A high-dimensional reliability analysis method for composite structures integrating MRBF and iCE-m

Abstract

The present invention discloses a high-dimensional reliability analysis method for composite structures that integrates MRBF and iCE-m. The method includes initializing a training sample set for a high-dimensional composite structure with a small failure probability and calculating the true value of an objective function to form an experimental design (DoE). Based on the current DoE, a full RBF model is trained to define a quasi-optimal iPDF. Important samples that obey the quasi-optimal iPDF are generated. An active learning function is constructed to obtain an optimal training point. Based on the optimal training point obtained in step S4, a stopping criterion for active learning is determined, and the failure probability of the high-dimensional composite structure with a small failure probability to be analyzed is output. The present invention proposes integrating MRBF and iCE-m to analyze the reliability of high-dimensional composite structures with small failure probabilities. Based on the prediction information of the MRBF model, a new learning function is proposed to better approximate the limit state plane in the reliability analysis problem, thereby significantly improving the analysis efficiency of the reliability analysis of high-dimensional composite structures with small failure probabilities.

Description

Technical Field

[0001] The present invention relates to the technical field of high-dimensional low-failure-probability composite materials, and more specifically to a high-dimensional reliability analysis method for composite material structures integrating MRBF and iCE-m. Background Art

[0002] Composite structures possess remarkable properties, including high mechanical strength, stiffness, corrosion resistance, thermal insulation, and a low weight-to-weight ratio. These structures can be tailored to specific application requirements to optimize structural performance and are widely used in industries such as aerospace, automotive, construction, and shipbuilding. However, their structural performance is often subject to a degree of uncertainty due to the complexity of the manufacturing process and the inherent variability of material parameters.

[0003] The performance of complex composite structures is often influenced by a variety of uncertain parameters, particularly material parameters, the number of layers, the thickness of each layer, and the angles between layers. These uncertainties can lead to uncertainty in the mechanical properties of composite structures. Therefore, it is crucial to comprehensively consider the uncertainties of these parameters and conduct reliability analysis for each input parameter.

[0004] Reliability analysis of composite structures is a typical high-dimensional problem. Most traditional reliability analysis methods require multiple calculations of the structural performance function. In practical engineering, the calculation of performance functions often requires the use of computationally intensive commercial software such as finite element analysis, multibody dynamics, and computational fluid dynamics. Therefore, developing efficient and highly accurate reliability analysis methods has long been a goal pursued by scholars both domestically and internationally. Currently, commonly used structural reliability analysis methods can be categorized into three main categories: approximate analytical methods, sampling simulation methods, and surrogate model methods. First-order reliability methods (FORMs) and second-order reliability methods (SORMs) are the most basic approximate methods, performing first- or second-order approximations on the function. Monte Carlo simulation and importance sampling are classic sampling simulation methods that can yield more accurate results through extensive function calculations. Commonly used surrogate models include polynomial response surfaces (PRS), kriging, radial basis functions (RBFs), artificial neural networks (ANNs), and support vector regression (SVR). These methods first use a surrogate model to approximate the function and then employ sampling simulation methods to determine the approximate failure probability.

[0005] Unlike surrogate models such as the Kriging model, PCE, SVR, and neural networks, which are susceptible to the curse of dimensionality, the RBF model does not require excessive training time to achieve high accuracy. This means that the RBF model can be trained directly in the high-dimensional source space without the need for feature screening or mapping dimensionality reduction, achieving high accuracy. Furthermore, cross-validation techniques can be used to obtain the prediction variance of the surrogate model, thereby completing active learning. Related research has been confirmed in the field of low-dimensional reliability analysis. However, in the context of high-dimensional reliability analysis, the computational time required to obtain the prediction mean and variance of the RBF model increases significantly, and the computational time of active learning itself (excluding the computation time of the performance function) will exceed acceptable limits.

