A structural reliability analysis method based on an adaptive variational fidelity model

Abstract

The application provides a structure reliability analysis method based on an adaptive variable fidelity model, and the method comprises the following steps: generating an initial sample point set with uniform distribution and representativeness through an improved random sampling method KMODMC, the initial sample point set comprising a low-fidelity sample set and a high-fidelity sample set; subsequently, training a BP neural network by using the low-fidelity sample set to obtain a low-fidelity BP neural network model; at the same time, training a Kriging model based on the error of the high-fidelity sample set and the predicted value of the low-fidelity model to construct an error correction Kriging model; combining the low-fidelity BP neural network model and the error correction Kriging model to form a multi-fidelity hybrid proxy model; and performing adaptive iterative optimization through a double-model alternating point sampling strategy to finally obtain a high-precision multi-fidelity hybrid proxy model for structure reliability evaluation. The application solves the problems of high cost of high-fidelity simulation calculation and insufficient precision of a low-fidelity model, and effectively improves the adaptability and prediction precision of the model in complex nonlinear problems.

Description

Technical Field

[0001] This invention relates to the field of mechanical structure reliability analysis technology, and in particular to a structural reliability analysis method based on an adaptive variable fidelity model. Background Technology

[0002] In the field of mechanical structure design and analysis, structural reliability analysis is a crucial step in ensuring the safety of mechanical structures, and numerical simulation methods such as finite element analysis have become important tools for assessing structural reliability. However, while high-fidelity simulation models can provide accurate analysis results, their computational costs are often very high, especially when dealing with complex structures, where computation time and resource consumption increase exponentially. Low-fidelity simulation models reduce computational load by simplifying the physical model or reducing mesh precision, but this also leads to a decrease in the accuracy of the analysis results. Therefore, how to improve the accuracy of analysis results while ensuring computational efficiency has become an urgent problem to be solved in the field of mechanical structure reliability analysis.

[0003] Furthermore, traditional random sampling methods, such as Monte Carlo and Latin hypercube sampling, while capable of covering the entire design space, often suffer from uneven sample point distribution, especially in high-dimensional design spaces. Sample points tend to cluster in certain regions while becoming sparse near the boundaries. This uneven sample distribution not only reduces the fitting accuracy of the surrogate model but also wastes valuable computational resources. Summary of the Invention

[0004] To address the problems of high computational cost of high-fidelity models, low computational accuracy of low-fidelity models, and uneven sample distribution in existing structural reliability analysis techniques, this invention provides a structural reliability analysis method based on an adaptive variable fidelity model.

[0005] The technical solution adopted by this invention to achieve the above objectives is: a structural reliability analysis method based on an adaptive variable fidelity model, comprising the following steps:

[0006] Step S1: Generate an initial sample point set, which includes a low-fidelity sample set and a high-fidelity sample set;

[0007] Step S2: Train the BP neural network using a low-fidelity sample set to obtain a trained low-fidelity BP neural network model.

[0008] Step S3: Train the Kriging model using the error between the predicted structural failure probability of the high-fidelity sample set and the predicted structural failure probability of the high-fidelity sample set in the low-fidelity BP neural network model to obtain the error-corrected Kriging model.

[0009] Step S4: Combine the low-fidelity BP neural network model and the error correction Kriging model to construct a multi-fidelity hybrid proxy model, and use the multi-fidelity hybrid proxy model to evaluate the structural reliability.

[0010] Further, in step S1, an initial sample point set is generated using the improved random sampling method KMODMC, including: randomly generating a candidate sample point set within the design space; selecting a point from the candidate sample point set that is furthest from the already selected sample point as a new sample point in each round of sample point selection; and further homogenizing the sample distribution through clustering to obtain the initial sample point set.

