A two-stage active learning reliability analysis method and apparatus based on multi-strategy optimization

Abstract

This application relates to the field of structural reliability analysis technology, providing a two-stage active learning reliability analysis method and apparatus based on multi-strategy optimization. This invention constructs a two-stage active learning framework oriented towards global exploration and local development, balancing global region traversal capability with local boundary fitting effect. By introducing a stage switching index value for stage switching judgment, high-value local optimization regions are accurately identified, achieving a smooth transition from global exploration to local development. By identifying transition anchor points and constructing local regions based on these anchor points, a stable transition from global exploration to local development is achieved, improving the targeting of subsequent sample updates and the efficiency of local development. By establishing a global-local dual-layer stopping criterion, the algorithm termination is controlled collaboratively from two levels: the sufficiency of local development and the statistical accuracy of global failure probability, effectively avoiding the problems of insufficient local fitting and large statistical errors in global failure probability.

Description

Technical Field

[0001] This application relates to the field of structural reliability analysis technology, and in particular to a two-stage active learning reliability analysis method and apparatus based on multi-strategy optimization. Background Technology

[0002] Structural reliability assessment is a core technology for ensuring the safe operation of complex engineering structures. Traditional Monte Carlo simulation (MCS) offers high accuracy but comes with extremely high computational costs. First-order reliability methods (FORM), second-order reliability methods (SORM), and conventional sampling methods are ill-suited for complex operating conditions with strong nonlinearity and implicit performance functions. Active learning Kriging surrogate models, with their ability to output predicted means and variances, have become a mainstream and efficient technique for reliability analysis.

[0003] Existing active learning kriging techniques suffer from several technical shortcomings: a single learning function cannot simultaneously address global region identification and local boundary refinement; hybrid learning functions lack stable collaborative mechanisms; and it is difficult to balance sample utilization efficiency with boundary fitting accuracy. Current two-stage learning frameworks lack accurate transition anchor point identification and information scale-driven local region construction strategies, resulting in poor stability during the transition from global exploration to local development and insufficient targeted sample updates. Furthermore, existing convergence criteria often rely on a single metric, failing to simultaneously verify the sufficiency of local boundary development and the statistical accuracy of global failure probability, leading to insufficient rationality in termination decisions. This results in poor algorithm stability, low failure probability estimation accuracy, and numerous function calls, making it difficult to meet the demands of high-precision, high-efficiency engineering reliability analysis. Summary of the Invention

[0004] Therefore, it is necessary to provide a two-stage active learning reliability analysis method and apparatus based on multi-strategy optimization to address the above-mentioned technical problems.

[0005] A two-stage active learning reliability analysis method based on multi-strategy optimization, the method comprising the following steps: S1. Generate a global test candidate pool within the global design domain, and generate global initial test samples based on the global test candidate pool and calculate the corresponding true responses to construct the initial training set; S2. Construct a global Kriging model based on the current training set, and predict the global test candidate pool. Calculate the EF value and stage switching index value based on the prediction results. S3. Make a switching judgment based on the stage switching index value. If the stage switching index value is less than the switching threshold, go to S4; otherwise, select the global update point to update the training set and return to S2. S4. Sort the candidate samples in the global test candidate pool in descending order according to their EF values, and select the top...m The candidate samples constitute a high-information subset. The geometric center of the high-information subset is calculated. The candidate sample with the smallest Euclidean distance from the geometric center in the high-information subset is used as the transition anchor point. A local region is constructed with the transition anchor point as the center. S5. Generate initial training samples in the local region and calculate the corresponding real responses, then update the training set and the global Kriging model. S6. Generate a local candidate pool in the local area, use the updated global Kriging model to predict the local candidate pool, and calculate the U function value and the maximum error of the failure probability based on the prediction results. S7. If the value of the U function is not less than the preset threshold and the maximum value of the failure probability error is not greater than the failure probability error termination threshold, then go to S8; otherwise, select the local update point to update the training set and the global Kriging model and return to S6. S8. Calculate the failure probability and coefficient of variation. If the coefficient of variation is less than the global failure probability statistical precision threshold, output the failure probability and coefficient of variation. Otherwise, expand the global test candidate pool and return to S4.

[0006] In one embodiment, a global Kriging model is constructed based on the current training set, and predictions are made on the global test candidate pool. The EF value and stage switching metric value are calculated based on the prediction results, including: A global Kriging model is constructed based on the current training set, and predictions are made on the global test candidate pool to obtain the prediction mean and prediction standard deviation. The EF value and the phase switching index value are calculated based on the predicted mean and predicted standard deviation. The phase switching index value is calculated according to the following formula: ; ; in, This refers to the indicator value for phase switching; For the first sample points The predicted mean; For the first sample points The standard deviation of the forecast; This serves as a global candidate sample pool. is the cumulative probability density function of the standard normal distribution.

