Application of maximum entropy principle for reliability-based design optimization

Abstract

The maximum entropy principle (MEP) is used to generate a natural probability distribution among the many possible that have the same moment conditions. The MEP can accommodate higher order moment information and therefore facilitate a higher quality PDF model. The performance of the MEP for PDF estimation is studied by using more than four moments. For the case with four moments, the results are compared with those by the Pearson system. It is observed that as accommodating higher order moment, the estimated PDF converges to the original one. A sensitivity analysis formulation of the failure probability based on the MEP is derived for reliability-based design optimization (RBDO) and the accuracy is compared with that by finite difference method (FDM). Two RBDO examples including a realistic three-dimensional wing design are solved by using the derived sensitivity formula and the MEP-based moment method. The results are compared with other methods such as TR-SQP, FAMM + Pearson system, FFMM + Pearson system in terms of accuracy and efficiency. It is also shown that an improvement in the accuracy by including more moment terms can increase numerical efficiency of optimization for the three-dimensional wing design. The moment method equipped with the MEP is found flexible and well adoptable for reliability analysis and design.