Random-interval hybrid uncertainty structure reliability analysis method and related device

Abstract

The invention provides a random-interval hybrid uncertainty structure reliability analysis method and a related device, and belongs to the technical field of structure reliability analysis. The method mainly comprises two improvements: 1, determining a selection mode of a sampling center of an important sampling density function of a kth layer, constructing the important sampling density function according to the determined sampling center of the important sampling density function of the kth layer, and extracting a random sample of the kth layer according to the constructed important sampling density function; and 2, constructing a Kriging model according to the function relationship between the POD coefficient and the interval variable, constructing a mixed Kriging model on the basis of the Kriging model according to the function relationship between the output and the interval variable, and carrying out adaptive learning on the mixed Kriging model. According to the method, the problem that the reliability analysis efficiency of the random-interval hybrid uncertainty structure is not high is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural reliability analysis, and in particular relates to a random-interval mixed uncertainty structural reliability analysis method and a related device. Background Art

[0002] Reliability analysis studies the behavior of output performance when uncertainty in the input link is transferred to the output link. Structural reliability analysis is not only an important tool for ensuring structural safety and reliability, but also a key research direction in practical engineering.

[0003] In practical problems, uncertainty includes both aleatory uncertainty and epistemic uncertainty. To date, reliability theory has focused on three main areas to address different types of uncertainty: probability-based reliability theory, non-probabilistic structural reliability theory, and hybrid reliability analysis (HRA), which incorporates both aleatory and epistemic uncertainty.

[0004] In actual engineering structures, for complex engineering problems, the situation where random variables are used to represent uncertainty when the information is complete and the situation where interval variables are used to represent uncertainty when the information is incomplete often exist at the same time.

[0005] The common methods currently used in the prior art for reliability analysis of random-interval mixed uncertainty structures are: 1) using Monte Carlo simulation (MCS) to perform reliability analysis on random-interval mixed uncertainty structures; 2) using interval optimization methods to perform reliability analysis on random-interval mixed uncertainty structures; 3) using direct modeling methods to perform reliability analysis on random-interval mixed uncertainty structures.

[0006] The Monte Carlo method is used to perform reliability analysis on random-interval mixed uncertainty structures. It is not only easy to implement and has high applicability, but also has high computational accuracy. Therefore, it often provides a reference solution for other improvement methods.

[0007] Interval optimization methods are used to perform reliability analysis on random-interval mixed uncertainty structures, such as the unified uncertainty analysis (UUA) method (FORM-UUA) based on the first-order reliability method (FORM). Compared with MCS, FORM-UUA offers significant advantages in computational efficiency when dealing with problems with small failure probabilities. However, due to the limitations of FORM, FORM-UUA may provide unstable and unacceptable results for performance functions with high nonlinearity or multiple design points.

[0008] The direct modeling method (i.e., using proxy model technology to directly model the structural performance function) is used to perform reliability analysis on random-interval mixed uncertainty structures. Although the direct modeling method has a simple process and is easy to implement, as the dimension of the input variables increases, the calculation time may exceed the time required to directly calculate the output using the performance function.

[0009] The PODK method, based on the leave-one-out error method, is constructed by combining a reduced-order model using orthogonal decomposition with a Kriging model. While this method can reduce the number of interval samples required during modeling and improve computational efficiency, it is inefficient for reliability analysis of random-interval mixed uncertainty structures due to the large random sample pool required for small failure probabilities. Summary of the Invention

[0010] The purpose of the present invention is to provide a random-interval mixed uncertainty structure reliability analysis method and related devices, which are used to solve the problem of low efficiency of random-interval mixed uncertainty structure reliability analysis due to the large size of random sample pool when performing random-interval mixed uncertainty analysis on small failure probabilities in the prior art.

[0011] In order to achieve the above object, the present invention adopts the following technical solutions:

[0012] In a first aspect, the present invention provides a random-interval mixed uncertainty structural reliability analysis method, comprising the following steps:

[0013] Extract interval sample pool and initial interval sample;

[0014] Determine a method for selecting a sampling center of the k-th layer importance sampling density function, construct an importance sampling density function based on the determined sampling center of the k-th layer importance sampling density function, and extract a random sample of the k-th layer based on the constructed importance sampling density function;

[0015] Based on the random sample of the kth layer and the initial interval sample, a first output matrix is ​​obtained, and POD calculation is performed on the first output matrix;

[0016] A Kriging model is constructed based on the functional relationship between the POD coefficient and the interval variable. Based on the Kriging model, a hybrid Kriging model is constructed based on the functional relationship between the output and the interval variable, and adaptive learning is performed on the hybrid Kriging model.

[0017] When the hybrid Kriging model converges, the hybrid Kriging model is used to predict the output corresponding to all interval samples to obtain a second output matrix. Based on the second output matrix, the extreme value of each random sample corresponding to the random sample pool of each layer is obtained;

[0018] Arrange the extreme values ​​of each random sample corresponding to the random sample pool of each layer in descending order to obtain the critical value of the intermediate failure event of each layer;

[0019] Based on the critical value of the intermediate failure event of each layer, estimate the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layers;

[0020] After the stratification is completed, the upper and lower boundary values ​​of the final failure probability are calculated based on the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probability corresponding to the subsequent layers.

