A structural reliability analysis method combining transfer learning and adaptive sampling

Abstract

The application discloses a structure reliability analysis method combining migration learning and adaptive sampling, and relates to the field of structure reliability analysis. In view of the problems of high calculation cost of a high-fidelity model and insufficient precision of a single surrogate model in the prior analysis, the method firstly acquires low-fidelity sample data and trains a first surrogate model representing global features; then, an initial sample is selected to acquire a high-fidelity response, and a second surrogate model is constructed based on the first surrogate model through migration learning; subsequently, candidate sample points are generated, and an importance evaluation index is calculated in combination with predicted response and random variable joint probability distribution information; based on the index, new samples are adaptively selected, a high-fidelity response is acquired to update the second surrogate model; finally, the failure probability is cyclically evaluated and a dynamic convergence condition is judged until the convergence requirement is met, and the final result is output. The application greatly reduces the number of high-fidelity model calls under the premise of ensuring evaluation precision, and significantly improves the efficiency and stability of reliability analysis.

Description

Technical Field

[0001] This invention relates to the field of engineering structure reliability analysis and risk assessment technology, specifically to a structural reliability analysis method that combines transfer learning and adaptive sampling. Background Technology

[0002] In the field of engineering structural design and reliability analysis, accurate assessment of failure probability is a core aspect of ensuring the safety of engineering systems. Typically, the assessment of failure probability is highly dependent on limit state functions and random variable models.

[0003] Currently, Monte Carlo simulation, as a classic structural reliability analysis method, is widely used due to its good versatility and adaptability to high-dimensional problems. However, with the increasing complexity of modern engineering structures, limit state functions often need to be characterized by high-precision numerical simulation models (i.e., high-fidelity models, such as complex finite element analysis models). In this case, traditional Monte Carlo simulation, due to its requirement for massive random sampling and repeated model calls, consumes extremely large amounts of computational resources and time, making it difficult to meet the urgent requirements for computational efficiency in practical engineering applications.

[0004] To reduce computational costs, existing technologies commonly employ surrogate models to approximate the limit state function, combined with adaptive sampling strategies to add sample points near the failure boundary, thus replacing expensive high-fidelity numerical simulations. However, when the limit state function of an engineering structure exhibits strong nonlinearity or complex variations, a single surrogate model often struggles to balance global prediction accuracy with local boundary accuracy under limited sample conditions. This results in the need to call the high-fidelity model a relatively high number of times to achieve convergence accuracy, leaving a heavy computational burden.

[0005] Furthermore, some existing technologies attempt to introduce multi-fidelity modeling strategies that combine low-fidelity models (such as simplified physical models or coarse mesh models) with high-fidelity models. However, in practical engineering applications, existing multi-fidelity modeling methods still have significant shortcomings: on the one hand, the information fusion between high-fidelity and low-fidelity models is often insufficient; on the other hand, existing adaptive sampling strategies are inefficient under complex joint probability distribution conditions, easily leading to excessive clustering of new sample points in local areas or failure to hit the critical areas that contribute the most to the failure probability. These problems collectively result in the need to further improve the stability and reliability of the final failure probability assessment results.

[0006] In summary, the engineering field urgently needs an engineering reliability analysis method that can fully utilize the inexpensive global information of low-fidelity models, effectively and significantly reduce the number of calls to high-fidelity models, and possess a stable and efficient adaptive sampling strategy, so as to balance computational efficiency and evaluation accuracy. Summary of the Invention

[0007] To address the problems existing in the background technology, this invention proposes a structural reliability analysis method combining transfer learning and adaptive sampling. This method constructs a transfer learning network fusion mechanism that preserves low-fidelity global features while correcting high-fidelity local accuracy; employs an adaptive sampling strategy that combines the joint probability density of predicted response and random variables based on sample importance; and introduces distance threshold constraints and dynamic relative change rate-based anti-aggregation and convergence stopping logic. This solves the technical problems of high computational cost in high-fidelity numerical simulation for assessing failure probability, difficulty in achieving both global and local accuracy under complex nonlinear extreme states with a single surrogate model, insufficient information fusion in traditional multi-fidelity models, and low efficiency in adaptive sampling. The method achieves stable and efficient engineering structural reliability analysis and risk assessment while significantly reducing the number of high-fidelity model calls, ensuring the accuracy of failure probability assessment.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A structural reliability analysis method combining transfer learning and adaptive sampling includes the following steps: S1. Determine the random variables and their probability distribution information of the engineering structure to be analyzed, generate low-fidelity sample data in the design space of the random variables, and call the low-fidelity limit state function to calculate the low-fidelity response corresponding to each low-fidelity sample data. S2. The first surrogate model is trained based on the low-fidelity sample data and its low-fidelity response. S3. Using a distance maximization strategy based on normalized design space, initial sample points are selected from low-fidelity sample data, and the corresponding high-fidelity response is calculated by calling the high-fidelity limit state function to obtain an initial high-fidelity training set; based on the first surrogate model, the initial high-fidelity training set is introduced, and a second surrogate model is constructed through transfer learning. S4. Based on the preset probability distribution of random variables, use the Monte Carlo sampling method to generate several candidate sample points in the design space of random variables, use the second surrogate model to calculate the predicted response value of the candidate sample points, and combine the joint probability distribution information of random variables to calculate the importance evaluation index of the candidate sample points. S5. Select new sample points from the candidate sample points according to the importance evaluation index, and call the high-fidelity limit state function to calculate the high-fidelity response of the new sample points in order to update the second proxy model. S6. Calculate the estimated failure probability of the engineering structure to be analyzed based on the updated second surrogate model, and determine whether the preset convergence condition is met. If the convergence condition is not met, return to execute steps S4 and S5 again until the convergence condition is met and the iteration is terminated. Calculate the final failure probability as the reliability analysis result.

