Reliability Based Design Optimization Formulations for Component and System Reliability

Reliability-based design optimization (RBDO) of mechanical systems is computationally intensive due to the presence of two types of iterative procedures – design optimization and reliability estimation. Single-loop RBDO algorithms offer tremendous savings in computational effort, but they have so far only been able to consider individual component reliability constraints. This paper presents a single-loop RBDO formulation and an equivalent formulation that can also include system-level reliability constraints. The formulations allow the allocation of optimal reliability levels to individual component limit states in order to satisfy both system-level and component-level reliability requirements. Four solution algorithms to implement the second, more efficient formulation are developed. A key feature of these algorithms is to remove the most probable points from the decision space, thus avoiding the need to calculate Hessians or gradients of limit state gradients. It is shown that with the proposed methods, systems-level RBDO can be accomplished with computational expense equivalent to several cycles of computationally inexpensive singleloop RBDO based on second-moment methods. Examples of this new approach applied to series, parallel, and combined systems are provided. Nomenclature