[0011] Furthermore, the generation of the initial sample point set using the improved random sampling method KMODMC includes:

[0012] Dimensions of given design variables and design space , ,in, For the real number field, a candidate sample point set is generated using random sampling, represented as:

[0013] ;

[0014] in, For the first One sample point, and These are the upper and lower bounds of the design variable, respectively. Indicates the generation of a A uniformly distributed vector of 3D random numbers, and a set of candidate sample points. ;

[0015] In the When selecting sample points in rounds, the point that is furthest from the set of already selected sample points is chosen from the candidate sample set, which is represented as:

[0016] ;

[0017] ;

[0018] in, The distance between two sample points. This is the currently selected set of sample points;

[0019] To further homogenize the distribution of sample points, the K-Means clustering algorithm is executed to divide the currently selected sample points into... Clusters, calculate the centroid of each cluster. :

[0020] ;

[0021] in, It is the first The set of sample points for each cluster is updated by using the centroid of each cluster as the new sample point. :

[0022] ;

[0023] The optimized initial sample point set is obtained, namely the optimized low-fidelity sample set and high-fidelity sample set.

[0024] Further, in step S2, a BP neural network is trained using a low-fidelity sample set. The BP neural network includes an input layer, a hidden layer, and an output layer. The input layer receives input variables, the hidden layer processes the input signal through a nonlinear activation function, and the output layer generates an output quantity, which is the predicted structural failure probability.

[0025] Furthermore, the working principle of a BP neural network is as follows:

[0026] Input variables are Corresponding to the input layer The hidden layer contains 100 neurons. There are neurons, and the output is . ,correspond One neuron;

[0027] The transitive relationships between the input layer and hidden layers, and between hidden layers and output layers, are represented by transformation functions, using the Sigmoid function:

[0028] Hidden layer The output of each neuron is transformed by a weighted sum of the input signals followed by an activation function:

[0029] ;

[0030] in, Represents the transformation function. For input layer variables With hidden layer variables The connection weights between them Hidden layer variables The threshold;

[0031] The number of neurons in the hidden layer was determined by trial and error. Initial value:

[0032] ;

[0033] in, It is a regulating factor.

[0034] Furthermore, in step S3, the low-fidelity BP neural network model is obtained through training with low-fidelity samples, specifically including:

[0035] ;

[0036] in, This represents the predicted failure probability value for a low-fidelity BP neural network model. This represents a low-fidelity backpropagation (BP) neural network model. These are the training parameters for a low-fidelity BP neural network model, which include weights and biases.

[0037] For error Modeling:

[0038] ;

[0039] in, For high-fidelity samples, This represents the probability value of structural failure in a true high-fidelity sample set. To predict the structural failure probability value of the low-fidelity model obtained by training a low-fidelity BP neural network model on high-fidelity samples, the Kriging model is trained using error data to obtain the error-corrected Kriging model.

[0040] Furthermore, in step S4, the low-fidelity BP neural network model and the error-corrected Kriging model are superimposed to obtain the multi-fidelity hybrid proxy model as follows: .

[0041] Furthermore, in step S4, the multi-fidelity hybrid proxy model is adaptively iterated, and a dual-model alternating sampling strategy is implemented in each iteration:

[0042] During even-numbered iterations, the uncertainty of the low-fidelity BP neural network model at the prediction point and the gradient of the predicted value are calculated. The results of both calculations are combined to generate an even-numbered iteration scoring function, and the sample point with the highest score is selected to be added to the training set of the adaptive iteration.

[0043] During odd-numbered iterations, the prediction variance of the error-corrected Kriging model and the distance term of the failure probability surface are calculated. The results of both calculations are combined to generate an odd-numbered iteration scoring function, and the sample point with the highest score is selected to be added to the training set of the adaptive iteration.

[0044] After each iteration, determine whether the model has converged. If it has converged, terminate the point addition iteration to obtain a high-precision multi-fidelity hybrid proxy model.

[0045] Furthermore, even-numbered iterations include:

[0046] Constructing a low-fidelity BP neural network model at the input point Predicted distribution on:

[0047] ;

[0048] in, The first BP neural network Second forward propagation, Indicates the same input point The number of samples to be sampled during random forward propagation has an uncertainty of:

[0049] ;

[0050] in, ;

[0051] The gradient of the predicted value is:

[0052] ;

[0053] The partial derivative, even-numbered iterations, and scoring function are:

[0054] ;

[0055] Select Before scoring High-quality sample points are added to the adaptive iterative training set.

