A sequential approximate programming strategy for reliability-based structural optimization

Although reliability-based structural optimization (RBSO) is recognized as a rational structural design philosophy that is more advantageous to deterministic optimization, most common RBSO is based on straightforward two-level approach connecting algorithms of reliability calculation and that of design optimization. This is achieved usually with an outer loop for optimization of design variables and an inner loop for reliability analysis. A number of algorithms have been proposed to reduce the computational cost of such optimizations, such as performance measure approach, semi-infinite programming, and mono-level approach. Herein the sequential approximate programming approach, which is well known in structural optimization, is extended as an efficient methodology to solve RBSO problems. In this approach, the optimum design is obtained by solving a sequence of sub-programming problems that usually consist of an approximate objective function subjected to a set of approximate constraint functions. In each sub-programming, rather than direct Taylor expansion of reliability constraints, a new formulation is introduced for approximate reliability constraints at the current design point and its linearization. The approximate reliability index and its sensitivity are obtained from a recurrence formula based on the optimality conditions for the most probable failure point (MPP). It is shown that the approximate MPP, a key component of RBSO problems, is concurrently improved during each sub-programming solution step. Through analytical models and comparative studies over complex examples, it is illustrated that our approach is efficient and that a linearized reliability index is a good approximation of the accurate reliability index. These unique features and the concurrent convergence of design optimization and reliability calculation are demonstrated with several numerical examples.