Small failure probability assessment method based on prior constraint integration and hierarchical correction sampling
By constructing a priori constraint integrated proxy model and performing hierarchical correction sampling, the accuracy and efficiency issues of small failure probability assessment for complex equipment components are solved. This achieves improved accuracy and stability under conditions of limited high-fidelity resources, and is applicable to the reliability design of complex equipment such as aerospace mechanisms, load-bearing structures, and connection and release devices.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2026-06-05
- Publication Date
- 2026-07-03
AI Technical Summary
In the reliability design of complex equipment components, existing methods suffer from problems such as high computational cost, long cycle, insufficient accuracy, inadequate characterization of failure boundaries, and omission of multimodal failure regions in the assessment of low failure probability. In particular, in high-dimensional, strongly nonlinear and multi-failure cluster scenarios, it is difficult to take into account both global exploration and local approximation, and there is a lack of integrated collaborative mechanism, resulting in inaccurate assessment results.
An integrated surrogate model based on prior constraint integration and hierarchical correction sampling is constructed to integrate multiple types of prior constraints. Through high-fidelity simulation or experimental correction, soft failure weights are calculated, failure samples are searched hierarchically, failure clusters are identified by clustering, a multi-scale hybrid proposal distribution is constructed, and bridging sampling and inverse probability weighted unbiased correction are performed to optimize the failure probability assessment.
It significantly improves the accuracy of failure boundary approximation under limited resources, prioritizes the exploration of key failure regions, covers multimodal regions, reduces the risk of single proposal distribution mismatch, and improves the accuracy and stability of the evaluation results. It is suitable for low failure probability evaluation of complex equipment components.
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Figure CN122334053A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of uncertainty quantification technology, and in particular to a method for assessing small failure probability based on prior constraint integration and hierarchical correction sampling. Background Technology
[0002] In the reliability design of complex equipment components such as aerospace mechanisms, load-bearing structures, and connection and release devices, failure events often correspond to local regions with extremely small volume and discrete distribution within the parameter space. For this type of problem, directly using Monte Carlo sampling requires a large number of high-fidelity simulations or experimental tests, which is computationally expensive and time-consuming, making it difficult to meet the dual requirements of efficiency and accuracy in engineering applications.
[0003] While existing reliability analysis methods based on surrogate models can reduce the cost of a single assessment, they are prone to problems such as insufficient characterization of failure boundaries, omission of local multimodal failure regions, and accumulation of low-fidelity surrogate bias under small sample conditions. Especially in high-dimensional, strongly nonlinear, and multi-failure cluster scenarios, a single proposal distribution often fails to take into account both global exploration and local approximation, leading to degradation of importance weights, increased estimation variance, and even systematic underestimation.
[0004] Meanwhile, high-fidelity assessment resources available for correcting surrogate errors in engineering are typically very limited. How to incorporate prior knowledge into surrogate modeling, couple failure search with proposal distribution construction, and achieve unbiased correction through targeted high-fidelity verification, all within a limited high-fidelity budget, is a key technical challenge in current low failure probability assessment.
[0005] Furthermore, existing methods often treat surrogate modeling, failure sample search, importance sampling, and high-fidelity verification as independent processing steps, lacking an integrated collaborative mechanism for low failure probability assessment tasks. As a result, front-end surrogate bias is difficult to propagate to subsequent proposal distribution corrections in a timely manner, and back-end high-fidelity verification information is difficult to use to update the front-end surrogate and failure boundary identification processes. Consequently, limited budgets are not prioritized for the key samples that most significantly impact the accuracy of the assessment results. Summary of the Invention
[0006] The purpose of this application is to provide a method for assessing the low failure probability based on prior constraint integration and hierarchical correction sampling. This method can improve the accuracy and stability of low failure probability assessment in scenarios with limited high-fidelity assessment resources, small sample sizes, and multimodal failure domains, and fully cover the failure area.
[0007] To achieve the above objectives, this application provides the following solution: A method for assessing the low failure probability based on prior constraint integration and hierarchical correction sampling is applied to the assessment of the low failure probability of complex equipment components. The method includes the following steps: Based on the engineering parameters of the complex equipment components to be analyzed, an integrated proxy model that incorporates multiple types of prior constraints is constructed. The residual of the integrated proxy model is then corrected using anchor point samples obtained from high-fidelity simulation or physical experiments to obtain the corrected proxy model. The engineering parameters include detonation impulse, yield strength, shear groove depth, assembly gap, and on-orbit temperature.
[0008] The soft failure weights of candidate engineering parameter samples are calculated based on the corrected surrogate model. Then, a hierarchical search is performed on the candidate engineering parameter samples according to the soft failure weights to obtain the failure sample set.
[0009] Clustering is performed on the failure samples in the failure sample set to identify multiple failure sample clusters corresponding to different failure modes of complex equipment components. A multi-scale hybrid proposal distribution is constructed based on multiple failure sample clusters.
