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At least 37 records · Page 2

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Matérn-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory to characterize the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and MAP estimators for nonlinear inverse problems. Furthermore, our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.

Bayesian inverse problem↗

Traffic safety analysis and model updating for freeways using Bayesian method

Freeway crash prediction models are the basic of traffic safety research, yet crash occurrence and the influencing factors change over time. In order to make sure the implemented safety models fit the current traffic environment, this study conducts a comparative analysis of 2017 and 2020 datasets collected from freeways in Suzhou, China. Herein, considering the spatial correlation among analysis units and the hierarchical data structure, a Bayesian conditional autoregressive negative binomial (CAR-NB) model and a Bayesian hierarchical CAR-NB (HCAR-NB) model were used to explore the safety influencing factors, and a traditional NB model was developed for further comparison. To update the HCAR-NB model from 2017 to 2020, Bayesian inference with informative priors was used to improve its goodness of fit and efficiency. Preliminary results showed that 1) the HCAR-NB model outperformed the NB model and CAR-NB model in prediction accuracy, and 2) the number of crashes was significantly correlated with average speed, speed variance, road segment length, number of lanes, and presence of ramps. The potential for safety improvement (PSI) method was applied to the modeling results to identify hotspots for the two years. The results confirmed that the hotspots spatiotemporally shifted among the freeways. The proposed crash prediction model and updating method are expected to assist implementation of informed countermeasures for freeway safety improvement.

97 MATHEMATICS AND COMPUTING↗

Adapting Reinforcement Learning Treatment Policies Using Limited Data to Personalize Critical Care

We report reinforcement learning (RL) demonstrates promise for developing effective treatment policies in critical care settings. However, existing RL methods often require large and comprehensive patient data sets and do not readily lend themselves to settings in which certain patient subpopulations are severely underrepresented. In this study, we develop a new method, noisy Bayesian policy updates (NBPU), for selecting high-performing reinforcement learning–based treatment policies for underrepresented patient subpopulations using limited observations. Our method uses variational inference to learn a probability distribution over treatment policies based on a reference patient subpopulation for which sufficient data are available. It then exploits limited data from an underrepresented patient subpopulation to update this probability distribution and adapts its recommendations to this subpopulation. We demonstrate our method’s utility on a data set of ICU patients receiving intravenous blood anticoagulant medication. Our results show that NBPU outperforms state-of-the-art methods in terms of both selecting effective treatment policies for patients with nontypical clinical characteristics and predicting the corresponding policies’ performance for these patients.

60 APPLIED LIFE SCIENCES↗

Quantifying modeling uncertainty in simplified beam models for building response prediction

The use of simple models for response prediction of building structures is preferred in earthquake engineering for risk evaluations at regional scales, as they make computational studies more feasible. The primary impediment in their gainful use presently is the lack of viable methods for quantifying (and reducing upon) the modeling errors/uncertainties they bear. This study presents a Bayesian calibration method wherein the modeling error is embedded into the parameters of the model. Here, the method is specifically described for coupled shear-flexural beam models here, but it can be applied to any parametric surrogate model. The major benefit the method offers is the ability to consider the modeling uncertainty in the forward prediction of any degree-of-freedom or composite response regardless of the data used in calibration. The method is extensively verified using two synthetic examples. In the first example, the beam model is calibrated to represent a similar beam model but with enforced modeling errors. In the second example, the beam model is used to represent the detailed finite element model of a 52-story building. Both examples show the capability of the proposed solution to provide realistic uncertainty estimation around the mean prediction.

47 OTHER INSTRUMENTATION↗

A Markov framework for generalized post-event systems recovery modeling: From single to multihazards