[0009] Specifically, in step S1, the method for generating low-fidelity sample data within the design space of random variables is as follows: based on the preset probability distribution of random variables, a preset number of low-fidelity sample points are generated using the Maximin LHS sampling method, and the low-fidelity sample points are uniformly distributed within the design space.

[0010] Specifically, step S2 includes: S21. Calculate the empirical mean and empirical standard deviation of each dimension of the random variables determined by the low-fidelity sample dataset, and normalize each random variable in the low-fidelity sample data. The calculation formula is as follows: ; in, For the low-fidelity sample set The first sample The original values ​​of a 3D random variable; and These are the first two samples in the low-fidelity sample dataset. The empirical mean and empirical standard deviation of a dimensional random variable; This represents the normalized value of the random variable; after all random variables have been normalized, a standardized low-fidelity sample dataset is obtained.

[0011] S22. Based on the standardized low-fidelity sample dataset and the corresponding low-fidelity response, a first surrogate model is trained; wherein the first surrogate model is a multi-layer feedforward neural network including at least two hidden layers, and the network parameters are optimized by a backpropagation algorithm based on Bayesian regularization until the mean square prediction error of the first surrogate model for low-fidelity samples is less than a preset training accuracy threshold.

[0012] Specifically, in step S3, the mathematical process for selecting initial sample points using a distance maximization strategy based on the normalized design space is as follows: a. Randomly select one low-fidelity sample point and add it to the initial high-fidelity training set; b. In the standardized low-fidelity sample dataset obtained in step S21, calculate the standardized low-fidelity sample points that have not yet been selected. With each point in the selected sample set The Euclidean distance between them is calculated, and the minimum spatial distance corresponding to each unselected sample point is recorded. : ; c. Select the minimum spatial distance The standardized low-fidelity sample points that reach the maximum value are added to the set as the original design space sample points, and this iterative calculation process is repeated until a preset number of initial sample points are obtained. This is to eliminate the measurement failure caused by the difference in the dimensions of multidimensional random variables and ensure that the initial sample points are uniformly covered in the multidimensional joint probability space.

[0013] Specifically, the process of constructing the second agent model through transfer learning in step S3 includes: S31. The network topology of the first surrogate model that has been trained, as well as the weight matrices and bias vectors of all its layers, are isomorphically mapped and initialized to form the initial transfer model. S32. Freeze the weight matrix connecting the input layer and the first hidden layer in the initial transfer model, as well as the bias vector of the neurons in the first hidden layer, to preserve the global manifold features of the limit state function learned by the first surrogate model from the low-fidelity sample data. S33. Using the Levenberg-Marquardt training algorithm, the parameters of subsequent network layers that have not been frozen are locally approximated and trained using the initial high-fidelity training set until the mean square prediction error of the model on the initial high-fidelity samples is less than the preset training accuracy threshold, thus obtaining a second surrogate model that integrates low-fidelity global physical laws and high-fidelity local accuracy.

[0014] Specifically, the joint training and optimization process of the first proxy model and the second proxy model satisfies the following conditions: (1) The first surrogate model is a multi-layer feedforward neural network, whose network topology includes an input layer, at least two hidden layers, and an output layer; during the training phase of the first surrogate model, a Bayesian regularized backpropagation algorithm is used, and its objective function is... Sum of squared prediction errors With the sum of squared network weights The linear combination of these terms is calculated using the following formula: ; in and The regularization parameter is dynamically updated based on the Bayesian criterion and is used to suppress overfitting during training with low-fidelity samples. (2) In the construction stage of the second proxy model, the Levenberg-Marquardt algorithm is used to locally correct the subsequent network layers that are not frozen. The iterative update formula for the network parameters is as follows: ; in, This refers to the update amount of network weights and biases. The Jacobian matrix of the network prediction error with respect to the parameters of the unfrozen layer. This represents the prediction error vector for high-fidelity samples. It is the identity matrix. This is the damping factor that is dynamically and adaptively adjusted.

[0015] Specifically, in step S4, the formula for calculating the importance evaluation index of candidate sample points is: ; in, To predict the first using the second surrogate model The predicted response value of each candidate sample point represents the degree of proximity of the candidate sample point to the failure boundary of the limit state function. For the first The weight index of each candidate sample point is used to characterize the joint probability density value of the candidate sample points appearing in the random variable design space; This is an adjustment factor used to balance the weights of failure boundary search and probability space coverage; The preset small positive regularization term is used to prevent numerical truncation and computational overflow caused when the joint probability density of the deep-tailed region approaches zero. For the first The smaller the value of the candidate sample point, the higher its potential contribution to the overall failure probability.

[0016] Specifically, no. Weight index of each candidate sample point The calculation is performed based on whether the random variables of the engineering structure being analyzed are independent of each other. (1) When the random variables of the engineering structure to be analyzed are independent of each other, the weight index of the candidate sample points is the product of the probability density functions of each random variable, and the calculation formula is: ; in, Let be the total dimension of the random variables in the engineering structure to be analyzed. For the first The first candidate sample point The original values ​​of a 3D random variable. For the first The probability density function of a 3D random variable; (2) When the random variables of the engineering structure to be analyzed are not independent of each other, the weight index of the candidate sample points is calculated by the multidimensional joint probability density function composed of all random variables. The calculation formula is as follows: ; in, for The joint probability density function of 3D random variables; The first The original values ​​of each candidate sample point in each dimension of the random variable.