[0010] Based on the multi-scale mixed proposal distribution, bridging sampling driven by effective sample size is performed to construct a series of bridging layers and summarize the samples and normalized weights of all bridging layers to obtain the initial failure probability estimate; each bridging layer corresponds to an intermediate distribution between the prior distribution and the target failure distribution.
[0011] Perform inverse probability weighted unbiased correction, perform high-fidelity verification on the samples obtained by bridging sampling, correct the initial failure probability estimate based on the verification results, and output the final failure probability of the complex equipment component to be analyzed.
[0012] Optionally, based on the engineering parameters of the complex equipment component to be analyzed, an integrated proxy model incorporating multiple types of prior constraints is constructed, specifically including the following steps: An initial sample set is obtained based on the engineering parameters of the complex equipment component to be analyzed.
[0013] Multiple basic surrogate models are trained using an initial sample set, and three types of constraints are introduced during the training process: prior knowledge of physical laws, prior knowledge of engineering experience, and prior knowledge of mathematical properties.
[0014] The combined weights of each basic proxy model are solved by non-negative least squares method to obtain the integrated proxy model.
[0015] Alternatively, during training, a comprehensive loss function can be constructed as shown in the following equation: in, This is the sample fitting error term. These are a priori constraints on physical laws. These are prior constraints based on engineering experience. These are a priori constraints on mathematical properties. , and These are the corresponding weight coefficients; each basic proxy model is trained based on the comprehensive loss function.
[0016] Optionally, the integrated surrogate model is residually corrected using anchor point samples obtained from high-fidelity simulation or physical experiments to obtain a corrected surrogate model, specifically including the following steps: Several high-fidelity anchor point samples are obtained through high-fidelity simulation or physical experiments, forming a high-fidelity anchor point sample set.
[0017] Calculate the prediction residuals of each sample in the high-fidelity anchor sample set under the integrated surrogate model.
[0018] The input features of high-fidelity anchor samples are mapped to a random feature space through random Fourier feature mapping. Combined with the corresponding prediction residuals, a ridge regression residual model is fitted and established. The ridge regression residual model is used to output the corresponding residual correction value based on the input features.
[0019] The output of the integrated surrogate model is superimposed with the residual correction value of the ridge regression residual model to obtain the corrected surrogate model.
[0020] Optionally, the soft failure weights of the candidate engineering parameter samples are calculated according to the following formula: in, Sample of candidate engineering parameters Soft failure weights, To correct the output of the surrogate model, For smoothing scale parameters, For e An exponential function with base 0.
[0021] Optionally, a hierarchical search is performed on the candidate engineering parameter samples based on soft failure weights to obtain a failure sample set, specifically including the following steps: Based on the corrected surrogate model, the soft failure weight of each candidate engineering parameter sample in the candidate engineering parameter sample set is calculated.
[0022] Based on the soft failure weights and the prediction uncertainty of the corrected surrogate model, the candidate engineering parameter sample set is divided into multiple regions; these regions include a highly suspicious region, a boundary tracking region, and a global exploration region.
[0023] Samples to be verified are selected from multiple regions according to a preset allocation ratio, and a high-fidelity evaluation is performed on the samples to be verified.
[0024] Add the samples to be checked that are marked as invalid by the high-fidelity evaluation results to the invalid sample set, and add all the samples to be checked that have undergone high-fidelity evaluation to the anchor sample set.
[0025] Incrementally update the corrected surrogate model, then proceed to step "Calculate the soft failure weight of each candidate engineering parameter sample in the candidate engineering parameter sample set based on the corrected surrogate model" until the preset stopping criterion is met.
[0026] Optionally, the failure samples in the failure sample set are clustered to identify multiple failure sample clusters corresponding to different failure modes of complex equipment components. A multi-scale hybrid proposal distribution is then constructed based on these multiple failure sample clusters, specifically including the following steps: Clustering operations are performed on the failure samples in the failure sample set to identify multiple failure sample clusters corresponding to different failure modes of complex equipment components.
[0027] For each cluster of failed samples, calculate its cluster center and standard deviation of each dimension, and construct locally compact and locally extended bounding regions.
[0028] Construct a global bounding domain that covers the entire parameter space.
[0029] Based on the locally compact bounding region, the locally extended bounding region, the global bounding region, and the prior distribution, defensive mixing is performed to obtain a multi-scale mixing proposal distribution.
[0030] Optionally, based on the multi-scale mixed proposal distribution, effective sample size-driven bridging sampling is performed to construct a series of bridging layers and aggregate the samples and normalized weights of all bridging layers to obtain an initial failure probability estimate. This specifically includes the following steps: Construct a series of bridging layers; each bridging layer corresponds to an intermediate distribution between the prior distribution and the target failure distribution.
[0031] For each bridging layer, bridging layer samples are drawn from the multi-scale mixed proposal distribution, and the importance weight of each bridging layer sample is calculated.
[0032] Calculate the effective sample size of the current bridging layer.
[0033] If the effective sample size is lower than the preset target threshold, the transition parameters of the current bridging layer are adjusted and the importance weights are recalculated until the effective sample size meets the preset target threshold.