State-dependent models can be used to represent the system recovery process as a series of stochastic transitions from lower to higher functional states. However, the applications of these models have been limited in scope and there is a lack of a generalized recovery modeling framework. A generalized framework would permit a robust forecasting of systems and system-of-systems recovery under multiple hazards, and more broadly, would contribute to community disaster preparedness. This paper develops a generalized post hazard-event recovery modeling framework based on state-dependent Markov-type processes. We then apply the proposed framework to solve a spectrum of problems that range from hind-casting single-system recovery following a single hazard event to forecasting post-event trajectories under multiple hazards and modeling the recovery of a system-of-systems. First, Markov chains are used to hind-cast the observed recovery for a portfolio of buildings affected by the 2014 South Napa, California, earthquake. Next, Markov processes are used to formulate a parametric post hazard-event recovery model, which can be updated using Bayesian statistics when relevant datasets become available. Semi-Markov processes are then used to develop a more general model of single hazard recovery, which accounts for the intensity of the loading and level of damage caused by the event. Semi-Markov processes with non-renewal features are then used to account for multihazard interactions in a post-event recovery model, and applied to a case study that involves a community in Charleston, South Carolina. Lastly, Markov-type processes are combined with Bayesian networks to model the recovery of residential, commercial, educational, and industrial buildings (system-of-systems) following a hazard event. Overall, these applications demonstrate the versatility of the Markov framework towards handling recovery problems with varying levels of complexity.

42 ENGINEERING↗

Data assimilation in operator algebras

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.

97 MATHEMATICS AND COMPUTING↗

Reliability Prediction using FMEA, FTA, and Related Techniques [Slides]

Summary: We presented a reliability analysis framework. We made point estimates of reliability using reliability block diagrams, fault trees, success trees and estimates with uncertainty using expert elicitation, Monte Carlo simulation, Bayesian analysis. Expert elicitation of failure modes and probabilities is labor-intensive, but critical. Bayesian analysis updates information from expert elicitation with data from reliability and aging tests (aging/compatibility data are needed to estimate lower-bound reliabilities at end of life). Estimation by more than one method helps insure consistency and accuracy.

97 MATHEMATICS AND COMPUTING↗

Reinforcement learning for adaptive maintenance policy optimization under imperfect knowledge of the system degradation model and partial observability of system states

Maintenance policy optimization usually is faced with challenges that arise from an imperfect knowledge of system degradation models and from the partial observability of system degradation states. Here, this paper proposes a reinforcement learning method to address these two challenges for a class of maintenance problems with Markov degradation processes. The reinforcement learning approach consists of a learning component and a planning component. Using sequentially collected observations, at each step of decision-making the learning component improves the knowledge of system degradation in terms of the probability distributions of the transition rates based on sequential Bayesian inference. Using the updated transition rates, at each step of decision-making the maintenance policy optimization problem is then formulated as a partially observable Markov decision problem, and the planning component computes the optimal maintenance policy that maximizes the expected cumulative reward. The proposed method is illustrated using a numerical example with repair and inspection maintenance actions. The result shows that as more observations are collected, the learning component progressively learns the true system degradation process, and the planning component adjusts the optimal maintenance policy accordingly as well, which leads to increased reward.

42 ENGINEERING↗

Development of a framework for sequential Bayesian design of experiments: Application to a pilot-scale solvent-based CO 2 capture process

In this paper, a methodology is developed for sequential design of experiments (SDoE) for process systems and applied to a solvent-based CO 2 capture system. In this approach, the prior knowledge of the system is used to prioritize process data collection at specific operating conditions. These data are then incorporated into a Bayesian inference methodology for updating a stochastic model by refining estimations of its underlying parameters, and the updated model is then used to generate the next set of test runs. Thus, the new knowledge obtained from the data is used to guide subsequent iterations of the experimental runs, ensuring that the overall data collection is maximally informative given that most experimental campaigns, especially at pilot or higher-scale plants, are costly, time-consuming, and resource-limited. The test run objective for this work was to minimize the maximum model prediction uncertainty for key output variables, but the methodology is generic and can be readily applied to other test run objectives. This methodology is applied to an aqueous monoethanolamine (MEA) pilot plant campaign at the National Carbon Capture Center (NCCC) in Wilsonville, Alabama, USA. The SDoE framework was utilized for two iterations, while collecting 18 sets of data representing different process conditions, and this resulted in an overall average reduction in uncertainty of approximately 50% in the prediction of CO 2 capture percentage. Moreover, 11 additional data sets were obtained with variation of absorber packing height for further model validation. This work shows the capability of the SDoE framework to maximize learning given limited resources, allowing for the reduction of model uncertainty, which is of great importance for many applications including reduction of technical risk associated with scale-up and economic analysis.

