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This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis with hybrid variables, that is, random and interval variables. This method can significantly improve the computational efficiency for the abovementioned hybrid reliability analysis (HRA), while generally providing sufficient precision. In the proposed procedure, the hybrid problem is reduced to standard reliability problem with the polar coordinates, where an n-dimensional limit-state function is defined only in terms of two random variables. Firstly, the linear Taylor series is used to approximate the limit-state function around the design point. Subsequently, with the approximation of the n-dimensional limit-state function, the new bidimensional limit state is established by the polar coordinate transformation. And the probability density functions (PDFs) of the two variables can be obtained by the PDFs of random variables and bounds of interval variables. Then, the interval of failure probability is efficiently calculated by the integral method. At last, one simple problem with explicit expressions and one engineering application of spacecraft docking lock are employed to demonstrate the effectiveness of the proposed methods.

In this presented work, a reliability sensitivity analyzing method was proposed for the resonance failures of gear-rotor systems with multiple random parameters. First, eigenvectors corresponding to the natural frequencies of a gear-rotor system governed by deterministic parameters were deduced. Mass and stiffness matrices were then decomposed into sub-matrices in the form of deterministic matrices multiplied by random parameters. Rayleigh quotient formula was utilized to derive the explicit expressions of natural frequencies of the system. Then, limit state functions of resonant failures of the system under an external load with random excited frequency was constructed based on vibration stability criterion. Reliability sensitivity analyzing method was applied to obtain sensitivities of random parameters on the resonant reliability of the gear-rotor system. Finally, a numerical case was given to illustrate the effectiveness and accuracy of the proposed method by comparing with Monte Carlo (MC) simulation.

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In order to improve the reliability analysis accuracy of the aircraft high-lift, an approach based on the Copula function theory and Bayesian updating is proposed. Considering the influence of the random variables' correlation in the process of updating, choosing the reasonable prior joint distribution and likelihood function is crucial. Under the condition of the incomplete probability information, the analytic expressions of the prior joint distribution and likelihood function of the correlated random variables are derived through the Copula function. Then, the posterior joint distribution is obtained by Bayesian updating. The reliability of the lifting device is calculated based on the posterior distribution. The case analysis shows that the reliability results based on the proposed approach are more accurate and more coincident with the factual situation than the reliability analysis results based on the independence assumption of random variables.