[0021] A further improvement of the present invention is that the method for determining the sampling center of the k-th layer importance sampling density function constructs an importance sampling density function based on the determined sampling center of the k-th layer importance sampling density function, and extracts the k-th layer random sample based on the constructed importance sampling density function, specifically including:

[0022] a. When the layers corresponding to the upper and lower boundaries of the failure probability have not yet ended, find random samples that fall into the failure domain of the k-1th layer. The point with the maximum joint probability density function in the intersection of the random samples that fall into the failure domain of the k-1th layer is used as the sampling center. The important sampling density function is constructed based on the sampling center, and the random sample of the kth layer is extracted based on the constructed important sampling density function.

[0023] b. When only the stratum corresponding to the upper boundary of the failure probability ends, select only the random sample with the largest joint probability density function from the failure domain corresponding to the lower boundary of the failure probability of the k-1th layer as the sampling center, construct the importance sampling density function based on the sampling center, and extract the kth layer random sample based on the constructed importance sampling density function.

[0024] A further improvement of the present invention is that, in the step of obtaining the first output matrix based on the k-th layer random samples and the initial interval samples and performing POD calculation on the first output matrix, the calculation formula of POD is:

[0025]

[0026] in, is the most characteristic structure function extracted from the snapshot matrix, and the corresponding coefficient c l (Z)(l=1,…L) is a function of interval variables, L is the number of retained POD bases, and the calculation formula for the number of retained POD bases L is:

[0027]

[0028] where ε is the user-defined error tolerance.

[0029] A further improvement of the present invention is to perform adaptive learning on the hybrid Kriging model based on the relationship between the maximum scale coefficient, the minimum scale coefficient and the convergence coefficient. The specific adaptive learning method includes:

[0030] When the maximum scale coefficient is greater than or equal to the convergence coefficient, and the minimum scale coefficient is greater than or equal to the convergence coefficient, the hybrid Kriging model is adaptively learned using interval samples for improving the maximum prediction accuracy at random samples, interval samples for improving the minimum prediction accuracy at random samples, and the true outputs corresponding to the two interval samples;

[0031] When the maximum scale coefficient is greater than or equal to the convergence coefficient and the minimum scale coefficient is less than the convergence coefficient, adaptive learning is performed on the hybrid Kriging model using interval samples for improving the maximum value prediction accuracy at the random samples and the true output corresponding to the interval samples;

[0032] When the maximum proportional coefficient is less than the convergence coefficient and the minimum proportional coefficient is greater than or equal to the convergence coefficient, adaptive learning is performed on the hybrid Kriging model using interval samples for improving the minimum value prediction accuracy at the random samples and the true output corresponding to the interval samples;

[0033] When the maximum scale coefficient is less than the convergence coefficient and the minimum scale coefficient is less than the convergence coefficient, the hybrid Kriging model converges and adaptive learning is not performed on the hybrid Kriging model.

[0034] A further improvement of the present invention is that the calculation formulas for the maximum scale factor and the minimum scale factor are:

[0035]

[0036] Among them, r max is the maximum proportional coefficient, r min is the minimum scale factor, is the first expected improvement function, Improve the function for the second expectation.

[0037] A further improvement of the present invention is that the calculation formulas of the first expected improvement function and the second expected improvement function are:

[0038]

[0039] Among them, Φ(·) and are the cumulative distribution function and probability density function of the normal distribution respectively;

[0040] The calculation formula is:

[0041]

[0042] in, For the mixed Kriging model exist The predicted value at

[0043] The calculation formula is:

[0044]

[0045] in, is the maximum value;

[0046] The calculation formula is:

[0047]

[0048] in, is the minimum value.

[0049] A further improvement of the present invention is that, after the stratification is completed, in the step of calculating the upper and lower boundary values ​​of the final failure probability based on the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probabilities corresponding to the subsequent layers, the calculation formulas for the upper and lower boundary values ​​of the final failure probability are:

[0050]

[0051] in, is the upper limit value of the final failure probability, is the lower boundary value of the final failure probability, is the upper boundary value of the conditional failure probability corresponding to the k-th layer sample, is the lower boundary value of the conditional failure probability corresponding to the k-th layer sample, m U and m L They are and The number of layers in the calculation process.

