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Research Papers: Design Theory and Methodology

# Q2S2: A New Methodology for Merging Quantitative and Qualitative Information in Experimental Design

[+] Author and Article Information
Rahul Rai

Automated Design Lab, Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712-0292rahulrai@mail.utexas.edu

Matthew Campbell1

Automated Design Lab, Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712-0292mc1@mail.utexas.edu

1

Corresponding author.

J. Mech. Des 130(3), 031103 (Feb 05, 2008) (12 pages) doi:10.1115/1.2829884 History: Received May 30, 2006; Revised October 10, 2007; Published February 05, 2008

## Abstract

Sequential sampling refers to a set of experimental design methods where the next sample point is determined by information from previous experiments. This paper introduces a new sequential sampling method where optimization and user knowledge are used to guide the efficient choice of sample points. This method combines information from multiple sources of varying fidelity including actual physical experiments, computer simulation models of the product, and first principles involved in design and designer’s qualitative intuition about the design. Both quantitative and qualitative information from different sources are merged together to arrive at a new sampling strategy. This is accomplished by introducing the concept of a confidence function $C$, which is represented as a field that is a function of the decision variables $x$ and the performance parameter $f$. The advantages of the approach are demonstrated using different example cases. The examples include design of a bistable microelectro mechanical system switch, a complex and relevant mechanical system.

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## Figures

Figure 1

A single experiment in the design of a heat sink shows that an experiment run at l=4in. yields a surface temperature of 600F

Figure 2

(a) The C field created by introducing the results of a single experiment and (b) the C field that results from including monotonicity information

Figure 3

The Q2S2 process is a cycle of six main steps

Figure 4

In Example 2, taken from Martin and Simpson (37)

Figure 5

In Example 2, the Q2S2 process slowly approximates the true oxidant-temperature relationship. (a) After five nearly evenly distributed sample points. (b) The C′ plot at this stage shows several local optima to sample next. (c) The relationship after ten points; many of which are between the ascribed monotonic regions.

Figure 6

Actual model for the projectile problem

Figure 7

The metamodel curve fit for the projectile problem: (a) using FF, (b) using Latin hypercube, (c) using generalized linear models, (d) using QS, and (e) using Q2S2

Figure 8

Comparison of sampling methods

Figure 9

(a) Potential energy as a function of changing configuration of a MSE system (b) Force versus displacement curve of a MSE system

Figure 10

Step-by-step decoding of the representation of the structure. (a) First beam of length l1 is attached at the origin at orientation angle θ1. (b) Second beam of length l2 and orientation angle θ2 is added to the end of the first beam. (c) The symmetrical half of the structure after adding all the beams and anchoring the beam ends. (d) The final structure. Also, note that the origin is considered as the loading point.

Figure 11

SLS manufactured “macro” prototypes

Figure 12

Feasible solutions generated in ANSYS

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