[0034] If the effective sample size is equal to or higher than the preset target threshold, proceed to the next bridging layer and jump to the step "Calculate the effective sample size of the current bridging layer" until the bridging transition parameter reaches 1. Summarize the samples and normalized weights of all bridging layers and obtain the initial failure probability estimate by weighted averaging.
[0035] Optionally, inverse probability weighted unbiased correction is performed to conduct a high-fidelity verification of the samples obtained by bridging sampling, and the initial failure probability estimate is corrected based on the verification results to output the final failure probability of the complex equipment component to be analyzed. This specifically includes the following steps: Based on the samples obtained from bridging sampling, a high-fidelity comprehensive review score is constructed.
[0036] The sampling probability for each sample is determined based on the comprehensive score of the high-fidelity review.
[0037] Based on the review sampling probability, review samples are randomly selected from the samples obtained by bridging sampling, and high-fidelity evaluation is performed on the review samples.
[0038] Calculate the difference between the high-fidelity failure indication and the proxy failure indication for each verification sample.
[0039] By using inverse probability weighting, a correction term is calculated based on the difference and the verification sampling probability. The correction term is then added to the initial failure probability estimate to obtain the final failure probability estimate of the complex equipment component to be analyzed.
[0040] Optionally, the high-fidelity review score is constructed based on at least one of the following: false negative risk, boundary risk, and true positive risk; the false negative risk is shown in the following formula: Boundary risk is shown in the following formula: The risk of a true positive result is shown in the following formula: in, To mitigate the risk of false negatives, For border risks, The risk of a true positive result. For the sample Soft failure weights, To correct the output of the surrogate model, For indicator functions, To act as a proxy for forecasting uncertainty, The importance weights of the samples.
[0041] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a method for assessing the low failure probability of complex equipment components based on prior constraint integration and hierarchical correction sampling. The method first constructs an integrated surrogate model that incorporates multiple types of prior constraints based on the engineering parameters of the complex equipment component to be analyzed. Residual correction is then performed using anchor point samples obtained from high-fidelity simulations or physical experiments to obtain a corrected surrogate model, which significantly improves the approximation accuracy near the failure boundary under limited sample conditions. Next, soft failure weights are calculated based on the corrected surrogate model, and a hierarchical search is performed on candidate engineering parameter samples according to these weights to obtain a failure sample set. This prioritizes the exploration of the most likely failure regions under a limited high-fidelity budget, improving sample utilization efficiency. Finally, the samples in the failure sample set are clustered to identify multiple corresponding complex equipment components with different failures. The system first identifies failure sample clusters and constructs a multi-scale hybrid proposal distribution based on these clusters. This effectively covers disconnected, multimodal failure regions and reduces the risk of mismatch in a single proposal distribution. Then, based on this hybrid proposal distribution, effective sample size-driven bridging sampling is performed. A series of bridging layers are constructed, and the samples and normalized weights of all bridging layers are aggregated. An initial failure probability estimate is obtained by adaptively controlling the transition step size, ensuring the stability of the sampling process and the effectiveness of the estimate. Finally, inverse probability weighted unbiased correction is performed. The samples obtained from bridging sampling undergo high-fidelity verification prioritizing false negative risk. The initial failure probability estimate is corrected based on the verification results, and the final failure probability of the complex equipment component to be analyzed is output. This achieves unbiased correction of the initial estimate with minimal high-fidelity calls, improving the statistical reliability of the final evaluation results. Attached Figure Description
[0042] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0043] Figure 1 The flowchart illustrates a method for assessing low failure probability based on prior constraint integration and hierarchical correction sampling, as provided in an embodiment of this application.
[0044] Figure 2 This is a flowchart of step S1 in a low failure probability assessment method based on prior constraint integration and hierarchical correction sampling, provided as an embodiment of this application.
[0045] Figure 3 This is a flowchart of step S14 in a low failure probability assessment method based on prior constraint integration and hierarchical correction sampling, provided as an embodiment of this application.
[0046] Figure 4 This is a flowchart of step S2 in a low failure probability assessment method based on prior constraint integration and hierarchical correction sampling, provided as an embodiment of this application.
[0047] Figure 5 This is a flowchart of step S3 in a low failure probability assessment method based on prior constraint integration and hierarchical correction sampling, provided as an embodiment of this application.
[0048] Figure 6 This is a flowchart of step S4 in a low failure probability assessment method based on prior constraint integration and hierarchical correction sampling, provided as an embodiment of this application.
[0049] Figure 7 This is a flowchart of step S5 in a low failure probability assessment method based on prior constraint integration and hierarchical correction sampling, provided as an embodiment of this application. Detailed Implementation
[0050] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0051] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0052] This application provides a low failure probability assessment method based on prior constraint integration and hierarchical correction sampling, applied to the low failure probability assessment of complex equipment components. In an exemplary embodiment, such as... Figure 1 As shown, the method includes the following steps: S1. Based on the engineering parameters of the complex equipment components to be analyzed, an integrated proxy model that incorporates multiple prior constraints is constructed. The residual of the integrated proxy model is corrected using anchor point samples obtained from high-fidelity simulation or physical experiments to obtain the corrected proxy model. The engineering parameters include detonation impulse, yield strength, shear groove depth, assembly gap, and on-orbit temperature.
