Reliability Analysis Method Based on Coupled Support Vector Regression and Quasi-Uniform Importance Sampling

Abstract

A reliability analysis method coupled with support vector regression and quasi-uniform importance sampling comprises the following steps: obtaining the composition of a structure to be evaluated, confirming the failure mode of the structure and the corresponding functional function; obtaining a proxy modeling sequence and a reliability evaluation sequence through Sobol sampling; converting the proxy modeling sequence and the reliability evaluation sequence into a first uniform sample and a second uniform sample respectively through uniform sampling conversion; calculating the system response of the first uniform sample according to the functional function to obtain a first system response sample; normalizing the first uniform sample and the first system response sample as training data to train a support vector regression model; inputting the second uniform sample into the trained support vector regression model to obtain structural reliability; the present invention proposes quasi-uniform importance sampling based on Sobol, which can better cover the failure space and has a lower dispersion in the sampling results. After coupling it with the support vector regression model, it can improve the accuracy and modeling efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of equipment manufacturing, and more particularly to a reliability analysis method of coupled support vector regression and quasi-uniform importance sampling. Background Art

[0002] At present, with the rapid development of major equipment design and manufacturing technology, engineering components are developing in the direction of precision, complexity, high speed, large size, and high performance, such as the reliability issues of aircraft engine hot end components, armored vehicle power units or transmission devices. However, uncertainty is widely present in the structure, which in turn causes uncertainties in materials, dimensions, loads and environments. At the same time, when products face harsh operating conditions, once a failure occurs, it may cause economic and property losses at the least, or even catastrophic accidents and threaten life safety. Therefore, carrying out reliability design and evaluation of equipment structures under uncertainty is the key foundation for ensuring the safe and reliable operation of major equipment structures. However, structural reliability analysis of complex equipment often involves finite element simulation. High reliability requires a low failure probability, which makes the computational cost unacceptable, and the related needs are becoming more and more urgent.

[0003] Research on structural reliability analysis methods has made significant progress. Scholars and engineers are eager to find a structural reliability analysis method that can solve practical engineering problems with low failure probabilities at high computational cost. Currently, mainstream approaches include analytical and simulation methods. Analytical methods often suffer from large computational errors because they rely on first-order Taylor series expansions to approximate the performance function. Among simulation methods, the most widely used is Monte Carlo simulation. While this method offers stable results, it requires a large sample size, making it difficult to apply to problems with low failure probabilities. Numerous simulation methods have been developed based on variance reduction techniques, and surrogate models have been established based on machine learning theory to solve computationally expensive problems. For example, to improve the efficiency and accuracy of reliability analysis, existing techniques have proposed the use of kriging as a surrogate modeling algorithm. However, this method is difficult to apply to scenarios with high data and high dimensionality. As the number of training samples and dimensionality increases, modeling becomes slow, potentially taking hours or more. Furthermore, the method focuses on local optima, and when evaluating performance function variations, the overall reliability assessment accuracy is low.

[0004] Therefore, how to further improve efficiency and accuracy is an urgent problem that needs to be solved by those skilled in the art. Therefore, how to further improve efficiency and accuracy is an urgent problem that needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a reliability analysis method that couples support vector regression and quasi-uniform importance sampling, which can further improve the accuracy and modeling efficiency.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A reliability analysis method coupled with support vector regression and quasi-uniform importance sampling includes the following steps:

[0008] Obtain the composition of the structure to be evaluated and identify the failure mode of the structure and the corresponding functional function.

[0009] The surrogate modeling sequence and reliability evaluation sequence are obtained through Sobol sampling.

[0010] The agent modeling sequence and the reliability evaluation sequence are respectively converted into a first uniform sample and a second uniform sample through uniform sampling conversion.

[0011] The system response of the first uniform sample is calculated according to the functional function to obtain a first system response sample.

[0012] The first uniform sample and the first system response sample are normalized respectively, and the normalized data are used as training data to train a support vector regression model.

[0013] The second uniform sample is input into the trained support vector regression model, and the structural reliability is confirmed by combining the weights of each sample in the second uniform sample.

[0014] Preferably, the support vector regression model is trained by K-fold cross validation and Bayesian optimization.

[0015] Preferably, the training step includes calculating a model error, wherein the model error is:

[0016]

[0017] Among them, Error is the model error, RMSE j is the root mean square error of the jth time in K-fold cross validation, K is the number of folds, is the predicted value of the i-th sample of the support vector regression model, y i is the system response value of the i-th sample.