[0007] In one embodiment, constructing a local region centered on a transition anchor point includes: Information scale is calculated based on transition anchor points: ; in, For transition anchor points; For information scale; The first in the high information subset One candidate sample; Calculating the radius of a local region based on information scale: ; in, r The radius of the local region; This is the scaling factor; Constructing a local region: ; Among them, Ω local Ω represents the local region; Ω represents the global design domain. These are sample points.

[0008] In one embodiment, the failure probability and the coefficient of variation are calculated according to the following formula: ; ; in, This represents the probability of failure. This represents the number of samples deemed invalid. This serves as a global candidate sample pool. is the coefficient of variation.

[0009] In one embodiment, the geometric center of the high-information subset is calculated according to the following formula: ; in, It is the geometric center of the high-information subset; The first in the high information subset 10 candidate samples.

[0010] In one embodiment, the global update point is selected according to the following formula: ; in, This is a global update point; For EF value; This is a pre-filtered set.

[0011] In one embodiment, the global initial test sample is generated using LCVT.

[0012] In one embodiment, the initial training samples are generated using Maximin LHS.

[0013] In one embodiment, the global test candidate pool is generated within the global design domain using the MCS method.

[0014] A two-stage active learning reliability analysis device based on multi-strategy optimization, the device comprising: The initial training set construction module is used to generate a global test candidate pool within the global design domain, generate global initial test samples based on the global test candidate pool, calculate the corresponding true responses, and construct the initial training set. The global prediction module is used to build a global Kriging model based on the current training set, predict the global test candidate pool, and calculate the EF value and stage switching index value based on the prediction results. The stage switching module is used to make switching judgments based on the stage switching index value. If the stage switching index value is less than the switching threshold, it will switch to the transition module; otherwise, it will select the global update point to update the training set and return to the global prediction module. The transition module is used to sort the candidate samples in the global test candidate pool in descending order according to their EF values, and select the top... m The candidate samples constitute a high-information subset. The geometric center of the high-information subset is calculated. The candidate sample with the smallest Euclidean distance from the geometric center in the high-information subset is used as the transition anchor point. A local region is constructed with the transition anchor point as the center. The local update module is used to generate initial training samples and calculate the corresponding true responses in local regions, and update the training set and the global Kriging model. The local prediction module is used to generate a local candidate pool within a local region, use the updated global Kriging model to predict the local candidate pool, and calculate the U function value and the maximum error of the failure probability based on the prediction results. The local stopping module is used to switch to the global stopping module if the U function value is not less than the preset threshold and the maximum value of the failure probability error is not greater than the failure probability error termination threshold; otherwise, it selects the local update point to update the training set and the global Kriging model and returns to the local prediction module. The global stop module is used to calculate the failure probability and coefficient of variation. If the coefficient of variation is less than the global failure probability statistical accuracy threshold, the failure probability and coefficient of variation are output; otherwise, the global test candidate pool is expanded and the process is returned to the transition module.

[0015] The aforementioned two-stage active learning reliability analysis method and apparatus based on multi-strategy optimization constructs a two-stage active learning framework for global exploration and local development. In the global stage, the EF function is used to screen high-information candidate samples, achieving accurate identification of potential limit state regions across the entire domain and ensuring the integrity of the global exploration. In the local stage, the U function is used to iteratively optimize local candidate samples, precisely refining key boundary regions of limit states and significantly improving the local approximation accuracy of structural failure boundaries, balancing global region traversal capability with local boundary fitting effect. A stage switching index is introduced for stage switching judgment. The EF value is used to screen high-information subsets, solve for the geometric center, and locate the optimal transition anchor point, accurately locking high-value local optimization regions and achieving a smooth transition from global exploration to local development. By identifying transition anchor points and constructing local regions based on them, a stable transition from global exploration to local development is achieved, improving the targeting of subsequent sample updates and the efficiency of local development. By establishing a global-local dual-layer stopping criterion, the algorithm termination is controlled collaboratively from two levels: the sufficiency of local development and the statistical accuracy of global failure probability. This effectively avoids the problems of insufficient local fitting and large global failure probability statistical error, and significantly improves the algorithm's iterative stability and result reliability. It can output high-precision and high-stability failure probability calculation results with fewer calls to the real performance function. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a two-stage active learning reliability analysis method based on multi-strategy optimization in one embodiment. Figure 2 This is a schematic diagram of the framework of a two-stage active learning reliability analysis method based on multi-strategy optimization in one embodiment; Figure 3 This is a graph showing the variation of the limit state surface with the number of update points for different methods in Example 1 of one embodiment. Figure 3 (a) is a graph showing the change of the AK-MCS+EF limit state surface with the number of update points. Figure 3 (b) is a graph showing the change of the AK-MCS+U limit state surface with the number of update points. Figure 3 (c) is a graph showing the change of the AK-MCS+EF-U limit state surface with the number of update points. Figure 3 (d) is a graph showing the change of the AK-TSEUAL limit state surface with the number of update points; Figure 4 This is a graph showing the variation of the limit state surface with the number of update points for different methods in Example 2 of one embodiment. Figure 4 (a) is a graph showing the change of the AK-MCS+EF limit state surface with the number of update points. Figure 4 (b) is a graph showing the change of the AK-MCS+U limit state surface with the number of update points. Figure 4(c) is a graph showing the change of the AK-MCS+EF-U limit state surface with the number of update points. Figure 4 (d) is a graph showing the change of the AK-TSEUAL limit state surface with the number of update points; Figure 5 This is a schematic diagram of a nonlinear oscillator affected by a rectangular load pulse in one embodiment; Figure 6 This is a diagram of a truss structure in one embodiment; Figure 7 This is a finite element model diagram of a bridge truss structure in one embodiment. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0018] In one embodiment, such as Figure 1 , Figure 2 As shown, a two-stage active learning reliability analysis method based on multi-strategy optimization is provided. The method includes the following steps: S1. Generate a global test candidate pool within the global design domain, and generate global initial test samples based on the global test candidate pool and calculate the corresponding true responses to construct the initial training set.