[0056] Furthermore, odd-numbered iterations include:

[0057] The Kriging model provides the prediction variance (MSE) through its own structure, measuring the prediction uncertainty at a certain point, including the design point. The MSE calculation method at this location is as follows:

[0058] ;

[0059] in, This is the correlation vector between the current point and the training points. The covariance parameter of the Kriging model. For the regression residuals, The correlation matrix represents the spatial correlation between sample points.

[0060] Introduce the following distance term:

[0061] ;

[0062] in, The output value of the multi-fidelity hybrid agent model. This is the failure detection threshold;

[0063] Using a weighted function in exponential form:

[0064] ;

[0065] in, This is a hyperparameter.

[0066] The odd-number iterative scoring function is:

[0067] ;

[0068] Select Before scoring High-quality sample points are added to the adaptive iterative training set.

[0069] The beneficial technical effects of this invention are as follows:

[0070] This invention combines the advantages of high-fidelity and low-fidelity models to improve computational efficiency and analytical accuracy. By employing a combination of BP neural networks and Kriging difference models, it fully utilizes the global information provided by the low-fidelity model and the high-precision characteristics of the high-fidelity model, enhancing the model's adaptability to complex nonlinear problems. This invention achieves higher prediction accuracy and better sample utilization efficiency with fewer equivalent high-fidelity model calls, effectively reducing costs. The improved KMODMC sampling method provided by this invention, by combining the maximum-minimum distance criterion and K-Means clustering optimization strategy, generates uniformly distributed and representative sample points within the design space, effectively avoiding the uneven distribution of sample points in traditional sampling methods and improving the initial fitting accuracy of the surrogate model. This invention introduces a gradient-uncertainty-driven and MSE-failure surface-driven point-addition sampling strategy, which adaptively selects key sample points for model updates during iteration, improving prediction accuracy near boundaries and failure surfaces, reducing sample distribution in redundant regions, and effectively lowering computational costs. Attached Figure Description

[0071] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] Figure 1 This is a flowchart illustrating a structural reliability analysis method based on an adaptive variable fidelity model provided in an embodiment of the present invention.

[0073] Figure 2This is a scatter plot of the Monte Carlo sampling method provided in the embodiments of the present invention;

[0074] Figure 3 This is a scatter plot of the Latin hypercube sampling method provided in the embodiments of the present invention;

[0075] Figure 4 This is a scatter plot of the Sobol sequence sampling method provided in the embodiments of the present invention;

[0076] Figure 5 This is a scatter plot of the KMODMCS sampling method provided in the embodiments of the present invention;

[0077] Figure 6 This is a model fitting diagram provided in an embodiment of the present invention. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] This invention provides a structural reliability analysis method based on an adaptive variable fidelity model, such as... Figure 1 As shown, the method includes the following steps:

[0080] S1. Generate an initial sample point set, which includes a low-fidelity sample set and a high-fidelity sample set. The initial sample point set is generated using an improved random sampling method, KMODMC (K-Means Optimized Distance-based Monte Carlo), including: randomly generating a candidate sample point set within the design space; selecting a new sample point from the candidate sample point set at each round of sample point selection, choosing the point furthest from the already selected sample points; and further homogenizing the sample distribution through clustering to obtain the initial sample point set. Here, the design space refers to the input variable space of the structural performance function, typically including random variables such as material strength, load, and geometric parameters. The first selected sample point is randomly chosen from the candidate sample points. Specifically:

[0081] Dimensions of given design variables and design space Design Space It is the field of real numbers On 3D space vector, that is In the design space Within, candidate sample points are generated using a random sampling formula:

[0082] ;

[0083] in, For the first One sample point, and These are the upper and lower bounds of the design variable, respectively. To generate a A uniformly distributed random number vector ensures the initial randomness of the sample points, forming the candidate sample point set. Design variables are the input parameters;

[0084] In the When selecting sample points in rounds, in order to maximize the distance between sample points and avoid the clustering of sample points in space, the point that is farthest from the already selected sample point set is selected as the new sample point from the candidate sample point set:

[0085] ;

[0086] ;

[0087] in, The distance between two sample points. The candidate sample point set typically includes the currently selected sample point set, in order to avoid insufficient coverage due to too few samples. A random point, This refers to the number of design parameters in the design space. For example, if the design parameters are three variables: material strength, cross-sectional dimensions, and load magnitude, then... The candidate sample point set C at this time contains 30 random points;