[0006] The MRBF model uses matrix operations to complete the prediction of massive candidate points, which greatly reduces the prediction time of the RBF model and makes active learning possible. However, this method is not suitable for problems with extremely small failure probabilities. Problems with extremely small failure probabilities (failure probability less than 10 -5 ), a large number of MCS samples are required to ensure the accuracy of the estimation. -5 ~10 -10 The magnitude of the function often requires 4×10 7 ~4×10 12 Only with a large number of simulation samples can MCS provide an estimation result with a coefficient of variation lower than 5%. The ALR method based on MCS requires response prediction for such a large number of MCS samples in each iteration, which takes an unacceptable amount of computation time. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a high-dimensional reliability analysis method for composite material structures that integrates MRBF and iCE-m. The fusion of iCE-m and MRBF based on the dimensionality reduction idea builds a bridge for collaboration between the two and helps select the optimal training point.

[0008] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows.

[0009] A high-dimensional reliability analysis method for composite structures that integrates MRBF and iCE-m includes the following steps:

[0010] S1. Initialize a training sample set of high-dimensional composite structures with low failure probability and calculate the true value of the objective function to form the experimental design DoE;

[0011] S2. Based on the current DoE, train the full RBF model and define the quasi-optimal iPDF;

[0012] S3. Generate important samples that obey the quasi-optimal iPDF;

[0013] S4. Build an active learning function to obtain the optimal training point;

[0014] S5. Based on the optimal training point obtained in step S4, determine the stopping criterion of active learning, and output the failure probability of the high-dimensional small failure probability composite material structure to be analyzed.

[0015] To further optimize the technical solution, in step S1, the high-dimensional small failure probability composite material training sample set is initialized using the Latin hypercube sampling method, the training sample set is extracted in the original high-dimensional variable space, and the true response value of the objective function is calculated to form the experimental design DoE (x (i) ,g(x (i) ))(i=1,…,m).

[0016] To further optimize the technical solution, in step S2, the RBF full model is trained and the method for defining the quasi-optimal iPDF is:

[0017] According to the given DoE(x (i) ,g(x (i) ))(i=1,…,m), the RBF model approximates the objective function as a linear combination of m RBFs, that is:

[0018]

[0019] Where: ||xx (i) || represents any point x and x (i) The spatial distance is usually the Euclidean distance. is the radial basis function; c is the shape parameter of the radial basis function; β=[β1,…,β m ] T is the coefficient vector of the basis function;

[0020] The unknown coefficients can be obtained as

[0021] β=Φ -1 g

[0022] Where Φ is the RBF matrix of the training point, g=[g(x (1) ),…,g(x (m) )] T ;

[0023] The expression for obtaining the optimal shape parameter of the full RBF model is as follows:

[0024]

[0025] Among them, β i is the i-th element of β, is Φ -1The i-th diagonal element of ;

[0026] The prediction mean and prediction variance of the RBF model are obtained by using LOOCV technology or Jackknife method as the mean and variance of the prediction values ​​of m RBF sub-models, that is,

[0027]

[0028]

[0029] in, is the predicted value of the ith sub-model, assuming Subject to the mean μ g (x), the standard deviation is Normal distribution;

[0030] The matrix formed by the prediction values ​​of all sub-models is The matrix formed by the RBF values ​​between the training points and the prediction points is F X , It can be expressed in matrix form, that is,

[0031]

[0032] in, and

[0033]

[0034] F X It can be expressed as

[0035]

[0036] Where D is the Euclidean distance matrix between all training points and prediction points.

