System RBDO With Correlated Variables Using Probabilistic Re-Analysis and Local Metamodels

A simulation-based, system reliability-based design optimization (RBDO) method is presented that can handle problems with multiple failure regions and correlated random variables. Copulas are used to represent dependence between random variables. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with a sequential trust-region optimization approach and local metamodels covering each trust region. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation per trust region. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing the use of a gradient-based optimizer. The PRRA method is based on importance sampling. One requirement for providing accurate results is that the support of the sampling PDF must contain the support of the joint PDF of the input random variables. The trust-region optimization approach satisfies this requirement. Local metamodels are constructed sequentially for each trust region taking advantage of the potential overlap of the trust regions. The metamodels are used to determine the value of the indicator function in MC simulation. An example with correlated input random variables demonstrates the accuracy and efficiency of the proposed RBDO method.