[0018] Preferably, the uniform sampling conversion includes:

[0019] X0=F -1 (p)+[F -1 (1-p)-F -1 (p)]*U0

[0020] X=F -1 (p)+[F -1 (1-p)-F -1 (p)]*U

[0021] Where X0 is the first uniform sample, X is the second uniform sample; F -1 (·) represents the inverse function of the cumulative distribution function of the random variable in the performance function, p is the interval boundary probability; U0 is the agent modeling sequence, and U is the reliability evaluation sequence.

[0022] Preferably, the normalization function is:

[0023]

[0024] Wherein, x represents the normalized result of the first uniform sample, which is the input sample of the proxy model; y represents the normalized result of the first system response sample, which is the output sample of the proxy model; X and Y are the first uniform sample and the first system response sample respectively; X min and Y max The minimum and maximum values ​​of the input samples, Y min and Y max are the minimum and maximum values ​​of the output samples.

[0025] Preferably, the structure to be evaluated is a cantilever beam structure, the failure mode of the cantilever beam structure is that the actual displacement exceeds the allowable displacement, and the functional function is:

[0026]

[0027] Where D0 is the allowable displacement, X=(E,L,h,t,P x ,P y ), representing 6 independent random variables; E is the elastic modulus, L is the length of the cantilever beam, h is the width of the cantilever beam, t is the height of the cantilever beam, P x is the horizontal load, P y is the vertical load.

[0028] Preferably, the structure to be evaluated is a two-dimensional steel beam structure, the failure mode of the two-dimensional steel beam structure is that the actual load exceeds the allowable load, and the functional function is:

[0029] Y(X0)=ZF Y -M

[0030] Where X=(Z,F Y ), represents two independent random variables, M is the allowable load, Z is the plastic modulus, F Y is the yield strength of steel.

[0031] A reliability analysis system coupled with support vector regression and quasi-uniform importance sampling, comprising an acquisition module, a quasi-uniform sampling module, a model training module and a reliability analysis module;

[0032] The acquisition module is used to obtain the composition of the structure to be evaluated and to confirm the failure mode of the structure and the corresponding functional function.

[0033] The quasi-uniform sampling module is used to obtain a proxy modeling sequence and a reliability evaluation sequence through Sobol sampling; and is used to convert the proxy modeling sequence and the reliability evaluation sequence into a first uniform sample and a second uniform sample respectively through uniform sampling conversion.

[0034] The model training module is used to construct a knowledge vector regression model as a proxy model; normalize the first uniform sample and the first system response sample respectively, and use the normalized data as training data; and train the support vector regression model through the training data, K-fold cross validation and Bayesian optimization.

[0035] The reliability analysis module is used to input the second uniform sample into the trained support vector regression model to calculate structural reliability.

[0036] A computer-readable storage medium stores a program or instruction, and when the program or instruction is executed by a processor, the steps of any of the above-described distributed data storage methods are implemented.

[0037] It can be seen from the above technical solution that compared with the prior art, the present invention discloses a reliability analysis method that couples support vector regression and quasi-uniform importance sampling, and proposes quasi-uniform importance sampling based on Sobol, which can better cover the failure space, and the sampling results have lower dispersion. After coupling it with the support vector regression model, it can simultaneously reduce the number of calls to system response and proxy model, thereby improving accuracy and modeling efficiency; through the uniform training samples generated by Sobol, the support vector regression model can realize global proxy modeling, and at the same time reduce the number of calls to functional functions with high computational costs, such as the number of calls to finite element simulation, thereby improving the overall efficiency of the structural reliability analysis method; the present invention introduces K-fold cross-validation and Bayesian optimization to simultaneously train the training set and validation set errors, which can improve the model generalization ability; the present invention can realize accurate global proxy modeling, and for performance functions involving verification of allowable loads and life, it can provide reliability curves under allowable load changes without the need to call additional system responses or proxy models. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0039] Figure 1 A flow chart of the reliability analysis method provided by the present invention;

[0040] Figure 2 The Sobol sequence for agent modeling provided by the present invention;

[0041] Figure 3 The quasi-uniform sample for proxy modeling provided by the present invention;

[0042] Figure 4 The curve of Bayesian optimization in Example 2 of the present invention;

