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First Order Reliability Method for Time-Variant Problems Using Series Expansions
Structural and Multidisciplinary Optimization
  • Zhen Hu
  • Xiaoping Du, Missouri University of Science and Technology
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
Document Type
Article - Journal
Document Version
File Type
© 2015 Springer Verlag, All rights reserved.
Publication Date
Citation Information
Zhen Hu and Xiaoping Du. "First Order Reliability Method for Time-Variant Problems Using Series Expansions" Structural and Multidisciplinary Optimization Vol. 51 Iss. 1 (2015) p. 1 - 21 ISSN: 1615147X
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