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Research Papers: Design Automation

Reduction of Epistemic Model Uncertainty in Simulation-Based Multidisciplinary Design

[+] Author and Article Information
Zhen Jiang

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: zhenjiang2015@u.northwestern.edu

Shishi Chen

School of Aerospace Engineering;
Key Laboratory of Dynamics
and Control of Flight Vehicle,
Ministry of Education of P.R. China,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: shishi.chen@northwestern.edu

Daniel W. Apley

Department of Industrial Engineering
and Management Sciences,
Northwestern University,
Evanston, IL 60208
e-mail: dapley@northwestern.edu

Wei Chen

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: weichen@northwestern.edu

1Z. Jiang and S. Chen contributed equally to this work.

2Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 8, 2015; final manuscript received June 5, 2016; published online June 30, 2016. Assoc. Editor: Nam H. Kim.

J. Mech. Des 138(8), 081403 (Jun 30, 2016) (13 pages) Paper No: MD-15-1693; doi: 10.1115/1.4033918 History: Received October 08, 2015; Revised June 05, 2016

Model uncertainty is a significant source of epistemic uncertainty that affects the prediction of a multidisciplinary system. In order to achieve a reliable design, it is critical to ensure that the disciplinary/subsystem simulation models are trustworthy, so that the aggregated uncertainty of system quantities of interest (QOIs) is acceptable. Reduction of model uncertainty can be achieved by gathering additional experiments and simulations data; however, resource allocation for multidisciplinary design optimization (MDO) and analysis remains a challenging task due to the complex structure of the system, which involves decision makings about where (sampling locations), what (disciplinary responses), and which type (simulations versus experiments) for allocating more resources. Instead of trying to concurrently make the above decisions, which would be generally intractable, we develop a novel approach in this paper to break the decision making into a sequential procedure. First, a multidisciplinary uncertainty analysis (MUA) is developed to identify the input settings with unacceptable amounts of uncertainty with respect to the system QOIs. Next, a multidisciplinary statistical sensitivity analysis (MSSA) is developed to investigate the relative contributions of (functional) disciplinary responses to the uncertainty of system QOIs. The input settings and critical responses to allocate resources are selected based on the results from MUA and MSSA, with the aid of a new correlation analysis derived from spatial-random-process (SRP) modeling concepts, ensuring the sparsity of the selected inputs. Finally, an enhanced preposterior analysis predicts the effectiveness of allocating experimental and/or computational resource to answer the question about which type of resource to allocate. The proposed method is applied to a benchmark electronic packaging problem to demonstrate how epistemic model uncertainty is gradually reduced via resource allocation for data gathering.

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Figures

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Fig. 1

Illustration of GP-based model bias correction

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Fig. 2

A notional multidisciplinary system with epistemic model uncertainty

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Fig. 3

Flowchart of the proposed resource allocation approach

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Fig. 4

The preposterior analysis

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Fig. 5

Electronic packaging system

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Fig. 6

Design of experiments for model bias correction in the thermal discipline: 40 experiments + 40 simulations sparsely over the six-dimensional space {x1, x2, x3, x4, y6, y7}. The data points are plotted by projecting them onto {y6, y7} for illustration.

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Fig. 7

Comparison between the validation data and the updated emulators of (a) y11 and (b) y12 after model bias correction

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Fig. 8

Two thousand LHS samples to explore the eight-dimensional design space x1x8 (projected onto {x1, x2} for illustration), and the final selected samples for resource allocation

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Fig. 9

MSSA of the selected ten input settings

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Fig. 10

Preposterior analysis: comparison between the current uncertainty and the expected reduced uncertainty (calculated by taking the average of the reduced uncertainty under 500 sets of hypothetical simulation data)

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Fig. 11

Locations and types of the allocated resources for y11 and y12: (a) y11, first iteration, (b) y11, second iteration, (c) y11, third iteration, (d) y11, fourth iteration, (e) y12, first iteration, (f) y12, second iteration, (g) y12, third iteration, and (h) y12, fourth iteration. Data are over the six-dimensional space {x1, x2, x3, x4, y6, y7} but projected onto {y6, y7} for illustration.

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