[0043] Figure 5 The prediction result of the agent modeling in Example 2 of the present invention;

[0044] Figure 6 is the prediction result of the reliability evaluation in Example 2 of the present invention;

[0045] Figure 7 The sample size in Example 2 of the present invention is 10 6 Boxplots of different simulation methods;

[0046] Figure 8 The results of the reliability index of Example 2 of the present invention changing with the allowable load;

[0047] Figure 9 This is a schematic diagram of the cantilever beam structure of Example 3 of the present invention;

[0048] Figure 10 The curve of Bayesian optimization in Example 3 of the present invention;

[0049] Figure 11 The sample size in Example 3 of the present invention is 10 6 Boxplots of different simulation methods;

[0050] Figure 12 This is the result of the reliability index changing with the allowable displacement in Example 3 of the present invention. DETAILED DESCRIPTION

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

[0052] Example 1

[0053] like Figure 1 The embodiment of the present invention discloses a reliability analysis method coupling support vector regression and quasi-uniform importance sampling, comprising the following steps:

[0054] S1-1: Obtain the composition of the structure to be evaluated, and confirm the failure mode of the structure and the corresponding functional function. Specifically, the instructions, design standards, expert opinions and historical data of the structure to be evaluated are analyzed, and a system response model is formed based on the composition, function and working conditions of the structure to be evaluated. When determining the variables that affect the functional function, such as the size, material properties, working load, etc. of the structure, it is necessary to understand that due to randomness and uncertainty, the value of the variable is usually random, and its uncertainty needs to be described by a probability distribution. As for the modeling of the probability distribution of variables, it can be obtained based on existing data or engineering experience. This belongs to the existing general technology and will not be elaborated in detail in the present invention.

[0055] S1-2: Obtain the surrogate modeling sequence and reliability assessment sequence through Sobol sampling.

[0056] S1-3: Convert the agent modeling sequence and reliability evaluation sequence into the first uniform sample and the second uniform sample respectively through uniform sampling conversion.

[0057] S1-4: Calculate the system response of the first uniform sample according to the performance function to obtain a first system response sample. Specifically, the first uniform sample is input into the system response model, the system response model performs simulation, and automatically calculates the true value of the system response according to the preset performance function.

[0058] S1-5: Normalize the first uniform sample and the first system response sample respectively, use the normalized data as training data, and train the support vector regression model through K-fold cross validation and Bayesian optimization;

[0059] S1-6: Input the second uniform sample into the trained support vector regression model and confirm the structural reliability by combining the weights of each sample in the second uniform sample. The sample weight refers to the probability density of the sample.

[0060] In this embodiment, S1-1 requires confirming the number and distribution function of random variables using a functional function. When performing Sobol sampling, the sampling dimension must be determined based on the number of random variables, thereby forming a sample of a specific capacity. S1-2 and S1-3 are quasi-uniform sampling processes. Sobol sampling is first performed to generate a pseudo-random Sobol sequence, namely, a surrogate modeling sequence and a reliability assessment sequence. Uniform sampling conversion is then performed to convert the Sobol sequence into intervals corresponding to the random variables, resulting in a first uniform sample for training the surrogate model and a second uniform sample for reliability analysis. S1-4 and S1-5 are the training processes for the surrogate model, which is a support vector regression model. The training data consists of sample pairs consisting of the first uniform sample and its corresponding system response sample, which serve as the input and output of the training model. The surrogate model is trained and the model parameters, namely, the kernel function coefficients, the error penalty factor, and the error interval, are updated using a Bayesian optimization strategy until the preset number of iterations is met. S1-6 is the reliability analysis process, which uses the model trained in S5 to analyze reliability under the conditions of the second uniform sample.

[0061] Among them, the specific steps of reliability analysis include inputting the second uniform sample into the trained support vector regression model to calculate the system response of each sample, confirming the structural validity, calculating the structural failure probability based on the sample weight, and calculating the reliability index based on the structural failure probability.

[0062] Specifically, the calculation formula for the structural failure probability is:

[0063]

[0064] in, represents the failure probability of the structure; X i represents the i-th reliability evaluation uniform sample X; I(X i ) represents the characteristic function, when When I(X i )=1, when When I(X i )=0;w(X i ) represents the weight of the i-th sample, d represents the dimension of the structure-function function, F j -1 (·) represents the jth random variable X j The inverse function of the cumulative distribution function, f(·) represents the j-th random variable X j The probability density function of , which can be obtained by the function type, mean and standard deviation of the random distribution.