[0052] In a second aspect, the present invention provides a random-interval hybrid uncertainty structural reliability analysis system, comprising a data extraction module, a k-layer random sample extraction module, a POD calculation module, a hybrid Kriging model construction module, an extreme value acquisition module, a failure event critical value acquisition module, a conditional failure probability boundary value acquisition module, and a final failure probability boundary value acquisition module;

[0053] The data extraction module is used to extract the interval sample pool and the initial interval sample;

[0054] The k-layer random sample extraction module is used to determine the selection method of the sampling center of the k-th layer importance sampling density function, construct the importance sampling density function according to the determined sampling center of the k-th layer importance sampling density function, and extract the k-th layer random sample according to the constructed importance sampling density function;

[0055] The POD calculation module is used to obtain a first output matrix based on the k-th layer random sample and the initial interval sample, and perform POD calculation on the first output matrix;

[0056] The hybrid Kriging model construction module is used to construct a Kriging model according to the functional relationship between the POD coefficient and the interval variable, and to construct a hybrid Kriging model based on the functional relationship between the output and the interval variable on the basis of the Kriging model, and to perform adaptive learning on the hybrid Kriging model;

[0057] The extreme value acquisition module is used to predict the output corresponding to all interval samples using the hybrid Kriging model after the hybrid Kriging model converges, obtain a second output matrix, and obtain the extreme value of each random sample corresponding to the random sample pool of each layer based on the second output matrix;

[0058] The failure event critical value acquisition module is used to arrange the extreme values ​​of each random sample corresponding to the random sample pool of each layer in descending order to obtain the critical value of the intermediate failure event of each layer;

[0059] The conditional failure probability boundary value acquisition module is used to estimate the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probability corresponding to subsequent layers based on the critical value of the intermediate failure event of each layer;

[0060] The final failure probability boundary value acquisition module is used to calculate the upper boundary value and the lower boundary value of the final failure probability according to the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layer after the layering is completed.

[0061] In a third aspect, the present invention provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the random-interval mixed uncertainty structural reliability analysis method introduced above when executing the computer program.

[0062] In a fourth aspect, the present invention provides a storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the random-interval mixed uncertainty structural reliability analysis method introduced above.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] The present invention is an improved invention. Compared with the existing random-interval mixed uncertainty structural reliability analysis method, on the one hand, the present invention introduces intermediate failure events to express the small failure probability as the product of a series of larger conditional failure probabilities. Specifically, the method gradually approaches the final failure probability boundary in a layered manner. On the other hand, the present invention extracts random samples that simultaneously meet the calculation of the upper and lower bounds of the conditional failure probability by determining the sampling center of the k-th layer important sampling density function, avoiding the extraction of additional random samples caused by separately calculating the upper and lower bounds of the failure probability when performing hybrid reliability analysis, thereby improving efficiency. In addition, the present invention constructs a Kriging model based on the functional relationship between the POD coefficient and the interval variable, and on the basis of the Kriging model, constructs a hybrid Kriging model based on the functional relationship between the output and the interval variable, and performs adaptive learning on the hybrid Kriging model. The PODK model (hybrid Kriging model) reduces the number of interval samples through adaptive learning, thereby greatly improving computational efficiency, thereby effectively solving the problem of the large random sample pool size in the prior art when performing random-interval mixed reliability analysis on the small failure probability, resulting in low efficiency of random-interval mixed uncertainty structural reliability analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a flow chart of the random-interval mixed uncertainty structural reliability analysis method of the present invention;

[0066] Figure 2 Schematic diagram of the random-interval hybrid uncertainty structural reliability analysis system of the present invention;

[0067] Figure 3 It is a schematic diagram of a planar ten-bar structure;

[0068] Figure 4 Schematic diagram of the structure of the electronic device of the present invention. DETAILED DESCRIPTION

[0069] In order to further understand the content of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0070] The random-interval hybrid uncertainty structural reliability analysis method proposed in this invention estimates the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to subsequent layers based on the critical value of the intermediate failure event of each layer. After the layering is completed, the upper and lower boundary values ​​of the final failure probability are calculated based on the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to subsequent layers. Compared with the existing technology, this invention effectively solves the problem of low efficiency of random-interval hybrid uncertainty structural reliability analysis due to the large random sample pool size when performing random-interval hybrid reliability analysis on small failure probabilities.

[0071] Example 1:

[0072] The flowchart of the random-interval mixed uncertainty structural reliability analysis method of the present invention is as follows: Figure 1 As shown, the random-interval mixed uncertainty structural reliability analysis method of the present invention includes the following steps:

[0073] S1. Extract the interval sample pool and the initial interval sample.

[0074] S2. Determine the method for selecting the sampling center of the k-th layer importance sampling density function, construct the importance sampling density function based on the determined sampling center of the k-th layer importance sampling density function, and extract the k-th layer random sample based on the constructed importance sampling density function.

[0075] S3. Based on the random samples of the kth layer and the initial interval samples, a first output matrix is ​​obtained, and a POD calculation is performed on the first output matrix.

[0076] S4. Construct a Kriging model based on the functional relationship between the POD coefficient and the interval variable. On the basis of the Kriging model, construct a hybrid Kriging model based on the functional relationship between the output and the interval variable. Perform adaptive learning on the hybrid Kriging model.

[0077] S5. After the hybrid Kriging model converges, the hybrid Kriging model is used to predict the outputs corresponding to all interval samples to obtain a second output matrix. Based on the second output matrix, the extreme value of each random sample corresponding to the random sample pool of each layer is obtained.

[0078] S6. Arrange the extreme values ​​of each random sample corresponding to the random sample pool of each layer in descending order to obtain the critical value of the intermediate failure event of each layer.

[0079] S7. Based on the critical value of the intermediate failure event of each layer, estimate the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layers.

