A Reliability-Based Robust Design Methodology

Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization however, can lead to undesired choices because it neglects input and model uncertainty. Reliability-based design optimization (RBDO) and robust design improve optimization by considering uncertainty. A design is called reliable if it meets all performance targets in the presence of variation/uncertainty and robust if it is insensitive to variation/uncertainty. Ultimately, a design should be optimal, reliable, and robust. Usually, some of the deterministic optimality is traded-off in order for the design to be reliable and/or robust. This paper describes the state-of-the-art in assessing reliability and robustness in engineering design and proposes a new unifying formulation. The principles of deterministic optimality, reliability and robustness are first defined. Subsequently, the design compromises for simultaneously achieving optimality, reliability and robustness are illustrated. Emphasis is given to a unifying probabilistic optimization formulation for both reliability-based and robust design, including variation of all performance measures. The robust engineering problem is investigated as a part of a “generalized” RBDO problem. Because conventional RBDO optimizes the mean performance, its objective is only a function of deterministic design variables and the means of the random design variables. The conventional RBDO formulation is expanded to include performance variation as a design criterion. This results in a multi-objective optimization problem even with a single performance criterion. A preference aggregation method is used to compute the entire Pareto frontier efficiently. Examples illustrate the concepts and demonstrate their applicability.