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DOE OSTI2017

Model Calibration with Censored Data

Here, the purpose of model calibration is to make the model predictions closer to reality. The classical Kennedy-O'Hagan approach is widely used for model calibration, which can account for the inadequacy of the computer model while simultaneously estimating the unknown calibration parameters. In many applications, the phenomenon of censoring occurs when the exact outcome of the physical experiment is not observed, but is only known to fall within a certain region. In such cases, the Kennedy-O'Hagan approach cannot be used directly, and we propose a method to incorporate the censoring information when performing model calibration. The method is applied to study the compression phenomenon of liquid inside a bottle. The results show significant improvement over the traditional calibration methods, especially when the number of censored observations is large.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Reduced chemistry model calibration using unsteady flames with repetitive extinction and ignition

In this paper, combustion in a narrow channel with an imposed temperature gradient is used to calibrate a reduced chemical mechanism. The focus is placed on unsteady flames with repetitive extinction and ignition (FREI) at high pressure. The reduced mechanism follows a hybrid approach, combining a small fuel-dependent submechanism with a detailed fuel-independent submechanism for the core species chemistry. The fuel-dependent submechanism consists of three species and nine reactions describing both the low and high-temperature fuel decomposition pathways. The sensitivity of the extinction and ignition locations to the fuel-dependent reactions is assessed and multiple reactions are found to affect the FREI behavior. The sensitive reactions are calibrated following a Bayesian approach. The calibrated reduced model is compared to a detailed model and good agreement in ignition delay times and laminar flame speeds is observed. Finally, this illustrates the potential of a micro flow reactor with a controlled temperature profile to test fuels, calibrate chemical models, and infer kinetic data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Geomechanical Simulation of Big Hill Strategic Petroleum Reserve (Model Calibration)

A finite element numerical analysis model has been constructed that consists of a realistic mesh capturing the geometries of Big Hill (BH) Strategic Petroleum Reserve (SPR) site using the multi-mechanism deformation (M-D) salt constitutive model and including data taken daily of the wellhead pressure and level of the oil-brine interface. The salt creep rate is not uniform in the salt dome, and creep test data for BH salt is limited. Therefore, a model calibration is necessary to simulate the geomechanical behavior of the salt dome. Cavern volumetric closures of SPR caverns calculated from sonar survey reports are used for the field baseline measurement. The structure factor, A 2 , and transient strain limit factor, K o , in the M-D constitutive model are used for model calibration. An A 2 value obtained experimentally from the BH salt and K o value of WIPP salt are used as the baseline values. To adjust the magnitude of A 2 and K o , multiplication factors A2F and KOF are defined, respectively. The A2F and KOF values of the salt dome and salt drawdown layer of elements surrounding each SPR cavern have been determined through a number of back fitting analyses. The trendlines of the predictions and sonar data match up well for BH 101, 103, 104, 106, 110, 111, and 113. The prediction curves are close to the sonar data for BH 102 and 114. However, the prediction curves for BH 105, 107, 108, 109, and 112 are not close to the sonar data. An inconsistency was found in the sonar data, i.e. the sonar measurements of cavern volumes increase with time, during some periods for BH 101, 104, 106, 107, and 112. A follow-up report in 2019 will provide a resolution for these issues.

02 PETROLEUM↗

DOE OSTI2024

Advancing earth system model calibration: a diffusion-based method

Understanding of climate impact on ecosystems globally requires site-specific model calibration. Here we introduce a novel diffusion-based uncertainty quantification (DBUQ) method for efficient model calibration. DBUQ is a score-based diffusion model that leverages Monte Carlo simulation to estimate the score function and evaluates a simple neural network to quickly generate samples for approximating parameter posterior distributions. DBUQ is stable, efficient, and can effectively calibrate the model given diverse observations, thereby enabling rapid and site-specific model calibration on a global scale. This capability significantly advances Earth system modeling and our understanding of climate impacts on Earth systems. We demonstrate DBUQ's capability in E3SM land model calibration at the Missouri Ozark AmeriFlux forest site. Both synthetic and real-data applications indicate that DBUQ produces accurate parameter posterior distributions similar to those generated by Markov Chain Monte Carlo sampling but with 30X less computing time. This efficiency marks a significant stride in model calibration, paving the way for more effective and timely climate impact analyses.