[0080] S8. After the stratification is completed, the upper and lower boundary values ​​of the final failure probability are calculated based on the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probability corresponding to the subsequent layers.

[0081] Example 2:

[0082] The schematic diagram of the random-interval hybrid uncertainty structural reliability analysis system of the present invention is as follows: Figure 2 As shown, the random-interval hybrid uncertainty structural reliability analysis system of the present invention includes a data extraction module, a k-layer random sample extraction module, a POD calculation module, a hybrid Kriging model construction module, an extreme value acquisition module, a failure event critical value acquisition module, a conditional failure probability boundary value acquisition module, and a final failure probability boundary value acquisition module.

[0083] The data extraction module is used to extract the interval sample pool and the initial interval sample.

[0084] The k-layer random sample extraction module is used to determine the selection method of the sampling center of the k-th layer important sampling density function, construct the important sampling density function according to the determined sampling center of the k-th layer important sampling density function, and extract the k-th layer random sample according to the constructed important sampling density function.

[0085] The POD calculation module is used to obtain a first output matrix based on the k-th layer random samples and the initial interval samples, and perform POD calculation on the first output matrix.

[0086] The hybrid Kriging model construction module is used to construct a Kriging model based on the functional relationship between the POD coefficient and the interval variable, and to construct a hybrid Kriging model based on the functional relationship between the output and the interval variable on the basis of the Kriging model, and to perform adaptive learning on the hybrid Kriging model.

[0087] The extreme value acquisition module is used to predict the output corresponding to all interval samples using the hybrid Kriging model after the hybrid Kriging model converges, obtain the second output matrix, and based on the second output matrix, obtain the extreme value of each random sample corresponding to the random sample pool of each layer.

[0088] The failure event critical value acquisition module is used to arrange the extreme values ​​of each random sample corresponding to the random sample pool of each layer in descending order to obtain the critical value of the intermediate failure event of each layer.

[0089] The conditional failure probability boundary value acquisition module is used to estimate the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to subsequent layers based on the critical value of the intermediate failure event of each layer.

[0090] The final failure probability boundary value acquisition module is used to calculate the upper and lower boundary values ​​of the final failure probability according to the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probability corresponding to the subsequent layers after the layering is completed.

[0091] Example 3:

[0092] S1. Extract the interval sample pool and the initial interval sample.

[0093] S2. Determine the method for selecting the sampling center of the k-th layer importance sampling density function, construct the importance sampling density function based on the determined sampling center of the k-th layer importance sampling density function, and extract the k-th layer random sample based on the constructed importance sampling density function.

[0094] The specific methods for extracting random samples in the kth layer in this step include:

[0095] a. When the layers corresponding to the upper and lower boundaries of the failure probability have not ended, find the random samples that fall into the failure domain of the k-1th layer, and combine the probability density function f in the intersection of the random samples that fall into the failure domain of the k-1th layer. X The largest point (x) is taken as the sampling center, and the important sampling density function is constructed based on the sampling center. And according to the constructed important sampling density function Draw a random sample from the kth layer;

[0096] b. When only the layer corresponding to the upper boundary of the failure probability ends, only the joint probability density function f is selected from the failure domain corresponding to the lower boundary of the failure probability of the k-1th layer. X (x) The largest random sample is used as the sampling center, and the important sampling density function is constructed based on the sampling center. And according to the constructed important sampling density function Draw a random sample from the kth level.

[0097] Specifically, first draw a random sample Extract interval samples based on interval boundaries And select any number from them Initial sample pool If it is the first layer, that is, k = 1, then according to the probability density function f X (x) Draw a random sample If it is not the first layer, that is, k≠1, then according to the constructed important sampling density function Draw a random sample from the kth layer if From the failure domain and Select the random sample point with the largest joint probability density function from the intersection of sampling center; if Importance Sampling Density Function The sampling centers will only be drawn from the failure domain are selected from random sample points.

[0098] S3. Based on the random samples of the kth layer and the initial interval samples, a first output matrix is ​​obtained, and a POD calculation is performed on the first output matrix.

[0099] Based on the random samples of the kth layer and the initial interval samples, the first output matrix Y0 is obtained (k) , and the first output matrix Y0 (k) Perform POD calculation.

[0100] The formula for calculating POD is:

[0101]

[0102] in, is the most characteristic structure function extracted from the snapshot matrix, and the corresponding coefficient c l (Z)(l=1,…L) is a function of interval variables, L is the number of retained POD bases, and the calculation formula for the number of retained POD bases L is:

[0103]

[0104] where ε is the user-defined error tolerance.

[0105] S4. Construct a Kriging model based on the functional relationship between the POD coefficient and the interval variable. On the basis of the Kriging model, construct a hybrid Kriging model based on the functional relationship between the output and the interval variable. Perform adaptive learning on the hybrid Kriging model.

[0106] Construct Kriging model c based on the functional relationship between POD coefficients and interval variables Kl (Z), in the Kriging model c Kl (Z) is used to construct a hybrid Kriging model based on the functional relationship between the output and interval variables. Adaptive learning of mixed Kriging models.