[0037] To further optimize the technical solution, in step S3, in the importance sampling method, the optimal iPDF is:

[0038]

[0039] Where f(x) is the probability density function, P f represents the true failure probability;

[0040] The basic idea of ​​iCE-IS is to use a probability density function h(x,q) with a parameter q to approximate h * (x), q by minimizing h(x,q) and h * (x) is determined by the KL divergence between

[0041]

[0042] In the case of small failure probability problems, it is usually difficult to directly obtain a large number of failure samples, and it is also difficult to directly approximate h * (x), therefore, iCE-IS approximates h in a hierarchical manner * (x), define the following iPDF series in

[0043]

[0044] Among them, P t is a normalizing constant, σ t represents the smoothness parameter, and ∞>σ1>…>σ T >0; as σ t The increase, Close to h * (x);

[0045] iCE-IS from approximate Start by using h(x,q t ) to approximate The importance sampling method was used to calculate h(x,q t )and The KL difference between the two, and using the smooth function Make all intermediate samples participate in q t To obtain better estimation results;

[0046] For Gaussian density, the parameter that needs to be estimated is q t =(μ t ,Σ t ), where μ t ∈R D is the mean of the Gaussian density, Σ t ∈R D×D is the covariance matrix of the Gaussian density,

[0047]

[0048]

[0049] in, in

[0050] For high-dimensional problems, the above covariance matrix estimation will suddenly collapse to 0, so a mapping dimensionality reduction strategy is proposed to estimate the covariance matrix in a one-dimensional subspace:

[0051] Map random samples into a low-dimensional subspace

[0052] y (i) =R T x(i)

[0053] in, The projection direction is defined;

[0054] Compute the variance of sample points in a low-dimensional subspace:

[0055]

[0056] Estimate the covariance matrix of samples in the high-dimensional original space:

[0057] Σ t =(v-1)RR T +I D

[0058] In this way, the covariance matrix is ​​estimated only in the direction of the mean of the multivariate Gaussian distribution;

[0059] To fuse iCE-m with the RBF model, we should first define the optimal iPDF as the target distribution of iCE-m, thereby extracting "high-quality" candidate samples;

[0060] Considering the uncertainty of the prediction results, is the area near the limit state plane, There is a high confidence level that it is the failure region; setting α = 1.96, the confidence level is 95%. Represents potential failure domains;

[0061] Based on this, the following quasi-optimal iPDF is proposed

[0062]

[0063] Among them, P is the normalization coefficient, g Sur (x) is the potential failure plane,

[0064] g Sur (x) = μ g (x)-ασ g (x)

[0065] H * (x) is the target distribution, and the generated samples will be mostly located in To meet the above needs; in order to obtain obedience An important sample, the iPDF series is defined as

[0066]

[0067] Then we can perform iCE-m, and the samples in the last layer are those that obey H * (x) is an important sample.

[0068] To further optimize the technical solution, in step S4, the method for obtaining the optimal training point is:

[0069] Since g(x) is random, we can find g 2 The mathematical expectation of (x),

[0070]

[0071] In order to keep the training points dispersed, g 2 Variance of (x):

[0072]

[0073] In order to balance the two objectives, i.e., minimizing E(g 2 (x)), maximize Var(g 2 (x)), using g 2 The coefficient of variation of (x) is used as a learning function:

[0074]

[0075] The optimal training point is

[0076] x*=argmax Cov(g 2 (x)).

[0077] Further optimizing the technical solution, in step S5,

[0078] The true failure probability is The failure probability predicted by the RBF model is The relative error of importance sampling is

[0079]

[0080] Among them, I WSP (x i ) and I F (x i ) are indicator functions, representing x i Is the sign of the position function incorrectly predicted? i Is it a failed sample? The relative error takes into account the weight W(x i ), for ε IS Perform interval estimation and use the upper bound of the confidence interval As the convergence condition of the relative error of failure probability;

[0081] It is also necessary to evaluate the ability of the sample set to estimate the true iPDF and monitor the sample set's Estimation capability; defining the coefficient of variation

[0082]

[0083] when and When both are less than a given threshold, the active learning process is stopped and the failure probability is calculated.

[0084] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is as follows.