Liu, Yanfang↗

DOE OSTI2016

A Method to Test Model Calibration Techniques

This paper describes a method for testing model calibration techniques. Calibration is commonly used in conjunction with energy retrofit audit models. An audit is conducted to gather information about the building needed to assemble an input file for a building energy modeling tool. A calibration technique is used to reconcile model predictions with utility data, and then the 'calibrated model' is used to predict energy savings from a variety of retrofit measures and combinations thereof. Current standards and guidelines such as BPI-2400 and ASHRAE-14 set criteria for 'goodness of fit' and assume that if the criteria are met, then the calibration technique is acceptable. While it is logical to use the actual performance data of the building to tune the model, it is not certain that a good fit will result in a model that better predicts post-retrofit energy savings. Therefore, the basic idea here is that the simulation program (intended for use with the calibration technique) is used to generate surrogate utility bill data and retrofit energy savings data against which the calibration technique can be tested. This provides three figures of merit for testing a calibration technique, 1) accuracy of the post-retrofit energy savings prediction, 2) closure on the 'true' input parameter values, and 3) goodness of fit to the utility bill data. The paper will also discuss the pros and cons of using this synthetic surrogate data approach versus trying to use real data sets of actual buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2016

A Method to Test Model Calibration Techniques: Preprint

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS2007

A Comparison of Two Balance Calibration Model Building Methods

Simulated strain-gage balance calibration data is used to compare the accuracy of two balance calibration model building methods for different noise environments and calibration experiment designs. The first building method obtains a math model for the analysis of balance calibration data after applying a candidate math model search algorithm to the calibration data set. The second building method uses stepwise regression analysis in order to construct a model for the analysis. Four balance calibration data sets were simulated in order to compare the accuracy of the two math model building methods. The simulated data sets were prepared using the traditional One Factor At a Time (OFAT) technique and the Modern Design of Experiments (MDOE) approach. Random and systematic errors were introduced in the simulated calibration data sets in order to study their influence on the math model building methods. Residuals of the fitted calibration responses and other statistical metrics were compared in order to evaluate the calibration models developed with different combinations of noise environment, experiment design, and model building method. Overall, predicted math models and residuals of both math model building methods show very good agreement. Significant differences in model quality were attributable to noise environment, experiment design, and their interaction. Generally, the addition of systematic error significantly degraded the quality of calibration models developed from OFAT data by either method, but MDOE experiment designs were more robust with respect to the introduction of a systematic component of the unexplained variance.

DeLoach, Richard↗

DOE OSTI2024

Reduced-dimension Bayesian optimization for model calibration of transient vapor compression cycles

Development and calibration of first-principles dynamic models of vapor compression cycles (VCCs) is of critical importance for applications that include control design and fault detection and diagnostics. Nevertheless, the inherent complexity of models that are represented by large systems of differential–algebraic equations leads to significant challenges for model calibration processes that utilize classical gradient-based methods. Bayesian optimization (BO) is a sample-efficient and gradient-free approach using a probabilistic surrogate model and optimal search over a feasible parameter space. Despite the benefits of BO in reducing computational costs, challenges remain in dealing with a high-dimensional calibration task resulting from a large set of parameters that have significant impacts on system behavior and need to be calibrated simultaneously. This paper presents a reduced-dimension BO framework for calibrating transient VCCs models where the calibration space is projected to a low-dimensional subspace for accelerating convergence of the solution algorithm and consequently reducing the number of transient simulations. The proposed approach was demonstrated via two case studies associated with different VCC applications where 10 parameters were calibrated in each case using laboratory measurements. The reduced-dimension BO framework only required 1 / 8 th of the iterations associated with a standard BO method that deals with high-dimensional calibration parameters for converged solutions and yielded comparable accuracy. Furthermore, both calibrated models revealed significant accuracy improvements compared to uncalibrated models.

Ma, Jiacheng↗

DOE OSTI2024

Rapid measurement of soluble xylo-oligomers using near-infrared spectroscopy (NIRS) and multivariate statistics: calibration model development and practical approaches to model optimization

