1
Introduction

1.1 Background

Optimization formalizes the century's old trial-and-error method which engineers have traditionally used to reason through the complexities of a design process where the merits and demerits of a large number of alternatives are evaluated and the best combination selected. Originally, this was done using hand-based calculation procedures but has evolved, in the modern design environment, into the application of sophisticated computer-based numerical algorithms. Whether done by hand calculation or by employing an advanced computer program, the underlying procedure is the same; the optimization process starts the search for a best solution from an initial guess and then iteratively seeks to find better alternatives. These alternative designs are generated by varying parameters that characterize the design problem. If the design is characterized by cost, these would be cost factors; if the design is to have minimum weight, structural parameters related to the volume of structural material would be used. These parameters are the design variables which are used as the defining terms in a design objective; for example, the cost of manufacture is defined in terms of economic cost factors; the total structural weight can be defined in terms of structural sizes. By the intelligent application of the trial-and-error process, a computer-based algorithm, or the engineer, evaluates the quality of the trial to decide on the next move. Employing a computer, the engineer can engage a numerical algorithmic process that brings the power of computational numerical methods into play which iteratively changes the values of the design variables to modify the numerical value(s) of the design objective(s) while adhering to the limitations on the design normally termed constraints. By proceeding in this manner, the algorithm is driving toward a design judged best for a given set of circumstances. While engineers naturally turn to computer methods to assist them in the design process, we should, nevertheless, not forget that the most innovative computer is the human brain and the best designs are always a result of the engineer thinking first and employing computers second.

In real world engineering where a large and complex system, for example, an aircraft, a ship, or a car, is being designed, a process involving trade-offs takes place both within disciplinary subsystem domains and across their boundaries. Optimization in this environment becomes multidisciplinary design optimization (MDO). The complexity of modern systems shows itself under a number of different headings: compositional, behavioral, modeling, and evaluative complexity. The compositional complexity relates to the high number of system elements in the design process and their connectivity; if we take into account manufacturing cost, structural mass, dynamic response, and so on, each of these interacts with each other and calls into play a wide range of associated software tools. The behavioral complexity comes from the many aspects that influence the behavior that the designer is looking for, or trying to avoid, and is well described by the adage that in a system "everything affects everything." Modeling complexity is associated with the complex (physical) phenomena that need to be taken into account to analyze the system's behavior such as major structural analysis programs, computational fluid dynamics software tools, and so on which also interact. Finally, evaluative complexity appears when conflicting design characteristics are aimed for and trade-offs are needed between disparate properties.

Many of the methods applied to design optimization originate from the world of operations research (OR) which aims at optimizing operations of existing systems while MDO extends the approach to the engineering system design process, explaining the D in MDO. However, as explained in Chapter 2, there is a long history to the development of optimization principles and methods that have migrated to the design environment from variety of mathematical sources. The totality of these inputs is made clear through the various chapters in this book.

MDO can be defined as an assemblage of methods, procedures, and algorithms for finding best designs measured against a set of specified criteria for complex engineering systems with interacting parts, whose behavior is governed by a number of coupled physical phenomena aligned with engineering disciplines. Such designs are brought to fruition by teams of engineers, often dispersed on a country or global scale, employing organization methods and processes that accommodate commercial realities which might involve human factors components, costs and profit considerations, market competitiveness, and so on. Within the design environment, uncertainties are always present, and handling them when employing optimizing methods is not always straightforward and currently a major research area. Coupled with the presence of uncertainties is the need to undertake reliability-based and robust (uncertainty tolerant) designs. It is in the resolution of this type of design problem, with its range of interactions and uncertainties, that MDO finds its application.

Knowledge-based engineering (KBE) aims at drawing together the knowledge required to construct an MDO system into a computer-based knowledge base which can be logically interrogated by an engineer. It supports those wishing to employ MDO methods by making knowledge directly available at each stage of the development and application of an MDO system-it cannot be expected that a designer is an expert in all aspects relating to this task. Currently, KBE tools are in a rapid state of development and as time passes will become directly linked with MDO in its successful support for generating optimized designs for complex products.

1.2 Aim of the Book

The aim of the book is to offer a basis for constructing a logical approach to the application and understanding of modern MDO methods and tools and provide a background to supporting MDO with KBE technology. This is an ambitious target, and it is not claimed the book gives a complete and totally comprehensive coverage of these major fields. Rather, it provides a door through which the reader is invited to step and after crossing the threshold absorb or possibly develop the ideas in these rapidly expanding areas. In essence, it provides a knowledge base that allows the reader to take advantage of this technology in engineering design. In the case of an inexperienced or new user of MDO/KBE technology, it represents a robust starting point. For an engineer experienced in the application of optimization tools for designing a product, we hope the book will give insight into a new set of optimization and optimization support tools for solving complex design problems.

In order to meet the book's aim, we recognize the need to progress through the necessary background knowledge before launching into the complexities of the full MDO application. Before reaching the chapters devoted to multidisciplinary design, the book introduces and explains the basics of optimization and the method employed for single-discipline optimum design problems. Prior exposure to these basic optimization methods will assist the reader but is not a requirement as we start along the pathway to complex methods with a review of the necessary fundamentals. Readers familiar with the basics of optimization and optimization method may wish to pass by the earlier chapters. However, we all, from time to time, forget what we have previously learned, and in this situation, the early chapters can be viewed as a convenient aide-memoire that can be consulted when required. As regards prerequisite knowledge, we assume the reader is familiar with the vector and matrix calculus and the analysis methods commonly taught in undergraduate engineering courses.

Recent years have seen rapid development in computer technology leading to major increases in computer power and speed that have proved beneficial in general applications and for engineering design in particular. One development of particular importance in the field of MDO is massively concurrent data processing (MCDP) also popularly known as parallel computing. Therefore, throughout the book, we repeatedly point to the use of MCDP as an enabler for solving problems that, previously, were regarded as intractable.

Our objective is simple: to provide sufficient information for the reader to understand the basics of the MDO process rooted in the realities of engineering design practices and benefiting from the rapid advance in computer technology, to see how uncertainty can be incorporated, and to illustrate how KBE tools can give support to the implementation of an MDO design solution system.

1.3 The Engineer in the Loop

It is probably worthwhile to discuss the fact that no optimization process exists to take us out of the box set by the definition of the design space implicit in the initialization and the underlying design concept. In this context, we may note that optimization is always reductionist. For example, an aircraft optimization starting with a biplane could evolve into a monoplane with a low, mid, or high wing; but a biplane will not arise from a configuration initialized as monoplane. This underscores the importance of the initial design concept and why the engineer will remain the designer for the foreseeable future and MDO will remain his subordinate.

Once an initial design configuration has been selected, the engineer has the...