A Modified Mean Value of Performance Measure Approach for Reliability-Based Design Optimization

Abstract

The advanced mean value (AMV) is generally implemented to evaluate the probabilistic constraints of reliability-based design optimization (RBDO) problems based on performance measure approach (PMA). The PMA-based AMV is efficient method but yields unstable results for highly nonlinear probabilistic constraints. In this paper, a modified mean value (MMV) method is proposed to improve the efficiency and robustness of inverse reliability method to evaluate the reliable level in RBDO-based PMA. The modified PMA using MMV is adaptively evaluated using a modified search direction based on the two previous performance values. The modified search direction is determined using an adaptive step size, which is simply computed based on a power function and adaptive factor between 0.95 and 1. The robustness and efficiency of proposed MMV are compared with several reliability methods-based PMA including the AMV, hybrid mean value (HMV), enriched HMV (HMV\(^{+}\)) and modified chaos control (MCC) through four mathematical and structural RBDO problems with nonlinear probabilistic constraints. The results illustrated that the proposed MMV is as robust as the MCC and HMV\(^{+}\) but is computationally more efficient. In addition, the MMV is more robust than the HMV and AMV for RBDO problems with highly probabilistic constraints.