[0017] Specifically, step S5 includes: S51. All candidate sample points are evaluated according to importance indicators. The values ​​are sorted from smallest to largest. The candidate sample points are then iterated and evaluated sequentially from the top-ranked points. Several sample points that satisfy the topological distance constraint are selected as new sample points. The specific topological distance constraint is as follows: Calculate the coordinate vector of the currently evaluated candidate sample point in the normalized design space. Normalized coordinate vectors of all existing samples in the current high-fidelity training set The Euclidean distance between them; only if the minimum distance between the current candidate sample point and any existing sample point in the high-fidelity training set is not less than a preset distance threshold. hour: ; The current candidate sample point is accepted as a new sample point to avoid historical sample redundancy and high clustering near the local failure boundary of the limit state function; if this constraint is not met, the candidate sample point is removed and the next candidate sample point is evaluated in sequence. S52. Call the high-fidelity limit state function to calculate the high-fidelity response of each newly added sample point, add each newly added sample point and its corresponding high-fidelity response to the current high-fidelity training set, and expand to form an updated high-fidelity training set. S53. Using the updated high-fidelity training set, the second proxy model is retrained and locally corrected and updated.

[0018] Specifically, step S6 includes: S61. After each update of the second surrogate model, generate a first preset number of Monte Carlo sample points based on the probability distribution of the random variable, and predict the response value of each Monte Carlo sample point using the current second surrogate model; count the proportion of failed samples with response values ​​less than 0 among all Monte Carlo samples, and obtain the first... Failure probability estimate for the next iteration ,in This is the sequence number of the current iteration; S62. Determine whether the preset convergence condition is met: (1) First determine the current iteration number. Does it meet the requirements? ,in The preset minimum number of iterations is used to force the second proxy model to complete the exploration and updating of basic local features within the design space of random variables; (2) Only when the above condition (1) is met, the relative rate of change of the failure probability estimate between two adjacent iterations is further calculated. Determine whether it satisfies: ; in, and The first Next and first The failure probability estimate obtained in the next iteration; The preset threshold for truncating very small normal numbers is used to prevent division-zero singularity divergence caused by the estimated failure probability being zero in early active learning iterations. This is the preset relative convergence threshold; If all convergence conditions are met, the iteration is terminated; otherwise, the process returns to steps S4 and S5. S63. After the iteration is terminated, a second preset number of Monte Carlo sample points are generated according to the probability distribution of the random variable. The response value of each Monte Carlo sample point is predicted using the converged second surrogate model. The proportion of failure samples with response values ​​less than 0 is counted, and the final failure probability is obtained as the reliability analysis result.

[0019] In summary, the beneficial technical effects of the present invention are as follows: 1. Reduced computational cost while balancing global and local accuracy: This invention pre-constructs a low-fidelity model to obtain the global overall trend of the engineering system response, and then extracts a very small number of high-fidelity samples. It uses a transfer learning mechanism that freezes the input layer weights and only updates the subsequent layers to fine-tune the surrogate model, achieving deep information fusion between the low-fidelity and high-fidelity models. Without losing the global physical laws, the surrogate model has extremely high local fitting accuracy, breaking the technical bottleneck of traditional single surrogate models relying on massive amounts of expensive high-fidelity data, and significantly reducing the time and computational cost of engineering reliability analysis.

[0020] 2. Improved adaptive sampling efficiency: To address the shortcomings of traditional active learning algorithms that blindly approach the failure boundary, leading to resource waste, this invention constructs a sample importance evaluation index that combines the predicted response with the joint probability density of random variables. This index not only examines the physical proximity of sample points to the failure boundary but also takes into account the probability weight of this condition occurring in the real random design space. This allows newly added expensive high-fidelity computing resources to be accurately and preferentially allocated to the core region that contributes the most to the final failure probability, significantly improving the utilization rate of computing resources.

[0021] 3. Avoids wasted computing power caused by blind iteration: This invention uses the relative change of the failure probability estimate obtained from two adjacent active learning iterations as the convergence criterion. This dynamic stopping strategy can accurately perceive the fitting maturity of the surrogate model in the high-probability failure region. Once the model has fully converged, the termination mechanism is automatically triggered, which reduces the computational redundancy of high-fidelity analysis while ensuring the accuracy of structural failure probability assessment.

[0022] 4. The algorithm has good decoupling, strong engineering applicability, and is easy to promote and integrate: The method provided by this invention does not rely on the mathematical expression of uncertainty of a specific surrogate model, nor does it require prior assumptions about the geometric characteristics of the limit state function. It has strong robustness to multidimensional, strongly nonlinear, and highly uncertain engineering problems. The method can be seamlessly connected and integrated into various existing industrial CAE high-precision simulation platforms, such as automobile collision safety assessment and aerospace reliability design, and has extremely high commercial application prospects and engineering promotion value. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0024] To make the technical means, creative features, objectives and effects of this invention clearer and easier to understand, the invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0025] Example This embodiment addresses the reliability assessment problem of vehicle side-impact collision structures. It employs the method proposed in this invention to model and calculate the failure probability of a multidimensional nonlinear limit state function, thereby verifying the applicability of the method in complex engineering scenarios. Those skilled in the art can refer to this embodiment to transfer the method to other engineering reliability analysis scenarios such as aerospace structures, civil engineering, and new energy equipment.