[0053] S2. Calculate the soft failure weights of candidate engineering parameter samples based on the corrected surrogate model, and perform a hierarchical search on the candidate engineering parameter samples according to the soft failure weights to obtain the failure sample set.
[0054] S3. Cluster the failure samples in the failure sample set to identify multiple failure sample clusters corresponding to different failure modes of complex equipment components, and construct a multi-scale hybrid proposal distribution based on multiple failure sample clusters.
[0055] S4. Based on the multi-scale mixed proposal distribution, perform effective sample size-driven bridging sampling, construct a series of bridging layers, and summarize the samples and normalized weights of all bridging layers to obtain the initial failure probability estimate; each bridging layer corresponds to an intermediate distribution between the prior distribution and the target failure distribution.
[0056] S5. Perform inverse probability weighted unbiased correction, perform high-fidelity verification on the samples obtained by bridging sampling, correct the initial failure probability estimate based on the verification results, and output the final failure probability of the complex equipment component to be analyzed.
[0057] In another exemplary embodiment of this application, the complex equipment component to be analyzed is a pyrotechnic separation nut of a certain type of spacecraft, and its on-orbit separation reliability is evaluated using a low failure probability assessment. This separation nut relies on the shock wave generated by the pyrotechnic detonation to drive the nut body to fracture along a pre-fabricated shear groove and eject axially, achieving compartment unlocking and separation. Its high-fidelity model is a multibody dynamics-finite element coupled simulation model (including the entire process of nut shear fracture and ejection motion), with a single call taking approximately 25 minutes. The high-fidelity budget upper limit is set to B=180 times. The failure criterion is that the axial ejection displacement d of the nut ≤ 3.0 mm (limit state function). , ( If the value is less than 0, the target is considered a failure (the probability of target failure is on the order of 10). -5 There are 5 random variables (d=5 dimensions), all of which follow an independent normal distribution. The main parameters are preset as follows: initial sample size n=30 (Latin hypercube sampling), candidate project parameter sample pool size N=100000, anchor point batch size 5 / round, bridging layer sample size Ns=2000 / layer, ESS target threshold 30% (i.e., 600), high-fidelity verification sample size m=50, and 3 basic proxies (Kriging, SVR, RBF).
[0058] like Figure 2 As shown, step S1 is achieved by the following steps S11 to S14: S11. Obtain an initial sample set based on the engineering parameters of the complex equipment component to be analyzed.
[0059] First, obtain n=30 initial samples (hereinafter referred to as...) Distinguish between sample serial numbers, ), denoted as Among them, subscript This only indicates the sample number. For random variable samples (5-dimensional input, detonation impulse) I Yield strength σ γ Shear groove depth h Assembly gap δ On-orbit temperatureT ), This corresponds to the limit state response (simulated pop-out displacement minus a threshold of 3.0 mm). In 30 simulations, There are 2 samples with a value <0 (i.e., failure), both distributed in the low impulse range ( I <1060 N·ms) and high strength ( σ γ The parameter combination range is >940MPa.
[0060] S12. Train multiple basic surrogate models using the initial sample set, and introduce three types of constraints during the training process: physical law priors, engineering experience priors, and mathematical property priors.
[0061] Three types of prior constraints are introduced during the training of the basic surrogate model: first, physical law priors, used to constrain the consistency between the surrogate response and the residuals of the governing equations or boundary conditions; second, engineering experience priors, used to constrain known monotonic relationships, trend relationships, or feasible region relationships; and third, mathematical property priors, used to limit the local oscillations and complexity of the response surface. In this embodiment, the physical law priors... The difference between the gradient of the constraint surrogate output in the impulse direction and the derived value of the momentum conservation equation (weight) =0.1); prior engineering experience Penalty for violating "through hinge loss" d Monotonically increasing I Monotonically decreasing σ γ "virtual samples (100 uniformly distributed, weighted)" =0.2); prior mathematical properties right h A secondary penalty (weight) is applied to regions where the local gradient exceeds the Lipschitz constant L = 8 mm / mm. =0.05). The training objective after comprehensive constraints can be written as: in, This is the sample fitting error term. These are a priori constraints on physical laws. These are prior constraints based on engineering experience. These are a priori constraints on mathematical properties. , and These are the corresponding weight coefficients; each basic proxy model is trained based on the comprehensive loss function.
[0062] The initial samples were divided into a training subset and a validation subset (24 training samples and 6 validation samples), and each basic proxy model ( For the Kriging model, For support vector regression models, The radial basis function model (RBF model) is trained on the training subset and then the prediction results are output on the validation subset. The RMSE values for the three basic surrogate validation sets are 0.22mm, 0.31mm, and 0.27mm, respectively.
