Accelerated PMA and its application in reliability-based design optimization

This paper proposes a novel approach based on the performance measure approach (PMA), which is termed accelerated PMA (aPMA) to overcome the non-convergence of the advanced mean value(AMV) and extend it to the reliability-based design optimization (RBDO). In aPMA, a threshold value by using inequality is integrated with the formula of AMV to make the efficiency and robustness of searching for the minimum performance target point (MPTP) better. The threshold value is able to eliminate the unnecessary probabilistic constraint in the inverse reliability analysis, thereby reducing the risk of numerical instability in AMV. Meanwhile, a judgment condition is defined according to the threshold value and reliability index in the design optimization, in which the active deterministic constraints can be quickly identified and updated. In addition, the recommended aPMA is merged into the double loop method (DLM) to consolidate the accuracy, efficiency and robustness of that for the high-dimensional RBDO problem. Since reliability analysis and structural optimization are carried out simultaneously, the convergence rate is enhanced. Besides, both the efficiency and robustness of the proposed aPMA are firstly trialed on six numerical/structural examples along with its performance on RBDO is tested through three RBDO problems quoted, showing significant merits.