A preposterior analysis to predict identifiability in the experimental calibration of computer models

Arendt, Paul D.; Apley, Daniel W.; Chen, Wei

doi:10.1080/0740817x.2015.1064554

Cited by 35 publications

(20 citation statements)

References 26 publications

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“…In the prediction setting, model calibration is typically employed to a set of 'best fitting' parameters that do not typically have a physical interpretation but improve the predictive ability of the model. When using computer models for physical parameter estimation, parameter identifiability and model misspecification must be carefully considered to obtain accurate and precise estimates of physical parameters Brynjarsdottir and O'Hagan, 2014;Arendt et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Estimating Material Properties Under Extreme Conditions by Using Bayesian Model Calibration with Functional Outputs

Brown

Hund

2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary Dynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto‐correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment‐specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.

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Section: Introductionmentioning

confidence: 99%

Estimating Material Properties Under Extreme Conditions by Using Bayesian Model Calibration with Functional Outputs

Brown

Hund

2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…To address this, in this subsection, we propose an enhanced preposterior analysis approach (see Fig. 4, based upon a similar idea in the earlier work [44,45]), which, prior to allocating the resources, can predict the posterior variance of y sys if the resources are actually gathered. Different from the existing work in the literature that focuses only on a single type of resource (usually experimental), the preposterior analysis proposed in this section provides insight for any combination of simulations and experiments.…”

Section: Deciding the Type Of Resource To Allocate For Eachmentioning

confidence: 99%

Reduction of Epistemic Model Uncertainty in Simulation-Based Multidisciplinary Design

Jiang

Chen

Apley

et al. 2016

Journal of Mechanical Design

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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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“…One primary objective of this paper is to address the issue of how to select the most appropriate subset of responses to measure experimentally, to best enhance identifiability. We use a preposterior analysis approach built upon the approach introduced in [9,13] that, prior to conducting the physical experiments but after conducting the computer simulations, can predict the relative improvement in identifiability that will result using different subsets of responses. Our preposterior analysis is based on Monte Carlo simulations within a modular Bayesian multi-response spatial random process (SRP) framework.…”

Section: International Journal For Uncertainty Quantificationmentioning

confidence: 99%

Surrogate Preposterior Analyses for Predicting and Enhancing Identifiability in Model Calibration

Jiang

Apley

Chen

2015

Int. J. UncertaintyQuantification

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In physics-based engineering modeling and uncertainty quantification, distinguishing the effects of two main sources of uncertainty-calibration parameter uncertainty and model discrepancy-is challenging. Previous research has shown that identifiability, which is quantified by the posterior covariance of the calibration parameters, can sometimes be improved by experimentally measuring multiple responses of the system that share a mutual dependence on a common set of calibration parameters. In this paper, we address the issue of how to select the most appropriate subset of responses to measure experimentally, to best enhance identifiability. We use a preposterior analysis approach that, prior to conducting physical experiments but after conducting computer simulations, can predict the degree of identifiability that will result using different subsets of responses to measure experimentally. It predicts identifiability via the preposterior covariance from a modular Bayesian Monte Carlo analysis of a multi-response spatial random process (SRP) model. Furthermore, to handle the computational challenge in preposterior analysis, we propose a surrogate preposterior analysis based on Fisher information of the calibration parameters. The proposed methods are applied to a simply supported beam example to select two out of six responses to best improve identifiability. The estimated preposterior covariance is compared to the actual posterior covariance to demonstrate the effectiveness of the methods.

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A preposterior analysis to predict identifiability in the experimental calibration of computer models

Cited by 35 publications

References 26 publications

Estimating Material Properties Under Extreme Conditions by Using Bayesian Model Calibration with Functional Outputs

Estimating Material Properties Under Extreme Conditions by Using Bayesian Model Calibration with Functional Outputs

Reduction of Epistemic Model Uncertainty in Simulation-Based Multidisciplinary Design

Surrogate Preposterior Analyses for Predicting and Enhancing Identifiability in Model Calibration

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