A Simulation-Based RBDO Method Using Probabilistic Re-Analysis and a Trust Region Approach

A simulation-based, system reliability-based design optimization (RBDO) method is presented which can handle problems with multiple failure regions. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with a trust-region optimization approach. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. The PRRA method is based on importance sampling. It provides accurate results, if the support (set of all values for which a function is non zero) of the sampling PDF contains the support of the joint PDF of the input random variables and, if the mass of the input joint PDF is not concentrated in a region where the sampling PDF is almost zero. A sequential, trust-region optimization approach satisfies these two requirements. The potential of the proposed method is demonstrated using the design of a vibration absorber, and the system RBDO of an internal combustion engine.