Robust and reliability-based design optimization under epistemic uncertainty

Abstract

This thesis proposes formulations and algorithms for robust design optimization with uncertainty representation and propagation considering both aleatory (e.g. produced due to natural variability) and epistemic (e.g. variability due to lack of information or imprecise information) uncertainty arising from interval data. Multiple interval data are treated for uncertainty representation including both overlapping and non-overlapping in characteristics. A general likelihood-based approach for uncertainty representation has been proposed in this research. Uncertainty analysis through the likelihood approach is capable of estimating the uncertainty for different distribution types and parameters. The proposed likelihood-based representation of epistemic uncertainty has been used in the framework for robustness-based design optimization to achieve computational efficiency. A methodology is also outlined for solving reliability-based design optimization (RBDO) under epistemic uncertainty using the proposed likelihood-based uncertainty representation. The proposed robust design optimization methodology is illustrated with two numerical examples including a general mathematical problem and a real engineering problem.