[0026] like Figure 1 As shown, the present invention provides a structural reliability analysis method combining transfer learning and adaptive sampling, which specifically includes the following steps: S1. Determine the random variables and their probability distribution information of the engineering structure to be analyzed, generate low-fidelity sample data in the design space of the random variables, and call the low-fidelity limit state function to calculate the low-fidelity response corresponding to each low-fidelity sample data. The specific method for generating low-fidelity sample data within the design space of random variables is as follows: based on the preset probability distribution of random variables, the Maximin LHS sampling method is used to generate a preset number of uniform sample points within the cumulative distribution function space of each random variable. Then, a mapping transformation is performed through the inverse cumulative distribution function corresponding to each random variable to obtain low-fidelity sample data that conforms to the probability distribution characteristics of the physical space. Compared with traditional random sampling, this method can ensure that the samples have good spatial filling and uniformity within the 7-dimensional design space, effectively avoiding global trend learning bias caused by the absence of samples in local areas.

[0027] The table below shows the seven random variables and their probability distributions involved in this embodiment: Table 1. Random variable information for vehicle side-impact structural reliability assessment

[0028] In this embodiment, two limit state functions are used to simulate the relationship between different fidelity analysis models in the vehicle side impact problem. The high-fidelity limit state function is obtained by approximating the function based on the mechanical mechanism analysis of the vehicle side impact and combined with the high-precision numerical simulation results. It is used to characterize the actual failure boundary of the structure under the collision condition. ; The low-fidelity limit state function is constructed by introducing engineering simplification assumptions on the basis of the high-fidelity model and weakening or approximating the coupling relationships of some variables. Its overall trend is consistent with that of the high-fidelity model, but there are differences in local accuracy. It is used to simulate simplified analysis models with lower computational costs in engineering. The limit state function determination rule is as follows: if the output value of the limit state function is less than 0, the structure is considered to have failed; if it is greater than 0, the structure is considered to be safe. In this embodiment, the low-fidelity limit state function is a simplified mechanical model. Its overall trend is consistent with that of the high-fidelity model, but there are local accuracy deviations, which conforms to the characteristics of high-fidelity and low-fidelity models in actual engineering.

[0029] S2. The first surrogate model is trained based on low-fidelity sample data and its low-fidelity response. The core purpose of this step is to use low-cost low-fidelity data to learn the global variation trend of the limit state function in the entire design space, so as to avoid starting from scratch for subsequent high-fidelity model training. The specific steps include: S21. Calculate the empirical mean and empirical standard deviation of each dimension of the random variables determined by the low-fidelity sample dataset, and normalize each random variable in the low-fidelity sample data. The calculation formula is as follows: ; in, For the low-fidelity sample set The first sample The original values ​​of a 3D random variable; and These are the first two samples in the low-fidelity sample dataset. The empirical mean and empirical standard deviation of a dimensional random variable; This represents the normalized value of the random variable; after all random variables have been normalized, a standardized low-fidelity sample dataset is obtained. S22. Based on the standardized low-fidelity sample dataset and the corresponding low-fidelity responses, a first surrogate model is trained. To ensure that the surrogate model can accurately capture the global topological relationship of the limit state function in the 7-dimensional random variable design space, in this embodiment, the first surrogate model adopts a feedforward neural network with multi-hidden-layer mapping capability. Its network topology is set to "7-20-20-1", that is: the input layer contains 7 neurons (corresponding to the 7 standardized random variables in Table 1), the hidden layer contains two layers, each with 20 neurons, and the output layer has 1 neuron (outputting the predicted response value). During the training phase, to address the numerical noise and local bias that may exist in the low-fidelity sample data, the Bayesian Regularization Backpropagation (trainbr) algorithm is used to optimize the network parameters. This algorithm reconstructs the traditional mean squared error (MSE) objective function by introducing the sum of squares of the weights as a penalty term into the objective function. ; in, For the sum of squared prediction errors, For the sum of squares of network weights, and The regularization parameters are dynamically and adaptively updated according to the Bayesian criterion.

[0030] Set the preset training accuracy threshold (network training objective parameter goal) of the first proxy model to [value]. Iterative solutions using Bayesian regularization not only effectively suppress the overfitting tendency of deep networks, but also ensure that the first surrogate model performs well under small sample conditions (…). =350) Smoothly approximate the global physical trend of the low-fidelity limiting state function until the training accuracy threshold is met, and then output the first surrogate model that has completed training.

[0031] S3. Select initial sample points from the low-fidelity sample data, call the high-fidelity limit state function to calculate the corresponding high-fidelity response, and obtain the initial high-fidelity training set; based on the first surrogate model, introduce the initial high-fidelity training set, and construct the second surrogate model through transfer learning; the core purpose of this step is to use a very small number of high-fidelity samples to calibrate the local error of the first surrogate model, while retaining the correct global trend it has learned, without having to train the high-fidelity surrogate model from scratch, thus greatly reducing the need for high-fidelity samples.

