CN-122021236-A - Complex system performance simulation boundary verification method based on probability inverse test

CN122021236ACN 122021236 ACN122021236 ACN 122021236ACN-122021236-A

Abstract

A complex system performance simulation boundary verification method based on probability inverse test mainly comprises the steps of preparing a complex system boundary performance simulation model, determining a complex system performance boundary index to be verified, obtaining complex system performance simulation data set distribution and prior data sets, constructing a boundary sensitive weighted likelihood function, executing improved subset simulation and importance sampling, namely taking an elite sample as a center, carrying out importance sampling expansion to obtain a posterior sample set, and reducing uncertainty and verifying boundary performance. According to the method, by introducing the importance sampling of boundary sensitivity, the traditional subset simulation is improved, limited real observation data is introduced into the inference process, and high-efficiency and high-confidence verification of the failure boundary with small probability can be realized.

Inventors

WU ZHAOCHONG
ZHANG XIAOJUN
XU HONGWU
CAI JIANPING
ZHU WEI
ZHANG YANRU
ZHANG JINCHAO
WANG WEI
CHEN SIQI
ZHOU JIANWEI
ZHANG RUI
LIU YANRONG

Assignees

中国航天标准化研究所

Dates

Publication Date: 20260512
Application Date: 20251209

Claims (8)

1. The complex system performance simulation boundary verification method based on the probability inverse test is characterized by comprising the following steps of: s1, preparing a complex system boundary performance simulation model, and determining a complex system performance boundary index to be verified; S2, acquiring the distribution of the complex system performance simulation data set; s3, acquiring a priori data set of a complex system performance model; S4, constructing a weighted likelihood function sensitive to the boundary, namely, the closer to the real observation data of the target boundary, the larger the weight in the likelihood function; S5, performing improved subset simulation and importance sampling, namely taking an elite sample as a center, and performing importance sampling expansion to obtain a posterior sample set; S6, uncertainty reduction and boundary performance verification.
2. The method according to claim 1, wherein the step S1 comprises: constructing a boundary performance simulation model of the complex system, defining input parameters and output data of the model, and determining the boundary indexes of the performance of the complex system to be verified 。
3. The method according to claim 2, wherein the step S2 comprises: Determining an input parameter vector theta and prior distribution pi (theta) of a simulation model; And (3) running a simulation model to obtain performance output f (theta) under different theta, and constructing an initial simulation data set.
4. A method according to claim 3, wherein said step S3 comprises: preparing a finite set of real boundary observations 。
5. The method according to claim 4, wherein the step S4 specifically includes: a weighted likelihood function of the form: Wherein the weight is The risk level at the observation point is determined by: Wherein K is a boundary sensitive factor, and T is a bandwidth parameter.
6. The method according to claim 5, wherein the step S5 specifically includes: S51, setting an initial threshold gamma_1, and extracting N samples from prior distribution pi (theta); s52, for the first layer: Calculating the performance value f (theta) and the weighted likelihood value L (theta) of all samples; Determining a threshold value gamma_l+1 of the next layer according to the performance value sequence, so that the sample proportion of the performance value which is superior to gamma_l+1 is p_0; screening an elite sample with a performance value superior to gamma_ { l+1 }; s53, taking each elite sample' theta_ elite as a center, extracting a plurality of new samples from a proposal distribution, wherein the weights of the new samples are as follows: ; In the formula, Representing elite likelihood function, which refers to likelihood value corresponding to one elite sample theta_ elite in the L layer; Representing a new candidate likelihood function value, in the importance sampling, taking θ_ elite as a center, and a likelihood value corresponding to a candidate sample θ_new which is newly proposed; S54, expert sample screening: Carrying out industry expert screening on the resampled sample to ensure that the resampled sample has no abnormal data; And S55, repeating the steps S52 and S53 until the defined final failure domain is reached, and outputting all samples falling in the failure domain and likelihood values thereof to form a posterior sample set S_post.
7. The method according to claim 6, wherein in the step S53, the proposed distribution uses a gaussian distribution N (θ_ elite, Σ).
8. The method according to claim 6 or 7, wherein the step S6 specifically comprises: Calculating key statistics of posterior distribution; Calculating uncertainty reduction URA to quantify cognitive gain brought by the verification process: In the formula, A trace representing an a priori covariance matrix that quantifies the total uncertainty in cognition of all simulation model parameters prior to fusing new observation data; The sum of all diagonal elements of a matrix, in the context of multidimensional Gaussian distribution, the trace is related to the total variance or the widening degree of the distribution ellipsoids, and the larger the trace is, the wider the range of possible values of the whole parameter is represented; a trace representing a posterior covariance matrix that quantifies the total uncertainty of the parameters remaining after fusion of the finite real observations; The closer the URA is to 1, the more uncertainty in the parameters is eliminated, and the higher the confidence of the validation conclusion is; Using the posterior samples, a breakthrough probability p_fail of the performance boundary y_lim and a confidence interval thereof are calculated, wherein p_fail=p (f (θ) < y_lim).

