Multi-objective robustness indicators for evaluation and exploration of design margins

Abstract

Specification of design margins serves the purpose of mitigating the ubiquitous uncertainty of the engineering design process. This paper addresses the twofold challenge of establishing a suitable concept of margins early in the design process, before the design is mature enough for detailed modelling, and evaluating margin inter-dependencies. As margins are often specified in an unstructured manner, there is a risk that one margin might lead to a need for more margins, e.g. tight tolerances, downstream. To avoid adverse margin dependencies, five Multi-Objective Robustness Indicators based on multi-objective design exploration are presented: The Relative Utopia Index, the Relative Pareto Shape Index, the Relative Compromise Index, the Relative Average Sensitivity Index, and the Average Feasible Variable Range. They aggregate optimality, trade-offs and sensitivity of design configurations. The indicators are applied to a case example, a flat head tank design, to illustrate the effect and inter-dependency of margin specification. Three margin types were identified. The first type affects only the Objective Space size, the second type affects only the Pareto set size and the third type affects Pareto set shape. The third margin type is the most critical as it leads to harder compromises between design objectives later in the design process.