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modeling mechanical behavior of an additively manufactured metal structure with local texture variations: a study on model form error

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modelLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING 2019年第2期27卷 025003-025003页

作者： Brown, Judith A. Bishop, Joseph E. Sandia Natl Labs Engn Sci Ctr POB 5800 Albuquerque NM 87185 USA

The repetitive rapid solidification that occurs in metal additive manufacturing (AM) processes creates microstructures distinctly different from wrought materials. Local variability in AM microstructures (either by design or unintentional) raises questions as to how AM structures should be modeled at the part-scale to minimize modeling error. The key goal of this work is to demonstrate a posteriori error estimation applied to an AM part. It is assumed that the actual microstructure is unknown and an approximate, spatially uniform material model is used. error bounds are calculated for many reference models based on AM microstructures with elongated grain morphology and localized or global fiber textures during a post-processing step. The current findings promote confidence that a posteriori model form error estimation could be used effectively in mechanical performance simulations of AM parts to quickly obtain quantitative error metrics between an approximate model result and many microstructure-based reference models. The a posteriori error estimation introduces significant time savings compared to computing the full reference model solutions. Tight bounds on model form error are obtained when texture variations in the reference models occur on large length scales. For materials with property variation at small length scales, multi-scale error estimation techniques are needed to properly account for the many interfaces present between areas with different properties.

关键词： additive manufacturing texture mechanical properties model form error microstructure variability a posteriori error estimation

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Physics-integrated hybrid framework for model form error identification in nonlinear dynamical systems

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2022年第0期173卷 1页

作者： Garg, Shailesh Chakraborty, Souvik Hazra, Budhaditya Indian Inst Technol Delhi Dept Appl Mech Hauz Khas New Delhi 110016 India Indian Inst Technol Delhi Yardi Sch Artificial Intelligence ScAI New Delhi 110016 India Indian Inst Technol Guwahati Dept Civil Engn Gauhati 781039 Assam India

For real-life nonlinear systems, the exact form of nonlinearity is often not known and the known governing equations are often based on certain assumptions and approximations. Such representation introduce model-form error into the system. In this paper, we propose a novel gray-box modeling approach that not only identifies the model-form error but also utilizes it to improve the predictive capability of the known but approximate governing equation. The primary idea is to treat the unknown model-form error as a residual force and estimate it using dual Bayesian filter based joint input-state estimation algorithms. For improving the predictive capability of the underlying physics, we first use machine learning algorithm to learn a mapping between the estimated state and the input (model-form error) and then introduce it into the governing equation as an additional term. This helps in improving the predictive capability of the governing physics and allows the model to generalize to unseen environment. Although in theory, any machine learning algorithm can be used within the proposed framework, we use Gaussian process in this work. To test the performance of proposed framework, case studies discussing four different dynamical systems are discussed;results for which indicate that the framework is applicable to a wide variety of systems and can produce reliable estimates of original system's states. Apart from this, the algorithm has also been tested for a case where the data has been taken from an experimental setup (Silver box dataset). The results produced further showcase the efficacy of the proposed framework.

关键词： model form error Dual Bayesian filters Gaussian process Gray-box modeling

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Quantified Validation with Uncertainty Analysis for Turbulent Single-Phase Friction models

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NUCLEAR TECHNOLOGY 2019年第12期205卷 1607-1617页

作者： Porter, Nathan W. Mousseau, Vincent A. Avramova, Maria N. North Carolina State Univ Dept Nucl Engn Burlington Engn Labs 3140 2500 Stinson Dr Raleigh NC 27695 USA Sandia Natl Labs Severe Accid Anal POB 5800 Albuquerque NM 87185 USA

This paper introduces a framework for model selection that includes parameter estimation, uncertainty propagation, and quantified validation. The framework is applied to single-phase turbulent friction modeling in CTF, which is a thermal-hydraulic code for nuclear engineering applications. The friction model is chosen because it is well understood and easy to separate from other physics, which allows focus to be on the model selection framework instead of on the particulars of the chosen model. Two different empirical models are compared: the McAdams Correlation and the Simplified McAdams Correlation. The parameter estimation is performed by calibrating each of the friction models to experimental data using the Delayed Rejection Adaptive Metropolis algorithm, which is a Markov Chain Monte Carlo method. State point uncertainties are also considered, which are determined based on measurement errors from the experiment. The input parameter distributions are propagated through CTF using a statistical method with samples. A variety of validation metrics is used to quantify which empirical model is more accurate. It is shown that model form uncertainty can be quantified using validation once all other sources of uncertainty-numerical, sampling, experimental, and parameter-have been quantitatively addressed. When multiple models are available, the one that has the smallest model form error can be selected. Though the framework is applied to a simple example here, the same process can quantify the model form uncertainty of more complicated physics, multiple models, and simulation tools in other fields. Therefore, this work is a demonstration of best practices for future assessments of model form uncertainty.

