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Research Papers

Integrating Bayesian Calibration, Bias Correction, and Machine Learning for the 2014 Sandia Verification and Validation Challenge Problem

[+] Author and Article Information
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

Shishi Chen

School of Aerospace Engineering,
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

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

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

Wei Chen

Department of Mechanical Engineering,
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 1(1), 011004 (Feb 19, 2016) (12 pages) Paper No: VVUQ-15-1007; doi: 10.1115/1.4031983 History: Received February 06, 2015; Revised October 15, 2015

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.

Copyright © 2016 by ASME
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References

Figures

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Fig. 2

General framework for model updating (calibration and bias correction), UQ, and model validation [10]

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Fig. 3

Detailed work flow for the challenge problem

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Fig. 12

Comparison between validation data and their corresponding predictions for the bias-corrected model without parameter calibration for displacement w under the pressure plus liquid loading conditions

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Fig. 11

Comparison of u-pooling metrics for the calibrated model and the bias-corrected model without parameter calibration

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Fig. 10

U-pooling approach: Transformation of observations through predictive distributions to a standard uniform probability scale

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Fig. 15

Two prediction scenarios

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Fig. 9

Comparison between reserved validation data and updated model predictions for displacement w after model bias correction under the pressure plus liquid loading conditions

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Fig. 8

Comparison between experimental data and model predictions for displacement w after model calibration under the pressure only loading conditions

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Fig. 7

Joint posterior distribution of calibration parameters E and T

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Fig. 6

Flowchart of the modular Bayesian approach

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Fig. 5

First-order sensitivity index of model parameters under the nominal loading condition (P = 73.5 psig, χ = 0.1, and H = 50 in.)

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Fig. 4

First-order sensitivity index of model parameters under the pressure only loading conditions: six different pressure loading levels are evenly spaced over [0, 150] psig

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Fig. 13

Displacements at neighboring locations, which serve as input variables in the machine learning model for predicting σ at location (x, φ)

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Fig. 14

Validation results of the neural network model for σ

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Fig. 16

Flow chart for maximizing the stress and estimating failure probability

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Fig. 17

Local maxima of stress predictions

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Fig. 18

Transformation between liquid composition χ and liquid-specific weight γ

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Fig. 19

Presampling scheme for efficiently locating the failure frontier

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Fig. 20

Failure frontiers in the operating space of P, χ, and H

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