R. A. Bates

Achieving Robust Design from Computer Simulations

Abstract Computer simulations are widely used during product development. In particular, computer experiments are often conducted in order to optimize both product and process performance while respecting constraints that may be imposed. Several methods for achieving robust design in this context are described and compared with the aid of a simple example problem. The methods presented compare classical as well as modern approaches and introduce the idea of a ‘stochastic response’ to aid the search for robust solutions. Emphasis is placed on the efficiency of each method with respect to computational cost and the ability to formulate objectives that encapsulate the notion of robustness.

A Global Selection Procedure for Polynomial Interpolators

The drive for efficient methods of testing design ideas and prototypes, particularly in engineering, has led to a rapid increase in the field of numerical simulation methods using computers, such as finite-element analysis. This increase in popularity has fueled the need for empirical models that interpolate data collected from these simulations. We propose a selection algorithm to efficiently explore an appropriate class of polynomial interpolators. The storage of polynomial models is made efficient and effective thanks to a special coding. Finally, the last stage of the algorithm returns a model that is no longer an interpolator but, having a smaller number of terms, is simpler and easier to handle and understand. In this way, a trade-off between accuracy and simplicity of the model is attained.

Lattices and dual lattices in optimal experimental design for Fourier models

Number-theoretic lattices, used in integration theory, are studied from the viewpoint of the design and analysis of experiments. For certain Fourier regression models lattices are optimal as experimental designs because they produce orthogonal information matrices. When the Fourier model is restricted, that is a special subset of the full factorial (cross-spectral) model is used, there is a difficult inversion problem to find generators for an optimal design for the given model. Asymptotic results are derived for certain models as the dimension of the space goes to infinity. These can be thought of as a complexity theory connecting designs and models or as special type of Nyquist sampling theory.

Tolerancing and optimization for model‐based robust engineering design

There are various methods for performing tolerancing and robust design within a computer-aided design (CAD) framework. Recent work on fitting statistical emulators to CAD systems can be used to facilitate fast optmimization geared towards robustness against input variation. After discussing available methods for tolerancing within a common framework, a comprehensive strategy for robust design is developed which involves a combination of circuit simulation, emulation and global optimization.

Robust optimization of cardiovascular stents: a comparison of methods

Modern engineering design contains both creative and analytic components. This paper discusses the design process and illustrates links between design optimization and conceptual design through the re-design of a cardiovascular stent. A comparison is presented of two methods for design improvement: genetic algorithms (GA) and model-based robust engineering design (RED). Computational fluid dynamics (CFD) models are used to generate measurements of the quality of competing designs based on the concept of dissipated power. Alternative performance measures are also discussed. Environmental noise is introduced into the analysis and consideration is given to the treatment of discrete and continuous design parameters. Improved designs are identified using both methods and verified with further CFD analyses, and the benefits of each method are discussed.

Feasible region approximation: a comparison of search cone and convex hull methods

The concept of the design space encapsulates the search for optimal design configurations of engineering systems. During this search, infeasible or unsafe regions may be encountered, representing particular combinations of parameter values which cause the system to fail. These regions need to be characterized so that they can be avoided during the search for improved designs. In addition, the proximity of a design to a feasible boundary may be related to the reliability and robustness of the design in the face of variation in manufacture and use. A chemical engineering example is used to show how feasible design regions can be modelled using integer lattices and kriging methods. An algorithm using Hilbert bases is developed and used to select points on the boundary of the feasible region with arbitrary closeness so that the properties of the kriging model are such that the model remains stable and the star-shaped necessary condition is met.

A finite-element-based formulation for sensitivity studies of piezoelectric systems

Sensitivity analysis is a branch of numerical analysis which aims to quantify the effects that variability in the parameters of a numerical model have on the model output. A finite-element-based sensitivity analysis formulation for piezoelectric media is developed here and implemented to simulate the operational and sensitivity characteristics of a piezoelectric-based distributed mode actuator (DMA). The work acts as a starting point for robustness analysis in the DMA technology.

Bond Graph Based Sensitivity and Uncertainty Analysis Modelling for Micro-Scale Multiphysics Robust Engineering Design

Components within micro-scale engineering systems are often at the limits of commercial miniaturization and this can cause unexpected behavior and variation in performance. As such, modelling and analysis of system robustness plays an important role in product development. Here schematic bond graphs are used as a front end in a sensitivity analysis based strategy for modelling robustness in multiphysics micro-scale engineering systems. As an example, the analysis is applied to a behind-the-ear (BTE) hearing aid. By using bond graphs to model power flow through components within dierent physical domains of the hearing aid, a set of dierential equations to describe the system dynamics is collated. Based on these equations, sensitivity analysis calculations are used to approximately model the nature and the sources of output uncertainty during system operation. These calculations represent a robustness evaluation of the current hearing aid design and oer a means of identifying potential for improved designs of multiphysics systems by way of key parameter identification.

Bond graph analysis in robust engineering design

Within engineering design, optimization often involves building models of working systems to improve design objectives such as performance, reliability and cost. Bond graph models express systems in terms of energy flow and can be used to identify key factors that influence system behaviour. Robust Engineering Design (RED) is a strategy for the optimization of systems through experimentation and empirical modelling; however, experiments can often be prohibitively expensive for large or complex systems. By using bond graphs as a front-end to RED, experiments on systems could be designed more efficiently, reducing the number of experiments required for accurate empirical modelling. Two case study examples are given which show that bond graphs can be used to good effect in the empirical analysis of engineering systems.

Smooth supersaturated models

In areas such as kernel smoothing and non-parametric regression, there is emphasis on smooth interpolation. We concentrate on pure interpolation and build smooth polynomial interpolators by first extending the monomial (polynomial) basis and then minimizing a measure of roughness with respect to the extra parameters in the extended basis. Algebraic methods can help in choosing the extended basis. We get arbitrarily close to optimal smoothing for any dimension over an arbitrary region, giving simple models close to splines. We show in examples that smooth interpolators perform much better than straight polynomial fits and for small sample size, better than kriging-type methods, used, for example in computer experiments.