Improving Identifiability in Model Calibration Using Multiple Responses

Arendt, Paul D.; Apley, Daniel W.; Chen, Wei; Lamb, David; Gorsich, David

doi:10.1115/1.4007573

Cited by 103 publications

(35 citation statements)

References 14 publications

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“…This approach is sufficient for the calibration of tuning parameters for prediction of model output but does not address calibration of physical parameters. Arendt, Apley, Chen, Lamb and Gorsich () discussed the use of multiple outputs to improve calibration of physical parameters but they did not provide an explicit approach for calibration of physical parameters with functional output. Brynjarsdottir and O'Hagan () discussed the issue of artificially decreasing posterior variance by increased sampling from the design space.…”

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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“…There is a closely-related alternative to the DIT assumption that one may be tempted to consider, which, for the reasons discussed below, is not appropriate in this approach. Specifically, in the co-kriging literature [16,35,[40][41][42][43] with a single computer model, it is common to assume that the simulation model y m .x/ is independent of the discrepancy function ı.x/. For our model formulation as Equation (8), if we had assumed that Cov.y m¹i º .x/; ı ¹j º .x 0 // D 0 (for all x; x 0 , and i; j 2 OE1; 2; : : : ; Q), this would imply that for any i ¤ j…”

Section: Approach 2: Parallel Combination Pcmentioning

confidence: 99%

“…An MRGP model is fitted to the simulation responses. Based on the previous work [40,41,43], the prior for this MRGP model can be denoted as:…”

Section: Approachmentioning

confidence: 99%

Nonhierarchical multi‐model fusion using spatial random processes

Chen

Jiang

Yang

et al. 2015

Numerical Meth Engineering

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SUMMARYNew model fusion techniques based on spatial-random-process modeling are developed in this work for combining multi-fidelity data from simulations and experiments. Existing works in multi-fidelity modeling generally assume a hierarchical structure in which the levels of fidelity of the simulation models can be clearly ranked. In contrast, we consider the nonhierarchical situation in which one wishes to incorporate multiple models whose levels of fidelity are unknown or cannot be differentiated (e.g., if the fidelity of the models changes over the input domain). We propose three new nonhierarchical multimodel fusion approaches with different assumptions or structures regarding the relationships between the simulation models and physical observations. One approach models the true response as a weighted sum of the multiple simulation models and a single discrepancy function. The other two approaches model the true response as the sum of one simulation model and a corresponding discrepancy function, and differ in their assumptions regarding the statistical behavior of the discrepancy functions, such as independence with the true response or a common spatial correlation function. The proposed approaches are compared via numerical examples and a real engineering application. Furthermore, the effectiveness and relative merits of the different approaches are discussed.

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“…The so-called "multiple response" calibration of these models is a possible way to overcome this problem [49].…”

Section: Proportional To )mentioning

confidence: 99%

Validation and Calibration of Nuclear Thermal Hydraulics Multiscale Multiphysics Models - Subcooled Flow Boiling Study

Bui¹,

Dinh²,

Williams³

2013

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A ABSTRACTIn addition to a validation data plan for quantification of data needs and strategy for data collection and characterization [1] [2], development of advanced techniques for calibration and validation of complex multiscale, multiphysics nuclear reactor simulation codes are a major component of the CASL VUQ plan.Advanced modeling of LWR systems normally involves a range of physicochemical models describing multiple interacting phenomena, such as thermal hydraulics, reactor physics, coolant chemistry, etc., which occur over a wide range of spatial and temporal scales. To a large extent, the accuracy of (and uncertainty in) overall model predictions is determined by the correctness of various sub-models, which are not conservation-laws based, but empirically derived from measurement data. Such sub-models normally require extensive calibration before the models can be applied to analysis of real reactor problems.This work demonstrates a case study of calibration of a common model of subcooled flow boiling, which is an important multiscale, multiphysics phenomenon in LWR thermal hydraulics. The calibration process is based on a new strategy of model-data integration, in which, all sub-models are simultaneously analyzed and calibrated using multiple sets of data of different types. Specifically, both data on large-scale distributions of void fraction and fluid temperature and data on smallscale physics of wall evaporation were simultaneously used in this work's calibration.In a departure from traditional (or common-sense) practice of tuning/calibrating complex models, a modern calibration technique based on statistical modeling and Bayesian inference was employed, which allowed simultaneous calibration of multiple sub-models (and related parameters) using different datasets. Quality of data (relevancy, scalability, and uncertainty) could be taken into consideration in the calibration process.This work presents a step forward in the development and realization of the CIPS Validation Data Plan [3] [1] at the Consortium for Advanced Simulation of LWRs to enable quantitative assessment of the CASL modeling of Crud-Induced Power Shift (CIPS) phenomenon, in particular, and the CASL advanced predictive capabilities, in general.This report is prepared for the Department of Energy's Consortium for Advanced Simulation of LWRs program's VUQ Focus Area. E EXECUTIVE SUMMARYThis milestone supports a case study of calibration and validation of a realistic and relatively complex subcooled flow boiling model, with the objective to develop recommendations on CASL-wide Model Calibration, Validation, and Uncertainty Quantification efforts. The SFB model utilized a common description of multiphase flow as inter-penetrating continua with conservation laws applied to each phase as a separate field. Small-scale physics related to thermal hydrodynamic inter-phase and flow-wall interactions were represented by various empirical/semi-empirical closure sub-models. In this SFB modeling, the sub-model of wall evaporation, which relied on...

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Improving Identifiability in Model Calibration Using Multiple Responses

Cited by 103 publications

References 14 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

Nonhierarchical multi‐model fusion using spatial random processes

Validation and Calibration of Nuclear Thermal Hydraulics Multiscale Multiphysics Models - Subcooled Flow Boiling Study

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