[0088] To further homogenize the sample distribution, the K-Means clustering algorithm is executed to divide the initially generated sample points into... Clusters, each sample point is a cluster, calculate the centroid of each cluster. :

[0089] ;

[0090] in, It is the first The set of sample points for each cluster is updated by using the centroid of each cluster as the new sample point. :

[0091] ;

[0092] The process is executed iteratively until convergence. The maximum number of iterations is set according to actual needs. The K-Means clustering algorithm is used to further enhance the overall uniformity of the sample points and avoid the local clustering problem that may be caused by the maximum and minimum distance optimization.

[0093] Finally, the optimized initial sample point set is obtained, namely the optimized low-fidelity sample set and high-fidelity sample set. The low-fidelity sample set and high-fidelity sample set are distinguished according to the simulation accuracy or the complexity of the calculation model.

[0094] S2. Train the BP neural network using a low-fidelity sample set to obtain a trained low-fidelity BP neural network model.

[0095] BP neural networks have the following characteristics: (1) Nonlinear fitting ability: With the help of the combined effect of multi-layer activation functions, they can accurately fit highly nonlinear input-output mapping relationships; (2) Generalization prediction performance: A well-trained network can reliably infer samples that have not participated in training based on learning experience; (3) Data fault tolerance feature: It is tolerant to input noise or local data defects, avoiding model failure caused by overfitting.

[0096] A backpropagation (BP) neural network is trained using a low-fidelity sample set. The topology of the BP neural network includes an input layer, a hidden layer, and an output layer. The input layer receives input variables, the hidden layer processes the input signal through a non-linear activation function, and the output layer generates an output value, which is the predicted probability of structural failure.

[0097] Input variables are Corresponding to the input layer The hidden layer contains 100 neurons. There are neurons, and the output is . ,correspond One neuron;

[0098] The transitive relationships between the input layer and the hidden layer, and between the hidden layer and the output layer, are represented by transformation functions. In this embodiment, the transformation function is the Sigmoid function, and the expression for the Sigmoid function is:

[0099] ;

[0100] Represents the transformation function The independent variable, the hidden layer The output of each neuron is transformed by a weighted sum of the input signals and then by an activation function, as shown in the formula:

[0101] ;

[0102] in, For input layer variables With hidden layer variables The connection weights between them Hidden layer variables The threshold;

[0103] The number of neurons in the hidden layer was determined by trial and error. Initial value:

[0104] ;

[0105] in, This is an adjustment factor, and its value is an integer from 1 to 10.

[0106] During the training of a BP neural network, the input signal is forward-propagated to the hidden layer, processed by the activation function, and then passed to the output layer to generate an initial response value. When the deviation between the output result and the target value exceeds the threshold, the error gradient is calculated and distributed backward along the network layers to each node. The inter-layer connection weights and neuron thresholds are dynamically adjusted to gradually correct the model prediction deviation until the preset convergence accuracy is reached, thus obtaining a well-trained low-fidelity BP neural network model.

[0107] S3. Train the Kriging model using the error between the predicted structural failure probability of the high-fidelity sample set and the predicted structural failure probability of the high-fidelity sample set in the low-fidelity BP neural network model, to obtain the error-corrected Kriging model, which specifically includes:

[0108] Construct a Kriging model and use Euclidean equations to quantify any two points in the design space. and The distance between them can be expressed as:

[0109] ;

[0110] in, In response to the predicted value, These are the basis function weights of Kriging. The basis functions are composed of regression functions. This is a systematic bias;

[0111] The systematic deviation between the predicted response and the actual structural response in the Kriging regression model It follows a distribution with a mean of 0 and a covariance as shown in the following formula:

[0112] ;

[0113] in, For systematic bias variance Sample points and Related functions, For the spatial correlation function parameters, this embodiment selects the widely used Gaussian process as the correlation function, and its expression is as follows:

[0114] ;

[0115] in, For input dimensions, This is a length scale parameter that controls the smoothness of this dimension. Let be the Euclidean distance between the sample points. , The input vector at the th The components of each dimension.

