This paper describes an integrated Bayesian calibration, bias correction, and machine learning approach to the validation challenge problem posed at the Sandia Verification and Validation Challenge Workshop, May 7–9, 2014. Three main challenges are recognized as: I—identification of unknown model parameters; II—quantification of multiple sources of uncertainty; and III—validation assessment when there are no direct experimental measurements associated with one of the quantities of interest (QoIs), i.e., the von Mises stress. This paper addresses these challenges as follows. For challenge I, sensitivity analysis is conducted to select model parameters that have significant impact on the model predictions for the displacement, and then a modular Bayesian approach is performed to calibrate the selected model parameters using experimental displacement data from lab tests under the “pressure only” loading conditions. Challenge II is addressed using a Bayesian model calibration and bias correction approach. For improving predictions of displacement under “pressure plus liquid” loading conditions, a spatial random process (SRP) based model bias correction approach is applied to develop a refined predictive model using experimental displacement data from field tests. For challenge III, the underlying relationship between stress and displacement is identified by training a machine learning model on the simulation data generated from the supplied tank model. Final predictions of stress are made via the machine learning model and using predictions of displacements from the bias-corrected predictive model. The proposed approach not only allows the quantification of multiple sources of uncertainty and errors in the given computer models, but also is able to combine multiple sources of information to improve model performance predictions in untested domains.
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March 2016
Research-Article
Integrating Bayesian Calibration, Bias Correction, and Machine Learning for the 2014 Sandia Verification and Validation Challenge Problem
Wei Li,
Wei Li
School of Aeronautics,
Northwestern Polytechnical University,
127 West Youyi Road,
Hangkong Building C506,
Xi'an, Shaanxi 710072, China
e-mail: liwiair@gmail.com
Northwestern Polytechnical University,
127 West Youyi Road,
Hangkong Building C506,
Xi'an, Shaanxi 710072, China
e-mail: liwiair@gmail.com
Search for other works by this author on:
Shishi Chen,
Shishi Chen
School of Aerospace Engineering,
Beijing Institute of Technology,
5 South Zhongshancun Street,
Beijing 100081, China
e-mail: shishi.chen@northwestern.edu
Beijing Institute of Technology,
5 South Zhongshancun Street,
Beijing 100081, China
e-mail: shishi.chen@northwestern.edu
Search for other works by this author on:
Zhen Jiang,
Zhen Jiang
Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road, Tech DG61,
Evanston, IL 60208
e-mail: ZhenJiang2015@u.northwestern.edu
Northwestern University,
2145 Sheridan Road, Tech DG61,
Evanston, IL 60208
e-mail: ZhenJiang2015@u.northwestern.edu
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Daniel W. Apley,
Daniel W. Apley
Department of Industrial Engineering and
Management Sciences,
Northwestern University,
2145 Sheridan Road, Tech C150,
Evanston, IL 60208
e-mail: apley@northwestern.edu
Management Sciences,
Northwestern University,
2145 Sheridan Road, Tech C150,
Evanston, IL 60208
e-mail: apley@northwestern.edu
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Zhenzhou Lu,
Zhenzhou Lu
School of Aeronautics,
Northwestern Polytechnical University,
127 West Youyi Road,
Hangkong Building C506,
Xi'an, Shaanxi 710072, China
e-mail: zhenzhoulu@nwpu.edu.cn
Northwestern Polytechnical University,
127 West Youyi Road,
Hangkong Building C506,
Xi'an, Shaanxi 710072, China
e-mail: zhenzhoulu@nwpu.edu.cn
Search for other works by this author on:
Wei Chen
Wei Chen
Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road, Tech A216,
Evanston, IL 60208
e-mail: weichen@northwestern.edu
Northwestern University,
2145 Sheridan Road, Tech A216,
Evanston, IL 60208
e-mail: weichen@northwestern.edu
Search for other works by this author on:
Wei Li
School of Aeronautics,
Northwestern Polytechnical University,
127 West Youyi Road,
Hangkong Building C506,
Xi'an, Shaanxi 710072, China
e-mail: liwiair@gmail.com
Northwestern Polytechnical University,
127 West Youyi Road,
Hangkong Building C506,
Xi'an, Shaanxi 710072, China
e-mail: liwiair@gmail.com
Shishi Chen
School of Aerospace Engineering,
Beijing Institute of Technology,
5 South Zhongshancun Street,
Beijing 100081, China
e-mail: shishi.chen@northwestern.edu
Beijing Institute of Technology,
5 South Zhongshancun Street,
Beijing 100081, China
e-mail: shishi.chen@northwestern.edu
Zhen Jiang
Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road, Tech DG61,
Evanston, IL 60208
e-mail: ZhenJiang2015@u.northwestern.edu
Northwestern University,
2145 Sheridan Road, Tech DG61,
Evanston, IL 60208
e-mail: ZhenJiang2015@u.northwestern.edu
Daniel W. Apley
Department of Industrial Engineering and
Management Sciences,
Northwestern University,
2145 Sheridan Road, Tech C150,
Evanston, IL 60208
e-mail: apley@northwestern.edu
Management Sciences,
Northwestern University,
2145 Sheridan Road, Tech C150,
Evanston, IL 60208
e-mail: apley@northwestern.edu
Zhenzhou Lu
School of Aeronautics,
Northwestern Polytechnical University,
127 West Youyi Road,
Hangkong Building C506,
Xi'an, Shaanxi 710072, China
e-mail: zhenzhoulu@nwpu.edu.cn
Northwestern Polytechnical University,
127 West Youyi Road,
Hangkong Building C506,
Xi'an, Shaanxi 710072, China
e-mail: zhenzhoulu@nwpu.edu.cn
Wei Chen
Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road, Tech A216,
Evanston, IL 60208
e-mail: weichen@northwestern.edu
Northwestern University,
2145 Sheridan Road, Tech A216,
Evanston, IL 60208
e-mail: weichen@northwestern.edu
1Corresponding author.
Manuscript received February 6, 2015; final manuscript received October 15, 2015; published online February 19, 2016. Guest Editor: Kenneth Hu.
J. Verif. Valid. Uncert. Mar 2016, 1(1): 011004 (12 pages)
Published Online: February 19, 2016
Article history
Received:
February 6, 2015
Revised:
October 15, 2015
Citation
Li, W., Chen, S., Jiang, Z., Apley, D. W., Lu, Z., and Chen, W. (February 19, 2016). "Integrating Bayesian Calibration, Bias Correction, and Machine Learning for the 2014 Sandia Verification and Validation Challenge Problem." ASME. J. Verif. Valid. Uncert. March 2016; 1(1): 011004. https://doi.org/10.1115/1.4031983
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