[0107] In this step, the hybrid Kriging model is adaptively learned based on the relationship between the maximum scale coefficient, the minimum scale coefficient, and the convergence coefficient. The adaptive learning method of the hybrid Kriging model specifically includes:

[0108] A. When the maximum proportional coefficient r max Greater than or equal to the convergence coefficient ε r, and the minimum proportional coefficient r min Greater than or equal to the convergence coefficient ε r When using interval samples to improve the accuracy of maximum prediction at random samples and interval samples for improving the accuracy of minimum prediction at random samples And the real output corresponding to the two interval samples is used to adaptively learn the hybrid Kriging model;

[0109] B. When the maximum proportional coefficient r max Greater than or equal to the convergence coefficient ε r , and the minimum proportional coefficient r min Less than the convergence coefficient ε r When using interval samples to improve the accuracy of maximum prediction at random samples Adaptively learn the hybrid Kriging model based on the real output corresponding to the interval samples;

[0110] C. When the maximum proportional coefficient r max Less than the convergence coefficient ε r , and the minimum proportional coefficient r min Greater than or equal to the convergence coefficient ε r When using interval samples to improve the accuracy of minimum prediction at random samples Adaptively learn the hybrid Kriging model based on the real output corresponding to the interval samples;

[0111] D. When the maximum proportional coefficient r max Less than the convergence coefficient ε r , and the minimum proportional coefficient r min Less than the convergence coefficient ε r When , the hybrid Kriging model converges and no adaptive learning is performed on the hybrid Kriging model.

[0112] The calculation formula for the maximum scale factor and the minimum scale factor is:

[0113]

[0114] Among them, r max is the maximum proportional coefficient, r min is the minimum scale factor, is the first expected improvement function, Improve the function for the second expectation.

[0115] The calculation formulas for the first expected improvement function and the second expected improvement function are:

[0116]

[0117]

[0118] Among them, Φ(·) and are the cumulative distribution function and probability density function of the normal distribution respectively;

[0119] The calculation formula is:

[0120]

[0121] in, For the mixed Kriging model exist The predicted value at

[0122] The calculation formula is:

[0123]

[0124] in, is the maximum value;

[0125] The calculation formula is:

[0126]

[0127] in, is the minimum value.

[0128] When the delamination corresponding to the upper and lower boundaries of the failure probability has not ended, the maximum proportional coefficient r max and the minimum proportionality factor r min Keep the calculated true value.

[0129] When only the delamination corresponding to the upper limit of the failure probability ends, the minimum proportional coefficient r min Equal to 0.

[0130] S5. After the hybrid Kriging model converges, the hybrid Kriging model is used to predict the outputs corresponding to all interval samples to obtain a second output matrix. Based on the second output matrix, the extreme value of each random sample corresponding to the random sample pool of each layer is obtained.

[0131] When the mixed Kriging model After convergence, the mixed Kriging model is used Predict the output corresponding to all interval samples and obtain the second output matrix Y1 (k) , and based on the second output matrix Y1 (k), get the extreme value (maximum and minimum) of each random sample corresponding to the random sample pool of each layer. The calculation formula of the extreme value (minimum and maximum) of each random sample corresponding to the random sample pool of each layer is:

[0132]

[0133] S6. Arrange the extreme values ​​of each random sample corresponding to the calculated random sample pool of each layer in descending order to obtain the critical value of the intermediate failure event of each layer.

[0134] Specifically, the minimum values ​​of the calculated random samples and interval samples are arranged in descending order as follows:

[0135] When k=1: No. response values Will be recorded as the first layer failure event F1 U The critical value if So like So The descending sorting method of the maximum value is the same as that of the minimum value, and is obtained in the same way. The numerical value of .

[0136] When k≠1, if Find the failure domain of Random samples and those falling into the failure domain of Random samples. Then, sort the minimum and maximum values ​​in descending order. response values As the k-th intermediate failure event The critical value Select response values As the k-th intermediate failure event The critical value if So if So if Find the failure domain of A random sample, select response values As the k-th intermediate failure event The critical value if

[0137] S7. Based on the critical value of the intermediate failure event of each layer, estimate the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layers.

[0138] Based on the critical value of each layer's intermediate failure event, estimate the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layers (the upper boundary value of the conditional failure probability and the lower bound of the conditional failure probability ).

[0139] Upper bound value of conditional failure probability The calculation formula is:

[0140]

[0141] in is the conditional probability density function, the conditional probability density function The calculation formula is:

[0142]

[0143] in is the importance sampling density function, To pass The random samples generated, is the indicator function, the indicator function The calculation formula is:

[0144]

[0145] in, is the critical value of the failure event, To calculate the minimum value.

[0146] Lower bound value of conditional failure probability and the upper bound of the conditional failure probability The calculation formula is similar.

[0147] S8. After the stratification is completed, the upper and lower boundary values ​​of the final failure probability are calculated based on the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probability corresponding to the subsequent layers.

[0148] After the stratification is completed, the upper and lower boundary values ​​of the final failure probability are calculated based on the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layers. The calculation formula for the upper and lower boundary values ​​of the final failure probability is:

[0149]

[0150]

[0151] in, is the upper limit value of the final failure probability, is the lower boundary value of the final failure probability, is the upper boundary value of the conditional failure probability corresponding to the k-th layer sample, is the lower boundary value of the conditional failure probability corresponding to the k-th layer sample, m U and m L They are and The number of layers in the calculation process.