[0032] Among them, a distance maximization strategy based on normalized design space is adopted to select initial sample points from low-fidelity sample data, and the rule is as follows: a. Randomly select one low-fidelity sample point and add it to the initial high-fidelity training set; b. In the standardized low-fidelity sample dataset obtained in step S21, calculate the standardized low-fidelity sample points that have not yet been selected. With each point in the selected sample set The Euclidean distance between them is calculated, and the minimum spatial distance corresponding to each unselected sample point is recorded. : ; c. Select the minimum spatial distance The standardized low-fidelity sample points that reach the maximum value are added to the set as the corresponding original design space sample points, and the iterative calculation process is repeated until a preset number of initial sample points are obtained. In this embodiment, the preset number of initial sample points is set to 30 to eliminate the measurement failure caused by the difference in the dimensions of multidimensional random variables and ensure the uniform coverage of the initial sample points in the multidimensional joint probability space.

[0033] The specific process of constructing the second agent model through transfer learning in step S3 includes: S31. The network topology of the first surrogate model that has been trained, as well as the weight matrices and bias vectors of all its layers, are isomorphically mapped and initialized to form the initial transfer model. S32. Freeze the weight matrix of the connection between the input layer and the first hidden layer in the initial transfer model, as well as the bias vector of the neurons in the first hidden layer, to preserve the global trend features learned by the first surrogate model from the low-fidelity sample data. S33. The Levenberg-Marquardt training algorithm (trainlm) is adopted. Using the initial high-fidelity training set, local calibration training is performed on the unfrozen subsequent network layers (i.e., the weights and biases between the second hidden layer and the output layer). Since the connection weight matrix from the input layer to the first hidden layer has been frozen, the network already possesses global prior physical knowledge of the low-fidelity model. When introducing computationally expensive high-fidelity samples for transfer learning, the core objective is to achieve fast, locally high-precision approximation. Therefore, this embodiment abandons the computationally time-consuming Bayesian regularization algorithm and instead uses the Levenberg-Marquardt algorithm, which combines the global search capability of gradient descent with the local second-order convergence speed of the Gauss-Newton method, for network fine-tuning. Its parameter update iteration rule is defined as: ; in, This is the Jacobian matrix for updating the weights of the activated network error. This represents the high-fidelity prediction error vector of the network. It is the identity matrix. This is the damping factor, which is dynamically adjusted during the iteration process based on the error reduction trend.

[0034] Set the preset training accuracy threshold (target parameter goal) of the second surrogate model to a stringent level. This extremely high-precision threshold, combined with the efficient second-order Hessian matrix approximation calculation of the Levenberg-Marquardt algorithm, ensures that high-precision calibration of local failure boundaries of the network can be completed in a very short time using only a very small number of initial high-fidelity samples (such as 30 samples), thus achieving deep fusion of multi-fidelity physical information.

[0035] S4. Based on the preset probability distribution of random variables, a number of candidate sample points are generated within the design space of the random variables using the Monte Carlo sampling method. The predicted response values ​​of the candidate sample points are calculated using the second surrogate model, and the importance evaluation index of the candidate sample points is calculated by combining the joint probability distribution information of the random variables. The formula for calculating the importance evaluation index of the candidate sample points is: ; in, To predict the first using the second surrogate model The predicted response value of each candidate sample point represents the degree of proximity of the candidate sample point to the failure boundary of the limit state function. For the first The weight index of each candidate sample point is used to characterize the joint probability density value of the candidate sample points appearing in the random variable design space; As an adjustment factor, it is used to balance the weights of failure boundary search and probability space coverage. In this embodiment, the adjustment factor... The value is set to 0.3; The preset small positive regularization term is used to prevent numerical truncation and computational overflow caused when the joint probability density of the deep-tailed region approaches zero. For the first The smaller the value of the candidate sample point, the higher its potential contribution to the overall failure probability.

[0036] No. Weight index of each candidate sample point The calculation is performed based on whether the random variables of the engineering structure being analyzed are independent of each other. (1) When the random variables of the engineering structure to be analyzed are independent of each other, the weight index of the candidate sample points is the product of the probability density functions of each random variable, and the calculation formula is: ; in, Let be the total dimension of the random variables in the engineering structure to be analyzed. For the first The first candidate sample point The original values ​​of a 3D random variable. For the first The probability density function of a 3D random variable; (2) When the random variables of the engineering structure to be analyzed are not independent of each other, the weight index of the candidate sample points is calculated by the multidimensional joint probability density function composed of all random variables. The calculation formula is as follows: ; in, for The joint probability density function of 3D random variables; The first The original values ​​of each candidate sample point in each dimension of the random variable.

[0037] In actual numerical calculations, to avoid numerical underflow caused by the product of the joint probability densities of multidimensional random variables, the weight index calculation in step S4 preferably uses logarithmic mapping, as follows: (1) Calculate the log joint probability density of each candidate sample point: ; in, This is a preset minimum value used to prevent overflow in logarithmic calculations; (2) Normalize the mapping by subtracting the maximum value term to restore the weight index: ; This step, by shifting the logarithmic space, ensures that the value after the exponential operation falls within the range of the computer's effective floating-point representation, thus guaranteeing the stability of weight allocation during adaptive sampling.

