Uncertainty quantification of property models: Methodology and its application to CO 2 -loaded aqueous MEA solutions
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CO2 capture↗
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Results for “Bayesian Engine for Uncertainty Analysis”
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Uncertainty Quantification and Sensitivity Analysis for Simulation of Hostile Blast Events [Slides]
A mesh convergence study shows that shock arrival times converge for basic flow shots. Sensitivity study reveals a surprisingly high sensitivity to the placement of the HE package. Bayesian inference tools used on the experimental datasets suggest this is a real effect. Sensitivity analysis of ambient conditions such as temperature and pressure reveal minimal effect. Porting of pressure data from QUINOA simulations to perform structural analysis on the aeroshell geometry was successful, and shows a strong dependence of payload response to the angle of attack.
42 ENGINEERING↗
Bayesian calibration of irradiated graphite property models under high temperatures
Graphite under high temperatures and irradiation is central to advanced reactors. We develop a Bayesian calibration framework for graphite property models that explicitly represents model-data mismatch via a Gaussian-process discrepancy. The approach propagates uncertainty from parameters, experimental noise, and model form, with a hierarchical variance structure to capture group and cross-group noise. Using two predictive models across five grades (IG-110, NBG-18, PCEA, NBG-17, 2114) and four properties-irradiation-induced dimension change, creep, Young’s modulus change ratio, and coefficient of thermal expansion change ratio-we obtain average predictive-error reductions of 54%, 65%, 17%, and 17% when discrepancy is included. We illustrate engineering impact with a multiphysics model of a very-high-temperature reactor prismatic reflector brick, analyzing stresses under high fluence and temperature. Accounting for model discrepancy markedly improves predictive accuracy and provides a robust basis for reliable graphite component design in advanced reactors.
36 - MATERIALS SCIENCE↗
Atikokan Digital Twin: Machine learning in a biomass energy system
The Atikokan Generating Station, operated by Ontario Power Generation, has a 200 MW, biomass-fired tower boiler that operates on a dispatch schedule with a five-minute cycle. The boiler is generally operated in the range of 40–100 MW using two of five burner levels. In order to optimize boiler performance, we propose the implementation of a unique digital twin. Our digital twin abstraction couples Bayesian inference from science-based models and from observations (machine learning) with decision theory to predict operating-variable set points that optimize the physical asset (the boiler) in the presence of uncertainty (artificial intelligence). We focus this paper on the continuous Bayesian machine learning part of the Atikokan Digital Twin; we discuss decision theory in a companion paper. We identify and learn about 12 operational, model, and measured-output parameters and their uncertainties from high-fidelity, science-based simulations of the Atikokan boiler and from the observed measurements at the power plant. Since the goal of the Atikokan Digital Twin is to implement it online in real time, we require fast function evaluations for the quantities of interest extracted from the simulations in the Bayesian analysis. We use Gaussian process regression/interpolation to create accurate, robust surrogate models. We define the Bayesian priors and likelihood function and solve for the posterior distributions of the 12 parameters. Here we then propagate these distributions (i.e., parameters with uncertainty) into the predicted distributions of 790 quantities of interest to learn about the relative importance of various sources of error including experimental, model, and operating-parameter errors.
09 BIOMASS FUELS↗
Decision Analyses Related to Groundwater Remediation - 17051
Traditional decision analyses of groundwater remediation scenarios frequently fail because the probability of adverse, unanticipated events occurring is often high. This is driven by many factors including that (1) the models developed to represent the flow and transport in contaminated aquifers are typically simpler than reality and do not account for all the important governing processes, (2) probability distributions are assigned to critical performance parameters (such as model inputs or characteristics of the engineered remediation systems) even though some of these parameters might be unknown or not be very well constrained. However, there is a novel decision analysis methodology and a computational tool based on Bayesian Information-Gap Decision Theory (BIG-DT) that are designed to mitigate the shortcomings of the models and probabilistic decision analyses by leveraging a non-probabilistic decision theory -- information-gap decision theory. The new decision analysis methodology considers possible models that have not been explicitly enumerated and does not require us to commit to a particular probability distribution for model and remediation-design parameters. Both the set of possible models and the set of possible probability distributions grow as the degree of uncertainty increases. The fundamental question that BIG-DT asks is 'How large can these sets be before a particular decision results in an undesirable outcome?'. The decision that allows these sets to be the largest is considered to be the best option. In this way, BIG-DT enables robust decision-support for groundwater remediation problems. Here, we apply BIG-DT to a representative groundwater remediation scenario where different options for hydraulic containment and pump and treat are being considered. BIG-DT requires many model runs and high-performance computing resources are needed when complex models are used. We demonstrate the BIG-DT analyses on a series of synthetic problems that are designed to be consistent with real-world problems such as Los Alamos National Laboratory (LANL) contamination sites. We also discuss a general framework for how the BIG-DT analyses will be carried out at the chromium groundwater contamination site at LANL. BIG-DT is implemented in Julia (a high-level, high-performance dynamic programming language for technical computing) and is part of the MADS framework (http://mads.lanl.gov and http://madsjulia.github.io/Mads.jl). (authors)
