Abstract
Structural reliability analysis is the key approach to assess uncertainties so that to increase the safety of engineering structures. Quantifying the failure probability (FP) is central to direct the result of the reliability assessment. In aerospace and military fields, normal samples collected from a structure are easily available, however, failure samples are extremely limited. Such imbalanced samples circumstance may lead to a large approximate bias of the failure probability. The critical problem in structural reliability analysis is how to use a smaller number of samples to get more precise failure probabilities. Although the Monte Carlo simulation (MCS) is the recognized benchmark, the high computational cost of calling limit state function has forced people to seek alternative ways. On the other hand, the surrogate model method, such as the adaptive Kriging model (abbreviated as AK-MCS), has been proposed to reduce the computational burden. To evaluate small failure probability, however, the number of the candidate points must be large for a convergent solution. To this end, this paper constructs a security domain identified model (SDIM) based on the one-class support vector machine (SVM) and imbalanced data. Different types of misjudged samples and approximate errors of the trained SDIM are analyzed. Two schemes are proposed accordingly to reduce the tested estimate error of the failure probability. Comparing with MCS and AK-MCS, the numerical and engineering examples demonstrate the accuracy and efficiency of the proposed method under different scenarios.
Highlights
Structural reliability analysis is the key approach to assess uncertainties for engineering structures or robotics systems, including the inherent randomness caused by structural systems and dynamic loads [1]–[5]
G(x)≤0 where Pf represents the failure probability (FP), Pr {·} is the probability, (x1, x2, . . . xn) are basic random variables, g(x) means the limit state function (LSF) of structural response, which implies if g(x) ≤ 0 the structure failed; if g(x) = 0 the structure achieves limit state, and f (x) is the joint probability density function (PDF) of variables (x1, x2, . . . xn)
PROPOSED SCHEME FOR APPROXIMATE FP 1) SCHEME ONE Since the security domain identified model (SDIM) has been established based on one-class support vector machine (SVM) with the training samples, the FP can be approximated through the proposed flowchart as shown in fig
Summary
Structural reliability analysis is the key approach to assess uncertainties for engineering structures or robotics systems, including the inherent randomness caused by structural systems and dynamic loads [1]–[5]. When there is one or a few very distant samples included in the samples training set, a large sphere will be usually obtained, so that the distribution of samples can not be well described In this regard, slack variables ξi is introduced to allow some distant samples outside the sphere, as is shown in the following in Figure 1: FIGURE 1. In order to balance the volume of the sphere and the number of target samples, penalty parameter C is introduced to get the objective function of the optimized sphere, which is given as follows:. THE PROPOSED SCHEME OF REDUCING THE APPROXIMATE PF ERRORS the SDIM from the training samples based on SVM will be introduced first.
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