Description

Complex system performance simulation boundary verification method based on probability inverse test Technical Field The invention relates to the technical field of digital tests and performance simulation researches of complex systems, in particular to a complex system performance simulation boundary verification method based on probability inverse test. Background The performance simulation is widely applied to the fields of boundary performance design, aeronautical pneumatic design, engineering optimization design and the like of the complex system, but the problem of reliability of boundary performance simulation of the complex system is always a key problem for restricting the application of digital tests and performance simulation. If the simulation is simply relied on, risk may be underestimated, and if only real data is used, the result is unstable due to sample scarcity. The method mainly comprises the steps of limiting accurate and usable reasons of performance simulation under boundary and limit conditions, namely firstly, extremely difficult acquisition of actual measurement data of boundary performance data scarcity (such as an aircraft stall boundary and an engineering structure failure critical point), wherein simulation errors of a large number of complex systems in a boundary area are obviously higher than those in a normal working area, secondly, high-dimensional parameter space influence is achieved, a complex system simulation model relates to tens to hundreds of parameters (such as aerodynamic parameters, material properties and environmental variables) which are mutually influenced, the traditional Monte Carlo method faces a dimension disaster when verifying boundary performance, and thirdly, performance boundary verification evaluation risks are caused by parameter uncertainty, probability propagation effects of model errors and boundary condition errors. When the existing Bayesian updating method solves the problem, standard Markov Chain Monte Carlo (MCMC) sampling is generally directly used, the sampling efficiency in a high-dimensional parameter space and a small probability failure domain is extremely low, and the calculation cost is not bearable. While the subset simulation (Subset Simulation) method can estimate the small probability event efficiently, the traditional form does not fully consider how to be fused with the limited, multi-source real observation data depth, so as to systematically correct the deviation of the simulation model in the boundary area. Therefore, there is an urgent need for a high-efficiency probability inversion framework that can integrate simulation and measured data and optimize against the boundary verification problem. Disclosure of Invention Aiming at the problems that the existing complex system simulation modeling method lacks of boundary physical object and measured data correction and causes boundary area simulation errors to be obviously higher than a normal working interval when boundary performance simulation analysis or simulation is carried out under extreme boundary conditions, the present disclosure provides a complex system performance simulation boundary verification method based on probability inverse test, and the method builds an efficient probability inversion framework for optimizing the boundary verification problem, which has the core that: A double-layer updating framework of 'simulation-data' collaboration is constructed, the traditional subset simulation is improved by introducing boundary-sensitive importance sampling, and limited real observation data is introduced into an inference process, so that high-efficiency and high-confidence verification of a small-probability failure boundary is realized. The method mainly comprises the following steps: s1, preparing a complex system boundary performance simulation model, and determining a complex system performance boundary index to be verified; s2, determining the distribution of the complex system performance simulation data set; s3, determining a priori data set of a complex system performance model; S4, constructing a weighted likelihood function sensitive to the boundary, namely, the closer to the real observation data of the target boundary, the larger the weight in the likelihood function; S5, performing improved subset simulation and importance sampling, namely taking an elite sample as a center, and performing importance sampling expansion to obtain a posterior sample set; S6, uncertainty reduction and boundary performance verification. The step S1 includes: constructing a boundary performance simulation model of the complex system, defining input parameters and output data of the model, and determining the boundary indexes of the performance of the complex system to be verified 。 Further, the step S2 includes: Determining an input parameter vector theta and prior distribution pi (theta) of a simulation model; And (3) running a simulation model to obtain performance o