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Unpacking model inadequacy: The quantification of silver release from TRISO fuel by considering empirical and mechanistic approaches
Increasing adoption of the proposed tristructural isotropic (TRISO) particle fuel for both advanced and existing reactors makes it critical to assess and address any uncertainties and inadequacies of TRISO fission product release models. Model inadequacy stems from simplifications made to the computational model when compared to the experiments. The modeling and simulation efforts conducted using the BISON fuel performance code, along with the experimental campaigns carried out under the Advanced Gas Reactor Fuel Development and Qualification Program, afford a unique opportunity to conduct a rigorous modeling inadequacy assessment within the Bayesian uncertainty quantification (UQ) framework. Here, this study compares the standard Bayesian framework against the Kennedy-O'Hagan (KOH) framework, which explicitly represents modeling inadequacy, in regard to UQ for TRISO silver release models. For this purpose, both the traditional Arrhenius equation fitted to experimental data and the more advanced lower-length-scale (LLS)-informed model, which considers microstructure information, are independently considered. Applying the inverse UQ process on the AGR-2 and -3/4 datasets revealed modeling inadequacy to be the most dominant source of uncertainty. Experimental noise uncertainty is also significant; however, model parameter uncertainty can be considered negligible. Interestingly, both the Arrhenius equation and the LLS-informed model demonstrated similar levels of modeling inadequacy. For the forward predictive UQ, the KOH framework improved both the accuracy and quality of quantified uncertainties in comparison to the standard Bayesian framework. This is true for both the Arrhenius equation and the LLS-informed model. In comparing these modeling approaches, both demonstrated similar performance at the engineering scale, while the LLS-informed model expectedly outperformed the Arrhenius equation at the mesoscale. These conclusions highlight the importance of explicitly accounting for modeling inadequacy in the UQ process, and reinforce the need for continuous refinement of physics-based models in order to address the modeling inadequacy.
Advanced reactors↗
A Markov chain Monte Carlo (MCMC) Bayesian inference approach to analyze apparent activation barriers and reaction orders from microreactor data
Statistical analysis of steady-state catalytic kinetic data is often limited by data sparsity due to the slow pace at which the data is collected. Data sparsity and limitations in statistical analysis make it difficult to differentiate between mechanistic models and catalytic sites. A Bayesian inference tool is reported for catalysis researchers to estimate error in the determination of reaction orders from steady state microreactor data. The benefits of a Bayesian inference approach are discussed, as an alternative to the more common frequentist approach. The approach incorporates prior knowledge of the system and the data collected to form an error estimate on reaction orders. We investigated the effects of three distinct data treatments—individual fitting of trials, pooled analysis, and constrained regression methods—on the precision and uncertainty of reaction order determinations. To assess the robustness of our findings, we conducted sensitivity analyses to evaluate the influence of Bayesian parameters on uncertainty estimation. Additionally, we utilized synthetic data to illustrate how data quality impacts the precision of uncertainty assessments. We show Bayesian analysis can obtain a more precise estimation of error with a sparse data set than a frequentist analysis. Finally, this work provides strong evidence that the adoption of Bayesian analysis of kinetic data may help researchers make more precise arguments as to the strength of their evidence for a particular mechanistic hypothesis, or in comparing across different catalysts.
42 ENGINEERING↗
Capabilities of multivariate Bayesian inference toward seismic hazard assessment
Multivariate Bayesian analysis can bring significant benefits to seismic hazard analysis: Its multivariate feature enables computing scalar and vector hazard without making any approximations; Correlations between intensity measures are implicitly modeled, permitting direct simulation of ground motion selection tools such as the conditional mean spectrum and the generalized conditioning intensity measure; and Its updating feature enables a seamless integration of new ground motion data into the hazard results. Here, we first develop a multivariate Bayesian ground motion model through the NGA-West2 database. The model functional form considers fault-type, magnitude, and distance dependencies, and also the linear and the rock intensity dependent site response. We use a hybrid Markov Chain Monte Carlo sampling to perform Bayesian inference consisting of Gibbs step and a multilevel Metropolis-Hastings step. We then perform several checks on the model and note that its performance is satisfactory. Finally, we illustrate the merits of this multivariate Bayesian analysis, which include: ground motion model updating with ground motion data recorded in the last four years not part of the NGA-West2 database; computation of scalar and vector seismic hazard using the un-updated and updated ground motion models for Los Angeles, CA; and simulation of the conditional mean spectrum under scalar and vector IM conditioning while accounting for different sources of aleatoric and epistemic uncertainties.
