Time-dependent failure possibility analysis under consideration of fuzzy uncertainty

The problem which is actually being addressed in this paper includes two parts. One is establishing the time-dependent failure possibility (TDFP) model to measure the safety degree for structure under the fuzzy uncertainty over a given time intervals. The other is presenting two methods to estimate the TDFP, involving the double-loop nested optimization method (DLOM) and the efficient single-loop optimization method (SLOM). For measuring the safety degree of the structure under the fuzzy uncertainty in the given time interval, the TDFP, defined as the possibility of the performance less than zero under the fuzzy uncertainty in the given time interval, is proposed based on the possibility theory of the safety measure. For evaluating the proposed TDFP, the DLOM is established firstly by the definition of TDFP, but the computational cost of the DLOM is too high to solve the problems of the practical engineering. Thus the SLOM which transforms the estimation of the TDFP to the time-independent failure possibility by the extreme value is established to save the computational cost. The equivalency between the DLOM and the SLOM is strictly proved. The comparison between TDFP and the time dependent failure probability is completely in the theory and implementation to show the advantages of the proposed TDFP. After the detailed implementation of the proposed TDFP is given, several examples are used to verify the rationality of the established TDFP and the efficiency of the SLOM.