[0063] S13. Solve for the combined weights of each basic proxy model using the non-negative least squares method to obtain the integrated proxy model. The integrated proxy model is shown in the following equation: in, For the first j The combined weights of the basic proxy models are obtained in this embodiment. , , After integration, RMSE = 0.19mm.
[0064] S14. Using anchor point samples obtained from high-fidelity simulation or physical experiments, residual correction is performed on the integrated surrogate model to obtain the corrected surrogate model. For example... Figure 3 As shown, this step specifically includes the following steps: S141. Obtain several high-fidelity anchor point samples through high-fidelity simulation or physical experiments, forming a high-fidelity anchor point sample set. From the initial sample set... Selecting anchor point sample set In this embodiment, we take All 30 samples were used as initial anchor points.
[0065] S142. Calculate the prediction residuals of each sample in the high-fidelity anchor sample set under the integrated surrogate model. Calculate the prediction residuals of the anchor samples under the integrated surrogate model according to the following formula: .
[0066] S143. The input features of the high-fidelity anchor point samples are mapped to a random feature space using random Fourier feature mapping. Combined with the corresponding prediction residuals, a ridge regression residual model is fitted and established. The ridge regression residual model is used to output the corresponding residual correction value based on the input features. The anchor point input... Through random Fourier feature mapping (D=200-dimensional, random frequencies are extracted from the spectral distribution corresponding to the RBF kernel, bandwidth...), γ =0.5) mapped to random feature space Establish a ridge regression residual model (regularization coefficient) λ =0.01, leave one for cross-validation to determine).
[0067] S144. The output of the ensemble surrogate model is superimposed with the residual correction value of the ridge regression residual model to obtain the corrected surrogate model. The corrected surrogate model is shown in the following equation: The mean absolute value of the residuals at the initial 30 anchor points was 0.19 mm, with a maximum residual of 0.42 mm near the boundary (in the region where |y| < 0.5 mm); after residual correction, With cross-validation at all anchor points, the RMSE decreased to 0.18 mm, and the local RMSE in the boundary region decreased to 0.11 mm.
[0068] like Figure 4 As shown, step S2 is achieved by the following steps S21 to S24: S21. Based on the corrected surrogate model, the soft failure weight of each candidate engineering parameter sample in the candidate engineering parameter sample set is calculated. First, from a 5-dimensional independent normal prior distribution... A candidate engineering parameter sample set with size N=100000 is generated using Monte Carlo sampling. The soft failure weight of the candidate engineering parameter sample is calculated according to the following formula: in, Sample of candidate engineering parameters Soft failure weights, To correct the output of the surrogate model, For smoothing scale parameters, For e An exponential function with base 0. In this embodiment, we take... =0.3mm, The larger the value, the closer the sample is to the failure domain. =1 corresponds to →-∞, =0.5 corresponds =0, =0.27 corresponds to =0.3mm).
[0069] S22. Based on the soft failure weight and the prediction uncertainty of the corrected surrogate model, the candidate engineering parameter sample set is divided into multiple regions; the multiple regions include the highly suspicious region, the boundary tracking region, and the global exploration region.
[0070] In this embodiment, the highly suspicious area is: (Right now A total of 4,872 candidates were identified, accounting for 4.9% of the candidate pool; boundary tracking area: and ( =0.27mm is the proxy prediction uncertainty), a total of 11,836, accounting for 11.8%; global exploration area: the remaining candidate engineering parameter samples, accounting for 83.3%.
[0071] S23. Select samples to be verified from multiple regions according to the preset allocation ratio, and perform high-fidelity evaluation on the samples to be verified. Allocation of each region in each round: 4 highly suspicious + 3 boundary tracking + 1 global exploration = 8 samples / round.
[0072] S24. Add the samples to be checked that are marked as failed by the high-fidelity evaluation results to the failed sample set, and add all the samples to be checked that have undergone high-fidelity evaluation to the anchor sample set. Incrementally update the corrected surrogate model, and jump to step S21 until the preset stopping criterion is met.
[0073] This embodiment performed 10 rounds of hierarchical search (8 simulations per round). The number of newly added failure samples in each round was 4, 6, 5, 5, 4, 6, 5, 5, 4, and 3, respectively, resulting in a total of 47 failure samples. A total of 80 high-fidelity calls were made (110 calls including the initial 30). The search ended after meeting the stopping criteria (no new failure clusters were found for 3 consecutive rounds, and the boundary prediction uncertainty decreased from 0.27 to 0.13 mm).
[0074] like Figure 5 As shown, step S3 is achieved by the following steps S31 to S34: S31. Perform clustering operations on the failure samples in the failure sample set to identify multiple failure sample clusters corresponding to different failure modes of complex equipment components.
[0075] This embodiment performs DBSCAN clustering on 47 failed samples. (MinPts=5, normalized space) Two spatially separated failure clusters were identified: Cluster 1 (31 samples, corresponding to the "low impulse + high intensity" region, center) Standard deviation Cluster 2 (16 samples, corresponding to the "low impulse + large gap + low temperature" region, center) Standard deviation ).