[0085] The present invention provides a high-dimensional reliability analysis method for composite structures that integrates MRBF and iCE-m. It proposes integrating MRBF and iCE-m to analyze the reliability of high-dimensional small failure probability problems. Based on the prediction information of the MRBF model, a new learning function is proposed to better approximate the limit state plane in the reliability analysis problem, thereby greatly improving the analysis efficiency of the reliability analysis of high-dimensional small failure probability composite structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is a logic flow chart of the present invention;

[0087] Figure 2 This is a schematic diagram of the composite material reinforced plate structure of the present invention;

[0088] Figure 3 is a graph showing changes in failure probability and estimated relative error of the present invention;

[0089] Figure 4 The convergence process of active learning and the distribution diagram of DoE. DETAILED DESCRIPTION

[0090] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0091] A high-dimensional reliability analysis method for composite materials that integrates MRBF and iCE-m is a method that integrates the matrix operation radial basis function (MRBF) model and the cross entropy importance sampling based on mean dimensionality reduction (iCE-m). The logical process is as follows Figure 1 As shown, it includes the following steps:

[0092] S1. Initialize a training sample set of high-dimensional composite structures with small failure probability, calculate the true value of the objective function, and form an experimental design DoE.

[0093] The Latin hypercube sampling method is used to initialize the training sample set of high-dimensional small failure probability composite materials. The training sample set is extracted in the original high-dimensional variable space, and the true response value of the objective function is calculated to form the experimental design DoE (x (i) ,g(x (i)))(i=1,…,m).

[0094] S2. Based on the current DoE, train the full RBF model and define the quasi-optimal iPDF.

[0095] The method for training the full RBF model and defining the quasi-optimal iPDF is:

[0096] According to the given DoE(x (i) ,g(x (i) ))(i=1,…,m), the RBF model approximates the objective function as a linear combination of m RBFs, that is:

[0097]

[0098] Where: ||xx (i) || represents any point x and x (i) The spatial distance is usually the Euclidean distance. is the radial basis function; c is the shape parameter of the radial basis function; β=[β1,…,β m ] T is the coefficient vector of the basis function;

[0099] The unknown coefficients can be obtained as

[0100] β=Φ -1 g

[0101] Where Φ is the RBF matrix of the training point, g=[g(x (1) ),…,g(x (m) )] T ;

[0102] The expression for obtaining the optimal shape parameter of the full RBF model is as follows:

[0103]

[0104] Among them, β i is the i-th element of β, is Φ -1 The i-th diagonal element of ;

[0105] The prediction mean and prediction variance of the RBF model are obtained by using LOOCV technology or Jackknife method as the mean and variance of the prediction values ​​of m RBF sub-models, that is,

[0106]

[0107]

[0108] in, is the predicted value of the ith sub-model, assuming Subject to the mean μ g (x), the standard deviation is Normal distribution.

[0109] The matrix formed by the prediction values ​​of all sub-models is The matrix formed by the RBF values ​​between the training points and the prediction points is F X , It can be expressed in matrix form, that is,

[0110]

[0111] Where B=[β1,…,β m ],and

[0112]

[0113] F X It can be expressed as

[0114]

[0115] Where D is the Euclidean distance matrix between all training points and prediction points.

[0116] S3. Generate important samples that obey the quasi-optimal iPDF.

[0117] In the importance sampling method, the optimal iPDF is:

[0118]

[0119] Where f(x) is the probability density function, P f represents the true failure probability;

[0120] The basic idea of ​​iCE-IS is to use a probability density function h(x,q) with a parameter q to approximate h * (x), q by minimizing h(x,q) and h * (x) is determined by the KL divergence between

[0121]

[0122] In the case of small failure probability problems, it is usually difficult to directly obtain a large number of failure samples, and it is also difficult to directly approximate h * (x), therefore, iCE-IS approximates h in a hierarchical manner * (x), define the following iPDF series in

[0123]

[0124] Among them, P tis a normalizing constant, σ t represents the smoothness parameter, and ∞>σ1>…>σ T >0; as σ t The increase, Close to h * (x);

[0125] iCE-IS from approximate Start by using h(x,q t ) to approximate The importance sampling method was used to calculate h(x,q t )and The KL difference between the two, and using the smooth function Make all intermediate samples participate in q t To obtain better estimation results;

