Towards a Better Understanding of the Equality Constraints in Robust Design Optimization

Abstract

Equality constraints in deterministic problems pose strict limitations on design feasibility because of the exactitude associated with such constraints. Equality constraints in robust design optimization (RDO) problems can be classified into two types: (1) those that must be satisfied regardless of uncertainty, examples include physics-based constraints, such as F = ma, and (2) those that cannot be satisfied because of uncertainty, which are typically designer-imposed, such as dimensional constraints. Our goal is to maintain design feasibility under uncertain conditions – to exactly satisfy physics based equality constraints, and to satisfy designer-imposed constraints exactly or as closely as possible. Whether or not a particular equality constraint can be exactly satisfied depends on the nature of the design variables that exist in the constraint. In this context, the contribution of this paper is two-fold. First, we present a rank-based matrix approach to interactively classify equality constraints into the above two types. Second, we present an approach to incorporate designer’s intra-constraint and inter-constraint preferences for designer-imposed constraints into the RDO formulation. Intra-constraint preference expresses how closely a designer wishes to satisfy a particular constraint, in terms of its mean and standard deviation. A designer may express inter-constraint preference if satisfaction of a particular designer-imposed constraint is more important than that of another. In other words, a designer might desire higher constraint satisfaction for some equality constraints, even if it is at the expense of lower constraint satisfaction for other equality constraints. The above discussed constraint satisfaction preferences give the designer the means to explore design space possibilities; and entail interesting implications in terms of decision making. An example is provided to illustrate the proposed approach.