[0019] S2. Construct a global Kriging model based on the current training set, and predict the global test candidate pool. Calculate the EF value and stage switching index value based on the prediction results.

[0020] It should be noted that the Kriging model is a surrogate model based on statistics and spatial interpolation theory. Its basic idea is to use the known spatial correlation between data points for prediction. The global Kriging model used in this invention is a commonly used Kriging model. The EF value is the output value of the EF learning function, which can be expressed as: ; in, The joint probability density function of the input random variables; An indicator related to error is defined as follows: ; ; in, This serves as the global candidate sample pool. Regions with larger EF values ​​typically correspond to candidate regions that simultaneously possess strong boundary proximity and high probability importance.

[0021] S3. Make a switching judgment based on the stage switching index value. If the stage switching index value is less than the switching threshold, go to S4. Otherwise, select the global update point to update the training set and return to S2.

[0022] S4. Sort the candidate samples in the global test candidate pool in descending order according to their EF values, and select the top... m The candidate samples constitute a high-information subset. The geometric center of the high-information subset is calculated. The candidate sample with the smallest Euclidean distance from the geometric center in the high-information subset is used as the transition anchor point. A local region is constructed with the transition anchor point as the center.

[0023] S5. Generate initial training samples in the local region and calculate the corresponding true responses, then update the training set and the global Kriging model.

[0024] S6. Generate a local candidate pool within the local region, use the updated global Kriging model to predict the local candidate pool, and calculate the maximum value of the U function value and the failure probability error based on the prediction results.

[0025] It should be noted that the U function is the U-learning function, which applies to any sample point. The learning function U can be expressed as: ; in, For the Kriging model The predicted mean; This represents the predicted standard deviation.

[0026] S7. If the value of the U function is not less than the preset threshold and the maximum value of the failure probability error is not greater than the termination threshold of the failure probability error, then go to S8; otherwise, select the local update point to update the training set and the global Kriging model and return to S6.

[0027] It should be noted that the local update points are sample points that are close to the boundary of the failure domain and have a high risk of misjudgment.

[0028] S8. Calculate the failure probability and coefficient of variation. If the coefficient of variation is less than the global failure probability statistical precision threshold, output the failure probability and coefficient of variation. Otherwise, expand the global test candidate pool and return to S4.

[0029] The aforementioned two-stage active learning reliability analysis method based on multi-strategy optimization constructs a two-stage active learning framework for global exploration and local development. In the global stage, the EF function is used to screen high-information candidate samples, achieving accurate identification of potential limit state regions across the entire domain and ensuring the integrity of the global exploration. In the local stage, the U function is used to iteratively optimize local candidate samples, precisely refining the key boundary regions of the limit states and significantly improving the local approximation accuracy of structural failure boundaries, balancing global region traversal capability with local boundary fitting effects. A stage switching index is introduced for stage switching judgment. The EF value is used to screen high-information subsets, solve for the geometric center, and locate the optimal transition anchor point, accurately locking high-value local optimization regions and achieving a smooth transition from global exploration to local development. By identifying transition anchor points and constructing local regions based on them, a stable transition from global exploration to local development is achieved, improving the targeting of subsequent sample updates and the efficiency of local development. By establishing a global-local dual-layer stopping criterion, the algorithm termination is controlled collaboratively from two levels: the sufficiency of local development and the statistical accuracy of global failure probability. This effectively avoids the problems of insufficient local fitting and large global failure probability statistical error, and significantly improves the algorithm's iterative stability and result reliability. It can output high-precision and high-stability failure probability calculation results with fewer calls to the real performance function.