20 FOSSIL-FUELED POWER PLANTS↗

Human reliability analysis studies from simulator experiments using Bayesian inference

Probabilistic Safety Assessment (PSA) of complex facilities is performed to arrive at the risk posed by them. PSA also accounts for the contribution of the human errors towards the overall risk through Human Reliability Analysis (HRA) in terms of Human Error Probability (HEP). Human operators are part of the system and do not work in isolation. Their performance is influenced by the context in which the actions are performed. As a result, quantification of HEP requires operator performance data under the given context. Some good sources of operator performance data are plant‘s operation data, simulator data and expert judgement. The plant operation data pertaining to HRA is generally sparse. In this situation, a full scope plant simulator provides a good alternative for operator performance data generation. Many of the currently practiced HRA methods have been developed by combining the empirical evidence with expert judgement and contain a lot of uncertainty in their estimates. Bayesian inference is suitable for updating the prior HRA estimates with the simulator evidence to obtain the posterior HEP. Here, posterior HEP has been calculated for postulated accident scenarios in advanced reactor (first of its kind) at design stage, using plant simulator.

97 MATHEMATICS AND COMPUTING↗

A Bayesian Multi-fidelity Neural Network to Predict Nonlinear Frequency Backbone Curves

The use of structural mechanics models during the design process often leads to the development of models of varying fidelity. Often low-fidelity models are efficient to simulate but lack accuracy, while the high-fidelity counterparts are accurate with less efficiency. Here, this paper presents a multi-fidelity surrogate modeling approach that combines the accuracy of a high-fidelity finite element model with the efficiency of a low-fidelity model to train an even faster surrogate model that parameterizes the design space of interest. The objective of these models is to predict the nonlinear frequency backbone curves of the Tribomechadynamics Research Challenge benchmark structure which exhibits simultaneous nonlinearities from frictional contact and geometric nonlinearity. The surrogate model consists of an ensemble of neural networks that learn the mapping between low and high-fidelity data through nonlinear transformations. Bayesian neural networks are used to assess the surrogate model's uncertainty. Once trained, the multi-fidelity neural network is used to perform sensitivity analysis to assess the influence of the design parameters on the predicted backbone curves. Additionally, Bayesian calibration is performed to update the input parameter distributions to correlate the model parameters to the collection of experimentally measured backbone curves.

42 ENGINEERING↗

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗

A Multirange Vehicle Speed Prediction With Application to Model Predictive Control-Based Integrated Power and Thermal Management of Connected Hybrid Electric Vehicles

Abstract Connectivity and automated driving technologies have opened up new research directions in the energy management of vehicles which exploit look-ahead preview and enhance the situational awareness. Despite this advancement, the vehicle speed preview that can be obtained from vehicle-to-vehicle/infrastructure (V2V/I) communications is often limited to a relatively short time-horizon. The vehicular energy systems, specifically those of the electrified vehicles, consist of multiple interacting power and thermal subsystems that respond over different time-scales. Consequently, their optimal energy management can greatly benefit from long-term speed prediction beyond that available through V2V/I communications. Accurately extending the look-ahead preview, on the other hand, is fundamentally challenging due to the dynamic nature of the traffic environment. To address this challenge, we propose a data-driven multirange vehicle speed prediction strategy for arterial corridors with signalized intersections, providing the vehicle speed preview for three different ranges, i.e., short-, medium-, and long-range. The short-range preview is obtained by V2V/I communications. The medium-range preview is realized using a neural network (NN), while the long-range preview is predicted based on a Bayesian network (BN). The predictions are updated in real-time based on the current state of traffic and incorporated into a multihorizon model predictive control (MH-MPC) for integrated power and thermal management (iPTM) of connected vehicles. The results of design and evaluation of the performance of the proposed data-informed MH-MPC for iPTM of connected hybrid electric vehicles (HEVs) using traffic data for real-world city driving are reported.

Automation & Control Systems↗

Stopping criteria for ending autonomous, single detector radiological source searches