[0076] S32. For each cluster of failed samples, calculate its cluster center and standard deviation of each dimension, and construct a locally compact bounding domain and a locally extended bounding domain.
[0077] In this embodiment, Cover the core of the identified failure area. Coverage of the boundary neighborhood .
[0078] S33. Construct a global bounding domain covering the entire parameter space. .
[0079] S34. Based on the locally compact bounding region, the locally extended bounding region, the global bounding region, and the prior distribution, a defensive mixing is performed to obtain a multi-scale mixing proposal distribution.
[0080] In this embodiment, the prior distribution is used. Conduct defensive hybrid ( β =0.05), and the final hybrid proposal distribution is shown in the following equation: The sampling density of the full parameter space is guaranteed to be positive by using a hybrid proposal distribution.
[0081] like Figure 6 As shown, step S4 is achieved by the following steps S41 to S46: S41. Construct a series of bridging layers; each bridging layer corresponds to an intermediate distribution between the prior distribution and the target failure distribution.
[0082] S42. For each bridging layer, draw bridging layer samples from the multi-scale mixture proposal distribution and calculate the importance weight of each bridging layer sample. N=2000 bridging layer samples are extracted. Importance weights are calculated using the following formula: in, Let the importance weight of the i-th sample be , Let i be the soft failure weight for the i-th sample. Let be the prior distribution of the i-th sample. Let be the multi-scale mixture proposal distribution of the i-th sample, and α be the bridging transition parameter with an initial value of 0.
[0083] S43. Calculate the effective sample size of the current bridging layer according to the following formula: Determine whether the effective sample size is lower than the preset target threshold. If so, execute S44; if the effective sample size is equal to or higher than the preset target threshold, execute S45.
[0084] S44. Adjust the transition parameters of the current bridging layer and recalculate the importance weights until the effective sample size meets the preset target threshold. For example, if ESS ≥ 600 (preset target threshold = 30% × N), then reduce the weights using a binary search method if ESS < 600. And update Then return to step S42 to recalculate the weights.
[0085] S45. Proceed to the next bridging layer, jump to step S43, until the bridging transition parameters are reached. Once step 1 is reached, execute S46.
[0086] S46. Summarize all samples and normalized weights from all bridging layers, and obtain the initial failure probability estimate by weighted averaging. .
[0087] This embodiment involves a total of 8 transition layers ( The values were 0.04, 0.11, 0.22, 0.37, 0.54, 0.70, 0.87, and 1.00, respectively, with the ESS for each layer maintained between 660 and 890. After layers 2 through 7 were completed, three additional high-fidelity simulation incremental updates were added to each layer. (Total 18 times). A weighted average of 16,000 samples from 8 layers, along with normalized importance weights, was used to obtain the initial failure probability estimate. By the end of this phase, the cumulative number of high-fidelity calls was: initial 30 + search 80 + bridging increment 18 = 128.
[0088] like Figure 7 As shown, step S5 is achieved by the following steps S51 to S55: S51. Construct a high-fidelity comprehensive review score based on the samples obtained from bridging sampling. The high-fidelity comprehensive review score is constructed based on at least one of the following: false negative risk, boundary risk, and true positive risk; the false negative risk is shown in the following formula: Boundary risk is shown in the following formula: The risk of a true positive result is shown in the following formula: in, To mitigate the risk of false negatives, For border risks, The risk of a true positive result. For the sample Soft failure weights, To correct the output of the surrogate model, For indicator functions, To act as a proxy for forecasting uncertainty, The importance weights of the samples.
[0089] The comprehensive score is constructed as shown in the following formula: S52. Determine the review sampling probability for each sample based on the high-fidelity review comprehensive score. The review sampling probability is obtained after normalizing the comprehensive score. .
[0090] S53. Based on the review sampling probability, a review sample is randomly selected from the sample obtained by bridging sampling, and a high-fidelity evaluation is performed on the review sample. According to... From the pool of 16,000 samples obtained by bridging sampling in the previous stage, m=50 verification samples are extracted with replacement. High-fidelity simulation is called for each verification sample (this stage consumes 50 times, for a total of 178 times).
[0091] S54. Calculate the difference between the high-fidelity failure indication and the proxy failure indication for each verification sample. .
[0092] The high-fidelity failure indication is for a single verification sample. This is a binary state indication of whether the sample has failed, obtained through a true high-fidelity evaluation method. If the high-fidelity evaluation result meets the failure criteria, the high-fidelity failure indication is set to 1; otherwise, it is set to 0.
[0093] The aforementioned proxy failure indication is for a single review sample. Through the corrected proxy model The predicted binary state indicator indicates whether the sample has failed. If the surrogate model prediction meets the failure criterion, the surrogate failure indicator is set to 1; otherwise, the surrogate failure indicator is set to 0.
[0094] S55. By using inverse probability weighting, a correction term is calculated based on the difference and the verification sampling probability. This correction term is then added to the initial failure probability estimate to obtain the final failure probability estimate of the complex equipment component to be analyzed. The final failure probability estimate is calculated using the following formula: in, m To verify the number of samples.