[0030] In one embodiment, the global test candidate pool is generated within the global design domain using the MCS method.

[0031] In one embodiment, the global initial test sample is generated using LCVT.

[0032] In this embodiment, LCVT is used to generate global initial test samples, which can make the global initial test samples have better spatial uniformity and spacing, so as to avoid local aggregation and improve the overall coverage effect.

[0033] In one embodiment, a global Kriging model is constructed based on the current training set, and predictions are made on the global test candidate pool. The EF value and stage switching metric value are calculated based on the prediction results, including: A global Kriging model is constructed based on the current training set, and predictions are made on the global test candidate pool to obtain the prediction mean and prediction standard deviation. The EF value and the phase switching index value are calculated based on the predicted mean and predicted standard deviation. The phase switching index value is calculated according to the following formula: ; ; in, This refers to the indicator value for phase switching; For the first sample points The predicted mean; For the first sample points The standard deviation of the forecast; This serves as a global candidate sample pool. is the cumulative probability density function of the standard normal distribution.

[0034] Understandably, in the expression for the stage switching index value, the numerator represents whether the distribution of sample points near the limit state surface in the global test candidate pool is significantly biased towards one side between the safe side and the failure side: if the distribution on both sides is relatively balanced, the numerator is smaller; if it is more concentrated on one side, the numerator is larger; the denominator represents the overall ambiguity of all sample points near the boundary in the candidate pool, which is used to standardize the numerator.

[0035] Switching decisions are made based on phase switching indicator values, and the switching status can be represented as follows: ; in, esp This is the switching threshold. In one embodiment, esp Set to 0.01. When the switching conditions are met, the global exploration phase is considered to be basically stable, and the transition phase begins.

[0036] In this embodiment, by introducing a stage switching index value, the problems of blind transition and poor sample update targeting in the traditional two-stage method are effectively solved, the invalid sample calls are significantly reduced, and the accuracy and efficiency of local development are improved.

[0037] In one embodiment, the geometric center of the high-information subset is calculated according to the following formula: ; in, It is the geometric center of the high-information subset; The first in the high information subset 10 candidate samples.

[0038] The candidate samples in the global test candidate pool are sorted in descending order according to their EF (Expert Frame) values, and the top [samples] are selected. m A subset of candidate samples is formed. The geometric center of the high-information subset is calculated, and the candidate sample with the smallest Euclidean distance from the geometric center in the high-information subset is used as the transition anchor point. Specifically, the high-information subset can be represented as... In one embodiment m Set the value to 10. From the high-information subset, select the candidate sample with the smallest Euclidean distance to the geometric center as the transition anchor point, i.e.: ; in, This serves as a transition anchor point.

[0039] Understandably, the selection of transition anchor points does not rely directly on single-point extrema, but rather on the spatial clustering characteristics of high EF regions to identify transition anchor points. This allows the identified transition anchor points to more stably represent the core positions of high-information regions discovered during the global exploration phase, providing a more stable and reliable central basis for the construction of local regions.

[0040] In one embodiment, constructing a local region centered on a transition anchor point includes: Information scale is calculated based on transition anchor points: ; in, For transition anchor points; For information scale; The first in the high information subset One candidate sample; Calculating the radius of a local region based on information scale: ; in, r The radius of the local region; This is the scaling factor, with a value ranging from 1.1 to 1.5; Constructing a local region: ; Among them, Ω local Ω represents the local region; Ω represents the global design domain. These are sample points.

[0041] Understandably, the information scale reflects the average dispersion of high-information samples relative to the transition anchor points, and can be regarded as a statistical representation of the local effective range of influence near the transition anchor points. If... A larger EF indicates that the high EF region is relatively dispersed; conversely, if A smaller value indicates that high-information samples are concentrated near the transition anchor point.

[0042] In this embodiment, a local region is constructed around the transition anchor point, creating an engineering-feasible local action zone. This allows subsequent samples to focus on the neighborhood with the highest development value. Compared to directly entering the next stage of learning within the global design space, constructing a local region around the transition anchor point significantly narrows the search range, enhances the local targeting of subsequent sampling, and improves the update efficiency for fine-grained boundary approximation.

[0043] In one embodiment, the initial training samples are generated using Maximin LHS.

[0044] In this embodiment, Maximin LHS is used to generate initial training samples, which can increase the minimum distance between sample points and improve local space filling while maintaining the hierarchical characteristics.