While the localization of radiological sources has traditionally been handled with statistical algorithms, such a task can be augmented with advanced machine learning methodologies. The combination of deep and reinforcement learning has provided learning-based navigation to autonomous, single-detector, mobile systems. However, these approaches lacked the capacity to terminate a surveying/search task without outside influence of an operator or perfect knowledge of source location (defeating the purpose of such a system). Two stopping criteria are investigated in this work for a machine learning navigated system: one based upon Bayesian and maximum likelihood estimation (MLE) strategies commonly used in source localization, and a second providing the navigational machine learning network with a “stop search” action. A convolutional neural network was trained via reinforcement learning in a 10 m × 10 m simulated environment to navigate a randomly placed detector-agent to a randomly placed source of varied strength (stopping with perfect knowledge during training). The network agent could move in one of four directions (up, down, left, right) after taking a 1 s count measurement at the current location. During testing, the stopping criteria for this navigational algorithm was based upon a Bayesian likelihood estimation technique of source presence, updating this likelihood after each step, and terminating once the confidence of the source being in a single location exceeded 0.9. A second network was trained and tested with similar architecture as the previous but which contained a fifth action: for self-stopping. The accuracy and speed of localization with set detector and source initializations were compared over 50 trials of MLE-Bayesian approach and 1000 trials of the CNN with self-stopping. The statistical stopping condition yielded a median localization error of ~1.41 m and median localization speed of 12 steps. The machine learning stopping condition yielded a median localization error of 0 m and median localization speed of 17 steps. This work demonstrated two stopping criteria available to a machine learning guided, source localization system.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Model-Form Epistemic Uncertainty Quantification for Modeling with Differential Equations: Application to Epidemiology

Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.

97 MATHEMATICS AND COMPUTING↗

Stochastic modeling and statistical calibration with model error and scarce data

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. Here, the Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

Bayesian inference↗

Application of Sequential Design of Experiments (SDoE) to Large Pilot-Scale Solvent-Based CO2 Capture Process at Technology Centre Mongstad (TCM)

The United States Department of Energy’s Carbon Capture Simulation for Industry Impact (CCSI2) program has developed a framework for sequential design of experiments (SDoE) that aims to maximize knowledge gained from budget- and schedule-limited pilot scale testing. SDoE was applied to the planning and execution of campaigns for testing CO2 capture systems at pilot-scale in order to optimally allocate resources available for the testing. In this methodology, a stochastic process model is developed by quantifying the parametric uncertainty in submodels of interest; for a solvent-based CO2 capture system, these may include physical properties and equipment performance submodels (e.g., mass transfer, interfacial area). This uncertainty is propagated through the full process model, over variable operating conditions, for estimating the resulting uncertainty in key model outputs (e.g., percentage of CO2 capture, solvent regeneration energy requirement). In developing a data collection plan, the predicted output uncertainty is incorporated into an algorithm that seeks simultaneously to select process operating conditions for which the predicted uncertainty is relatively high and to ensure that the entire space of operation is well represented. This test plan is then used to guide operation of the pilot plant at varying steady-state conditions, with resulting process data incorporated into the existing model using Bayesian inference to refine parameter distributions. The updated stochastic model, with reduced parametric uncertainty from data collected, is then used to guide additional data collection, thus the sequential nature of the experimental design. The SDoE process was implemented at the pilot test unit (12 MWe in scale) at Norway’s Technology Centre Mongstad (TCM) in a summer 2018 test campaign with aqueous monoethanolamine (MEA). During the test campaign, the varied operating conditions included the flowrates of circulated solvent, flue gas, and reboiler steam and the CO2 concentration in the flue gas. The process data were used to update probability distributions of mass transfer and interfacial area parameters of a stochastic process model developed by the CCSI2 team. Two iterations of the SDoE process were executed, resulting in the uncertainty in model predicted CO2 capture percentage decreasing by an average of 58.0 ± 4.7% over the full input space of interest. This work demonstrates the potential of the SDoE process for model refinement through reduction in process model parametric uncertainty, and ultimately risk in scale-up, in CO2 capture technology performance.

carbon capture↗

On‐site surrogates for large‐scale calibration

Abstract Motivated by a computer model calibration problem from the oil and gas industry, involving the design of a honeycomb seal, we develop a new Bayesian methodology to cope with limitations in the canonical apparatus stemming from several factors. We propose a new strategy of on‐site design and surrogate modeling for a computer simulator acting on a high‐dimensional input space that, although relatively speedy, is prone to numerical instabilities, missing data, and nonstationary dynamics. Our aim is to strike a balance between data‐faithful modeling and computational tractability in a calibration framework—tailoring the computer model to a limited field experiment. Situating our on‐site surrogates within the canonical calibration apparatus requires updates to that framework. We describe a novel yet intuitive Bayesian setup that carefully decomposes otherwise prohibitively large matrices by exploiting the sparse blockwise structure. Empirical illustrations demonstrate that this approach performs well on toy data and our motivating honeycomb example.

Huang, Jiangeng↗