A simulation method for reliability-based design optimization using probabilistic re-analysis and approximate metamodels

A simulation-based, system reliability-based design optimization (RBDO) method is presented which can in general 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 the system reliability of a design efficiently by performing a single Monte Carlo (MC) simulation. 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. It provides accurate results if the support (set of all values for which a function is non zero) of the joint sampling PDF contains the support of the joint PDF of the input random variables. The sequential, trust-region optimization approach satisfies this requirement. PRRA improves the design within each trust region using a single MC simulation per trust region. Local approximate metamodels are constructed sequentially for each trust region taking advantage of the potential overlap of the trust regions. The metamodels are "accurate-on-demand," and serve as indicators to determine the failure and safe regions. Sample points close to limit states define transition regions between the safe and failure domains. A clustering technique identifies all transition regions which can be in general disjoint, and local metamodels of the actual limit states are generated for each transition region. Importance sampling generates sample points only in the identified transition and failure regions, providing accuracy in the areas near the failure boundary without using any computational effort for sample points in the safe domain. A robust maximin "space-filling" sampling technique is used to construct the metamodels. Examples demonstrate the accuracy and efficiency of the developed metamodeling, PRRA and trust-region RBDO methods.