58 GEOSCIENCES↗
Geomechanical risk assessment for subsurface fluid disposal operations
Numerical models are commonly used to estimate the state of stress in the subsurface for various engineering applications. These estimates are subject to considerable uncertainty, and yet, the estimates are almost always deterministic, yielding no information about the certainty of the prediction. For some applications, unquantified uncertainties in stress are often acceptable, because the risks related to geomechanics may be of low relative importance compared to other risks (e.g. recoverable resource volume), for which uncertainties are often quantified. Furthermore, many geomechanics-related risks in the petroleum industry are relatively short lived (e.g. well bore stability), and decrease in importance with time. In contrast, for waste water injection or geologic carbon sequestration (GCS), geomechanics-related risks (e.g. seal integrity, induced seismicity) are on par with resource-related risks and are of long-term concern, with the risk generally increasing in importance for a significant period of time. For these reasons, the deterministic stress estimation and risk analysis approaches generally applied in the petroleum industry are insufficient for GCS applications. This paper describes a Bayesian approach to geomechanical uncertainty quantification and risk assessment. The method is demonstrated using data from an active enhanced oil recover/geologic carbon sequestration field as a case study
Burghardt, Jeffrey A.↗
EGS Stimulation Design with Uncertainty Quantification at the EGS Collab Site
Engineering a robust hydraulic connection between wells is one of the most difficult aspects of enhanced geothermal systems (EGS). Designing and constructing such hydraulic connections requires and understanding of the in situ state of stress and the heterogeneities and discontinuities that naturally exist and may control the stimulation. Even with comprehensive stress and formation characterization programs substantial uncertainty remains in these key parameters. This is especially the case in high-temperature EGS environments where drilling conditions are often difficult and a far fewer logging and testing options are available. This paper presents a new approach for explicitly quantifying the uncertainties in the state of stress using a Bayesian Markov Chain Monte Carlo method. This approach produces a probability distribution for the stress tensor, including a general 3D orientation, that reflects the uncertainties in all the observations or indicators used to constrain the stress state. This method is demonstrated on the characterization data for the EGS Collab Experiment 2 site. The output of the analysis is used to guide the design of the planned stimulations. In the case of research projects like EGS Collab, explicitly quantifying the uncertainties in the stress state allow for more rigorous hypothesis testing by allowing conclusions drawn from the experiments to be interpreted in the context of the uncertain knowledge about conditions in the test bed.
Burghardt, Jeffrey A.↗
A comparison of material flow strength models using Bayesian cross-validation
Predicting material flow strength over a range of conditions, such as temperature and strain rate, is necessary for many engineering applications. In this paper, we consider how to compare the predictiveness of several different strength models using a statistical technique called Bayesian cross-validation. Given a dataset of flow strength measurements obtained from mechanictesting experiments, the procedure consists of performing a Bayesian calibration of each strength model on a subset of the data and evaluating how well the trained models predict the remaining data. The predictiveness of a calibrated strength model is quantifiable probabilistically, which provides an interpretable metric for comparing the different models. As an illustrative example, we compare the Johnson-Cook (JC), Zerilli-Armstrong (ZA), Preston-Tonks-Wallace (PTW), and Mechanical Threshold Stress (MTS) flow strength models for the tantalum stress-strain curve data from Chen and Gray (1996). We show that prediction intervals for the four strength models cover the held-out data at most experimental conditions, but also that prediction interval coverage and prediction uncertainty varies by model and experimental condition. Finally, the analysis further allows us to identify experimental regimes for which one of the strength models predicts better than the other three.
36 MATERIALS SCIENCE↗
Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments
In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.
42 ENGINEERING↗
A Gaussian Process Enhancement to Linear Parameter Varying Models
Simulation and analysis for modern engineering systems now routinely requires the merging of multiple disciplines, physical-domains, time-scales, and data sets — all at ever increasing levels. These capabilities are especially needed in the domain of Advanced Air Mobility, where rapidly emerging vehicle designs are significantly more complex, while having to be both cost-effective and safe. To meet these engineering challenges, machine learning methods are an attractive option for merging models and data across multiple areas while providing uncertainty quantification and maintaining computational efficiency. This paper examines the use of Gaussian process machine learning to generalize and enhance the commonly used class of quasi-Linear Parameter Varying models for fast full-envelope simulation while also supporting control system design and analysis with model uncertainty. Gaussian process machine learning is selected because it: can fuse multiple data sets, enables an easy trade-off between data fitting and smoothing, provides model uncertainty quantification, scales well with increasing complexity, and does not generally require starting from a large training data set. To demonstrate the benefits of the approach, a robust stability analysis with Gaussian process uncertainty is shown for a NASA reference design of an electric quad-rotor air-taxi concept vehicle with motor parameter uncertainty.
