First Order Reliability Method for Time-Variant Problems Using Series Expansions


Time-variant reliability is often evaluated by Rice's formula combined with the First Order Reliability Method (FORM). To improve the accuracy and efficiency of the Rice/FORM method, this work develops a new simulation method with the first order approximation and series expansions. The approximation maps the general stochastic process of the response into a Gaussian process, whose samples are then generated by the Expansion Optimal Linear Estimation if the response is stationary or by the Orthogonal Series Expansion if the response is non-stationary. As the computational cost largely comes from estimating the covariance of the response at expansion points, a cheaper surrogate model of the covariance is built and allows for significant reduction in computational cost. In addition to its superior accuracy and efficiency over the Rice/FORM method, the proposed method can also produce the failure rate and probability of failure with respect to time for a given period of time within only one reliability analysis.


Mechanical and Aerospace Engineering

Keywords and Phrases

Fourier analysis; Random processes; Reliability; Stochastic systems; Structural analysis; Approximation; Computational costs; First order reliability methods; First-order approximations; Gaussian Processes; Linear estimation; Probability of failure; Time-variant reliability; Reliability analysis

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Article - Journal

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© 2015 Springer Verlag, All rights reserved.

Publication Date

01 Jan 2015