A Modified Conjugate Gradient Approach for Reliability-Based Design Optimization

To improve the efficiency of structural reliability-based design optimization (RBDO) based on the performance measure approach (PMA), a modified conjugate gradient approach (MCGA) is proposed for RBDO with nonlinear performance function. In PMA, the advanced mean value (AMV) approach is widely used in engineering because its simplicity and efficiency. However, the AMV method shows the inefficient and unstable results for structural performance function with high nonlinearity in RBDO. To overcome this shortcoming, the proposed MCGA method improves the efficiency of solution by modifying the relevant parameters of conjugate gradient approach (CGA) and the direction of conjugate gradient algorithm for searching the optimal design point. Finally, three numerical examples with highly nonlinear performance function and an optimization design example of speed reducer are presented. Compared with different methods, the results show that the MCGA method exhibited the better efficiency and robustness in structural reliability and RBDO analyses.