Gaussian Process↗
A Bayesian Approach to the Eagar–Tsai Model for Melt Pool Geometry Prediction with Implications in Additive Manufacturing of Metals
Here, this paper focuses on improving the melt pool geometry predictions and quantifying uncertainties using an adapted version of the Eagar–Tsai (E–T) model that incorporates temperature-dependent properties of the material as well as powder conditions. Additionally, Bayesian inference is employed to predict distributions for the E–T model input parameters of laser absorptivity and powder bed porosity by incorporating experimental results into the analysis. Monte Carlo uncertainty propagation is then used with these parameter distributions to estimate the melt pool depth and associated uncertainty. Our results for the 316L stainless steel suggest that both the absorptivity and powder bed porosity are strongly influenced by the laser power. In contrast, the scanning speed has only a marginal effect on both the absorptivity and powder bed porosity. We constructed a printability map using the Bayesian E–T model based on power-dependent input parameter values to demonstrate the merit of the approach. The Bayesian approach improved the accuracy in predicting the keyhole regions in the laser power-scan speed parameter space for the 316L stainless steel. Although applied to a specific adaptation of the E–T model, the method put forth can be extended to quantify uncertainties in other numerical models as well as in the estimation of unknown parameters.
316L Stainless Steel (SS).↗
Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference
Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.
Bayesian optimal experimental design↗
Preliminary Results on Applying Nonparametric Clustering and Bayesian Consensus Clustering Methods to Multimodal Data
In this report, we present preliminary research into nonparametric clustering methods for multi-source imagery data and quantifying the performance of these models. In many domain areas, data sets do not necessarily follow well-defined and well-known probability distributions, such as the normal, gamma, and exponential. This is especially true when combining data from multiple sources describing a common set of objects (which we call multimodal analysis), where the data in each source can follow different distributions and need to be analyzed in conjunction with one another. This necessitates nonparametric density estimation methods, which allow the data to better dictate the distribution of the data. One prominent example of multimodal analysis is multimodal image analysis, when we analyze multiple images taken using different radar systems of the same scene of interest. We develop uncertainty analysis methods, which are inherent in the use of probabilistic models but often not taken advance of, to assess the performance of probabilistic clustering methods used for analyzing multimodal images. This added information helps assess model performance and how much trust decision-makers should have in the obtained analysis results. The developed methods illustrate some ways in which uncertainty can inform decisions that arise when designing and using machine learning models.
42 ENGINEERING↗
Operation Optimization using Reinforcement Learning with Integrated Artificial Reasoning Framework
In large and complex systems, operational decision-making requires a systematic analysis with a vast amount of data from both process parameters and component status monitoring. In this paper, we present an integrated artificial reasoning approach for system state transition models that can help operational decision-making with explainable and traceable reasoning. The integrated artificial reasoning framework is a physics-based approach of defining the system structure in a Bayesian network, so we leveraged it in a Markov decision process (MDP) for finding optimal operational solutions. In our proposed framework, the MDP is implemented on a dynamic Bayesian network (DBN), which represents causalities in a system. The multilevel flow modeling was utilized in order to extract these causalities in a more efficient and objective manner. Since multilevel flow modeling is based on the fundamental energy and mass conservation laws, the target system is decomposed into several mass, energy, and information structures, which serve as the basis for a DBN. The MDP consists of the processes of finding a solution for the Bellman equation, which can be derived from the conditional probability equations of the constructed DBN. System operators can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from the component degradation process or random failures. We analyzed a simplified example system to illustrate finding an optimal operational policy with this approach.
99 GENERAL AND MISCELLANEOUS↗
Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks
The computational cost of high-fidelity numerical models makes outer-loop analysis, which requires repeated interrogation of the model such as uncertainty quantification, computationally demanding. Multi-fidelity methods, which construct a surrogate model using data from an ensemble of models of varying cost and accuracy, can substantially reduce the cost of outer-loop analysis. However, these methods can be difficult to apply when the model ensemble does not admit a clear hierarchy a priori and the correlations between models are low. Consequently, in this paper, we present a multi-fidelity method that leverages dimension reduction to enhance the correlation between models, thereby reducing the amount of data needed to train a surrogate from an unordered ensemble of models. Our method utilizes basis adaptation to build low-dimensional polynomial chaos expansions of each model and employs Multi-fidelity Networks to encode the relationships among models. We show that the resulting method exhibit two notable advantages over its counterpart: (1) enhanced accuracy (both reduced bias and variance); and (2) reduced dependency on the graph structure encoding relationships among models. We demonstrate the approach on an analytical test problem and a challenging finite element model for a spent nuclear fuel. Our method produces a surrogate model that is significantly more accurate than either a single-fidelity surrogate or a multi-fidelity surrogate constructed without basis adaptation.
42 ENGINEERING↗