[0065] Confirm the reliability index β:

[0066]

[0067] Among them, Φ -1 (·) is the inverse function of the cumulative distribution function of the standard normal distribution.

[0068] In order to further implement the above technical solution, K-fold cross-validation is introduced when training the model. The training data is divided into a training set and a validation set according to the K value, and the model error Error under cross-validation is calculated. The specific formula is:

[0069]

[0070] Among them, Error is the model error, RMSE j is the root mean square error of the jth time in K-fold cross validation, K is the number of folds, is the predicted value of the i-th sample of the support vector regression model, y i is the system response value of the i-th sample.

[0071] It should be noted that using a combination of K-fold cross-validation and Bayesian optimization to train the surrogate model and find the optimal hyperparameters for support vector regression can improve the generalization ability of the surrogate model, that is, the model has high prediction accuracy on both training samples and reliability assessment samples. Specifically, appropriate hyperparameters are required to improve the prediction accuracy of the support vector regression model. Bayesian optimization can achieve hyperparameter optimization, but optimizing only the training set can lead to overfitting, resulting in worse accuracy when predicting new data. Therefore, K-fold cross-validation is introduced to improve the model's generalization ability, that is, the accuracy of predicting new data (the prediction accuracy of reliability assessment data not used for training).

[0072] In order to further implement the above technical solution, the formula for uniform sampling conversion is:

[0073] X0=F -1 (p)+[F -1 (1-p)-F -1 (p)]*U0

[0074] X=F -1 (p)+[F -1 (1-p)-F -1 (p)]*U

[0075] Where X0 is the first uniform sample, X is the second uniform sample; F -1 (·) represents the inverse function of the cumulative distribution function of the random variable in the performance function, p is the interval boundary probability, and for the structural reliability analysis problem to be analyzed, the lower the failure probability, the smaller the value of p; U0 is the agent modeling sequence, and U is the reliability evaluation sequence.

[0076] Furthermore, the interval boundary probability can be set to p = 1 × 10 -10 .

[0077] In order to further implement the above technical solution, the normalization function used when constructing training data is:

[0078]

[0079] Wherein, x represents the normalized result of the first uniform sample, which is the input sample of the proxy model; y represents the normalized result of the first system response sample, which is the output sample of the proxy model; X and Y are the first uniform sample and the first system response sample respectively; X min and X max The minimum and maximum values ​​of the input samples, Y min and Y max The minimum and maximum values ​​of the output samples are obtained by normalizing the input and output values ​​of the training model to between -1 and 1, which facilitates the training of the support vector regression model.

[0080] Example 2

[0081] Based on the same inventive concept, the method in Example 1 is used to implement structural reliability analysis of a two-dimensional steel beam. The specific steps include:

[0082] S2-1: Determine the failure mode of the structure and the corresponding performance function Y(X) based on the composition, function, and operating conditions of the structure to be evaluated, and obtain the dimension d of the random variable X that affects the structural performance function and the distribution function of the random variable X;

[0083] The functional function in this embodiment is expressed as:

[0084] Y(X0)=ZF Y -M

[0085] Where X=(X,F Y ), representing two independent random variables. M is the allowable load, which is a constant and can be set to 2500 initially. Other values ​​can be used when evaluating the relationship between reliability and allowable load. The dimension of the structural function is d = 2; the distribution information of the random variables is: Z is the plastic modulus, F Y is the yield strength of steel, Z and F Y Independent of each other, Z follows a maximum Gumbel distribution with a mean of 100 and a standard deviation of 4, F Y It follows a maximum lognormal distribution with a mean of 40 and a standard deviation of 4.

[0086] S2-2: According to the dimension d of the random variable, Sobol sampling is used to obtain the Sobol agent modeling sequence U0 and reliability evaluation sequence U with sample sizes N0 and N.

[0087] Among them, the sample size of the Sobol sampling agent modeling sequence U0 is N0=50d=100 and the sample size of the reliability evaluation sequence U is N=10 5 . Figure 2 The sample capacity of the Sobol agent modeling sequence is N0=50d=100, where U1 and U2 in the horizontal and vertical coordinates represent two groups of Sobol sequences between 0 and 1, U1 corresponds to the Sobol sequence of Z, and U2 corresponds to the Sobol sequence of Fy.

