Fuzzy First-Order and Second Moment Method for Failure Credibility Analysis in the Presence of Fuzzy Uncertainty

A fuzzy first-order and second moment (FFOSM) method is proposed to efficiently estimate time-independent and time-dependent failure credibility in the presence of fuzzy uncertainty. For the time-independent linear performance function with independently, regularly, and identically distributed fuzzy inputs, the analytical relationship is first derived between the failure credibility and fuzzy safety index, and the relation form is established between fuzzy safety index and fuzzy first two moments of the performance function. Second, in the standard space of fuzzy inputs, the minimum infinite norm distance from the coordinate origin to the linear limit state surface is analytically derived, and the point with the smallest infinite norm distance located on the limit state surface is defined as the fuzzy design point. Based on this definition, the geometric and physical meanings are explained for the fuzzy safety index and fuzzy design point, and the FFOSM method for time-independent failure credibility analysis is established for both linear and nonlinear performance function. Third, for time-dependent performance functions, the equivalence is proved between time-dependent fuzzy safety index and the minimum value of transient fuzzy safety indices, on which the iteration steps of the FFOSM method is designed for time-dependent fuzzy safety index and failure credibility estimation. Since the proposed FFOSM method is an approximately analytical approach, it has higher efficiency than the fuzzy simulation method and the cut level optimization method. Finally, the effectiveness and applicability of the proposed method are demonstrated by different examples.