[0152] In order to verify the effectiveness of the random-interval hybrid uncertainty structure reliability analysis method proposed in this invention, this embodiment performs reliability analysis on a planar ten-bar structure. The schematic diagram of the planar ten-bar structure is shown in FIG. Figure 3 As shown, the left end of the structure is fixed, node 4 bears a vertical load F1, and node 2 bears a vertical load F2 and a horizontal load F3.

[0153] The input variables are the length L of all horizontal and vertical rods, the elastic modulus L and the cross-sectional area A of all rods. i (i=1,…10).

[0154] The input variables are the length L of all horizontal and vertical rods, the elastic modulus L and the cross-sectional area A of all rods. i (i=1,…10). Construct the performance function g based on the vertical displacement y of node 2. The expression of performance function g is:

[0155] g=0.057-y

[0156] The calculation formula for the vertical displacement y of node 2 is:

[0157]

[0158] When F1=F3=0, F2=0, is the axial internal force of each rod. The internal forces of rods 8 and 10 can be obtained according to the node equilibrium equation, which is as follows:

[0159] a 11 N8+a 12 N 10 =b1

[0160] a 21 N8+a 22 N 10 =b2

[0161] in,

[0162]

[0163]

[0164] The internal forces of the remaining members can be obtained according to the following formulas:

[0165]

[0166] The distribution types and parameters of the above input variables are shown in Table 1. For random variables, parameters 1 and 2 in Table 1 represent the mean and standard deviation of the normal distribution, respectively. For interval variables, parameters 1 and 2 in Table 1 represent the lower limit and upper limit of the interval distribution, respectively.

[0167] Table 1 Distribution parameters of input variables of the planar ten-bar structure

[0168]

[0169] This embodiment uses three methods to perform reliability analysis on the planar ten-bar structure. The analysis results of the three methods are shown in Table 2. In Table 2, cov is the coefficient of variation, N call The actual number of function calls.

[0170] Table 2 Hybrid reliability analysis results of planar ten-bar structure

[0171]

[0172] The calculation results of the MCS method are used as the reference solution. During the calculation process of the MCS method, the number of random samples is 10 6 ,The number of interval samples is 161051.

[0173] In the process of reliability analysis of the planar ten-bar structure using SSIS, the upper and lower bounds of the conditional failure probability are finally obtained through three-layer stratification. The calculation process of each layer uses 10 4 random samples and 161,051 interval samples.

[0174] To accommodate the characteristics of random interval hybrid reliability analysis, the proposed random interval hybrid uncertainty structural reliability analysis method (SSIS-PODK) simultaneously calculates both the upper and lower bounds of the failure probability, saving computational cost. The MCS calculation results reveal that the upper and lower bounds of the failure probability differ significantly in magnitude, necessitating a different number of layers when performing the SSIS calculation.

[0175] When using the SSIS method for reliability analysis of a planar ten-bar structure, the calculation of the upper bound of the failure probability requires only one simulation layer, while the calculation of the lower bound of the failure probability requires three simulation layers. As shown in Table 2, the SSIS method successfully reduces the size of the random sample pool during the reliability analysis process.

[0176] In order to further improve the computational efficiency of reliability analysis of planar ten-bar structures, the present invention constructs the SSIS-PODK model (SSIS-PODK) based on SSIS. The second-order Kriging model is used in the SSIS-PODK calculation process, which means that the number of initial interval samples cannot be less than (n I +1)(n I +2) / 2, the 21 interval samples in Table 2 are used to construct the initial Kriging model. During the SSIS-PODK construction process, the number of random samples drawn in each layer is consistent with the SSIS method. During the SSIS-PODK calculation process, the upper and lower bounds of the failure probability are finally obtained through three-layer stratification. The calculation process of each layer uses 10 4 The results in Table 2 show that the proposed random-interval hybrid uncertainty structural reliability analysis method (SSIS-PODK) not only ensures the calculation accuracy, but also further reduces the size of the interval sample pool in the analysis process based on SSIS.

[0177] The proposed random-interval hybrid uncertainty structural reliability analysis method improves the prediction accuracy of interval extreme values ​​by combining POD calculations with the Kriging model to establish an adaptive learning PODK model based on the expected lift criterion. This model also improves computational efficiency by reducing the number of interval samples. Subsequently, based on the adaptive PODK model and combined with the improved SSIS method, the SSIS-PODK model is proposed to further reduce the number of random samples, thereby improving the efficiency of reliability analysis. Ultimately, this overcomes the low efficiency of the original method when performing random interval hybrid reliability analysis.

[0178] Example 4:

[0179] See also Figure 4 As shown, the present invention also provides an electronic device 100 for a random-interval mixed uncertainty structural reliability analysis method; the electronic device 100 includes a memory 101, at least one processor 102, a computer program 103 stored in the memory 101 and executable on the at least one processor 102, and at least one communication bus 104.

