Optimization Algorithms For Structural Reliability Study

On the basis of the available research, three reliability models are studied intensively in this contribution. The main innovative points are listed as follows.(1) In case that failure domain or safe domain of the single failure mode is convex, three sections truncated sampling methods, including β-section samplingmethod, β -section importance sampling method and multi-sections truncated importance sampling method, are presented to evaluate the failure probability. In the presented methods, the computational cost is greatly decreased by reducing the sampling domain, and this advantage of the presented methods also can be extended to the failure probability of parallel system.(2) For reliability analysis of the series and parallel systems with multiple failure modes, the simulated annealing optimization based adaptive importance sampling method is presented to evaluate the failure probability. Based on optimizing characteristics of the simulated annealing, the importance sampling function is optimized in the sampling process, thereby the efficiency of system reliability analysis is improved greatly.(3) The mixed genetic algorithm is used to optimize the importance sampling function and to estimate the radius of β -sphere, then a β -sphere importance sampling method is composed to evaluate the failure probability of random reliability model.(4) On the basis of the simulated annealing algorithm for global optimization, an adaptive importance sampling method is presented to evaluate the reliability sensitivity. In the presented method, the simulated annealing optimization is employed to seek the most probable failure point (MPFP) gradually, which is used as the sampling center of the adaptive importance sampling function. The samples generated from the adaptive importance sampling functions are utilized to calculate the unbiased estimation of reliability sensitivity. The advantage of the presented method also can be extended to the reliability sensitivity of structure system with multiple failure modes.(5) For computation of fuzzy-random failure probability, an adaptive importance sampling algorithm is presented by taking the fuzziness and randomness in basic variables into account simultaneously. After the fuzzy-random failure probability is transformed into the random failure probability equivalently, a simulated annealing...