[0038] S5. Based on the importance assessment index, select new sample points from the candidate sample points, and call the high-fidelity limit state function to calculate the high-fidelity response of the new sample points to update the second surrogate model. This step only selects the sample that contributes the most to the failure probability to call the high-fidelity model, maximizing the value of each high-fidelity calculation and further reducing the cost of high-fidelity calls. The specific steps include: S51. All candidate sample points are evaluated according to importance indicators. The values ​​are sorted from smallest to largest. The candidate sample points are iterated and evaluated sequentially from the top-ranked points. Several sample points that satisfy the topological distance constraint are selected as new sample points. In this embodiment, the number of new sample points in each round is 1. The topological distance constraint is specifically: Calculate the coordinate vector of the currently evaluated candidate sample point in the normalized design space. Normalized coordinate vectors of all existing samples in the current high-fidelity training set The Euclidean distance between them; only if the minimum distance between the current candidate sample point and any existing sample point in the high-fidelity training set is not less than a preset distance threshold. hour: ; In this embodiment, the preset distance threshold The value of is set to 0.3. The current candidate sample point is accepted as a new sample point to avoid historical sample redundancy and high aggregation near the local failure boundary of the limit state function; if this constraint is not met, the candidate sample point is removed and the next candidate sample point is evaluated in sequence. S52. Call the high-fidelity limit state function to calculate the high-fidelity response of each newly added sample point, add each newly added sample point and its corresponding high-fidelity response to the current high-fidelity training set, and expand to form an updated high-fidelity training set. S53. Using the updated high-fidelity training set, the second proxy model is retrained and locally corrected and updated.

[0039] S6. Calculate the estimated failure probability of the engineering structure to be analyzed based on the updated second surrogate model, and determine whether it meets the preset convergence condition. If the convergence condition is not met, return to steps S4 and S5 again until the convergence condition is met, at which point the iteration terminates, and the final failure probability is calculated as the reliability analysis result. The core purpose of this step is to directly use the stability of the failure probability as the convergence criterion, without relying on the uncertainty assumptions of the surrogate model, which is especially suitable for the accuracy requirements of low failure probability scenarios. The steps specifically include: S61. After each update of the second surrogate model, generate a first preset number of Monte Carlo sample points based on the probability distribution of the random variable, and predict the response value of each Monte Carlo sample point using the current second surrogate model; count the proportion of failed samples with response values ​​less than 0 among all Monte Carlo samples, and obtain the first... Failure probability estimate for the next iteration ,in This is the sequence number of the current iteration; S62. Determine whether the preset convergence condition is met: (1) First determine the current iteration number. Does it meet the requirements? ,in The preset minimum number of iterations is used to force the second surrogate model to complete the exploration and updating of basic local features within the random variable design space. In this embodiment, the preset minimum number of iterations... The value of is set to 6; (2) Only when the above condition (1) is met, the relative rate of change of the failure probability estimate between two adjacent iterations is further calculated. Determine whether it satisfies: ; in, and The first Next and first The failure probability estimate obtained in the next iteration; The preset threshold for truncating very small normal numbers is used to prevent division-zero singularity divergence caused by the estimated failure probability being zero in early active learning iterations. In this embodiment, the preset relative convergence threshold is... The value is set to 0.01; If all convergence conditions are met, the iteration is terminated; otherwise, the process returns to steps S4 and S5. S63. After the iteration is terminated, a second preset number of Monte Carlo sample points are generated according to the probability distribution of the random variable. The response value of each Monte Carlo sample point is predicted using the converged second surrogate model. The proportion of failure samples with response values ​​less than 0 is counted, and the final failure probability is obtained as the reliability analysis result.

[0040] To verify the effectiveness of this method, a cost function is further introduced. To evaluate the relative simulation costs at different fidelity levels: ; in, Set the value to 1. The number of times the high-fidelity HF model is called; the cost is determined by comparing the relative simulation time with that of the high-fidelity HF model. The value, specifically, the cost = 0.1 indicates that the simulation time for the low-fidelity LF sample is 10% of that for the high-fidelity HF sample. This is for the number of calls to the low-fidelity LF model.

[0041] Considering the randomness of initial sample sampling during the agent model construction process, to eliminate accidental errors, this embodiment uses different random number seeds to conduct 30 independent repeated tests on the above-mentioned analysis method combining transfer learning and adaptive sampling. Subsequently, the final average failure probability is calculated based on the samples. Standard deviation and coefficient of variation The table below lists the statistical average results of direct Monte Carlo simulation (MCS, as an accurate reference baseline), traditional multifidelity surrogate model, and the method of this invention after 30 independent runs: Table 2 Average results of tests using different methods

[0042] Statistical results show that after 30 independent random tests, the mean final failure probability predicted by the method of this invention is and consume a lot of computing power Compared to the MCS benchmark solution, the relative error is only 0.29%. More importantly, the coefficient of variation (CoV) of the method in this invention is strictly controlled at 2.72%, which is significantly better than the 4.6% of the traditional multifidelity model. This proves that while significantly reducing the computational cost of high fidelity (total cost is only 85.8), the dynamic convergence mechanism of this method effectively suppresses the evaluation fluctuation of the algorithm in the deep-tail region, demonstrating excellent algorithm robustness and extremely high engineering applicability.

[0043] Through the above steps, this embodiment can stably and accurately estimate the failure probability of a vehicle side collision structure under limited high-fidelity computing resources. Compared with traditional single surrogate models or direct Monte Carlo simulation methods, the method of this invention significantly reduces the number of high-fidelity calculations while maintaining analytical accuracy.