[0045] In one embodiment, the failure probability and the coefficient of variation are calculated according to the following formula: ; ; in, This represents the probability of failure. This represents the number of samples deemed invalid. This serves as a global candidate sample pool. is the coefficient of variation.

[0046] It should be noted that the failure probability is used to construct the current global candidate sample pool from the input random space. The failure determination is based on the current proxy model. The coefficient of variation is used as a global accuracy indicator to quantify the statistical uncertainty of the failure probability.

[0047] The U-function value is not less than a preset threshold and the maximum failure probability error is not greater than the failure probability error termination threshold, which can be expressed as: ; ; in, This represents the maximum error value for the failure probability. This is the termination threshold for the failure probability error; U limit This is a preset threshold.

[0048] If the coefficient of variation is less than the global failure probability statistical precision threshold, then the output failure probability and coefficient of variation can be expressed as: ; in, The preset global failure probability statistical accuracy threshold is set to 5% in one embodiment.

[0049] In one embodiment, the global update point is selected according to the following formula: ; in, This is a global update point; For EF value; This is a pre-filtered set.

[0050] It should be noted that, According to Filter from largest to smallest The system consists of several candidate points, and in one embodiment, these points constitute a network of candidate points. Select the sample point with the largest EF value from the pre-screened set as the global update point. Calculate using the following formula: ; in, This is the error contribution value.

[0051] To assess the consistency between the present invention and the MCS reference results, the MCS is used to directly evaluate the true performance function. Let's assume... Among a number of independent random samples, the failure condition is met. The number of samples is The MCS reference failure probability is defined as follows: ; The relative error between the failure probability and the MCS reference failure probability is defined as: ; The final results evaluation phase used a sample size of [number missing]. An independent evaluation sample set was obtained, and... This is to ensure consistency with the MCS reference results.

[0052] To verify the effectiveness of this invention, it was compared with three other methods—AK-MCS+U, AK-MCS+EF, and AK-MCS+EF-U—under the same computational examples. To ensure a fair comparison, all methods employed the same global candidate pool generation method, initial sample design method, and Kriging modeling framework. Specifically, all methods generated a global candidate pool based on MCS, generated initial samples based on LCVT, and used the same DACE-Kriging model and related parameter settings. A common feature of the three methods is that their learning and update processes always occur within the global candidate pool: AK-MCS+U performs global iterative point selection solely based on the U learning function; AK-MCS+EF performs global error-driven updates solely based on the EF learning function; and although AK-MCS+EF-U can switch from EF to U based on a switching criterion, the search and update are still performed within the same global candidate pool before and after the switch, thus essentially remaining a global search framework. Furthermore, the comparison methods used the ESC single-layer global stopping criterion, while this invention (AK-TSEUAL) uses the HESC double-layer stopping criterion.

[0053] definition The performance parameter is the number of function calls, i.e., the total number of samples required to build the surrogate model, including initial training samples and subsequent update samples. To comprehensively evaluate the computational efficiency, accuracy, and stability of each method, we select... Relative error The coefficient of variation (COV) was used as an evaluation index, and the stability of each method was analyzed based on the results of 10 independent runs.

[0054] Example 1 is a series system with four discrete failure domains. The performance function expression of the series system is: ; in, and They are mutually independent standard normal random variables.

[0055] To compare the differences in training sample selection mechanisms among different methods, Figure 3 The spatial distribution of newly added samples and corresponding limit state fitting results under four learning strategies are presented. It can be seen that the updated samples of AK-MCS+EF are mainly distributed along the failure boundary, possessing strong global search capabilities, but the samples are relatively scattered, with insufficient focus on key local boundary segments; the updated samples of AK-MCS+U are more concentrated in local boundary regions, exhibiting strong local approximation capabilities, but limited overall coverage of multi-branch discrete failure domains; AK-MCS+EF-U, to some extent, balances global exploration and local refinement, but still suffers from insufficient sample utilization efficiency and update targeting in branch transition regions. In contrast, this invention, through transition anchor point identification, local region construction, and collaborative updating of local initial samples and U-learned samples, makes the updated samples more concentrated in the key transition areas and high curvature regions of multi-branch failure boundaries, thereby significantly improving the local characterization capability of real failure boundaries while maintaining necessary global coverage. It can be observed that the actual results analyzed through the limit function fitting diagram are basically consistent with the theoretical analysis method.

[0056] To mitigate the impact of randomness in a single calculation on the evaluation of results, Table 1 lists the average results of each method under 10 repeated trials as well as the results of one representative calculation.

