An investigation of nonlinearity of reliability-based design optimization approaches

Because deterministic optimum designs obtained without taking uncertainty, into account could lead to unreliable designs, a reliability-based approach to design optimization is preferable using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in all original random space (X-space) and a reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mappings between X- and U-spaces for various probability distributions. Therefore, the nonlinearity, of the RBDO problem will depend oil the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity, into the reliability-based performance measures evaluated during the RBDO process. The evaluation of probabilistic constraints in RBDO call be carried out in two ways: using either the Reliability, Index Approach (RIA), or the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity for RIA and PMA in the RBDO process. In this paper it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of the highly nonlinear transformations that art involved. However PMA is rather independent of probability, distributions because it only, has a small involvement with a nonlinear transformation.