[0126] For Gaussian density, the parameter that needs to be estimated is q t =(μ t ,Σ t ), where μ t ∈R D is the mean of the Gaussian density, Σ t ∈R D×D is the covariance matrix of the Gaussian density,

[0127]

[0128]

[0129] in, in

[0130] For high-dimensional problems, the above covariance matrix estimation will suddenly collapse to 0, so a mapping dimensionality reduction strategy is proposed to estimate the covariance matrix in a one-dimensional subspace:

[0131] Map random samples into a low-dimensional subspace

[0132] y (i) =R T x (i)

[0133] in, The projection direction is defined;

[0134] Compute the variance of sample points in a low-dimensional subspace:

[0135]

[0136] Estimate the covariance matrix of samples in the high-dimensional original space:

[0137] Σ t =(v-1)RR T +I D

[0138] In this way, the covariance matrix is ​​estimated only in the direction of the mean of the multivariate Gaussian distribution;

[0139] To fuse iCE-m with the RBF model, we should first define the optimal iPDF as the target distribution of iCE-m, thereby extracting "high-quality" candidate samples;

[0140] Considering the uncertainty of the prediction results, is the area near the limit state plane, There is a high confidence level that it is the failure region; setting α = 1.96, the confidence level is 95%. Represents potential failure domains;

[0141] Based on this, the following quasi-optimal iPDF is proposed

[0142]

[0143] Among them, P is the normalization coefficient, g Sur (x) is the potential failure plane,

[0144] g Sur (x) = μ g (x)-ασ g (x)

[0145] H * (x) is the target distribution, and the generated samples will be mostly located in To meet the above needs; in order to obtain obedience An important sample, the iPDF series is defined as

[0146]

[0147] Then we can perform iCE-m, and the samples in the last layer are those that obey H * (x) is an important sample.

[0148] S4. Build an active learning function to obtain the optimal training point.

[0149] The method to obtain the optimal training point is:

[0150] Since g(x) is random, we can find g 2 The mathematical expectation of (x),

[0151]

[0152] In order to keep the training points dispersed, g 2 Variance of (x):

[0153]

[0154] In order to balance the two objectives, i.e., minimizing E(g 2 (x)), maximize Var(g 2 (x)), using g 2 The coefficient of variation of (x) is used as a learning function:

[0155]

[0156] The optimal training point is

[0157] x*=argmax Cov(g 2 (x)).

[0158] S5. Based on the optimal training point obtained in step S4, determine the stopping criterion of active learning, and output the failure probability of the high-dimensional small failure probability composite material structure to be analyzed.

[0159] The true failure probability is The failure probability predicted by the RBF model is The relative error of importance sampling is

[0160]

[0161] Among them, I WSP (x i ) and I F (x i ) are indicator functions, representing x i Is the sign of the position function incorrectly predicted? i Is it a failed sample? The relative error takes into account the weight W(x i ), for ε IS Perform interval estimation and use the upper bound of the confidence interval As the convergence condition of the relative error of failure probability;

[0162] It is also necessary to evaluate the ability of the sample set to estimate the true iPDF and monitor the sample set's Estimation capability; defining the coefficient of variation

[0163]

[0164] when and When both are less than a given threshold, the active learning process is stopped and the failure probability is calculated.

[0165] An explicit nonlinear function is introduced as a test to verify the above steps. The dimension D is set to 100 and 200, where:

[0166]

[0167] The experimental results are shown in Table 1:

[0168] Table 1 Comparison of results of different methods

[0169]

[0170] It can be seen that the AL-MRBF-iCE-m method proposed in this invention requires fewer training points than other methods. AL-MRBF-MCS and AL-MRBF-iCE do not require dimensionality reduction or feature screening, and directly identify the optimal training points in the high-dimensional space. Therefore, the number of required performance function calculations is greatly reduced. AL-MRBF-MCS only needs to convert 1×10 7 MCS sample points are used as prediction samples, while AL-MRBF-iCE uses iCE-m samples as prediction samples. Therefore, the computation time of AL-MRBF-iCE is significantly lower than that of AL-MRBF-MCS.

