Convergence Control Of Sequential Optimization And Reliability Assessment Method

In reliability analysis and design for engineering structures, because of the existence of lots of uncertainties which come from parameters themselves, we can only obtain the limited data samples. Therefore, to adopt the model considering the uncertainty is much more reasonable in practical engineering design. Actually, the reliability based design optimization (RBDO) is one of the most widely-used models. To develop the efficient and stable structure reliability optimization algorithms is currently one key research topic of uncertainty optimization design.During the procedure for solving the reliability based design optimization problems, the traditional two-level methods need expensive computational cost. Thus, many efficient single-level decoupled optimization methods were established. Sequential optimization and reliability assessment method (SORA) based on the most probable point under uncertainty analysis is a single-level RBDO approach proposed recently, which has higher efficiency. Nevertheless, SORA possibly does not converge for solving some nonlinear problems and its computational procedure is quite complex.Firstly, the present paper adopts the performance measure approach (PMA) for structural reliability assessment. Although its calculated process is simple and convenient, it could not converge sometimes. Consequently, the stability transformation method of chaos feedback control is suggested to overcome the problem of iterative failure such as periodic oscillation and chaos, and achieve the convergence control for iterative scheme of probabilistic constraint evaluation. The numerical results of several representative examples show that, the performance measure approach with chaos control has simpler operation procedure and better stability than the method of the most probable point based uncertainty analysis (MPPUA).Furthermore, instead of the MPPUA method the PMA method under chaos control is embedded into the SORA algorithm to avoid the non-convergence caused by SORA for reliability based design optimization. Some computational examples illustrate that the proposed algorithm is effective and stable.