Increasing the discriminatory power of bounding models using problem-specific knowledge when viewing design as a sequential decision process

Abstract

A recent design paradigm seeks to overcome the challenges associated with broadly exploring a design space requiring computationally expensive model evaluations by formally viewing design as a sequential decision process (SDP). With the SDP, a set of computational models of increasing fidelity are used to sequentially evaluate and systematically eliminate inefficient design alternatives from further consideration. Key to the SDP are concept models that are of lower fidelity than the true function and are constructed in such a way that when used to evaluate a given design, they return two-sided limits that bound the precise value of the decision criteria, hence referred to as bounding models. Efficiency in the SDP is achieved by using such low-fidelity, inexpensive models, early in the design process to eliminate inefficient design alternatives from consideration after which a higher fidelity, more computationally expensive model, is executed, but only on those design alternatives that appear promising. In general, low-fidelity models trade off discriminatory power for computational complexity; however, it can be demonstrated that knowledge of the underlying physics and/or mathematics can be used to increase the discriminatory power of the lower fidelity models for a given computational cost. Increasing the discriminatory power of the bounding models directly translates into an increase in the efficiency of the SDP. This paper discusses and demonstrates how knowledge of the underlying physics and/or mathematics, otherwise referred to as “problem-specific knowledge,” such as monotonicity and concavity can be used to increase the discriminatory power of the bounding models in the context of the SDP and for engineering designs characterized by demand and capacity relationships. Furthermore, the concept of constructing the bounding models to systematically defer decisions on a subset of design variables, for example for a subsystem, is demonstrated, while retaining the desirable convergence guarantees to the optimal set. The utility of leveraging knowledge to increase discriminatory power and systematically deferring decisions through bounding models in the context of the SDP is demonstrated through two design problems: (1) the notional design of an engine-propeller combination to minimize takeoff distance for a light civil aircraft, and (2) the design of a building’s seismic force resisting structural-foundation system where the performance is evaluated on the basis of minimizing drift and total system cost.