Reliability-Based Optimization (RBO) for engineering design deals mainly with two design attributes, namely the merit, for example cost, and the reliability of the design. In this work the class of design problems which are considered, are designs characterized by a minimum merit function and that satisfy certain reliability constraints. The reliability constraints are typically constraints on the probabilities of failure due to component failure events or a system failure event. These are obtained using standard reliability analysis techniques such as First Order Reliability Method (FORM), Second Order Reliability Methods (SORM) and Monte Carlo Simulation (MCS) techniques.
The reliability analysis and RBO are very expensive for multidisciplinary systems consisting of various disciplines that are dependent on each other or coupled, for example, an aeroelastic structure. Hence, the primary goal of the research is to develop efficient methodologies that perform RBO for multidisciplinary systems. The methodologies considered incorporates a Concurrent Subspace Optimization technique that allows concurrent design optimization in each discipline. The methodologies also incorporate approximation concepts to reduce the computational costs. There are essentially two methodologies, one that uses a traditional reliability analysis method and the other that uses a new reliability analysis method geared towards reduction of computational expenses for coupled multidisciplinary problems. A new reliability analysis tool based on Trust Region methods was developed for the latter case. Both methodologies were applied to multidisciplinary test problems and about 20%-30% computational savings were observed.
A second goal of the research was to investigate the use of Monte Carlo Simulation (MCS) techniques for reliability analysis in RBO, that are more accurate but more expensive than FORM or SORM. In this work, conditional expectation MCS was selected over indicator-based MCS techniques based on smoothness criteria and the availability of analytic sensitivities. A MCS-based RBO methodology was developed and successfully implemented to problems with both component and series failure events. It was observed that designs with significantly lower merit functions were obtained for the application problems considered, compared to a FORM-based RBO approach. It was also observed that the computational costs were extremely high for one of the application problems. Some suggestions for future research are made regarding development of efficient methodologies for the MCS-based RBO.