[0180] The memory 101 can be used to store the computer program 103. The processor 102 implements the steps of the random-interval mixed uncertainty structural reliability analysis method described in Example 1 by running or executing the computer program stored in the memory 101 and calling the data stored in the memory 101. The memory 101 can mainly include a program storage area and a data storage area. The program storage area can store an operating system, at least one application required for a function (such as a sound playback function, an image playback function, etc.); the data storage area can store data (such as audio data) created based on the use of the electronic device 100. In addition, the memory 101 can include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, at least one disk storage device, a flash memory device, or other non-volatile solid-state storage device.

[0181] The at least one processor 102 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor 102 may be a microprocessor or any conventional processor, etc. The processor 102 is the control center of the electronic device 100 and connects various parts of the entire electronic device 100 using various interfaces and lines.

[0182] The memory 101 in the electronic device 100 stores a plurality of instructions to implement a random-interval hybrid uncertainty structural reliability analysis method, and the processor 102 can execute the plurality of instructions to implement:

[0183] Extract interval sample pool and initial interval sample;

[0184] Determine a method for selecting a sampling center of the k-th layer importance sampling density function, construct an importance sampling density function based on the determined sampling center of the k-th layer importance sampling density function, and extract a random sample of the k-th layer based on the constructed importance sampling density function;

[0185] Based on the random sample of the kth layer and the initial interval sample, a first output matrix is ​​obtained, and POD calculation is performed on the first output matrix;

[0186] A Kriging model is constructed based on the functional relationship between the POD coefficient and the interval variable. Based on the Kriging model, a hybrid Kriging model is constructed based on the functional relationship between the output and the interval variable, and adaptive learning is performed on the hybrid Kriging model.

[0187] When the hybrid Kriging model converges, the hybrid Kriging model is used to predict the output corresponding to all interval samples to obtain a second output matrix. Based on the second output matrix, the extreme value of each random sample corresponding to the random sample pool of each layer is obtained;

[0188] Arrange the extreme values ​​of each random sample corresponding to the random sample pool of each layer in descending order to obtain the critical value of the intermediate failure event of each layer;

[0189] Based on the critical value of the intermediate failure event of each layer, estimate the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layers;

[0190] After the stratification is completed, the upper and lower boundary values ​​of the final failure probability are calculated based on the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probability corresponding to the subsequent layers.

[0191] Example 5:

[0192] If the module / unit integrated in the electronic device 100 is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device that can carry the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory and read-only memory (ROM, Read-Only Memory).

[0193] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0194] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0195] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0196] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0197] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A random-interval hybrid uncertainty structural reliability analysis method, characterized by: The following steps are involved: Extract interval sample pool and initial interval sample; Determine a method for selecting a sampling center of the k-th layer importance sampling density function, construct an importance sampling density function based on the determined sampling center of the k-th layer importance sampling density function, and extract a random sample of the k-th layer based on the constructed importance sampling density function; Based on the random sample of the kth layer and the initial interval sample, a first output matrix is ​​obtained, and POD calculation is performed on the first output matrix; A Kriging model is constructed based on the functional relationship between the POD coefficient and the interval variable. Based on the Kriging model, a hybrid Kriging model is constructed based on the functional relationship between the output and the interval variable, and adaptive learning is performed on the hybrid Kriging model. When the hybrid Kriging model converges, the hybrid Kriging model is used to predict the output corresponding to all interval samples to obtain a second output matrix. Based on the second output matrix, the extreme value of each random sample corresponding to the random sample pool of each layer is obtained; Arrange the extreme values ​​of each random sample corresponding to the random sample pool of each layer in descending order to obtain the critical value of the intermediate failure event of each layer; Based on the critical value of the intermediate failure event of each layer, estimate the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layers; After the stratification is completed, the upper and lower boundary values ​​of the final failure probability are calculated based on the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probability corresponding to the subsequent layers.

2. The random-interval hybrid uncertainty structural reliability analysis method according to claim 1 is characterized in that: The method for determining the sampling center of the k-th layer importance sampling density function is to construct an importance sampling density function according to the determined sampling center of the k-th layer importance sampling density function, and extract the k-th layer random sample according to the constructed importance sampling density function, specifically including: a. When the layers corresponding to the upper and lower boundaries of the failure probability have not yet ended, find random samples that fall into the failure domain of the k-1th layer. The point with the maximum joint probability density function in the intersection of the random samples that fall into the failure domain of the k-1th layer is used as the sampling center. The important sampling density function is constructed based on the sampling center, and the random sample of the kth layer is extracted based on the constructed important sampling density function. b. When only the stratum corresponding to the upper boundary of the failure probability ends, select only the random sample with the largest joint probability density function from the failure domain corresponding to the lower boundary of the failure probability of the k-1th layer as the sampling center, construct the importance sampling density function based on the sampling center, and extract the kth layer random sample based on the constructed importance sampling density function.

3. The random-interval hybrid uncertainty structural reliability analysis method according to claim 1 is characterized in that: In the step of obtaining the first output matrix based on the k-th layer random samples and the initial interval samples, and performing POD calculation on the first output matrix, the calculation formula of POD is: in, is the most characteristic structure function extracted from the snapshot matrix, and the corresponding coefficient c l (Z)(l=1,…L) is a function of interval variables, L is the number of retained POD bases, and the calculation formula for the number of retained POD bases L is: where ε is the user-defined error tolerance.