[0057] Table 1 Comparison of Calculation Results of Different Methods in Example 1

[0058] Based on the average results of 10 repeated trials, AK-TSEUAL demonstrates significant advantages in both the number of update points and method error. Compared to AK-MCS+U, AK-MCS+EF, and AK-MCS+EF-U, it reduces the number of update points by 17.17%, 12.01%, and 10.14%, respectively, indicating higher sample utilization efficiency. In terms of error performance, AK-TSEUAL reduces the relative error by 59.91%, 71.29%, and 74.93% compared to the other three methods, and its failure probability estimate is closest to the MCS reference result, with a relative error of only 0.091%, the lowest among all compared methods. Simultaneously, its coefficient of variation is 4.758%, on the same order of magnitude as the other methods, indicating that while significantly reducing the need for update samples, AK-TSEUAL maintains good statistical stability and high estimation accuracy. In summary, AK-TSEUAL achieves a better balance between sample efficiency, error control, and result stability, demonstrating superior overall performance.

[0059] Example 2 is a highly nonlinear function, and its performance function expression is: ;

[0060] In the formula , They are mutually independent standard normal random variables; This represents the entire two-dimensional standard normal domain.

[0061] To compare the differences in training sample update mechanisms among different methods, Figure 4 The spatial distribution of newly added samples and the corresponding limit state fitting results are presented under four learning strategies. For complex boundaries like Example 2, which have obvious fluctuations and local high curvature features, AK-MCS+EF has strong global search capabilities, but the samples are relatively scattered; AK-MCS+U focuses more on local boundary approximation, but the overall coverage is limited; AK-MCS+EF-U achieves a certain balance between global search and local refinement, but the sample distribution in key transition regions is still insufficient. In contrast, AK-TSEUAL, through the identification of transition anchor points and adaptive updating of local regions, makes the updated samples more concentrated in key transition segments and high curvature regions, thereby improving the fitting accuracy of the true limit state boundary. It can be found that the actual results analyzed through the limit function fitting graph are basically consistent with the theoretical analysis method.

[0062] To avoid the influence of randomness in a single calculation, Table 2 also presents the average results of each method under 10 repeated trials and one representative result.

[0063] Table 2 Comparison of Calculation Results of Different Methods in Example 2

[0064] The average results from 10 repeated trials show that AK-TSEUAL exhibits significant advantages in both the number of update points and method error. Compared to AK-MCS+U, AK-MCS+EF, and AK-MCS+EF-U, it reduces the number of update points by 34.38%, 21.96%, and 10.81%, respectively, indicating a more prominent advantage in sample utilization efficiency. In terms of error performance, AK-TSEUAL reduces the relative error by 83.42%, 85.78%, and 87.55% compared to the other three methods, and its failure probability estimate is closest to the MCS reference result, with a relative error of only 0.032%, the smallest among all compared methods. Meanwhile, its coefficient of variation is 1.248%, on the same order of magnitude as the other methods, indicating that while significantly reducing the need for update samples, AK-TSEUAL maintains good statistical stability and high estimation accuracy.

[0065] Example 3 is a medium-dimensional problem, involving a nonlinear, single-degree-of-freedom undamped oscillator system, such as... Figure 5 As shown in the figure, Let be the instantaneous horizontal displacement of the mass block over time. For the time-varying external horizontal excitation load, the performance function expression of the structure is: ; in, , (Stiffness coefficient of linear segment under small deformation) (Correlation coefficient for nonlinear hardening / softening stiffness under large deformation) (quality), (Displacement limit threshold) (Rectangular pulse load amplitude) and (Duration of rectangular pulse load) is a uniform input variable, and its distribution parameters are shown in Table 3. Normal indicates a normal distribution.

[0066] Table 3 Random Parameters

[0067] To mitigate the impact of randomness in a single calculation on the evaluation of results, Table 4 lists the average results of each method under 10 repeated trials as well as the results of one representative calculation.

[0068] Table 4 Comparison of Calculation Results of Different Methods in Example 3

[0069] The average results from 10 repeated trials show that AK-TSEUAL also demonstrates significant advantages in both the number of update points and error control. Compared to AK-MCS+U, AK-MCS+EF, and AK-MCS+EF-U, the number of update points is reduced by 14.25%, 15.90%, and 10.97%, respectively, indicating that this method still has a strong advantage in sample utilization efficiency. In terms of error performance, AK-TSEUAL reduces the relative error by 86.81%, 85.68%, and 86.08% compared to the above three methods, respectively, and its failure probability estimate is closest to the MCS reference result, with a relative error of only 0.177%, the smallest among all compared methods. Meanwhile, its coefficient of variation is 1.311%, on the same order of magnitude as the other methods, indicating that while significantly reducing the need for update samples, AK-TSEUAL can still maintain good statistical stability and high estimation accuracy.