[0116] The low-fidelity BP neural network model is obtained by training with low-fidelity samples:

[0117] ;

[0118] in, This represents the predicted failure probability value for a low-fidelity BP neural network model. These are the training parameters for a low-fidelity BP neural network model, which include weights and biases.

[0119] Since BP networks may contain systematic errors, the Kriging method is used to analyze the error term. Modeling:

[0120] ;

[0121] in, For high-fidelity samples, This represents the probability value of structural failure in a true high-fidelity sample set. The low-fidelity model, which predicts the structural failure probability value of high-fidelity samples in a pre-trained low-fidelity BP neural network model, is used to obtain the structural failure probability value of the real high-fidelity sample set through high-fidelity numerical simulation (such as finite element analysis) or experimental calculation. The Kriging model is trained using error data to obtain the error-corrected Kriging model. The Kriging model is trained using high-fidelity samples as input and error values ​​as output.

[0122] S4. Combining the low-fidelity BP neural network model and the error-corrected Kriging model, a multi-fidelity hybrid agent model is constructed, specifically including:

[0123] The low-fidelity BP neural network model and the error-corrected Kriging model are superimposed to obtain a multi-fidelity hybrid surrogate model:

[0124] .

[0125] Adaptively iterate the multi-fidelity hybrid proxy model, i.e., establish an adaptive variable fidelity model, and implement a dual-model alternating sampling strategy in each iteration:

[0126] In even-numbered iterations, a gradient-uncertainty-driven sampling strategy is adopted. By calculating the uncertainty of the low-fidelity BP neural network model at the prediction point and the gradient of the predicted value, regions with high uncertainty and drastic gradient changes are identified. The uncertainty and the gradient of the predicted value are combined to generate an even-numbered iteration scoring function. The sample point with the highest score is selected and added to the adaptive iteration training set to improve the generalization ability of the low-fidelity BP neural network model near the boundary. Specifically:

[0127] Constructing a low-fidelity BP neural network model at the input point Predicted distribution on:

[0128] ;

[0129] in, The first BP neural network Secondary forward propagation (simulating dropout or network disturbance). Indicates the same input point The number of samples to be sampled during random forward propagation has an uncertainty of:

[0130] ;

[0131] in, ;

[0132] The gradient of the predicted value is:

[0133] ;

[0134] The partial derivative, even-numbered iterations, and scoring function are:

[0135] ;

[0136] Select Before scoring High-quality sample points are added to the adaptive iterative training set. The settings can be adjusted according to the actual situation. In this embodiment, .

[0137] In odd-numbered iterations, a sampling strategy based on MSE-failure surface-driven sampling is adopted. By calculating the prediction variance of the Kriging model to correct the error and introducing a failure probability surface distance term, the sample points are guided closer to the structural failure surface. The prediction variance and the introduced failure probability surface distance term are combined to generate an odd-numbered iteration sampling score function. The sample point with the highest score is selected and added to the training set for adaptive iteration to improve the accuracy of the hybrid model in failure probability estimation. Specifically:

[0138] The Kriging model can provide prediction variance (mean squared error, MSE) through its own structure, measuring the prediction uncertainty at a certain point, including the design point. The formula for calculating MSE at this location is:

[0139] ;

[0140] in, This is the correlation vector between the current point and the training points. The correlation vector is calculated by the correlation function (also known as the kernel function). The covariance parameter of the Kriging model. For the regression residuals, The correlation matrix represents the spatial correlation between sample points.

[0141] To make the sampling points close to the structural failure surface (i.e., the limit state function) Introducing the following distance term:

[0142] ;

[0143] in, The output value of the multi-fidelity hybrid agent model. In this embodiment, the failure detection threshold is set to 0;

[0144] To enhance the sampling weights near the failure boundary, an exponential weighting function is used:

[0145] ;

[0146] in, As a hyperparameter, it is set to 15 in this embodiment to control the sampling concentration.

[0147] The odd-number iterative scoring function is:

[0148] ;

[0149] Select Before scoring High-quality sample points are added to the adaptive iterative training set. The settings can be adjusted according to the actual situation. In this embodiment, .