4. The random-interval hybrid uncertainty structural reliability analysis method according to claim 1 is characterized in that: Adaptive learning of the hybrid Kriging model is performed based on the relationship between the maximum scale coefficient, the minimum scale coefficient, and the convergence coefficient. Specific adaptive learning methods include: When the maximum scale coefficient is greater than or equal to the convergence coefficient, and the minimum scale coefficient is greater than or equal to the convergence coefficient, the hybrid Kriging model is adaptively learned using interval samples for improving the maximum prediction accuracy at random samples, interval samples for improving the minimum prediction accuracy at random samples, and the true outputs corresponding to the two interval samples; When the maximum scale coefficient is greater than or equal to the convergence coefficient and the minimum scale coefficient is less than the convergence coefficient, adaptive learning is performed on the hybrid Kriging model using interval samples for improving the maximum value prediction accuracy at the random samples and the true output corresponding to the interval samples; When the maximum proportional coefficient is less than the convergence coefficient and the minimum proportional coefficient is greater than or equal to the convergence coefficient, adaptive learning is performed on the hybrid Kriging model using interval samples for improving the minimum value prediction accuracy at the random samples and the true output corresponding to the interval samples; When the maximum scale coefficient is less than the convergence coefficient and the minimum scale coefficient is less than the convergence coefficient, the hybrid Kriging model converges and adaptive learning is not performed on the hybrid Kriging model.

5. The random-interval hybrid uncertainty structural reliability analysis method according to claim 4 is characterized in that: The calculation formula for the maximum scale factor and the minimum scale factor is: Among them, r max is the maximum proportional coefficient, r min is the minimum scale factor, is the first expected improvement function, Improve the function for the second expectation.

6. The random-interval hybrid uncertainty structural reliability analysis method according to claim 5 is characterized in that: The calculation formulas for the first expected improvement function and the second expected improvement function are: Among them, Φ(·) and are the cumulative distribution function and probability density function of the normal distribution respectively; The calculation formula is: in, For the mixed Kriging model exist The predicted value at The calculation formula is: in, is the maximum value; The calculation formula is: in, is the minimum value.

7. The random-interval hybrid uncertainty structural reliability analysis method according to claim 1 is characterized in that: After the stratification is completed, in the step of calculating the upper boundary value and the lower boundary value of the final failure probability based on the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent stratification, the calculation formulas for the upper boundary value and the lower boundary value of the final failure probability are: in, is the upper limit value of the final failure probability, is the lower boundary value of the final failure probability, is the upper boundary value of the conditional failure probability corresponding to the k-th layer sample, is the lower boundary value of the conditional failure probability corresponding to the k-th layer sample, m U and m L They are and The number of layers in the calculation process.

8. A random-interval hybrid uncertainty structural reliability analysis system, characterized by: It includes data extraction module, k-layer random sample extraction module, POD calculation module, hybrid Kriging model construction module, extreme value acquisition module, failure event critical value acquisition module, conditional failure probability boundary value acquisition module, and final failure probability boundary value acquisition module; The data extraction module is used to extract the interval sample pool and the initial interval sample; The k-layer random sample extraction module is used to determine the selection method of the sampling center of the k-th layer importance sampling density function, construct the importance sampling density function according to the determined sampling center of the k-th layer importance sampling density function, and extract the k-th layer random sample according to the constructed importance sampling density function; The POD calculation module is used to obtain a first output matrix based on the k-th layer random sample and the initial interval sample, and perform POD calculation on the first output matrix; The hybrid Kriging model construction module is used to construct a Kriging model according to the functional relationship between the POD coefficient and the interval variable, and to construct a hybrid Kriging model based on the functional relationship between the output and the interval variable on the basis of the Kriging model, and to perform adaptive learning on the hybrid Kriging model; The extreme value acquisition module is used to predict the output corresponding to all interval samples using the hybrid Kriging model after the hybrid Kriging model converges, obtain a second output matrix, and obtain the extreme value of each random sample corresponding to the random sample pool of each layer based on the second output matrix; The failure event critical value acquisition module is used to arrange the extreme values ​​of each random sample corresponding to the random sample pool of each layer in descending order to obtain the critical value of the intermediate failure event of each layer; The conditional failure probability boundary value acquisition module is used to estimate the boundary value of the failure probability of the first layer and the boundary values ​​of the conditional failure probability corresponding to subsequent layers based on the critical value of the intermediate failure event of each layer; The final failure probability boundary value acquisition module is used to calculate the upper boundary value and the lower boundary value of the final failure probability according to the boundary value of the failure probability of the first layer and the boundary value of the conditional failure probability corresponding to the subsequent layer after the layering is completed.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the random-interval hybrid uncertainty structural reliability analysis method according to any one of claims 1 to 7 are implemented.

10. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the random-interval hybrid uncertainty structural reliability analysis method according to any one of claims 1 to 7 are implemented.

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