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.
Z. Hu and X. Du, "First Order Reliability Method for Time-Variant Problems Using Series Expansions," Structural and Multidisciplinary Optimization, vol. 51, no. 1, pp. 1-21, Springer Verlag, Jan 2015.
The definitive version is available at https://doi.org/10.1007/s00158-014-1132-9
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
International Standard Serial Number (ISSN)
Article - Journal
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