[0095] In this embodiment, 47 out of 50 resampled samples were correctly identified by proxy, and 3 were false negatives; based on 500 bootstrap resampling runs (250 for bridging sampling and 250 for resampled samples), sampling fluctuations were observed. Correcting fluctuations 95% confidence interval With 10 7 Subdirect Monte Carlo simulation results (Standard error) Using [a specific method] as a benchmark, the relative error of the method in this application is 2.8%, and the benchmark value falls within the 95% confidence interval. The failure probability of cluster 1 contribution is approximately 2.1 × 10⁻⁶. -5 The probability of cluster 2 contributing to failure is approximately 1.2 × 10⁻⁶. -5 The low-impulse + high-strength combination (cluster 1) is the dominant failure mode; therefore, it is recommended to focus on controlling the initiation impulse during engineering projects. I lower deviation and yield strength σ γ The upper deviation.
[0096] Compared with the prior art, the method provided in the above embodiments of this application has the following beneficial effects: (1) Combining prior knowledge constraints, heterogeneous proxy integration and residual correction into the same modeling framework can improve the approximation accuracy near the failure boundary when the sample size is small.
[0097] (2) Improve the utilization efficiency of the limited high-fidelity budget for suspected failure areas and boundary areas by using a hierarchical search mechanism driven by soft failure weights.
[0098] (3) By clustering failed samples and constructing multi-scale enclosing domains, it is possible to better cover multimodal and disconnected failed regions and reduce the risk of single proposal distribution mismatch.
[0099] (4) By controlling the bridging step size with an effective sample size and combining it with inverse probability weighted unbiased correction, the statistical reliability of the final result can be improved while ensuring the stability of the estimation.
[0100] (5) The method flow of this embodiment is compatible with finite element simulation, dynamic simulation, experimental measurement or multi-source hybrid high-fidelity evaluation methods, which is convenient for deployment and application in the low failure probability assessment tasks of aerospace institutions, complex mechanical structures and high reliability components.
[0101] Based on the same inventive concept, this application also provides an apparatus for implementing the aforementioned method for assessing low failure probability based on prior constraint integration and hierarchical correction sampling. The solution provided by this apparatus is similar to the implementation described in the above method, and will not be repeated here.
[0102] 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.
[0103] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for assessing low failure probability based on prior constraint integration and hierarchical correction sampling, characterized in that, The method, applied to the assessment of low failure probability of complex equipment components, includes: Based on the engineering parameters of the complex equipment components to be analyzed, an integrated proxy model that incorporates multiple types of prior constraints is constructed. The residual of the integrated proxy model is then corrected using anchor point samples obtained from high-fidelity simulation or physical experiments to obtain the corrected proxy model. The engineering parameters include detonation impulse, yield strength, shear groove depth, assembly gap, and on-orbit temperature. The soft failure weights of the candidate engineering parameter samples are calculated based on the corrected surrogate model, and a hierarchical search is performed on the candidate engineering parameter samples according to the soft failure weights to obtain a failure sample set. Cluster the failure samples in the failure sample set to identify multiple failure sample clusters corresponding to different failure modes of complex equipment components, and construct a multi-scale hybrid proposal distribution based on the multiple failure sample clusters. Based on the multi-scale hybrid proposal distribution, effective sample size-driven bridging sampling is performed to construct a series of bridging layers and summarize the samples and normalized weights of all bridging layers to obtain an initial failure probability estimate; each bridging layer corresponds to an intermediate distribution between the prior distribution and the target failure distribution; Perform inverse probability weighted unbiased correction, perform high-fidelity verification on the samples obtained by bridging sampling, and correct the initial failure probability estimate based on the verification results, and output the final failure probability of the complex equipment component to be analyzed.
2. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 1, characterized in that, Based on the engineering parameters of the complex equipment components to be analyzed, an integrated proxy model incorporating multiple types of prior constraints is constructed, specifically including: Based on the engineering parameters of the complex equipment component to be analyzed, an initial sample set is obtained; Multiple basic surrogate models are trained using the initial sample set, and three types of constraints are introduced during the training process: prior physical laws, prior engineering experience, and prior mathematical properties. The combined weights of each basic proxy model are solved by non-negative least squares method to obtain the integrated proxy model.
3. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 2, characterized in that, During training, a comprehensive loss function is constructed as shown in the following equation: in, This is the sample fitting error term. These are a priori constraints on physical laws. These are prior constraints based on engineering experience. These are a priori constraints on mathematical properties. , and These are the corresponding weight coefficients; each basic proxy model is trained based on the comprehensive loss function.
4. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 1, characterized in that, The integrated surrogate model is subjected to residual correction using anchor point samples obtained from high-fidelity simulation or physical experiments to obtain a corrected surrogate model, specifically including: Several high-fidelity anchor point samples are obtained through high-fidelity simulation or physical experiments, forming a high-fidelity anchor point sample set; Calculate the prediction residuals of each sample in the high-fidelity anchor sample set under the integrated proxy model; The input features of high-fidelity anchor samples are mapped to a random feature space through random Fourier feature mapping. Combined with the corresponding prediction residuals, a ridge regression residual model is fitted and established. The ridge regression residual model is used to output the corresponding residual correction value according to the input features. The output of the integrated surrogate model is superimposed with the residual correction value output by the ridge regression residual model to obtain the corrected surrogate model.
5. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 1, characterized in that, The soft failure weights of the candidate engineering parameter samples are calculated using the following formula: in, Sample of candidate engineering parameters Soft failure weights, To correct the output of the surrogate model, For smoothing scale parameters, For e An exponential function with base 0.
6. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 1, characterized in that, Based on the soft failure weights, a hierarchical search is performed on the candidate engineering parameter samples to obtain a failure sample set, specifically including: Based on the corrected proxy model, the soft failure weight of each candidate engineering parameter sample in the candidate engineering parameter sample set is calculated; Based on the soft failure weights and the prediction uncertainty of the corrected surrogate model, the candidate engineering parameter sample set is divided into multiple regions; the multiple regions include a highly suspicious region, a boundary tracking region, and a global exploration region; Samples to be verified are selected from the multiple regions according to a preset allocation ratio, and high-fidelity evaluation is performed on the samples to be verified. Add the samples to be checked that are indicated as invalid by the high-fidelity evaluation results to the invalid sample set, and add all the samples to be checked that have undergone high-fidelity evaluation to the anchor sample set; The incrementally updated and corrected proxy model is then used to proceed to the step "Calculate the soft failure weight of each candidate engineering parameter sample in the candidate engineering parameter sample set based on the corrected proxy model" until the preset stopping criterion is met.
7. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 1, characterized in that, Clustering is performed on the failure samples in the failure sample set to identify multiple failure sample clusters corresponding to different failure modes of complex equipment components. Based on these multiple failure sample clusters, a multi-scale hybrid proposal distribution is constructed, specifically including: Clustering operations are performed on the failure samples in the failure sample set to identify multiple failure sample clusters corresponding to different failure modes of complex equipment components; For each cluster of failed samples, calculate its cluster center and standard deviation of each dimension, and construct locally compact and locally extended bounding regions. Construct a global bounding domain that covers the entire parameter space; Based on the locally compact bounding region, the locally extended bounding region, the global bounding region, and the prior distribution, defensive mixing is performed to obtain a multi-scale mixing proposal distribution.
8. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 1, characterized in that, Based on the multi-scale hybrid proposal distribution, effective sample size-driven bridging sampling is performed to construct a series of bridging layers and aggregate the samples and normalized weights of all bridging layers to obtain an initial failure probability estimate, specifically including: Construct a series of bridging layers; each bridging layer corresponds to an intermediate distribution between the prior distribution and the target failure distribution; For each bridging layer, bridging layer samples are drawn from the multi-scale mixed proposal distribution, and the importance weight of each bridging layer sample is calculated. Calculate the effective sample size of the current bridging layer; If the effective sample size is lower than the preset target threshold, the transition parameters of the current bridging layer are adjusted and the importance weights are recalculated until the effective sample size meets the preset target threshold. If the effective sample size is equal to or higher than the preset target threshold, proceed to the next bridging layer and jump to the step "Calculate the effective sample size of the current bridging layer" until the bridging transition parameter reaches 1. Summarize the samples and normalized weights of all bridging layers and obtain the initial failure probability estimate by weighted averaging.
9. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 1, characterized in that, Perform inverse probability weighted unbiased correction, perform high-fidelity verification on the samples obtained from bridging sampling, and correct the initial failure probability estimate based on the verification results. Output the final failure probability of the complex equipment component to be analyzed, specifically including: Based on the samples obtained from the bridging sampling, a high-fidelity comprehensive review score is constructed. The sampling probability for each sample is determined based on the high-fidelity review comprehensive score. Based on the aforementioned verification sampling probability, verification samples are randomly selected from the samples obtained by bridging sampling, and high-fidelity evaluation is performed on the verification samples. Calculate the difference between the high-fidelity failure indication and the proxy failure indication for each verification sample; By using inverse probability weighting, a correction term is calculated based on the difference and the verification sampling probability, and the correction term is added to the initial failure probability estimate to obtain the final failure probability estimate of the complex equipment component to be analyzed.
10. The method for assessing small failure probabilities based on prior constraint integration and hierarchical correction sampling according to claim 9, characterized in that, The high-fidelity review comprehensive score is constructed based on at least one of false negative risk, boundary risk, and true positive risk; the false negative risk is shown in the following formula: The boundary risk is shown in the following formula: The true positive risk is shown in the following formula: in, To mitigate the risk of false negatives, For border risks, The risk of a true positive result. For the sample Soft failure weights, To correct the output of the surrogate model, For indicator functions, To act as a proxy for forecasting uncertainty, The importance weights of the samples.