The applications of an importance sampling method to reliability analysis of the inside flap of an aircraft

Abstract

Based on the cross-entropy method and modified Metropolis–Hastings algorithm, an efficient importance sampling method is proposed to perform reliability analysis for the inside flap of an aircraft. In the proposed method, the cross-entropy method is utilized to estimate the optimal importance sampling probability density function. The derivation shows that the distribution parameters of the optimal importance sampling probability density function can be estimated by the failure sample points generated according to the original probability density function. The crude Monte Carlo method can be employed to simulate the failure sample points but its computational cost is prohibitive. In order to circumvent the difficulties, the modified Metropolis–Hasting algorithm is employed to generate failure sample points distributed as the original probability density function. After the distribution parameters of the optimal importance sampling probability density function have been obtained, the importance sampling probability density function can be constructed, then the proposed importance sampling method combined with the quasi-Monte Carlo simulation can be utilized to perform the reliability analysis. Meanwhile, the confidence interval and its length for the results have also been derived. Various numerical examples demonstrate the efficiency and accuracy of the presented importance sampling method. Finally, the reliability analysis and sensitivity analysis of an inside flap are solved by the proposed importance sampling method.

A surrogate‐based iterative importance sampling method for structural reliability analysis

“…This false classification may lead to the following outlier case that a safe point may be served as the estimation of the MPP ( l ) . To avoid such a case, we can employ the Markov Chain Monte Carlo (MCMC) to generate the failure points, in which we have to evaluate the real LSF, and it may be time consuming. In addition, the MCMC has 2 issues .…”

“…To avoid such a case, we can employ the Markov Chain Monte Carlo (MCMC) to generate the failure points, in which we have to evaluate the real LSF, and it may be time consuming. In addition, the MCMC has 2 issues . The first is how to determine the “burn‐in” period (the time reaching the equilibration), and the second is how to determine the length of the step due to the fact that the length is vital to the convergence of the MCMC, and these 2 issues may be deteriorated when dealing with the high‐dimensional LSF and the highly nonlinear LSF, which are common in practical engineering .…”

“…It is evident that the accuracy of the MCMC is vital to these methods in other works . The MCMC has to meet with 2 issues . The first is how to determine the “burn‐in” period (the time reaching the equilibration) of the MCMC, and the “burn‐in” period may be very long for the high‐dimensional problems and highly nonlinear problems, which may be very time consuming.…”

“…It is important to select a reasonable IS PDF h(x) for Equations (5) and (6), which will affect the computational efficiency and the computational burden of the IS method (Tang et al 6 ). A good choice of h(x) can considerably improve the computational efficiency and reduce the computational burden, and vice versa.…”

“…Structural reliability analysis has been extensively studied, and various methods have been proposed to estimate failure probability (FP) for complex structures, including the Advanced First Order Second Moment (AFOSM) (Hasofer and Lind), the moment method (Zhao and Ono), the second order reliability method (Hohenbichler and Rackwitz), the Monte Carlo simulation (MCS) (Liu), the importance sampling (IS) (Melchers, Tang et al, Dai et al, and Papaioannou et al), the subset simulation (Au and Beck and Li and Au), the line sampling (LS) (Schuëller et al and Depina et al), the directional sampling (Jinsuo and Ellingwood), the response surface method (RSM) (Rajashekhar and Ellingwood and Zhou et al), the dimension reduction (Xu and Rahman, Rahman and Wei, Wei and Rahman, and Li and Ma), the polynomial chaos expansion (Sudret and Der Kiureghian and Berveiller), the eigenvector dimension reduction (Byeng et al), the asymptotic sampling (Bucher, Tang et al, and Tang et al), the hierarchical clustering (Yin and Ahsan Kareem), and many other techniques. These methods have considerably promoted the state‐of‐the‐art in the structural reliability analysis.…”