[0070] Example 4 uses a planar ten-bar truss structure as the verification object, and its geometry is as follows: Figure 6 As shown, it contains 10 independent random variables, and their distribution parameters are listed in Table 5. The finite element analysis results of the truss structure are as follows: Figure 7 As shown. The limit state function expression of the structure is: ; In the formula, Represents an input vector of random variables; For nodes V Deflection response at the location; for The threshold value was obtained from finite element analysis and was set to 0.09m. Lognormal represents the log-normal distribution; Gumbel represents the Gumbel distribution.

[0071] Table 5 Distribution information of trellis structure variables

[0072] To mitigate the impact of randomness in a single calculation on the evaluation of results, Table 6 also lists the average results of each method under 10 repeated trials and the results of one representative calculation.

[0073] Table 6 Comparison of Calculation Results of Different Methods in Example 4

[0074] The average results from 10 repeated trials show that AK-TSEUAL exhibits significant advantages in both the number of update points and method error. Compared to AK-MCS+U, AK-MCS+EF, and AK-MCS+EF-U, it reduces the number of update points by 52.18%, 49.08%, and 44.87%, respectively, indicating a more prominent advantage in sample utilization efficiency. In terms of error performance, AK-TSEUAL reduces the relative error by 93.53%, 95.27%, and 89.73% compared to the other three methods, respectively. Furthermore, its failure probability estimate is closest to the MCS reference result, with a relative error of only 0.065%, the lowest among all compared methods. Simultaneously, its coefficient of variation is 1.021%, on the same order of magnitude as the other methods, indicating that while significantly reducing the need for update samples, AK-TSEUAL maintains good statistical stability and high estimation accuracy.

[0075] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0076] In one embodiment, a two-stage active learning reliability analysis device based on multi-strategy optimization is provided, the device comprising: The initial training set construction module is used to generate a global test candidate pool within the global design domain, generate global initial test samples based on the global test candidate pool, calculate the corresponding true responses, and construct the initial training set. The global prediction module is used to build a global Kriging model based on the current training set, predict the global test candidate pool, and calculate the EF value and stage switching index value based on the prediction results. The stage switching module is used to make switching judgments based on the stage switching index value. If the stage switching index value is less than the switching threshold, it will switch to the transition module; otherwise, it will select the global update point to update the training set and return to the global prediction module. The transition module is used to sort the candidate samples in the global test candidate pool in descending order according to their EF values, and select the top... mThe candidate samples constitute a high-information subset. The geometric center of the high-information subset is calculated. The candidate sample with the smallest Euclidean distance from the geometric center in the high-information subset is used as the transition anchor point. A local region is constructed with the transition anchor point as the center. The local update module is used to generate initial training samples and calculate the corresponding true responses in local regions, and update the training set and the global Kriging model. The local prediction module is used to generate a local candidate pool within a local region, use the updated global Kriging model to predict the local candidate pool, and calculate the U function value and the maximum error of the failure probability based on the prediction results. The local stopping module is used to switch to the global stopping module if the U function value is not less than the preset threshold and the maximum value of the failure probability error is not greater than the failure probability error termination threshold; otherwise, it selects the local update point to update the training set and the global Kriging model and returns to the local prediction module. The global stop module is used to calculate the failure probability and coefficient of variation. If the coefficient of variation is less than the global failure probability statistical accuracy threshold, the failure probability and coefficient of variation are output; otherwise, the global test candidate pool is expanded and the process is returned to the transition module.

[0077] Specific limitations regarding the two-stage active learning reliability analysis device based on multi-strategy optimization can be found in the limitations of the two-stage active learning reliability analysis method based on multi-strategy optimization mentioned above, and will not be repeated here. Each module in the aforementioned two-stage active learning reliability analysis device based on multi-strategy optimization can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0078] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0079] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A two-stage active learning reliability analysis method based on multi-strategy optimization, characterized in that, The method includes the following steps: S1. Generate a global test candidate pool within the global design domain, and generate global initial test samples based on the global test candidate pool and calculate the corresponding true responses to construct the initial training set; S2. Construct a global Kriging model based on the current training set, and predict the global test candidate pool. Calculate the EF value and stage switching index value based on the prediction results. S3. Make a switching judgment based on the stage switching index value. If the stage switching index value is less than the switching threshold, go to S4; otherwise, select the global update point to update the training set and return to S2. S4. Sort the candidate samples in the global test candidate pool in descending order according to their EF values, and select the top... m The candidate samples constitute a high-information subset. The geometric center of the high-information subset is calculated. The candidate sample with the smallest Euclidean distance from the geometric center in the high-information subset is used as the transition anchor point. A local region is constructed with the transition anchor point as the center. S5. Generate initial training samples in the local region and calculate the corresponding real responses, then update the training set and the global Kriging model. S6. Generate a local candidate pool in the local area, use the updated global Kriging model to predict the local candidate pool, and calculate the U function value and the maximum error of the failure probability based on the prediction results. S7. If the value of the U function is not less than the preset threshold and the maximum value of the failure probability error is not greater than the failure probability error termination threshold, then go to S8; otherwise, select the local update point to update the training set and the global Kriging model and return to S6. S8. Calculate the failure probability and coefficient of variation. If the coefficient of variation is less than the global failure probability statistical precision threshold, output the failure probability and coefficient of variation. Otherwise, expand the global test candidate pool and return to S4.

