estimates for each performance index through post-processing. The performance indexes include stability response factor, inter-fiber failure factor and fatigue failure factor. Establish system response The parameters in each dimension follow a functional relationship. The system response estimate is obtained based on sparse orthogonal lattice points: ； Among them, It is the total number of material parameters. As a level factor, For sparse orthogonal lattice point set The weight, To be related to the level factor Relationship between functions Related estimation errors; One method for selecting input quantities from normally distributed random variables is to construct a sparse orthogonal lattice set. Based on meeting the grid configuration requirements Global orthogonal grid set The values ​​of each sample in the subset are used as input values; S3. Evaluate the response of each performance index to determine whether the reliability threshold is met: Based on the influence of the variability of material density, elastic modulus in each direction, and shear modulus on the system response, several uncertainty variables are introduced. The finite element model is treated as a linear system, and the sparse orthogonal lattice point set in step S2 is considered. Evaluate the mean of the system response. and variance And calculate reliability Given reliability thresholds for each performance metric, determine the reliability of the performance metric. Is it greater than the reliability threshold? If the reliability... If the reliability threshold is ≥, then the reliability is satisfied, and the reliability is output. If reliability If the reliability threshold is not met, proceed to steps S4 and S5. S4. Quantitative Sensitivity Analysis: Compare the simulated results of each sparse point under each performance index with the mean of the evaluation. The response difference is calculated, and the absolute value is taken to obtain the maximum deviation result. The elastic modulus corresponding to the main direction perpendicular to the ply material is identified as the first key material parameter. S5. Modify the dispersion of key material parameters for reliability assessment: Given a tolerance limit for the dispersion of the first key material parameter, reduce the tolerance limit at set intervals until it reaches the lowest threshold; update the orthogonal grid points under the new distribution based on the first key material parameter generated in step S2, and only change the value of the first key material parameter in the finite element model to the newly generated orthogonal grid points. Perform two finite element simulations for stability and inter-fiber failure respectively to obtain a secondary reliability assessment; when the tolerance limit drops to the lowest threshold, control the dispersion of the first key material parameter within the lowest threshold. Based on step S4, identify the material parameter with the second largest impact on the response of the finite element model as the second key material parameter, modify the dispersion, and repeat the above process until reliability is achieved. It is greater than the reliability threshold in step S3.

2. The high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points as described in claim 1, characterized in that: In step S1, after establishing the finite element model, it is verified, including: assigning all material parameters in the finite element model to their pre-set design values, performing modal analysis using finite element analysis software, calculating the first few natural frequencies, comparing the calculation results with the corresponding first few natural frequencies of the simulation software with the same parameter settings, and outputting qualified finite element model parameters if the error is within the specified range.

3. The high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points as described in claim 1, characterized in that: In step S2, the method for generating sparse orthogonal grid points and calculating the finite element simulation results for each sample is as follows: given the number of orthogonal grid points to be generated. The weight function generated by the Schmidt orthogonalization process is a distribution function of certain material parameters. orthogonal polynomials When the material parameters follow a normal distribution, the orthogonal polynomial corresponding to the standard normal distribution is obtained. for ； by Solve the system of linear equations with algebraic precision and use the inverse division operator to obtain the weights corresponding to each orthogonal lattice point.

4. The high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points as described in any one of claims 1-3, characterized in that: In step S3, the mean of the system response is evaluated. and variance And calculate reliability The method is: to adopt The sparse orthogonal lattice points are used to quantify various performance indicators of the blade. Let the sparse orthogonal lattice point set be... The corresponding weight is The system response and the parameters of each dimension follow a functional relationship. Evaluate the mean of the system response. ,variance and reliability for: （1）； （2）； （3）； reliability This represents the probability that the response factor falls within the reliability range.

5. The high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points as described in claim 4, characterized in that: When performing stability analysis If the value is greater than the given first threshold, the stability analysis changes the values ​​of each material parameter in the finite element model to the sparse orthogonal lattice point set generated in step S2, and performs buckling analysis. The first eigenvalue of buckling that is not concentrated at the blade tip is extracted as the response factor. If the response factor is less than or equal to the stability threshold, it is considered a failure.

6. The high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points as described in claim 4, characterized in that: When performing inter-fiber failure analysis When the strain is less than a given second threshold, the inter-fiber failure analysis first extracts the strain of each node from the finite element simulation results. Based on the rotation axis matrix Decompose it into fiber directions, based on the two-dimensional stiffness matrix. The stress along the fiber direction was calculated. ; The stress along the fiber direction was calculated using the PUCK criterion and based on the finite element simulation results. Then, the inter-fiber failure factor was calculated. for ； ； in, It is the calculated stress perpendicular to the fiber direction. Tensile strength perpendicular to the fiber direction. The compressive strength is perpendicular to the fiber direction. In-plane shear strength For stretching PUCK parameters, To compress the PUCK parameter, the threshold is 1. If the evaluation result is greater than 1, it is considered a failure.

7. The high-dimensional wind turbine blade reliability optimization method based on sparse orthogonal grid points as described in claim 4, characterized in that: When performing fatigue strength analysis Fatigue strength analysis was performed at the blade tip. shaft and A unit load of 1 Nm was applied along the axial direction, and the strain of each component under the unit force was extracted to obtain the relationship between the unit bending moment and the stress in the fiber direction. The fatigue failure factor was calculated based on the Markov distribution. ； ； in, , These are the characteristic values ​​of the tensile and compressive strength of the material; ; It is the average value of fiber stress cycles. It is the stress cycle amplitude. is the number of cycles under different mean and amplitude values ​​in the Markov distribution, and m is the fatigue strength index.

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