[0150] After each iteration, the convergence of the model is determined using an information criterion based on uncertainty aggregation. This criterion integrates the prediction uncertainties of the low-fidelity BP neural network model and the error-corrected Kriging model, and is defined as follows:

[0151] ;

[0152] in, This represents the total number of pre-generated test sample points used for convergence assessment. Indicates the index of the test sample point. Indicates the first One test sample point;

[0153] When the total uncertainty is below a preset threshold At that time, that is In this embodiment, a preset threshold is used. The model is considered to have sufficient global predictive ability, so the point addition iteration is terminated. Thus, a high-precision multi-fidelity hybrid surrogate model is obtained. The high-precision multi-fidelity hybrid surrogate model is used for structural reliability analysis. By combining the global information of low-fidelity data with the error correction of high-fidelity data, a high-precision multi-fidelity hybrid surrogate model is efficiently constructed. It can accurately capture the failure boundary and realize accurate prediction of structural failure probability and reliability assessment.

[0154] S5. Use a high-precision multi-fidelity hybrid surrogate model to assess structural reliability, calculate the predicted failure probability of the structure, compare the predicted failure probability with the actual failure probability or the calculation results of a reference method (such as the traditional Monte Carlo method MCS), verify the prediction accuracy and efficiency of the model, and adjust the model parameters or sampling strategy according to the verification results to further optimize the model performance.

[0155] This embodiment provides the following examples to verify the feasibility of the improved random sampling KMODMC method:

[0156] First, Monte Carlo sampling (MCS), Latin hypercube sampling (LHS), and Sobol sequence sampling (Sobol) were selected as comparison methods, considering two-dimensional dimensionless design variables. and Follows an independent normal distribution Design space definition Each sampling method generates The sampling distribution of the sample points is as follows: Figure 2-5 As shown, where, Figure 2 A scatter plot of the Monte Carlo sampling method. Figure 3 This is a scatter plot of the Latin hypercube sampling method. Figure 4A scatter plot of the Sobol sequence sampling method. Figure 5 The scatter plot of the improved random sampling KMODMC method provided by this invention shows that the traditional MCS method has strong randomness and often exhibits locally dense or empty areas due to the lack of distribution control, resulting in low sample utilization. The LHS method achieves hierarchical control in dimensional distribution, but still suffers from point clustering and boundary stacking problems in the two-dimensional joint space, resulting in poor uniformity. Sobol sequences, as low-discrepancy sequences, can improve uniformity to some extent, but their overall distribution in high-dimensional space still shows structural regularity, which is not conducive to global random coverage. In contrast, the improved random sampling method KMODMC of this invention combines the spatial adaptability of K-means clustering with a density-driven candidate sample generation mechanism, which can effectively control local clustering while ensuring global coverage. Its sampling results show high uniformity and reasonable randomness throughout the design space. The sample points are not only evenly distributed in various regions of the space, but also automatically avoid boundary stacking, improving the representativeness and information utilization of the samples. More importantly, the KMODMC method combines the importance sampling concept with data-driven control capabilities, making it suitable for the initial sample construction needs in multifidelity modeling and significantly improving the robustness and accuracy of surrogate model construction.

[0157] In summary, the improved KMODMC method of this invention has significant advantages over traditional methods such as MCS, LHS and Sobol in terms of sample selection uniformity, spatial coverage and information representation ability, and is suitable as an initial sample generation scheme for multi-fidelity surrogate models in structural reliability analysis.

[0158] This embodiment also provides the following structural reliability verification example based on a multi-fidelity hybrid proxy model:

[0159] This example selects a typical multimodal function for structural reliability assessment. This function contains multiple local extrema and a non-convex failure domain, which places high demands on the surrogate model. This embodiment uses a low-fidelity BP neural network model to fit the response trend of the function function, combined with a high-fidelity error correction Kriging model, and utilizes an adaptive dual-model alternating point addition strategy to iteratively improve the model accuracy and failure surface capture capability.

