Convergence control of probabilistic structural design optimization based on performance measure approach

The evaluation of probabilistic constraints inProbabilistic Structural Design Optimization (PSDO) can be carried out usingthe recently proposed performance measure approach (PMA). The advancedmean-value (AMV) method is well suitable for PMA due to its simplicity andefficiency. However, when the AMV iterative scheme is applied to search forthe minimum performance target point for some nonlinear performancefunctions, the iterative sequences could fall into the periodic oscillationand even chaos. Then both PMA Two-level and PMA with SAP (SequentialApproximate Programming), which are based on this evaluation ofprobabilistic constraints, could yield convergent failure. In the presentpaper, the convergence control of AMV iterative procedure is firstimplemented by using the stability transformation method of chaos feedbackcontrol. The unstable fixed points embedded in the periodic and chaoticorbit are stabilized and the expected stable convergent solutions areobtained. Once the evaluation of probabilistic constraints can be carriedout successfully, the design optimization is performed by PMA Two-level orPMA with SAP. The numerical results demonstrate that the convergence controlusing stability transformation method is effective and PMA with SAP is moreefficient.