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Research Papers: Design Automation

Sensitivity-Based Parameter Calibration and Model Validation Under Model Error

[+] Author and Article Information
Na Qiu

Mechanical and Electrical Engineering College,
Hainan University,
Haikou 570228, China;
Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: nnaqiu@163.com

Chanyoung Park

Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611

Yunkai Gao

School of Automotive Studies,
Tongji University,
Shanghai 201804, China

Jianguang Fang

School of Civil and Environmental Engineering,
University of Technology Sydney,
Sydney 2007, NSW, Australia
e-mail: fangjg87@gmail.com

Guangyong Sun

School of Aerospace, Mechanical
and Mechatronic Engineering,
The University of Sydney,
Sydney 2006, NSW, Australia
e-mail: sgy800@126.com

Nam H. Kim

Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: nkim@ufl.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 5, 2017; final manuscript received September 16, 2017; published online November 9, 2017. Assoc. Editor: Xiaoping Du.

J. Mech. Des 140(1), 011403 (Nov 09, 2017) (9 pages) Paper No: MD-17-1317; doi: 10.1115/1.4038298 History: Received May 05, 2017; Revised September 16, 2017

In calibrating model parameters, it is important to include the model discrepancy term in order to capture missing physics in simulation, which can result from numerical, measurement, and modeling errors. Ignoring the discrepancy may lead to biased calibration parameters and predictions, even with an increasing number of observations. In this paper, a simple yet efficient calibration method is proposed based on sensitivity information when the simulation model has a model error and/or numerical error but only a small number of observations are available. The sensitivity-based calibration method captures the trend of observation data by matching the slope of simulation predictions and observations at different designs and then utilizing a constant value to compensate for the model discrepancy. The sensitivity-based calibration is compared with the conventional least squares calibration method and Bayesian calibration method in terms of parameter estimation and model prediction accuracies. A cantilever beam example, as well as a honeycomb tube crush example, is used to illustrate the calibration process of these three methods. It turned out that the sensitivity-based method has a similar performance with the Bayesian calibration method and performs much better than the conventional method in parameter estimation and prediction accuracy.

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Copyright © 2017 by ASME
Topics: Calibration , Errors
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Figures

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Fig. 1

Schematic of model calibration and model validation

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Fig. 2

Illustration of sensitivity-based calibration method

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Fig. 3

Cantilever beam model

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Fig. 4

Comparison of the results of the true model and the conventional calibration methods using least squares based on one training point

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Fig. 5

Comparison of the results of true model, conventional least squares and sensitivity-based calibration methods based on two training points

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Fig. 6

Comparison of the results of sensitivity-based and Bayesian calibration methods based on two training points

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Fig. 7

Comparison of the calibration and validation error based on more observation data

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Fig. 8

Cross-sectional configurations of honeycomb tubes

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Fig. 9

Honeycomb tube structure under axial load

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Fig. 10

Experiment of the honeycomb tubes: (a) specimen and (b) test machine

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Fig. 11

Comparison of three aluminum honeycomb tubes with different parameters: (a) C6T5, (b) C3T7, and (c) C3T8

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Fig. 12

Comparison of the calibration and validation results for honeycomb structures

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Fig. 13

Comparison of the relative error of calibration and validation result for different methods

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