[0160] This example uses the traditional Monte Carlo method (MCS), the AK-MCS method based on single-fidelity Kriging, the simple BP neural network method (NN), and the multi-fidelity Co-Kriging method as comparison methods. Each method is run independently, and the prediction failure probability, relative error, and equivalent high-fidelity call count (i.e., the number of high-fidelity samples plus the weighted average of the number of low-fidelity samples and the cost ratio) of each method are recorded to evaluate the accuracy and efficiency of each method.

[0161] The evaluation results are shown in the table below. As can be seen from the table, the MCS method uses more than [a certain number of methods]. The second-high-fidelity call calculated the true failure probability to be 0.0330. The AK-MCS method, employing an active learning strategy, predicted a value of 0.0348 with an error of approximately 5.45%, consuming 110 equivalent high-fidelity calls, resulting in high computational cost. The NN method, trained with 50 high-fidelity samples, predicted a value of 0.0289 with an error of approximately 12.4%. The neural network is unstable in highly nonlinear regions, and the predicted surface fluctuates significantly near the failure domain. The Co-kriging method integrates high- and low-fidelity information, but when dealing with complex response functions, co-modeling struggles to capture the dynamic characteristics of global structure and local errors, resulting in a high predicted value of 0.0352 with a relative error of approximately 6.67%. The method of this invention uses only approximately 82 equivalent high-fidelity calls, accurately predicting a failure probability of 0.0323, close to the true value, with an average relative error of only 2.91%. The model fitting graph is shown below. Figure 6 As shown, thanks to the low-fidelity BP neural network model capturing the overall response trend well, the error correction Kriging model efficiently models the high-fidelity residuals, and the alternating point addition strategy guides the sample addition to be concentrated near the failure surface, reducing the distribution of redundant samples. While keeping the computational cost controllable, the model accuracy is improved, and the stability and adaptability are good.

[0162] Table 1 Comparison of Evaluation Results between the Invention Method and Traditional Methods

[0163]

[0164] In summary, the proposed solution has higher prediction accuracy and better sample utilization efficiency under multimodal functions. It has significant advantages and strong applicability in the context of complex limit state functions, strong nonlinearity, and multi-peak distribution of response structure.

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A structural reliability analysis method based on an adaptive variable fidelity model, characterized in that, The method includes the following steps: Step S1: Generate an initial sample point set. The initial sample point set is generated using the improved random sampling method KMODMC. The initial sample point set includes a low-fidelity sample set and a high-fidelity sample set. Step S2: Train the BP neural network using a low-fidelity sample set to obtain a trained low-fidelity BP neural network model. Step S3: Train the Kriging model using the error between the predicted structural failure probability of the high-fidelity sample set and the predicted structural failure probability of the high-fidelity sample set in the low-fidelity BP neural network model to obtain the error-corrected Kriging model. Step S4: Combine the low-fidelity BP neural network model and the error correction Kriging model to construct a multi-fidelity hybrid proxy model. Adaptively iterate the multi-fidelity hybrid proxy model and implement the dual-model alternating sampling strategy in each iteration. Finally, use the multi-fidelity hybrid proxy model to evaluate the structural reliability. In step S4, the multi-fidelity hybrid proxy model is adaptively iterated, and a dual-model alternating sampling strategy is implemented in each iteration, including: During even-numbered iterations, the uncertainty of the low-fidelity BP neural network model at the prediction point and the gradient of the predicted value are calculated. The results of both calculations are combined to generate an even-numbered iteration scoring function, and the sample point with the highest score is selected to be added to the training set of the adaptive iteration. During odd-numbered iterations, the prediction variance of the error-corrected Kriging model and the distance term of the failure probability surface are calculated. The results of both calculations are combined to generate an odd-numbered iteration scoring function, and the sample point with the highest score is selected to be added to the training set of the adaptive iteration. After each iteration, determine whether the model has converged. If it has converged, terminate the point addition iteration to obtain a high-precision multi-fidelity hybrid proxy model. Furthermore, even-numbered iterations include: Constructing a low-fidelity BP neural network model at the input point Predicted distribution on: ； in, The first BP neural network Second forward propagation, Indicates the same input point The number of samples to be sampled during random forward propagation has an uncertainty of: ； in, ; The gradient of the predicted value is: ； The partial derivative, even-numbered iterations, and scoring function are: ； Select Before scoring High-quality sample points are added to the adaptive iterative training set; Odd iterations include: The Kriging model provides the prediction variance (MSE) through its own structure, measuring the prediction uncertainty at a certain point, including the design point. The MSE calculation method at this location is as follows: ； in, This is the correlation vector between the current point and the training points. The covariance parameter of the Kriging model. For the regression residuals, The correlation matrix represents the spatial correlation between sample points. Introduce the following distance term: ； in, The output value of the multi-fidelity hybrid agent model. This is the failure detection threshold; Using a weighted function in exponential form: ； in, For hyperparameters; The odd-number iterative scoring function is: ； Select Before scoring High-quality sample points are added to the adaptive iterative training set.

