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

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.