A Model-Based Formulation of Robust Design

Abstract

Laid down in this paper are the foundations on which the design of engineering systems, in the presence of an uncontrollable changing environment, can be based. The changes in environment conditions are accounted for by means of robustness. To this end, a theoretical framework as well as a general methodology for model-based robust design are proposed. Within this framework, all quantities involved in a design task are classified into three sets: the design variables (DV), grouped in vector x, which are to be assigned values as an outcome of the design task; the design-environment parameters (DEP), grouped in vector p, over which the designer has no control; and the performance functions (PF), grouped in vector f, representing the functional relations among performance, DV, and DEP. A distinction is made between global robust design and local robust design, this paper focusing on the latter. The robust design problem is formulated as the minimization of a norm of the covariance matrix of the variations in PF upon variations in the DEP, aka noise in the literature on robust design. Moreover, one pertinent concept is introduced: design isotropy. We show that isotropic designs lead to robustness, even in the absence of knowledge of the statistical properties of the variations of the DEP. To demonstrate our approach, a few examples are included.