Rapid monitoring of biomass conversion processes using techniques such as near-infrared (NIR) spectroscopy can be substantially quicker and less labor-, resource-, and energy-intensive than conventional measurement techniques such as gas or liquid chromatography (GC or LC) due to the lack of solvents and preparation methods, as well as removing the need to transfer samples to an external lab for analytical evaluation. The purpose of this study was to determine the feasibility of rapid monitoring of a biomass conversion process using NIR spectroscopy combined with multivariate statistical modeling, and to examine the impact of (1) subsetting the samples in the original dataset by process location and (2) reducing the spectral range used in the calibration model on model performance. We develop multivariate calibration models for the concentrations of soluble xylo-oligosaccharides (XOS), monomeric xylose, and total solids at multiple points in a biomass conversion process which produces and then purifies XOS compounds from sugar cane bagasse. A single model using samples from multiple locations in the process stream showed acceptable performance as measured by standard statistical measures. However, compared to the single model, we show that separate models built by segregating the calibration samples according to process location show improved performance. We also show that combining an understanding of the sample spectra with simple multivariate analysis tools can result in a calibration model with a substantially smaller spectral range that provides essentially equal performance to the full-range model. We demonstrate that real-time monitoring of soluble xylo-oligosaccharides (XOS), monomeric xylose, and total solids concentration at multiple points in a process stream using NIR spectroscopy coupled with multivariate statistics is feasible. Segregation of sample populations by process location improves model performance. Models using a reduced spectral range containing the most relevant spectral signatures show very similar performance to the full-range model, reinforcing the importance of performing robust exploratory data analysis before beginning multivariate modeling.

09 BIOMASS FUELS↗

DOE OSTI2024

A Diffusion‐Based Uncertainty Quantification Method to Advance E3SM Land Model Calibration

Abstract Calibrating land surface models and accurately quantifying their uncertainty are crucial for improving the reliability of simulations of complex environmental processes. This, in turn, advances our predictive understanding of ecosystems and supports climate‐resilient decision‐making. Traditional calibration methods, however, face challenges of high computational costs and difficulties in accurately quantifying parameter uncertainties. To address these issues, we develop a diffusion‐based uncertainty quantification (DBUQ) method. Unlike conventional generative diffusion methods, which are computationally expensive and memory‐intensive, DBUQ innovates by formulating a parameterized generative model and approximates this model through supervised learning, which enables quick generation of parameter posterior samples to quantify its uncertainty. DBUQ is effective, efficient, and general‐purpose, making it suitable for site‐specific ecosystem model calibration and broadly applicable for parameter uncertainty quantification across various earth system models. In this study, we applied DBUQ to calibrate the Energy Exascale Earth System Model land model at the Missouri Ozark AmeriFlux forest site. Results indicated that DBUQ produced accurate parameter posterior distributions similar to those from Markov Chain Monte Carlo sampling but with 30 times less computing time. This significant improvement in efficiency suggests that DBUQ can enable rapid, site‐level model calibration at a global scale, enhancing our predictive understanding of climate impacts on terrestrial ecosystems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

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

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.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Geomechanical Simulation of Bayou Choctaw Strategic Petroleum Reserve - Model Calibration.

A finite element numerical analysis model has been constructed that consists of a realistic mesh capturing the geometries of Bayou Choctaw (BC) Strategic Petroleum Reserve (SPR) site and multi - mechanism deformation ( M - D ) salt constitutive model using the daily data of actual wellhead pressure and oil - brine interface. The salt creep rate is not uniform in the salt dome, and the creep test data for BC salt is limited. Therefore, the model calibration is necessary to simulate the geomechanical behavior of the salt dome. The cavern volumetric closures of SPR caverns calculated from CAVEMAN are used for the field baseline measurement. The structure factor, A 2 , and transient strain limit factor, K 0 , in the M - D constitutive model are used for the calibration. The A 2 value obtained experimentally from the BC salt and K 0 value of Waste Isolation Pilot Plant (WIPP) salt are used for the baseline values. T o adjust the magnitude of A 2 and K 0 , multiplication factors A2F and K0F are defined, respectively. The A2F and K0F values of the salt dome and salt drawdown skins surrounding each SPR cavern have been determined through a number of back fitting analyses. The cavern volumetric closures calculated from this model correspond to the predictions from CAVEMAN for six SPR caverns. Therefore, this model is able to predict past and future geomechanical behaviors of the salt dome, caverns, caprock , and interbed layers. The geological concerns issued in the BC site will be explained from this model in a follow - up report .

58 GEOSCIENCES↗

DOE OSTI2016

A frequentist approach to computer model calibration

The paper considers the computer model calibration problem and provides a general frequentist solution. Under the framework proposed, the data model is semiparametric with a non-parametric discrepancy function which accounts for any discrepancy between physical reality and the computer model. In an attempt to solve a fundamentally important (but often ignored) identifiability issue between the computer model parameters and the discrepancy function, the paper proposes a new and identifiable parameterization of the calibration problem. It also develops a two-step procedure for estimating all the relevant quantities under the new parameterization. This estimation procedure is shown to enjoy excellent rates of convergence and can be straightforwardly implemented with existing software. For uncertainty quantification, bootstrapping is adopted to construct confidence regions for the quantities of interest. As a result, the practical performance of the methodology is illustrated through simulation examples and an application to a computational fluid dynamics model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

