Hybrid Structural Reliability Analysis under Multisource Uncertainties Based on Universal Grey Numbers - Xingfa Yang; Jie Liu; Xiaoyue Chen; Qixiang Qing; Guilin Wen (Shock and Vibration)
Nondeterministic parameters of certain distribution are employed to model structural uncertainties, which are usually assumed as stochastic factors. However, model parameters may not be precisely represented due to some factors in engineering practices, such as lack of sufficient data, data with fuzziness, and unknown-but-bounded conditions. To this end, interval and fuzzy parameters are implemented and an efficient approach to structural reliability analysis with random-interval-fuzzy hybrid parameters is proposed in this study. Fuzzy parameters are first converted to equivalent random ones based on the equal entropy principle. 3σ criterion is then employed to transform the equivalent random and the original random parameters to interval variables. In doing this, the hybrid reliability problem is transformed into the one only with interval variables, in other words, nonprobabilistic reliability analysis problem. Nevertheless, the problem of interval extension existed in interval arithmetic, especially for the nonlinear systems. Therefore, universal grey mathematics, which can tackle the issue of interval extension, is employed to solve the nonprobabilistic reliability analysis problem. The results show that the proposed method can obtain more conservative results of the hybrid structural reliability.