[0171] The following is an example of a high-dimensional small failure probability composite structure reliability analysis problem:

[0172] like Figure 2 The figure shows a composite reinforced panel with a skin width of W = 610 mm and a length of L = 865 mm. The rib spacing S = 17.8 mm. The thickness of the composite laminate is 0.125 mm. The material parameters are: elastic modulus in the first direction E1, elastic modulus in the second direction E2, Poisson's ratio μ, shear modulus G 12 ,G 13 and G 23 The skin consists of 16 layers with ply angles θ1 to θ 16 The reinforcement cap is laid with 50 layers and the laying angle is θ 17 ~θ 66 . The stiffener web is laid with 22 layers and the laying angle is θ 67 ~θ 88 . The reinforcement flange is laid with 22 layers, and the laying angle is θ 89 ~θ 110. Four sets of stiffeners are bonded to the skin using BSL322 film adhesive with a thickness of 0.1 mm, an elastic modulus of 1000 GPa, and a shear modulus of 1000 GPa. The random variables in this case are 6 material parameters and 110 ply angle parameters. The distribution type and distribution parameters of the random variables are shown in Table 2. The finite element model of the composite stiffened panel was established using ABAQUS, in which the laminate was simulated using shell elements, the adhesive layer was simulated using cohesive elements, and the adhesive layer and the shell were bound using Tie connections. A unit load was applied along the laminate stiffener direction (Z axis), and a linear buckling analysis was performed.

[0173] Table 2 Random variable distribution parameters

[0174]

[0175] In the presence of random parameters, there is a certain dispersion in the buckling load that the panel can withstand. According to the design requirements, this value should be greater than 90kN. Therefore, the performance function is defined as

[0176] g(x)=λ(x)F0-90

[0177] Where F0 = 10.32 kN is the total load applied to the structure, and λ(x) is the first-order buckling factor of the structure.

[0178] The proposed method is used to solve the failure probability, and the calculation results are shown in Table 3. The present invention uses 100 initial training points and calls the finite element software 100 times as the initial DoE of AL-MRBF-iCE. 61 new training points are added and the finite element software is called 61 times, and the proposed method completes convergence. The total cost of active learning is 4577 seconds, of which about 4336 seconds are used for finite element model calculation and only 241 seconds are used for the algorithm itself. Figure 3 As shown in Figure 2, most of the added training points are located near the limit state surface. The change curves of failure probability and estimated relative error during the iteration process are shown in Figure 2. Figure 3 shown.

[0179] Table 3 Calculation results of composite stiffened panels

[0180]

[0181] In order to verify the accuracy of the proposed method, in the variable space [μ j -6σ j ,μ j +6σ j] extracted 1000 sets of samples, of which 700 were used as training points to approximate the global MRBF model, and 300 were used as verification points. The accuracy of the MRBF model was verified, and its determination coefficient R2 was obtained to be 0.9998. Based on this global MRBF model, the failure probability obtained by iCE-m is 2.91×10 -6 This shows that the calculation results of AL-MRBF-iCE have high accuracy. The convergence process of active learning is similar to the distribution of DoE. Figure 4 As shown in Figure 2, it can be seen that the proposed method can robustly complete active learning, and the added training points are concentrated near the limit state.

[0182] The above example results demonstrate that the proposed AL-MRBF-iCE-m model is highly effective in evaluating the reliability of high-dimensional, low-failure-probability composite structures. In terms of computational cost, the proposed AL-MRBF-iCE-m model requires fewer than 200 sample points and calculates failure probabilities with high accuracy, which is generally considered computationally feasible in engineering practice. Compared to existing methods, this model solves the difficult problem of reliability analysis for high-dimensional, low-probability composite structures, significantly reducing the computational effort and improving computational efficiency.

