A New Method for Reliability-Based Sensitivity Analysis of Dynamic Random Systems

A novel numerical method for investigating time-dependent reliability and sensitivity issues of dynamic systems is proposed, which involves random structure parameters and is subjected to stochastic process excitation simultaneously. The Karhunen–Loève (K-L) random process expansion method is used to express the excitation process in the form of a series of deterministic functions of time multiplied by independent zero-mean standard random quantities, and the discrete points are made to be the same as Legendre integration points. Then, the precise Gauss–Legendre integration is used to solve the oscillation differential functions. Considering the independent relationship of the structural random parameters and the parameters of random process, the time-varying moments of the response are evaluated by the point estimate method. Combining with the fourth-moment method theory of reliability analysis, the dynamic reliability response can be evaluated. The dynamic reliability curve is useful for getting the weakness time so as to avoid breakage. Reliability-based sensitivity analysis gives the importance sort of the distribution parameters, which is useful for increasing system reliability. The result obtained by the proposed method is accurate enough compared with that obtained by the Monte Carlo simulation (MCS) method.