关键词： model form error uncertainty analysis validation friction factor

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error estimation in coupled multi-physics models

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JOURNAL OF COMPUTATIONAL PHYSICS 2019年 395卷 19-37页

作者： Subramanian, Abhinav Mahadevan, Sankaran Vanderbilt Univ Dept Civil & Environm Engn Nashville TN 37235 USA

model predictions often exhibit discrepancy with respect to experimental observations, due to assumptions and approximations in the model. Bayesian approaches for estimating discrepancy in single models have been studied in the past. In this paper, we approach the problem of discrepancy estimation in coupled models (especially multi-disciplinary models) using Bayesian state estimation methods. The proposed state estimation-based approach is found to have significant advantages over the previously studied Kennedy-O'Hagan method, in the estimation of discrepancies of hidden states, and in the identification of the sources (namely, model form errors) of the discrepancies. We adopt a partitioned approach to estimate discrepancies in weakly coupled systems and perform state estimation separately for the individual disciplines. The proposed approach is illustrated for a four-discipline problem related to aero-thermo-elastic response prediction of a hypersonic aircraft panel. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Discrepancy estimation model form error Multi-disciplinary analysis Hypersonic aircraft panel Bayesian state estimation

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Hierarchical model form uncertainty quantification for turbulent combustion modeling

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COMBUSTION AND FLAME 2020年 221卷 288-295页

作者： Klemmer, Kerry S. Mueller, Michael E. Princeton Univ Dept Mech & Aerosp Engn Princeton NJ 08544 USA

All models invoke assumptions that result in model errors. The objective of model form uncertainty quantification is to translate these assumptions into mathematical statements of uncertainty. If each assumption in a model can be isolated, then the uncertainties associated with each assumption can be independently assessed. In situations where a series of assumptions leads to a hierarchy of models with nested assumptions, physical principles from a higher-fidelity model can be used to directly estimate a physics-based uncertainty in a lower-fidelity model. Turbulent nonpremixed combustion models fall into a natural hierarchy from the full governing equations to Conditional Moment Closure to flamelet-like models to thermodynamic equilibrium, and, at each stage of the hierarchy, a single assumption can be isolated. In this work, estimates are developed for the uncertainties associated with each assumption in the hierarchy. The general method identifies a trigger parameter that can be obtained with information only from the lower-fidelity model that is used to estimate the error in the lower-fidelity model using only physical principles from the higher-fidelity model. Starting from the lowest fidelity model, the trigger parameters identified in this work are the product of a chemical time scale and the scalar dissipation rate for the equilibrium chemistry model, which characterizes the errors associated with neglecting finite-rate chemistry and transport;the reciprocal of the product of a generalized Lagrangian flow time and the scalar dissipation rate for the steady flamelet model, which characterizes the errors associated with neglecting flow history effects;and the relative magnitude of the conditional fluctuations for Conditional Moment Closure. The approach is applied in LES to a turbulent nonpremixed simple jet flame to quantify the errors associated with the equilibrium chemistry model and the steady flamelet model. The results indicate that errors associated wi

关键词： Uncertainty quantification model form error Turbulent combustion modeling Large Eddy Simulation

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error and Uncertainty Analysis of Inexact and Imprecise Computer models

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JOURNAL OF COMPUTING IN CIVIL ENGINEERING 2013年第4期27卷 407-418页

作者： Farajpour, Ismail Atamturktur, Sez Clemson Univ Dept Civil Engn Clemson SC 29634 USA

Computer simulations are routinely executed to predict the behavior of complex systems in many fields of engineering and science. These computer-aided predictions involve the theoretical foundation, numerical modeling, and supporting experimental data, all of which come with their associated errors. A natural question then arises concerning the validity of computer model predictions, especially in cases where these models are executed in support of high-consequence decision making. This article lays out a methodology for quantifying the degrading effects of incompleteness and inaccuracy of the theoretical foundation, numerical modeling, and experimental data on the computer model predictions. Through the method discussed in this paper, the validity of model predictions can be judged and communicated between involved parties in a quantitative and objective manner.

关键词： Optimization Uncertainty principles Parameters Calibration Validation errors Computer models Computer aided simulation Optimization Uncertainty propagation Discrepancy bias Parameter calibration Bias correction model validation model form error Test-analysis correlation

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model form uncertainty quantification in turbulent combustion simulations: Peer models

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COMBUSTION AND FLAME 2018年第Jan.期187卷 137-146页

作者： Mueller, Michael E. Raman, Venkat Princeton Univ Dept Mech & Aerosp Engn Princeton NJ 08544 USA Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