[0088] S2-3: Convert the Sobol sequence to the interval corresponding to the random variable according to the uniform sampling formula to obtain the first uniform sample for agent modeling and the second uniform sample for reliability evaluation.

[0089] In this embodiment, the interval boundary probability p=1×10 -10 The sample boundaries of random variables are shown in Table 1. The uniform sampling formula is used to convert the Sobol sequence into the first uniform sample of the random variable corresponding interval. Figure 3 As shown, where Z in the horizontal and vertical coordinates is the plastic modulus, F Y is the yield strength of steel.

[0090] Table 1 Sampling boundaries of random variables

[0091] random variable <![CDATA[Lower boundary: F -1 (p)]]> <![CDATA[Upper boundary: F -1 (1 - p)]]> Z 88.42 170.01 <![CDATA[F Y ]]> 21.10 75.02

[0092] S2-4: Input the first uniform sample X0 into the pre-built system response model to obtain the system response Y(X0).

[0093] S2-5: Normalize the first uniform sample and the first system response sample respectively, use the normalized data as training data, and train the support vector regression model through K-fold cross validation and Bayesian optimization.

[0094] S2-6: Input the second uniform sample into the trained support vector regression model, calculate the structural failure probability based on the sample weight, and confirm the structural reliability.

[0095] Figure 4 This is a diagram of the training process of the Bayesian optimization support vector regression model for K-fold cross validation in this embodiment, where the number of training points for Bayesian optimization is 20, the number of iterations is 100, and the objective function is It establishes a proxy model of support vector regression hyperparameters and training error based on the Gaussian process regression algorithm, and minimizes the training error through the algorithm's own learning function, thereby improving the performance of support vector regression proxy modeling. Because Bayesian optimization is a general algorithm, it will not be described in detail here.

[0096] Table 2 Model training results

[0097] index RMSE <![CDATA[R 2 ]]> Proxy Modeling Sample <![CDATA[7.12×10 -4 ]]> 1 Reliability Assessment Sample <![CDATA[7.24×10 -5 ]]> 1

[0098] Figure 5 The training results of the proxy model are shown in Table 2. The horizontal axis is the actual system response, and the vertical axis is the predicted system response. The root mean square error (RMSE) is calculated based on the training results. The closer the RMSE is to 0, the better the training results are, as shown in Table 2. At the same time, in order to further quantify the training results, the coefficient of determination (R 2 ) This indicator, among which R 2 The closer it is to 1, the better the training result.

[0099] The calculation method of the coefficient of determination is:

[0100]

[0101] in, is the mean of the first system response sample.

[0102] Figure 6 Table 2 also shows the comparison between the prediction results of the support vector regression surrogate model and the actual system response.

[0103] Next, the effectiveness of the present invention is verified through this example.

[0104] First, the effectiveness of quasi-importance sampling is investigated. Without using the support vector regression model, taking the allowable load M = 2500 as an example, each method is simulated 20 times, and the mean and coefficient of variation of the results of each method are compared.

[0105] Table 3 Comparison of the results of the basic simulation method in Example 2

[0106]

[0107] As shown in Table 3, MCS represents Monte Carlo simulation, and QMC represents Quasi-Monte Carlo simulation. Both methods are general techniques and will not be described here. UIS represents uniform importance sampling, and QUIS represents the quasi-uniform importance sampling proposed in the present invention. The difference between the two is that the sampling methods are different, and the reliability index calculation method is the same. As shown in Table 3, N represents the sample capacity of the simulation method. Under the same sample capacity, the dispersion of the quasi-uniform importance sampling proposed in the present invention is the smallest. Under low sample capacity, the present invention can provide accurate evaluation results of reliability indicators, which the general method cannot do. Figure 7 As shown, the sample size is 10 6 The box plot below compares the results of different methods. For each box plot, each horizontal line from top to bottom represents the maximum value, upper quartile, median, lower quartile and minimum value of the result in 20 repeated simulations. The narrower the plot, the better the result. The quasi-uniform importance sampling proposed in this invention has the lowest dispersion.

