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The aircraft Structure Health Monitoring System (SHMS) is an important system for the old age or future aircrafts. The main components of this system includes many new and advanced sensors like fiber optic sensor etc. in the principal structure elements of aircraft structures, and the data processing module which needs to collect and demodulate the massive data, and the data analysis and storage which can be used to predict the structure’s life and evaluate the health status of the whole aircraft.

Importance analysis is aimed at finding the contributions of the inputs to the output uncertainty. For structural models involving correlated input variables, the variance contribution by an individual input variable is decomposed into correlated contribution and uncorrelated contribution in this study. Based on point estimate, this work proposes a new algorithm to conduct variance based importance analysis for correlated input variables. Transformation of the input variables from correlation space to independence space and the computation of conditional distribution in the process ensure that the correlation information is inherited correctly. Different point estimate methods can be employed in the proposed algorithm, thus the algorithm is adaptable and evolvable. Meanwhile, the proposed algorithm is also applicable to uncertainty systems with multiple modes. The proposed algorithm avoids the sampling procedure, which usually consumes a heavy computational cost. Results of several examples in this work have proven the proposed algorithm can be used as an effective tool to deal with uncertainty analysis involving correlated inputs.

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.