Structural Design Optimization Based on Reliability Analysis Using Evidence Theory

Over the last decade uncertainty quantification techniques of probability theory have been studied and embedded in multidisciplinary optimization problems, instead of simply assigning safe factors to the uncertain parameters in a system. However, recently it has been found by the scientific and engineering community that there are limitations for using only one framework (probability theory) to quantify the uncertainty in a general information situation. In a general situation, the available information may not be so complete and perfect for the uncertainty quantification modeling of a system using only probability theory. Dempster-Shafer theory, which is called evidence theory, is proposed to handle this general situation as an alternative to classical probability theory for the mathematical representation of uncertainty. Evidence theory allows us to express partial beliefs when it is impossible or impractical to assess the complete probability distribution confidently. Though there are plenty of studies for quantification of uncertainty using probability theory, uncertainty quantification for a structural problem using evidence theory is barely explored. In this paper, it is our attempt to apply Dempster-Shafer theory for uncertainty quantification and reliability-based optimization problem in a general imprecise and incomplete informative situation. In this paper, a cost effective and more accurate algorithm is adopted for a real structural optimization problem with multidisciplinary performance functions such as used in preliminary aircraft wing design.