CN-121766163-B - Aviation structure system minimum failure probability high-efficiency high-precision prediction method based on index punishment learning mechanism

CN121766163BCN 121766163 BCN121766163 BCN 121766163BCN-121766163-B

Abstract

The invention provides an index punishment learning mechanism-based aviation structure system minimum failure probability high-efficiency high-precision prediction method, and relates to the technical field of structure reliability analysis. Generating initial samples and candidate samples according to probability density functions of random variables of a function to be analyzed, calculating real function responses of the corresponding initial samples to form an initial training sample set, constructing an initial Kriging proxy model, selecting optimal sample points from the candidate sample set through the proposed EPAL functions, combining the optimal samples and the real responses thereof into the initial training sample set, iteratively updating the Kriging model until an error-based stopping criterion is met, judging whether a failure probability variation coefficient meets the requirement, and finally calculating the failure probability of the structure based on the trained Kriging model and a Monte Carlo method.

Inventors

ZHANG XUFANG
HUANG JINPENG
WANG YI
LIU HAINIAN
ZHAO BINGFENG
LI HE
WANG YONGFU
LV HAO
WANG JIAN

Assignees

东北大学
中国航发沈阳发动机研究所

Dates

Publication Date: 20260508
Application Date: 20260305

Claims (7)

1. An efficient high-precision prediction method for minimum failure probability of an aviation structure system based on an index punishment learning mechanism is characterized by comprising the following steps: step S1, acquiring a probability density function of a random input variable according to a function corresponding to a mechanical mechanism to be analyzed, extracting an alternative sample set for the random input variable by adopting a Monte Carlo simulation method, and extracting an initial sample set by adopting a Latin hypercube sampling method, wherein the input variable is a random field parameter of the elastic modulus of a material in the cross section of a turbine disk; S2, constructing an initial training sample set based on the initial sample set and a corresponding real response value, and constructing an initial Kriging proxy model about a limit state function to be analyzed; s3, calculating the prediction mean and variance of candidate sample points in all candidate sample sets according to the current Kriging model, substituting the prediction mean and variance into EPAL learning functions based on index penalty, selecting the sample point with the maximum EPAL value and calculating the real response value; the EPAL learning function based on the exponential penalty is as follows: ; Wherein, the For the mean value predicted by the Kriging proxy model, Standard deviation predicted for Kriging proxy model; step S4, based on the current Kriging agent model, and combining a bootstrap resampling method to evaluate the maximum relative error of the current failure probability When the maximum relative error is less than or equal to the preset error threshold value If not, combining the new sample point and its response value into the initial training sample set, updating the prediction accuracy of Kriging agent model, repeating steps S3-S4 until the maximum relative error is less than or equal to the preset error threshold value ; S5, calculating predicted failure probability and variation coefficient of the predicted failure probability based on the current Kriging agent model and the MCS sample; Step S6, judging whether the algorithm stopping condition is met or not, if the predicted variation coefficient of the failure probability is And if the number of the samples is larger than 0.05, the steps S1-S5 are needed to be re-executed again by increasing the number of the candidate samples, otherwise, the accuracy of the predicted failure probability is considered to meet the requirement, and the failure probability is output.
2. The method for predicting the minimum failure probability of the aviation structure system with high efficiency and high precision based on the exponential penalty learning mechanism according to claim 1, wherein the step S2 is specifically that an initial Kriging proxy model is built according to an initial sample data set obtained by Latin hypercube, and the mean value and variance of the Kriging proxy model prediction are obtained, and the calculation formula is as follows: ; Wherein, the , For the mean value predicted by the Kriging proxy model, The variance predicted for the Kriging proxy model, Is a polynomial regression model of the type, Is the basis function of the Kriging proxy model, The subscript of x denotes the index of the sample vector, n denotes the total number of training samples, As the coefficient of regression of the coefficient of the data, Is a regression coefficient Is a generalized least squares estimate of (1), For the random process variance of the Kriging proxy model, In order to input the variable(s), For inputting variables The corresponding response of the real performance function, To train sample rooms I and j represent the ith and jth samples, respectively, To predict the correlation matrix formed between the samples and the existing training samples, For the relevant model parameters, the superscript T of the parameter represents the transpose of the corresponding matrix, and the superscript-1 represents the inverse of the corresponding matrix.
3. The method for efficiently predicting the minimum failure probability of an aeronautical structure system based on an exponential penalty learning mechanism according to claim 2, wherein the maximum relative error of the failure probability in step S4 is as follows: ; Wherein, the Is a preset threshold value of the error, To predict the number of failure samples according to the current Kriging proxy model, An upper confidence bound representing the number of samples in a true failure region misclassified as a safe region, Confidence upper bound representing the number of samples in the true safe region misclassified as dead region, based on the probability of sample predicted symbol misclassification and bootstrap resampling method And Upper bound of confidence interval of the current failure probability is obtained And is matched with a preset error threshold value And comparing and judging.
4. The method for predicting the minimum failure probability of an aeronautical structure system with high efficiency and high precision based on an exponential penalty learning mechanism according to claim 3, wherein the failure probability calculated based on the current Kriging proxy model and the MCS sample in step S5 is: ; Wherein, the For the final predicted failure probability, N MCS is the number of MCS samples, As an indication function, when predicting the mean When the ratio is not less than 0, the ratio, Otherwise ; The calculation formula of the variation coefficient is as follows: ; Wherein, the For the final predicted probability of failure, The coefficient of variation of the predicted failure probability, N MCS , is the number of MCS samples.
5. An electronic device comprising one or more processors and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform a method of high-efficiency and high-precision prediction of the minimum probability of failure of an aero-structure system based on an exponential penalty learning mechanism as claimed in any one of claims 1-4.
6. A computer readable storage medium storing executable instructions which when executed cause a processor to perform a method of high efficiency and high accuracy prediction of the minimum probability of failure of an aeronautical structure system based on an exponential penalty learning mechanism as claimed in any one of claims 1 to 4.
7. A computer program product comprising a computer program or instructions which, when executed by a processor, implements a method for efficient and high-precision prediction of the minimum failure probability of an aeronautical structure system based on an exponential penalty learning mechanism as claimed in any one of claims 1 to 4.

