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Research Papers: Design Automation

Model Discrepancy Quantification in Simulation-Based Design of Dynamical Systems

[+] Author and Article Information
Zhen Hu

Department of Industrial and Manufacturing
Systems Engineering,
University of Michigan-Dearborn,
2340 Heinz Prechter Engineering Complex
(HPEC)
Dearborn, MI 48128
e-mail: zhennhu@umich.edu

Chao Hu

Assistant Professor
Department of Mechanical Engineering,
Iowa State University,
2026 Black Engineering,
Ames, IA 50011;
Department of Electrical and Computer Engineering,
Iowa State University,
2026 Black Engineering,
Ames, IA 50011
e-mail: chaohu@iastate.edu

Zissimos P. Mourelatos

Professor
Mechanical Engineering Department,
Oakland University,
Engineering Center,
Room 402D, 115 Library Drive,
Rochester, MI 48309
e-mail: mourelat@oakland.edu

Sankaran Mahadevan

John R. Murray Sr. Professor of Engineering,
Department of Civil and Environmental
Engineering,
Vanderbilt University,
2201 West End Avenue, Box 1831, Station B,
Nashville, TN 37235
e-mail: sankaran.mahadevan@vanderbilt.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 26, 2018; final manuscript received September 9, 2018; published online October 8, 2018. Assoc. Editor: Xiaoping Du.

J. Mech. Des 141(1), 011401 (Oct 08, 2018) (13 pages) Paper No: MD-18-1148; doi: 10.1115/1.4041483 History: Received February 26, 2018; Revised September 09, 2018

Discrete-time state-space models have been extensively used in simulation-based design of dynamical systems. These prediction models may not accurately represent the true physics of a dynamical system due to potentially flawed understanding of the system, missing physics, and/or numerical approximations. To improve the validity of these models at new design locations, this paper proposes a novel dynamic model discrepancy quantification (DMDQ) framework. Time-instantaneous prediction models are constructed for the model discrepancies of “hidden” state variables, and are used to correct the discrete-time prediction models at each time-step. For discrete-time models, the hidden state variables and their discrepancies are coupled over two adjacent time steps. Also, the state variables cannot be directly measured. These factors complicate the construction of the model discrepancy prediction models. The proposed DMDQ framework overcomes these challenges by proposing two discrepancy modeling approaches: an estimation-modeling approach and a modeling-estimation approach. The former first estimates the model discrepancy and then builds a nonparametric prediction model of the model discrepancy; the latter builds a parametric prediction model of the model discrepancy first and then estimates the parameters of the prediction model. A subsampling method is developed to reduce the computational effort in building the two types of prediction models. A mathematical example and an electrical circuit dynamical system demonstrate the effectiveness of the proposed DMDQ framework and highlight the advantages and disadvantages of the proposed approaches.

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Figures

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Fig. 1

Illustration of a discrete-time dynamical system in state-space form

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Fig. 2

A DBN representation illustrating connections between different variables

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Fig. 3

Bayesian network after arrow reversing at ti+1

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Fig. 4

Time-dependent inputs of the five experiments

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Fig. 5

Prediction and observation for experiments 1 and 2

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Fig. 6

Prediction and observation for experiments 3–5

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Fig. 7

Model discrepancy of state variable: (a) true model and (b) prediction model by approach one

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Fig. 8

Approximated model discrepancy by approach two

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Fig. 9

Prediction for a new input after correction using approach one

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Fig. 10

Prediction for a new input after correction using approach two

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Fig. 11

Absolute prediction errors of different methods

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Fig. 12

An electrical circuit dynamical system

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Fig. 13

Observations, prediction, and selected points of three experiments (electrical circuit)

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Fig. 14

Model discrepancy of “hidden” state variable: (a) true model and (b) approach one

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Fig. 15

Model discrepancy of “hidden” state variable: (a) approach one-linear and (b) approach two

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Fig. 16

Model discrepancy of “hidden” state variable: (a) true model and (b) approach one

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Fig. 17

Model discrepancy of “hidden” state variable: (a) approach one-linear and (b) approach two

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Fig. 18

True versus predicted observations at a new input condition

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