Optimization in Practice with MATLAB® For Engineering Students and Professionals

Overview

The previous chapters presented deterministic optimization methods. These do not implicitly take into account the inherent uncertainties typically present in the design process, in the system being designed, or in the models describing the system behavior. Uncertainties emanates from myriad sources. These include imperfect manufacturing processes and material properties, fluctuating loading conditions, over-simplified engineering models, or uncertain operating environment. All of these may have a direct impact on the system performance in its use or in the market place. To obtain a reliable and robust design (these terms are defined later), these uncertainties must be considered as part of the design process.

In the past, empirical safety factors were often used to guard against engineering design failure [1]. Safety factors resulted in overly conservative designs, increasing the probability that businesses may lose their competitive edge in terms of cost and performance. More recently, design optimization methods under uncertainty have gained broad recognition. These approaches explicitly consider uncertainties of various forms, and search for designs that are insensitive to variations or uncertainty to a significant extent.

This chapter introduces the concept of design optimization under uncertainty, and discusses the pertinent popular approaches available. Section 16.2 defines a generic example that is used throughout the book to facilitate the presentation of the material. The next Section (Sec. 16.3) defines five generic components/STEPS involved in design under uncertainty. This is followed by the presentation of these STEPS in the following five Sections: (1) uncertainty types identification (Sec. 16.4), (2) uncertainty quantification (Sec. 16.5), (3) uncertainty propagation (Sec. 16.6), (4) formulation of optimization under uncertainty (Sec. 16.7), and (5) results analysis (Sec. 16.8). Section 16.9 briefly discussed other popular methods. A chapter summary is provided in Sec 16.10.

Chapter Example

This section defines a generic example that it used throughout the chapter to illustrate the various concepts involved in design under uncertainty. Consider the optimization of a two bar truss shown in Fig. 16.1.