[0044] Therefore, this invention provides a structural reliability analysis method combining transfer learning and adaptive sampling. This method achieves efficient fusion of global trend and local accuracy by constructing a transfer learning network architecture with low-fidelity pre-training and high-fidelity frozen layer fine-tuning; employs a sample importance assessment strategy based on fused predicted response and joint probability density of random variables to ensure accurate allocation of expensive high-fidelity computing resources to high-contribution failure regions; and designs an adaptive sampling logic based on distance threshold constraints and dynamic relative rate of change convergence criteria to avoid local redundancy of high-fidelity samples and achieve minimal computational cost. This complete and reliable process achieves low-fidelity global baseline construction—high-fidelity transfer fine-tuning—joint probability density weighted sampling—dynamic convergence accurate assessment. The reliability analysis closed loop solves the problems of high computational costs caused by the inability of existing high-fidelity numerical simulation and single surrogate models to balance global and local accuracy under complex nonlinear conditions, the insufficient integration of low-fidelity and high-fidelity physical information features in existing traditional multi-fidelity modeling strategies, and the waste of computing power caused by the blind approximation of failure boundaries in existing adaptive sampling methods and the lack of intelligent iteration stopping criteria. It improves the computational timeliness, numerical stability and generalization prediction ability of failure probability assessment of complex engineering structures, and provides efficient and practical technical support for reliability evaluation and safety design optimization of complex industrial systems facing high-dimensional nonlinear extreme states, such as vehicle collision safety structures and aerospace service components.

[0045] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A structural reliability analysis method combining transfer learning and adaptive sampling, characterized in that, Includes the following steps: S1. Determine the random variables and their probability distribution information of the engineering structure to be analyzed, generate low-fidelity sample data in the design space of the random variables, and call the low-fidelity limit state function to calculate the low-fidelity response corresponding to each low-fidelity sample data. S2. The first surrogate model is trained based on the low-fidelity sample data and its low-fidelity response. S3. Using a distance maximization strategy based on normalized design space, initial sample points are selected from low-fidelity sample data, and the corresponding high-fidelity response is calculated by calling the high-fidelity limit state function to obtain the initial high-fidelity training set. Based on the first agent model, the initial high-fidelity training set is introduced, and a second agent model is constructed through transfer learning; S4. Based on the preset probability distribution of random variables, use the Monte Carlo sampling method to generate several candidate sample points in the design space of random variables, use the second surrogate model to calculate the predicted response value of the candidate sample points, and combine the joint probability distribution information of random variables to calculate the importance evaluation index of the candidate sample points. S5. Select new sample points from the candidate sample points according to the importance evaluation index, and call the high-fidelity limit state function to calculate the high-fidelity response of the new sample points in order to update the second proxy model. S6. Calculate the estimated failure probability of the engineering structure to be analyzed based on the updated second surrogate model, and determine whether the preset convergence condition is met. If the convergence condition is not met, return to execute steps S4 and S5 again until the convergence condition is met and the iteration is terminated. Calculate the final failure probability as the reliability analysis result.

2. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 1, characterized in that, The specific method for generating low-fidelity sample data in the design space of random variables in step S1 is as follows: based on the preset probability distribution of random variables, a preset number of low-fidelity sample points are generated using the maximum-minimum distance Latin hypercube sampling method, and the low-fidelity sample points are uniformly distributed in the design space.

3. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 1, characterized in that, Step S2 specifically includes: S21. Calculate the empirical mean and empirical standard deviation of each dimension of the random variables determined by the low-fidelity sample dataset, and normalize each random variable in the low-fidelity sample data. The calculation formula is as follows: ； in, For the low-fidelity sample set The first sample The original values ​​of a 3D random variable; and These are the first two samples in the low-fidelity sample dataset. The empirical mean and empirical standard deviation of a dimensional random variable; This represents the normalized value of the random variable; after all random variables have been normalized, a standardized low-fidelity sample dataset is obtained. S22. Based on the standardized low-fidelity sample dataset and the corresponding low-fidelity response, a first surrogate model is trained; wherein the first surrogate model is a multi-layer feedforward neural network including at least two hidden layers, and the network parameters are optimized by a backpropagation algorithm based on Bayesian regularization until the mean square prediction error of the first surrogate model for low-fidelity samples is less than a preset training accuracy threshold.

4. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 3, characterized in that, In step S3, the specific mathematical process for selecting initial sample points using a distance maximization strategy based on the normalized design space is as follows: a. Randomly select one low-fidelity sample point and add it to the initial high-fidelity training set; b. In the standardized low-fidelity sample dataset obtained in step S21, calculate the standardized low-fidelity sample points that have not yet been selected. With each point in the selected sample set The Euclidean distance between them is calculated, and the minimum spatial distance corresponding to each unselected sample point is recorded. : ； c. Select the minimum spatial distance The standardized low-fidelity sample points that reach the maximum value are added to the set as the original design space sample points, and this iterative calculation process is repeated until a preset number of initial sample points are obtained. This is to eliminate the measurement failure caused by the difference in the dimensions of multidimensional random variables and ensure that the initial sample points are uniformly covered in the multidimensional joint probability space.

5. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 1, characterized in that, The specific process of constructing the second agent model through transfer learning in step S3 includes: S31. The network topology of the first surrogate model that has been trained, as well as the weight matrices and bias vectors of all its layers, are isomorphically mapped and initialized to form the initial transfer model. S32. Freeze the weight matrix of the connection between the input layer and the first hidden layer in the initial transfer model, as well as the bias vector of the neurons in the first hidden layer, to preserve the global trend features learned by the first surrogate model from the low-fidelity sample data. S33. Using the Levenberg-Marquardt training algorithm, the parameters of subsequent network layers that have not been frozen are locally approximated and trained using the initial high-fidelity training set until the mean square prediction error of the model on the initial high-fidelity samples is less than the preset training accuracy threshold, thus obtaining a second surrogate model that integrates low-fidelity global physical laws and high-fidelity local accuracy.

6. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 5, characterized in that, The joint training and optimization process of the first proxy model and the second proxy model satisfies the following conditions: (1) The first surrogate model is a multi-layer feedforward neural network, whose network topology includes an input layer, at least two hidden layers, and an output layer; during the training phase of the first surrogate model, a Bayesian regularized backpropagation algorithm is used, and its objective function is... Sum of squared prediction errors With the sum of squared network weights The linear combination of these terms is calculated using the following formula: ； in and The regularization parameter is dynamically updated based on the Bayesian criterion and is used to suppress overfitting during training with low-fidelity samples. (2) In the construction stage of the second proxy model, the Levenberg-Marquardt algorithm is used to locally correct the subsequent network layers that are not frozen. The iterative update formula for the network parameters is as follows: ； in, This refers to the update amount of network weights and biases. The Jacobian matrix of the network prediction error with respect to the parameters of the unfrozen layer. This represents the prediction error vector for high-fidelity samples. It is the identity matrix. This is the damping factor that is dynamically and adaptively adjusted.

7. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 1, characterized in that, In step S4, the formula for calculating the importance assessment index of candidate sample points is: ； in, To predict the first using the second surrogate model The predicted response value of each candidate sample point represents the degree of proximity of the candidate sample point to the failure boundary of the limit state function. For the first The weight index of each candidate sample point is used to characterize the joint probability density value of the candidate sample points appearing in the random variable design space; This is an adjustment factor used to balance the weights of failure boundary search and probability space coverage; The preset small positive regularization term is used to prevent numerical truncation and computational overflow caused when the joint probability density of the deep-tailed region approaches zero. For the first The smaller the value of the candidate sample point, the higher its potential contribution to the overall failure probability.

8. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 7, characterized in that, No. Weight index of each candidate sample point The calculation is performed based on whether the random variables of the engineering structure being analyzed are independent of each other. (1) When the random variables of the engineering structure to be analyzed are independent of each other, the weight index of the candidate sample points is the product of the probability density functions of each random variable, and the calculation formula is: ； in, Let be the total dimension of the random variables in the engineering structure to be analyzed. For the first The first candidate sample point The original values ​​of a 3D random variable. For the first The probability density function of a 3D random variable; (2) When the random variables of the engineering structure to be analyzed are not independent of each other, the weight index of the candidate sample points is calculated by the multidimensional joint probability density function composed of all random variables. The calculation formula is as follows: ； in, for The joint probability density function of 3D random variables; The first The original values ​​of each candidate sample point in each dimension of the random variable.

9. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 8, characterized in that, Step S5 specifically includes: S51. All candidate sample points are evaluated according to importance indicators. The values ​​are sorted from smallest to largest. The candidate sample points are then iterated and evaluated sequentially from the top-ranked points. Several sample points that satisfy the topological distance constraint are selected as new sample points. The specific topological distance constraint is as follows: Calculate the coordinate vector of the currently evaluated candidate sample point in the normalized design space. Normalized coordinate vectors of all existing samples in the current high-fidelity training set The Euclidean distance between them; only if the minimum distance between the current candidate sample point and any existing sample point in the high-fidelity training set is not less than a preset distance threshold. hour: ； The current candidate sample point is accepted as a new sample point to avoid historical sample redundancy and high clustering near the local failure boundary of the limit state function; if this constraint is not met, the candidate sample point is removed and the next candidate sample point is evaluated in sequence. S52. Call the high-fidelity limit state function to calculate the high-fidelity response of each newly added sample point, add each newly added sample point and its corresponding high-fidelity response to the current high-fidelity training set, and expand to form an updated high-fidelity training set. S53. Using the updated high-fidelity training set, the second proxy model is retrained and locally corrected and updated.

10. The structural reliability analysis method combining transfer learning and adaptive sampling according to claim 1, characterized in that, Step S6 specifically includes: S61. After each update of the second surrogate model, generate a first preset number of Monte Carlo sample points based on the probability distribution of the random variable, and predict the response value of each Monte Carlo sample point using the current second surrogate model; count the proportion of failed samples with response values ​​less than 0 among all Monte Carlo samples, and obtain the first... Failure probability estimate for the next iteration ,in This is the sequence number of the current iteration; S62. Determine whether the preset convergence condition is met: (1) First determine the current iteration number. Does it meet the requirements? ,in The preset minimum number of iterations is used to force the second proxy model to complete the exploration and updating of basic local features within the design space of random variables; (2) Only when the above condition (1) is met, the relative rate of change of the failure probability estimate between two adjacent iterations is further calculated. Determine whether it satisfies: ； in, and The first Next and first The failure probability estimate obtained in the next iteration; The preset threshold for truncating very small normal numbers is used to prevent division-zero singularity divergence caused by the estimated failure probability being zero in early active learning iterations. This is the preset relative convergence threshold; If all convergence conditions are met, the iteration is terminated; otherwise, the process returns to steps S4 and S5. S63. After the iteration is terminated, a second preset number of Monte Carlo sample points are generated according to the probability distribution of the random variable. The response value of each Monte Carlo sample point is predicted using the converged second surrogate model. The proportion of failure samples with response values ​​less than 0 is counted, and the final failure probability is obtained as the reliability analysis result.

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