Step length adjustment iterative algorithm for inverse reliability analysis

Abstract

Performance Measure Approach (PMA) is an alternative way for evaluation of probabilistic constraints in reliability-based design optimization other than traditional Reliability Index Approach (RIA). In PMA, the probabilistic performance measure (PPM) is obtained through locating the minimum performance target point (MPTP) with the specified target reliability index in standard normal space, which is also called inverse reliability analysis. The advanced mean-value (AMV) method is well suitable for locating MPTP due to its simplicity and efficiency. However, AMV may have difficult to converge for highly nonlinear performance function. In this paper a step length adjustment (SLA) iterative algorithm, which introduces a "new" step length to control the convergence of the sequence, is proposed. This step length is new because the line search process for step length selection is not needed and it may be constant during the whole iteration process or decrease successively several times using a self-adjust strategy. It is proved that the AMV method is a special case of the SLA algorithm when the step length tends to infinity and the reason why AMV diverges is illustrated. SLA is as simple as AMV and does not need the prior knowledge of convexity or concavity of the performance function as other modified algorithms do. Numerical results of several highly nonlinear performance functions including an engineering application indicate that SLA is effective and robust.