Dimension Reduction Method for Design under Uncertainty

The objective of this book is to study new methods for inverse reliability analysis and robust design optimization using the univariate dimension reduction method (DRM). The current research effort involves: (1) reliability-based robust design optimization (RBRDO) method using the mean-based DRM; (2) reliability-based design optimization (RBDO) method using the inverse reliability analysis and the most probable point (MPP)-based DRM; (3) design sensitivity analyses for RBDO using the MPP-based DRM; and (4) system inverse reliability analysis and RBDO using the MPP-based DRM and Ditlevsen''s second order upper bound. For robust design optimization (RDO), the mean-based DRM improves the accuracy of estimation of statistical moments which are used as a cost function of RDO. For component and system RBDO, the MPP-based DRM improves the accuracy and efficiency of estimation of probability of failure.