Gradient projection for reliability-based design optimization using evidence theory

Abstract

Uncertainty quantification and risk assessment in the optimal design of structural systems has always been a critical consideration for engineers. When new technologies are developed or implemented and budgets are limited for full-scale testing, the result is insufficient datasets for construction of probability distributions. Making assumptions about these probability distributions can potentially introduce more uncertainty to the system than it quantifies. Evidence theory represents a method to handle epistemic uncertainty that represents a lack of knowledge or information in the numerical optimization process. Therefore, it is a natural tool to use for uncertainty quantification and risk assessment especially in the optimization design cycle for future aerospace structures where new technologies are being applied. For evidence theory to be recognized as a useful tool, it must be efficiently applied in a robust design optimization scheme. This article demonstrates a new method for projecting the reliability gradient, based on the measures of belief and plausibility, without gathering any excess information other than what is required to determine these measures. This represents a huge saving in computational time over other methods available in the current literature. The technique developed in this article is demonstrated with three optimization examples.

Keywords:

• evidence theory
• reliability
• epistemic uncertainty
• belief
• plausibility

Acknowledgements

This work was sponsored by the office of Naval Research under Grant N00014-03-1-0057. Dr Kam Ng is the program manager.