[0108] The second is the overall effectiveness of the invention, e.g. Figure 8 , which is the relationship between the allowable load M and the reliability index result of the proposed method. The number of times the Monte Carlo calls the system response is N=106, the number of times the method proposed in the present invention calls the system response is 100 times, and the number of times the proxy model is called is N=105 times, and the sample capacity is N. On the one hand, the proposed method reduces the number of times the system response is called by establishing a support vector regression proxy model, which greatly reduces the computational cost for complex finite element simulation problems. In this embodiment, the reliability index of the system decreases with the increase of the allowable load. In the case of low reliability, that is, when the failure probability is high, the results of the Monte Carlo method and the method of the present invention are consistent. With the increase of reliability, that is, when the failure probability is low, the error of the Monte Carlo simulation method gradually increases. When the allowable load is lower than 2300, the Monte Carlo method can no longer evaluate the reliability, while the method proposed in the present invention always gives the correct results.

[0109] Example 3

[0110] Based on the same inventive concept, the effectiveness of the cantilever beam structure is analyzed using the method in Example 1. The specific steps include:

[0111] S3-1: Determine the failure mode of the structure and the corresponding performance function Y(X) based on the composition, function, and operating conditions of the structure to be evaluated, and obtain the dimension d of the random variable that affects the structural performance function and the distribution function of the random variable;

[0112] This embodiment is a cantilever beam structure, such as Figure 9 As shown in Figure 2, the failure mode is that the actual displacement exceeds the allowable displacement, so the functional function of the structure is expressed as:

[0113]

[0114] Where D0 is the allowable displacement, which is a constant and can be taken as 1.2. The dimension of the structural function is n = 6; X = (E, L, h, t, P x , P y ), representing 6 independent random variables, E is the elastic modulus, L is the length of the cantilever beam, h is the width of the cantilever beam, t is the height of the cantilever beam, P x is the horizontal load, P y is the vertical load. The distribution information of random variables is shown in Table 4. Each random variable is independent of each other.

[0115] Table 4 Statistical characteristics of random variables of cantilever beam structure in Example 2

[0116] random variable mean Standard deviation Distribution type E <![CDATA[3×10 7 ]]> <![CDATA[1×10 5 ]]> Lognormal distribution L 100 1 normal distribution h 2 0.025 normal distribution t 4 0.04 normal distribution <![CDATA[P x ]]> 100 20 Maximum Gumbel distribution <![CDATA[P y ]]> 200 20 Maximum Gumbel distribution

[0117] S3-2: According to the dimension d of the random variable, Sobol sampling is used to obtain the Sobol agent modeling sequence U0 and reliability evaluation sequence U with sample sizes N0 and N.

[0118] The sample size of the Sobol sampling agent modeling sequence U0 is N0=50d=300 and the sample size of the reliability assessment sequence U is N=10 5 .

[0119] S3-3: According to the uniform sampling formula and the distribution characteristics of the random variables in Table 4, the Sobol sequence is converted to the interval corresponding to the random variable to obtain the first uniform sample for agent modeling and the second uniform sample for reliability evaluation.

[0120] Specifically, set the interval boundary probability p = 1×10 -10 , the sample boundaries of each random variable are shown in Table 5.

[0121] Table 5 Sampling boundaries of random variables

[0122] random variable <![CDATA[Lower boundary: F -1 (p)]]> <![CDATA[Upper boundary: F -1 (1 - p)]]> E <![CDATA[2.43×10 7 ]]> <![CDATA[3.71×10 7 ]]> L 93.64 106.36 h 1.84 2.16 t 3.75 4.25 <![CDATA[P x ]]> 42.09 450.06 <![CDATA[P y ]]> 142.09 550.06

[0123] S3-4: Input the first uniform sample X0 into the support vector regression model to obtain the system response Y(X0).

[0124] S3-5: Normalize the first uniform sample and the first system response sample respectively, use the normalized data as training data, and train the support vector regression model through K-fold cross validation and Bayesian optimization.

[0125] S3-6: Input the second uniform sample into the trained support vector regression model, calculate the structural failure probability based on the sample weight, and confirm the structural reliability.

[0126] Figure 10 This is the training process of the support vector regression model. The number of training points for Bayesian optimization is 20, and the number of iterations is 100. Since Bayesian optimization is a general algorithm, its detailed description is omitted here. As can be seen from the figure, as the number of iterations increases, the model error, i.e., the optimized objective function, gradually decreases and eventually converges, thereby improving the performance of the support vector regression agent modeling. This embodiment can stabilize the model with a relatively small number of iterations.