2. The structural reliability analysis method based on an adaptive variable fidelity model according to claim 1, characterized in that, In step S1, the generation of the initial sample point set by the improved random sampling method KMODMC includes: randomly generating a candidate sample point set within the design space; selecting a point from the candidate sample point set that is furthest from the already selected sample point as a new sample point in each round of sample point selection; and further homogenizing the sample distribution through clustering to obtain the initial sample point set.

3. The structural reliability analysis method based on the adaptive variable fidelity model according to claim 2, characterized in that, The generation of the initial sample point set using the improved random sampling method KMODMC further includes: Dimensions of given design variables and design space , ,in, For the real number field, a candidate sample point set is generated using random sampling, represented as: ； in, For the first One sample point, and These are the upper and lower bounds of the design variable, respectively. Indicates the generation of a A uniformly distributed vector of 3D random numbers, and a set of candidate sample points. ; In the When selecting sample points in rounds, the point that is furthest from the set of already selected sample points is chosen from the candidate sample set, which is represented as: ； ； in, The distance between two sample points. This is the currently selected set of sample points; To further homogenize the distribution of sample points, the K-Means clustering algorithm is executed to divide the currently selected sample points into... Clusters, calculate the centroid of each cluster. : ； in, It is the first The set of sample points for each cluster is updated by using the centroid of each cluster as the new sample point. : ； The optimized initial sample point set is obtained, namely the optimized low-fidelity sample set and high-fidelity sample set.

4. The structural reliability analysis method based on an adaptive variable fidelity model according to claim 1, characterized in that, In step S2, a BP neural network is trained using a low-fidelity sample set. The BP neural network includes an input layer, a hidden layer, and an output layer. The input layer receives input variables, the hidden layer processes the input signal through a nonlinear activation function, and the output layer generates an output quantity, which is the predicted probability of structural failure.

5. The structural reliability analysis method based on the adaptive variable fidelity model according to claim 4, characterized in that, The working principle of a BP neural network is as follows: Input variables are Corresponding to the input layer The hidden layer contains 100 neurons. There are neurons, and the output is . ,correspond One neuron; The transitive relationships between the input layer and hidden layers, and between hidden layers and output layers, are represented by transformation functions, using the Sigmoid function: Hidden layer The output of each neuron is transformed by a weighted sum of the input signals followed by an activation function: ； in, Represents the transformation function. For input layer variables With hidden layer variables The connection weights between them Hidden layer variables The threshold; The number of neurons in the hidden layer was determined by trial and error. Initial value: ； in, It is a regulating factor.

6. The structural reliability analysis method based on the adaptive variable fidelity model according to claim 5, characterized in that, In step S3, the low-fidelity BP neural network model is obtained through training with low-fidelity samples, specifically including: ； in, This represents the predicted failure probability value for a low-fidelity BP neural network model. This represents a low-fidelity backpropagation (BP) neural network model. These are the training parameters for a low-fidelity BP neural network model, which include weights and biases. For error Modeling: ； in, For high-fidelity samples, This represents the probability value of structural failure in a true high-fidelity sample set. To predict the structural failure probability value of the low-fidelity model obtained by training a low-fidelity BP neural network model on high-fidelity samples, the Kriging model is trained using error data to obtain the error-corrected Kriging model.

7. The structural reliability analysis method based on an adaptive variable fidelity model according to claim 6, characterized in that, In step S4, the low-fidelity BP neural network model and the error-corrected Kriging model are superimposed to obtain the multi-fidelity hybrid proxy model as follows: .

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