Turbulent combustion simulations invoke a number of component models for chemical kinetics, turbulence, flame structure, etc., each of which has an error associated with its structural form and contributes to overall uncertainties in simulation results. These model form errors arise from the necessity of making assumptions in deriving a model. Conventional approaches to estimating model form errors rely on an ad hoc additive error that is then calibrated against experimental or computational data. These approaches inherently neglect any a priori knowledge of physics in developing the model error estimate. Instead, in this work, an inherently physics-based approach to estimating model form error is developed based on the notion of "peer" models. In the generic approach, the error in a candidate model is determined by taking the difference between it and an equally plausible alternative "peer" model with a different set of assumptions. The generic approach is applied in this work to the modeling of the subfilter mixture fraction dissipation rate, which is typically modeled as the ratio of the subfilter mixture fraction variance and a time scale. The typical time scale approximation invokes a turbulent time scale, and a "peer" model is proposed in which a chemical time scale is invoked to estimate the model form error. Using stochastic collocation, the subfilter mixture fraction dissipation rate model form error as well as the uncertainty in a model parameter are propagated through LES calculations of the Sandia D Flame utilizing the steady flamelet model. The results indicate that the mixture fraction, temperature, and carbon monoxide uncertainties increase with downstream distance due to an increase in the relative subfilter mixture fraction variance and increased sensitivity to the time scale approximations, which diverge in magnitude with downstream distance. Uncertainties in these quantities arising from the model form error are shown to be more significant than u

关键词： Uncertainty quantification model form error Turbulent combustion Large Eddy Simulation

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model discrepancy calibration across experimental settings

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2020年 200卷 106818-106818页

作者： Maupin, Kathryn A. Swiler, Laura P. Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA

Despite continuing advances in the reliability of computational modeling and simulation, model inadequacy remains a pervasive concern across scientific disciplines. Further challenges are introduced into the already complex problem of "correcting" an inadequate model when experimental data is collected at varying experimental settings. This paper introduces a general approach to calibrating a model discrepancy function when the model is expected to perform for multiple experimental configurations and give predictions as a function of temporal and/or spatial coordinates.

关键词： Computational modeling model inadequacy model form error model discrepancy Inverse problems Bayes' Rule

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Prediction Uncertainties beyond the Range of Experience: A Case Study in Inertial Confinement Fusion Implosion Experiments

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SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION 2019年第2期7卷 604-633页

作者： Osthus, Dave Vander Wiel, Scott A. Hoffman, Nelson M. Wysocki, Frederick J. Los Alamos Natl Lab Stat Sci Grp Los Alamos NM 87545 USA Los Alamos Natl Lab Plasma Theory & Applicat Los Alamos NM 87545 USA Los Alamos Natl Lab Computat Phys Los Alamos NM 87545 USA

Scientists often predict physical outcomes, e.g., experimental results, with the assistance of computer codes that, at their best, only coarsely approximate reality. Coarse predictions are challenging in large part due to the multitude of seemingly arbitrary yet consequential decisions that must be made such as choice of relevant data, calibration of code parameters, and construction of empirical discrepancy forms. In this paper, we present a case study in the context of inertial confinement fusion (ICF) implosion experiments where extrapolative predictions are needed with quantified uncertainties. The purpose of this case study is to illustrate relevant statistical methods, as applied to ICF model fitting and prediction, to document the numerous decisions that must be made in the prediction pipeline, to extend a complex example in extrapolation to the uncertainty quantification (UQ) community, and to reflect on the challenges we encountered supporting extrapolations with imperfect models and thereby recommend several future research directions. We end with a discussion about the UQ community's role in less than ideal predictive scenarios like our ICF exercise.

关键词： model form error prediction uncertainties discrepancy modeling inertial confinement fusion

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Learning about physical parameters: the importance of model discrepancy

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INVERSE PROBLEMS 2014年第11期30卷 114007-114007页

作者： Brynjarsdottir, Jenny O'Hagan, Anthony Case Western Reserve Univ Cleveland OH 44106 USA Univ Sheffield Sheffield S Yorkshire England

Science-based simulation models are widely used to predict the behavior of complex physical systems. It is also common to use observations of the physical system to solve the inverse problem, that is, to learn about the values of parameters within the model, a process which is often called calibration. The main goal of calibration is usually to improve the predictive performance of the simulator but the values of the parameters in the model may also be of intrinsic scientific interest in their own right. In order to make appropriate use of observations of the physical system it is important to recognize model discrepancy, the difference between reality and the simulator output. We illustrate through a simple example that an analysis that does not account for model discrepancy may lead to biased and over-confident parameter estimates and predictions. The challenge with incorporating model discrepancy in statistical inverse problems is being confounded with calibration parameters, which will only be resolved with meaningful priors. For our simple example, we model the model-discrepancy via a Gaussian process and demonstrate that through accounting for model discrepancy our prediction within the range of data is correct. However, only with realistic priors on the model discrepancy do we uncover the true parameter values. Through theoretical arguments we show that these findings are typical of the general problem of learning about physical parameters and the underlying physical system using science-based mechanistic models.

关键词： computer models uncertainty quantification model form error calibration extrapolation simulation model structural uncertainty

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