[0127] Table 6 Model training results

[0128] index RMSE <![CDATA[R 2 ]]> Proxy Modeling Sample 0.0159 1 Reliability Assessment Sample 0.0031 1

[0129] Table 6 shows the numerical indicator results of support vector regression. It can be seen that the accuracy of the surrogate model is very high in terms of the number of samples in the training set and reliability evaluation.

[0130] Next, the effects of the present invention will be specifically described using this embodiment.

[0131] First, the effectiveness of quasi-uniform importance sampling is verified. Without using the support vector regression model, taking the allowable displacement D0=1.2 as an example, the simulation is repeated 20 times for each method, and the mean and coefficient of variation of the results of each method are compared. As shown in Table 7, N represents the sample size of the simulation method. Under the same sample size, the dispersion of the quasi-uniform importance sampling proposed by the present invention is the smallest. Under low sample size, the present invention can provide accurate evaluation results of reliability indicators, which cannot be achieved by general methods. Figure 11 As shown in FIG, it is a box plot comparing the results of different methods. The results show that the quasi-uniform importance sampling proposed in the present invention has the lowest dispersion.

[0132] The second is to verify the effectiveness of the present invention as a whole, such as Figure 12 The figure shows the relationship between the allowable displacement D0 and the reliability index results of the proposed method. The number of Monte Carlo system responses is N = 10 6 The method proposed in this invention calls the system response 300 times and calls the proxy model 300 times. The sample size is N=10. 5 On the one hand, the proposed method reduces the number of system responses by establishing a support vector regression proxy model, which will greatly reduce the computational cost for complex finite element simulation problems. Figure 10As shown, in this embodiment, the reliability index of the system increases with the increase of the allowable displacement. In the case of low reliability, that is, when the failure probability is high, the results of the Monte Carlo method are consistent with those of the method of the present invention. With the increase of reliability, that is, when the failure probability is low, the error of the Monte Carlo simulation method gradually increases. When the allowable displacement is higher than 1.4, the Monte Carlo method can no longer evaluate the reliability, while the method proposed in the present invention always gives the correct results. Finally, this embodiment completes the reliability evaluation of 300 training samples in 6 dimensions and 1 million prediction samples in about 30 minutes, which is a huge improvement compared to the active Kriging model combined with uniformity sampling in the prior art, which takes about 24 hours.

[0133] Example 4

[0134] Based on the same inventive concept, this embodiment provides a reliability analysis system that couples support vector regression and quasi-uniform importance sampling, including an acquisition module, a quasi-uniform sampling module, a model training module, and a reliability analysis module.

[0135] The acquisition module is used to obtain the composition of the structure to be evaluated and to confirm the failure mode of the structure and the corresponding functional function.

[0136] The quasi-uniform sampling module is used to obtain a proxy modeling sequence and a reliability evaluation sequence through Sobol sampling; and is used to convert the proxy modeling sequence and the reliability evaluation sequence into a first uniform sample and a second uniform sample respectively through uniform sampling conversion.

[0137] The model training module is used to construct a knowledge vector regression model as a proxy model; normalize the first uniform sample and the first system response sample respectively, and use the normalized data as training data; and train the support vector regression model through training data, K-fold cross-validation and Bayesian optimization.

[0138] The reliability analysis module is used to input the second uniform sample into the trained support vector regression model and calculate the structural reliability through the weight of the sample.

[0139] Example 5

[0140] Based on the same inventive concept, an embodiment of the present invention provides a computer-readable storage medium, which stores a program or instruction. When the program or instruction is executed by a processor, it can implement the steps of the distributed data storage method described in Example 1.

[0141] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0142] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A reliability analysis method coupling support vector regression and quasi-uniform importance sampling, characterized in that: The following steps are involved: Obtain the composition of the structure to be evaluated and identify the failure mode of the structure and the corresponding functional function; The surrogate modeling sequence and reliability evaluation sequence are obtained through Sobol sampling; Converting the agent modeling sequence and the reliability evaluation sequence into a first uniform sample and a second uniform sample respectively through uniform sampling conversion; calculating a system response of the first uniform sample according to the functional function to obtain a first system response sample; The first uniform sample and the first system response sample are normalized respectively, and the normalized data are used as training data to train the support vector regression model; specifically, the support vector regression model is trained through K-fold cross validation and Bayesian optimization; wherein the model error under K-fold cross validation is: Among them, Error is the model error, RMSE j is the root mean square error of the jth time in K-fold cross validation, K is the number of folds, is the predicted value of the i-th sample of the support vector regression model, y i is the system response value of the i-th sample; Calculating the sample weight of each sample in the second uniform sample; The second uniform sample is input into the trained support vector regression model, and the structural failure probability is calculated in combination with the sample weight to confirm the structural reliability.