Claims

1. A high-dimensional reliability analysis method for composite structures that integrates MRBF and iCE-m, characterized by: The following steps are involved: S1. Initialize a training sample set of high-dimensional composite structures with low failure probability and calculate the true value of the objective function to form an experimental design DoE; S2. Based on the current DoE, train the full MRBF model and define the quasi-optimal iPDF. Defining the quasi-optimal iPDF includes: Fusion of iCE-m and MRBF models is performed, and the quasi-optimal iPDF is defined as the target distribution of iCE-m to extract "high-quality" candidate samples; Considering the uncertainty of the prediction results, is the area near the limit state plane, It is the failure area with greater confidence; set , with a confidence level of 95%, Represents potential failure domains; Based on this, the following quasi-optimal iPDF is proposed in, is the normalization coefficient, is the potential failure plane, is the probability density function, in, is the predicted mean of the MRBF model, is the predicted standard deviation of the MRBF model; by As the target distribution, the generated samples will be mostly located in ; To gain obedience The quasi-optimal iPDF series is defined as ； in, To propose the optimal iPDF series, is a smooth function, represents the smoothing parameter, for The normalization coefficient of by For the target distribution, perform iCE-m, and the samples in the last layer are subject to Important samples of S3. Generate important samples that obey the quasi-optimal iPDF; S4. Build an active learning function to obtain the optimal training point; use The coefficient of variation of is used as a learning function: in, for The variance of for The mathematical expectation of is the square of the objective function value; S5. Based on the optimal training point obtained in step S4, determine the stopping criterion of active learning, and output the failure probability of the high-dimensional small failure probability composite material structure to be analyzed.

2. The high-dimensional reliability analysis method for composite material structures integrating MRBF and iCE-m according to claim 1, characterized in that: In step S1, the high-dimensional small failure probability composite material training sample set is initialized using the Latin hypercube sampling method to extract the training sample set in the original high-dimensional variable space, and calculate the true response value of the objective function to form the experimental design DoE .

3. The high-dimensional reliability analysis method for composite material structures integrating MRBF and iCE-m according to claim 1, characterized in that: In step S2, training the full MRBF model includes: According to the given DoE , the MRBF model approximates the objective function as a linear combination of m RBFs, namely: in: Represents any point and The spatial distance is usually Euclidean distance. is the radial basis function; is the shape parameter of the radial basis function; is the coefficient vector of the basis function; The unknown coefficients can be obtained as in, is the RBF matrix of the training point, ; The expression for obtaining the optimal shape parameter of the full MRBF model is as follows: in, yes No. i elements, yes No. i diagonal elements; The predicted mean and predicted variance of the MRBF model are obtained by using LOOCV technology or Jackknife method as the mean and variance of the predicted values ​​of m RBF sub-models, that is, in, It is i The predicted value of each sub-model, set Obey the mean , the variance is Normal distribution; The matrix formed by the prediction values ​​of all sub-models is , the matrix formed by the RBF values ​​between the training points and the prediction points is , It can be expressed in matrix form, that is, in, ,and It can be expressed as in, is the Euclidean distance matrix between all training points and prediction points.

4. The high-dimensional reliability analysis method for composite material structures integrating MRBF and iCE-m according to claim 1, characterized in that: In the step S4, The mathematical expectation of is, In order to keep the training points dispersed, Variance of: In order to balance the two objectives, namely, minimizing ,maximize , The optimal training point is 。 5. The high-dimensional reliability analysis method for composite material structures integrating MRBF and iCE-m according to claim 1, characterized in that: In the step S5, The true failure probability is , the failure probability predicted by the RBF model is , then the relative error of importance sampling is in, and is the indicator function, representing Whether the sign of the position function is mispredicted or not Is it a failed sample? The relative error takes into account the weight of each sample. ,right Perform interval estimation and use the upper bound of the confidence interval As the convergence condition of the relative error of failure probability; It is also necessary to evaluate the ability of the sample set to estimate the true iPDF and monitor the sample set's Estimation capability; defining the coefficient of variation when and When both are less than a given threshold, the active learning process is stopped and the failure probability is calculated.

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