High Accuracy Transistor Compact Model Calibrations

Typically, transistors are modeled by the application of calibrated nominal and range models. These models consists of differing parameter values that describe the location and the upper and lower limits of a distribution of some transistor characteristic such as current capacity. Correspondingly, when using this approach, high degrees of accuracy of the transistor models are not expected since the set of models is a surrogate for a statistical description of the devices. The use of these types of models describes expected performances considering the extremes of process or transistor deviations. In contrast, circuits that have very stringent accuracy requirements require modeling techniques with higher accuracy. Since these accurate models have low error in transistor descriptions, these models can be used to describe part to part variations as well as an accurate description of a single circuit instance. Thus, models that meet these stipulations also enable the calculation of quantification of margins with respect to a functional threshold and uncertainties in these margins. Given this need, new model high accuracy calibration techniques for bipolar junction transistors have been developed and are described in this report.

42 ENGINEERING↗

DOE OSTI2020

Accuracy of High Explosive Data used for Reactive Burn Model Calibration

Reactive burn models for a high explosive (HE) have three components: an equation of state (EOS) for the products, an EOS for the reactants and a reaction rate. For the products, we discuss the uncertainty in data for the planar detonation state and its release isentrope. For the reactants, the uncertainty in the principal shock locus data is discussed. For the reaction rate, we discuss uncertainties in shock initiation data (distance-of-run to detonation as a function of shock pressure), and curvature effect data (detonation speed as a function of front curvature). An important source of uncertainty for calibrating the reaction rate for a plastic-bonded explosive (PBX) results from variations in heterogeneities; that is the mesoscale structure of HE grains, binder and porosity. This shows up in the scatter of both shock initiation data and curvature effect data with small changes in initial density and initial temperature, and systematic changes with PBX lot. As illustrative examples, we use data for the conventional HMX based PBX 9501 and the insensitive TATB based PBX 9502 since these explosives have been extensively studied and high quality data are readily available in the literature.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2020

Dealing with Measurement Uncertainties as Nuisance Parameters in Bayesian Model Calibration

In the presence of model discrepancy, the calibration of physics-based models for physical parameter inference is a challenging problem. Lack of identifiability between calibration parameters and model discrepancy requires additional identifiability constraints to be placed on the model discrepancy to obtain unique physical parameter estimates. If these assumptions are violated, the inference for the calibration parameters can be systematically biased. In many applications, such as in dynamic material property experiments, many of the calibration inputs refer to measurement uncertainties. Here, we develop a metric for identifying overfitting of these measurement uncertainties, propose a prior capable of reducing this overfitting, and show how this leads to a diagnostic tool for validation of physical parameter inference. The approach is demonstrated for a benchmark example and applied for a material property application to perform inference on the equation of state parameters of tantalum.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

An asynchronous parallel high-throughput model calibration framework for crystal plasticity finite element constitutive models

Crystal plasticity finite element model (CPFEM) is a powerful numerical simulation in the integrated computational materials engineering toolboxes that relates microstructures to homogenized materials properties and establishes the structure–property linkages in computational materials science. However, to establish the predictive capability, one needs to calibrate the underlying constitutive model, verify the solution and validate the model prediction against experimental data. Bayesian optimization (BO) has stood out as a gradient-free efficient global optimization algorithm that is capable of calibrating constitutive models for CPFEM. Here in this paper, we apply a recently developed asynchronous parallel constrained BO algorithm to calibrate phenomenological constitutive models for stainless steel 304 L, Tantalum, and Cantor high-entropy alloy.

304L stainless steel↗

DOE OSTI2019

Bayesian Model Calibration for Extrapolative Prediction via Gibbs Posteriors

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to quantify uncertainty in physical parameters for extrapolative prediction, then there is no need to perform inference on the discrepancy term. With this in mind, we introduce Gibbs posteriors as an alternative Bayesian method for model calibration, which updates the prior with a loss function connecting the data to the parameter. The target of inference is the physical parameter value which minimizes the expected loss. We propose to tune the loss scale of the Gibbs posterior to maintain nominal frequentist coverage under assumptions of the form of model discrepancy, and present a bootstrap implementation for approximating coverage rates. Our approach is highly modular, allowing an analyst to easily encode a wide variety of such assumptions. Furthermore, we provide a principled method of combining posteriors calculated from data subsets. We apply our methods to data from an experiment measuring the material properties of tantalum.

36 MATERIALS SCIENCE↗