2. A reliability analysis method of coupling support vector regression and quasi-uniform importance sampling according to claim 1, characterized in that: The uniform sampling conversion includes: X0=F -1 (p)+[F -1 (1-p)-F -1 (p)]*U0 X=F -1 (p)+[F -1 (1-p)-F -1 (p)]*U Where X0 is the first uniform sample, X is the second uniform sample; F -1 (·) represents the inverse function of the cumulative distribution function of the random variable in the performance function, p is the interval boundary probability; U0 is the agent modeling sequence, and U is the reliability evaluation sequence.

3. The reliability analysis method of coupling support vector regression and quasi-uniform importance sampling according to claim 1, characterized in that: The normalization function is: Wherein, x represents the normalized result of the first uniform sample, which is the input sample of the proxy model; y represents the normalized result of the first system response sample, which is the output sample of the proxy model; X and Y are the first uniform sample and the first system response sample respectively; X min and X max The minimum and maximum values ​​of the input samples, Y min and Y max are the minimum and maximum values ​​of the output samples.

4. The reliability analysis method of coupling support vector regression and quasi-uniform importance sampling according to claim 1, characterized in that: The structure to be evaluated is a cantilever beam structure, the failure mode of the cantilever beam structure is that the actual displacement exceeds the allowable displacement, and the functional function is: Where D0 is the allowable displacement, X=(E,L,h,t,P x ,P y ), representing 6 independent random variables; E is the elastic modulus, L is the length of the cantilever beam, h is the width of the cantilever beam, t is the height of the cantilever beam, P x is the horizontal load, P y is the vertical load.

5. The reliability analysis method of coupling support vector regression and quasi-uniform importance sampling according to claim 1, characterized in that: The structure to be evaluated is a two-dimensional steel beam structure, the failure mode of the two-dimensional steel beam structure is that the actual load exceeds the allowable load, and the functional function is: Y(X0)=ZF Y -M Where X0=(Z,F Y ), represents two independent random variables, M is the allowable load, Z is the plastic modulus, F Y is the yield strength of steel.

6. The reliability analysis method of coupling support vector regression and quasi-uniform importance sampling according to claim 1, characterized in that: The steps for confirming the structural reliability include: Calculate the probability of failure of the structure: in, represents the failure probability of the structure; X i represents the i-th reliability evaluation uniform sample X; I(X i ) represents the characteristic function, when When I(X i )=1, when When I(X i )=0;w(X i ) represents the weight of the i-th sample, d represents the dimension of the structure-function function, F j -1 (·) represents the jth random variable X j The inverse function of the cumulative distribution function, f(·) represents the j-th random variable X j The probability density function of , which is obtained by the function type, mean and standard deviation of the random distribution, Confirm reliability: Among them, β is the reliability index; Φ -1 (·) is the inverse function of the cumulative distribution function of the standard normal distribution.

7. A reliability analysis system coupled with support vector regression and quasi-uniform importance sampling, characterized in that: The reliability analysis method according to any one of claims 1 to 6 is adopted, comprising an acquisition module, a quasi-uniform sampling module, a model training module and a reliability analysis module; The acquisition module is used to obtain the composition of the structure to be evaluated and to confirm the failure mode of the structure and the corresponding functional function; The quasi-uniform sampling module is used to obtain a proxy modeling sequence and a reliability evaluation sequence through Sobol sampling; and is used to convert the proxy modeling sequence and the reliability evaluation sequence into a first uniform sample and a second uniform sample respectively through uniform sampling conversion; The model training module is used to construct a knowledge vector regression model as a proxy model; normalize the first uniform sample and the first system response sample respectively, and use the normalized data as training data; and train the support vector regression model using the training data; The reliability analysis module is used to input the second uniform sample into the trained support vector regression model to calculate structural reliability.

8. A computer-readable storage medium, characterized in that The readable storage medium stores a program or instruction, and when the program or instruction is executed by a processor, the steps of the reliability analysis method according to any one of claims 1 to 6 are implemented.

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