Description

Aviation structure system minimum failure probability high-efficiency high-precision prediction method based on index punishment learning mechanism Technical Field The invention relates to the technical field of structural reliability analysis, in particular to an efficient and high-precision prediction method for the minimum failure probability of an aviation structural system based on an index punishment learning mechanism. Background The structural reliability analysis aims at evaluating the failure probability of the engineering structure under the influence of uncertainty factors such as material properties, external loads and the like, and is a key link for guaranteeing engineering safety and economy. In the field of high-end equipment such as aviation, aerospace and the like, the requirements on the reliability of parts are extremely severe, and the analyzed failure probability often belongs to the category of extremely small failure probability (usually less than 10 -4 orders of magnitude). While conventional numerical modeling methods such as the Monte Carlo Simulation (MCS) method have wide applicability, when dealing with the problem of very small failure probability, the required sample size typically needs to be on the order of 10 (k+2) (where k is on the order of failure probability), resulting in the need to invoke a large number of finite element models, which are expensive to compute, and the computational cost is prohibitive. While improved sampling methods such as importance sampling and subset modeling can improve efficiency to some extent, engineering computation costs remain challenging to achieve acceptable estimation accuracy. Approximation methods such as first and second order reliability methods (FORM/SORM) are computationally efficient, but often suffer from inadequate approximation accuracy when dealing with highly nonlinear or complex problems with multiple most likely points, and are difficult to meet the engineering requirements of high reliability assessment. The reliability analysis method based on the agent model approximates complex real limit state functions by constructing a mathematical model with high calculation efficiency, can greatly reduce the reliability analysis cost, and becomes an effective means for solving the engineering problem of high calculation cost. In various proxy models, a Kriging (Kriging) model can provide a predicted value of an unknown point and uncertainty measurement thereof, so that the Kriging (Kriging) model is easy to combine with an active learning framework, and self-adaptive sampling driven by a historical sample is realized, so that a core of an active learning Kriging (AL-Kriging) method in structural reliability analysis is formed. The typical AL-Kriging analysis framework mainly relies on three interrelated technical links, namely a sampling mechanism, an active learning function and a stopping criterion. However, the adaptability of the existing method to the problem of extremely small failure probability in the links still has obvious optimization space, and the calculation efficiency and the numerical robustness of the existing method in the high-reliability analysis of key components such as the aero-engine blade, the turbine disc and the like are restricted. In the aspect of sampling mechanism, in order to alleviate the aggregation of training samples in local areas and promote the effective exploration of training samples in an input space, a constraint based on distance or a sample rejection strategy is often required to be introduced. The introduction of such external rules often brings additional empirical parameters, reducing the adaptivity and versatility of the method. In the aspect of active learning functions of cores, although various functions such as U, H, EFF, REIF and the like are proposed, the defects of sample aggregation and the need of external subjective parameter modulation are easy to occur when the problem of small failure probability is solved. In summary, in the face of the requirements of the aviation field on high reliability and long service life, which are provided for a key structural system, there is an urgent need to develop a novel active learning function, which can adaptively balance global exploration and local utilization, effectively avoid sample clustering without relying on external parameters, and realize efficient and uniform sampling, so as to construct a more accurate, efficient and robust structural reliability analysis framework, thereby meeting the high-efficiency and high-precision analysis requirements of research and development of high-end equipment in the modern aviation field on extremely small failure probability. Disclosure of Invention Aiming at the defects of the prior art, the invention provides an efficient and high-precision prediction method for the minimum failure probability of an aviation structure system based on an index punishment learning mechanism, which aims t