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First and second order approximate reliability analysis methods using evidence theory

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  • Zhang, Z.
  • Jiang, C.
  • Wang, G.G.
  • Han, X.

Abstract

The first order approximate reliability method (FARM) and second order approximate reliability method (SARM) are formulated based on evidence theory in this paper. The proposed methods can significantly improve the computational efficiency for evidence-theory-based reliability analysis, while generally provide sufficient precision. First, the most probable focal element (MPFE), an important concept as the most probable point (MPP) in probability-theory-based reliability analysis, is searched using a uniformity approach. Subsequently, FARM approximates the limit-state function around the MPFE using the linear Taylor series, while SARM approximates it using the quadratic Taylor series. With the first and second order approximations, the reliability interval composed of the belief measure and the plausibility measure is efficiently obtained for FARM and SARM, respectively. Two simple problems with explicit expressions and one engineering application of vehicle frontal impact are presented to demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Zhang, Z. & Jiang, C. & Wang, G.G. & Han, X., 2015. "First and second order approximate reliability analysis methods using evidence theory," Reliability Engineering and System Safety, Elsevier, vol. 137(C), pages 40-49.
    • Handle: RePEc:eee:reensy:v:137:y:2015:i:c:p:40-49
    DOI: 10.1016/j.ress.2014.12.011
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    1. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L. & Sallaberry, C.J., 2006. "Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1414-1434.
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