2. The two-stage active learning reliability analysis method based on multi-strategy optimization according to claim 1, characterized in that, A global Kriging model is constructed based on the current training set, and predictions are made for the global test candidate pool. Based on the prediction results, the EF value and stage switching metric value are calculated, including: A global Kriging model is constructed based on the current training set, and predictions are made on the global test candidate pool to obtain the prediction mean and prediction standard deviation. The EF value and the phase switching index value are calculated based on the predicted mean and predicted standard deviation. The phase switching index value is calculated according to the following formula: in, This refers to the indicator value for phase switching; For the first sample points The predicted mean; For the first sample points The standard deviation of the forecast; This serves as a global candidate sample pool. is the cumulative probability density function of the standard normal distribution.

3. The two-stage active learning reliability analysis method based on multi-strategy optimization according to claim 1, characterized in that, A local region is constructed centered on the transition anchor point, including: Information scale is calculated based on transition anchor points: in, For transition anchor points; For information scale; For the first in the high information subset One candidate sample; Calculating the radius of a local region based on information scale: in, r The radius of the local region; This is the scaling factor; Constructing a local region: Among them, Ω local Ω represents the local region; Ω represents the global design domain. These are sample points.

4. The two-stage active learning reliability analysis method based on multi-strategy optimization according to claim 1, characterized in that, The failure probability and coefficient of variation are calculated according to the following formula: in, This represents the probability of failure. This represents the number of samples deemed invalid. This serves as a global candidate sample pool. is the coefficient of variation.

5. The two-stage active learning reliability analysis method based on multi-strategy optimization according to claim 1, characterized in that, The geometric center of the high-information subset is calculated according to the following formula: in, It is the geometric center of the high-information subset; For the first in the high information subset 10 candidate samples.

6. The two-stage active learning reliability analysis method based on multi-strategy optimization according to claim 1, characterized in that, The global update point is selected according to the following formula: in, This is a global update point; For EF value; This is a pre-filtered set.

7. The two-stage active learning reliability analysis method based on multi-strategy optimization according to claim 1, characterized in that, The initial global test samples were generated using LCVT.

8. The two-stage active learning reliability analysis method based on multi-strategy optimization according to claim 1, characterized in that, The initial training samples were generated using Maximin LHS.

9. The two-stage active learning reliability analysis method based on multi-strategy optimization according to claim 1, characterized in that, The global test candidate pool is generated within the global design domain using the MCS method.

10. A two-stage active learning reliability analysis device based on multi-strategy optimization, characterized in that, The device includes: The initial training set construction module is used to generate a global test candidate pool within the global design domain, generate global initial test samples based on the global test candidate pool, calculate the corresponding true responses, and construct the initial training set. The global prediction module is used to build a global Kriging model based on the current training set, predict the global test candidate pool, and calculate the EF value and stage switching index value based on the prediction results. The stage switching module is used to make switching judgments based on the stage switching index value. If the stage switching index value is less than the switching threshold, it will switch to the transition module; otherwise, it will select the global update point to update the training set and return to the global prediction module. The transition module is used to sort the candidate samples in the global test candidate pool in descending order according to their EF values, and select the top... m The candidate samples constitute a high-information subset. The geometric center of the high-information subset is calculated. The candidate sample with the smallest Euclidean distance from the geometric center in the high-information subset is used as the transition anchor point. A local region is constructed with the transition anchor point as the center. The local update module is used to generate initial training samples and calculate the corresponding true responses in local regions, and update the training set and the global Kriging model. The local prediction module is used to generate a local candidate pool within a local region, use the updated global Kriging model to predict the local candidate pool, and calculate the U function value and the maximum error of the failure probability based on the prediction results. The local stopping module is used to switch to the global stopping module if the U function value is not less than the preset threshold and the maximum value of the failure probability error is not greater than the failure probability error termination threshold; otherwise, it selects the local update point to update the training set and the global Kriging model and returns to the local prediction module. The global stop module is used to calculate the failure probability and coefficient of variation. If the coefficient of variation is less than the global failure probability statistical accuracy threshold, the failure probability and coefficient of variation are output; otherwise, the global test candidate pool is expanded and the process is returned to the transition module.

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