Integration of Possibility-Based Optimization to Robust Design for Epistemic Uncertainty

1. Abstract In practical engineering applications, there exist two different types of uncertainties: aleatory and epistemic uncertainties. Aleatory uncertainty is classified as objective and irreducible uncertainty with sufficient information on input uncertainty data, whereas epistemic uncertainty is a subjective and reducible uncertainty that stems from lack of knowledge on input uncertainty data. This study attempts to develop a robust design optimization with epistemic uncertainty. For epistemic uncertainties, a possibility-based design optimization deals with the failure rate, while a robust design optimization minimizes the product quality loss. In general, product quality loss is described using the first two statistical moments for aleatory uncertainty: mean and standard deviation. However, there is no metric for product quality loss defined when having epistemic uncertainty. This paper proposes a new metric for product quality loss with epistemic uncertainty, such that a possibility-based design optimization is integrated to a robust design. For numerical efficiency and stability, an enriched performance measure approach (PMA+) is employed for possibility-based robust design optimization, and the maximal possibility search (MPS) is used for a possibility analysis. Three different types of robust objectives are considered for possibility-based robust design optimization: smaller-the-better type (S-Type), larger-the-better type (L-Type), and nominal-the-better type (N-Type). Examples are used to demonstrate the effectiveness of possibility-based robust design optimization using the proposed metric for produce quality loss with epistemic uncertainty.