Reasoning about relationships among design constraints can facilitate objective and effective decision making at various stages of engineering design. Exploiting dominance among constraints is one particularly strong approach to simplifying design problems and to focusing designers’ attention on critical design issues.

Three distinct approaches to constraint dominance identification have been reported in the literature. We study the basic principles of these approaches with simple examples and then study their relative advantages and disadvantages (Figure 2).

We apply these methods to a practical linear electric actuator design problem. The task is to design a direct drive electric actuator as an alternative to the existing hydraulic cylinder drive of a Universal Modular Mast (or periscope
hoist assembly) of a submarine as shown in Figure 1. Linear Synchronous Motors (LSM) are potential design options (Figure 3). A number of configurations are possible for a LSM including single-sided, double sided or tubular LSMs.

With the help of the design problem we demonstrate strategies to synergistically employ the dominance identification methods. Specifically, we present an approach that utilizes the transitive nature of the dominance relation. The identification of dominance provides insight into the design of linear actuators, which leads to effective decisions at the conceptual stage of the design.

We show that the dominance determination methods can be synergistically employed with other constraint reasoning methods such as Interval Propagation methods and Monotonicity Analysis to achieve an optimal solution for a particular design configuration of the linear actuator. The dominance determination methods and strategies for their employment are amenable for automation and can be part of a suite of tools available to assist the designer in detailed as well as conceptual design.
 

Dominance among constraints exists when the satisfaction of one constraint guarantees the satisfaction of another, rendering the second constraint irrelevant. Identifying dominance not only facilitates numerical solution but may also focus the designer’s attention on critical aspects of the design. A number of dominance identification methods have been described in the literature, including the Constraint Difference Method, the Constraint Transformation Method, and the Necessary-Sufficient Interval Method.

We elaborate on the basis for and the character of these methods and we discuss relative similarities, differences, strengths, and weaknesses of the methods. We also discuss computational issues relevant to the application of these methods, most specifically function range determination and interval analysis issues. We observe that the differences among the methods lead to advantages for each method in circumstances that depend on the nature of the constraints and the extent of the design space. These distinct advantages suggest a synergism among the methods in the identification of constraint dominance in complex design problems.