VTechWorks Repository :: Browsing by Author "Gramacy, Robert B."

Browsing by Author "Gramacy, Robert B."

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Bayesian Methods for Mineral Processing Operations
Koermer, Scott Carl (Virginia Tech, 2022-06-07)
Increases in demand have driven the development of complex processing technology for separating mineral resources from exceedingly low grade multi- component resources. Low mineral concentrations and variable feedstocks can make separating signal from noise diﬃcult, while high process complexity and the multi-component nature of a feedstock can make testwork, optimization, and process simulation diﬃcult or infeasible. A prime example of such a scenario is the recovery and separation of rare earth elements (REEs) and other critical minerals from acid mine drainage (AMD) using a solvent extraction (SX) process. In this process the REE concentration found in an AMD source can vary site to site, and season to season. SX processes take a non-trivial amount of time to reach steady state. The separation of numerous individual elements from gangue metals is a high-dimensional problem, and SX simulators can have a prohibitive computation time. Bayesian statistical methods intrinsically quantify uncertainty of model parameters and predictions given a set of data and a prior distribution and model parameter prior distributions. The uncertainty quantiﬁcation possible with Bayesian methods lend well to statistical simulation, model selection, and sensitivity analysis. Moreover, Bayesian models utilizing Gaussian Process priors can be used for active learning tasks which allow for prediction, optimization, and simulator calibration while reducing data requirements. However, literature on Bayesian methods applied to separations engineering is sparse. The goal of this dissertation is to investigate, illustrate, and test the use of a handful of Bayesian methods applied to process engineering problems. First further details for the background and motivation are provided in the introduction. The literature review provides further information regarding critical minerals, solvent extraction, Bayeisan inference, data reconciliation for separations, and Gaussian process modeling. The body of work contains four chapters containing a mixture of novel applications for Bayesian methods and a novel statistical method derived for the use with the motivating problem. Chapter topics include Bayesian data reconciliation for processes, Bayesian inference for a model intended to aid engineers in deciding if a process has reached steady state, Bayesian optimization of a process with unknown dynamics, and a novel active learning criteria for reducing the computation time required for the Bayesian calibration of simulations to real data. In closing, the utility of a handfull of Bayesian methods are displayed. However, the work presented is not intended to be complete and suggestions for further improvements to the application of Bayesian methods to separations are provided.
Bayesian Modeling of Complex High-Dimensional Data
Huo, Shuning (Virginia Tech, 2020-12-07)
With the rapid development of modern high-throughput technologies, scientists can now collect high-dimensional complex data in different forms, such as medical images, genomics measurements. However, acquisition of more data does not automatically lead to better knowledge discovery. One needs efficient and reliable analytical tools to extract useful information from complex datasets. The main objective of this dissertation is to develop innovative Bayesian methodologies to enable effective and efficient knowledge discovery from complex high-dimensional data. It contains two parts—the development of computationally efficient functional mixed models and the modeling of data heterogeneity via Dirichlet Diffusion Tree. The first part focuses on tackling the computational bottleneck in Bayesian functional mixed models. We propose a computational framework called variational functional mixed model (VFMM). This new method facilitates efficient data compression and high-performance computing in basis space. We also propose a new multiple testing procedure in basis space, which can be used to detect significant local regions. The effectiveness of the proposed model is demonstrated through two datasets, a mass spectrometry dataset in a cancer study and a neuroimaging dataset in an Alzheimer's disease study. The second part is about modeling data heterogeneity by using Dirichlet Diffusion Trees. We propose a Bayesian latent tree model that incorporates covariates of subjects to characterize the heterogeneity and uncover the latent tree structure underlying data. This innovative model may reveal the hierarchical evolution process through branch structures and estimate systematic differences between groups of samples. We demonstrate the effectiveness of the model through the simulation study and a brain tumor real data.
A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951–1980
Graves, Timothy; Gramacy, Robert B.; Watkins, Nicholas; Franzke, Christian (MDPI, 2017-08-23)
Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here, we discuss the original motivation of the development of long memory and Mandelbrot’s influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities.
Computer Experimental Design for Gaussian Process Surrogates
Zhang, Boya (Virginia Tech, 2020-09-01)
With a rapid development of computing power, computer experiments have gained popularity in various scientific fields, like cosmology, ecology and engineering. However, some computer experiments for complex processes are still computationally demanding. A surrogate model or emulator, is often employed as a fast substitute for the simulator. Meanwhile, a common challenge in computer experiments and related fields is to efficiently explore the input space using a small number of samples, i.e., the experimental design problem. This dissertation focuses on the design problem under Gaussian process surrogates. The first work demonstrates empirically that space-filling designs disappoint when the model hyperparameterization is unknown, and must be estimated from data observed at the chosen design sites. A purely random design is shown to be superior to higher-powered alternatives in many cases. Thereafter, a new family of distance-based designs are proposed and their superior performance is illustrated in both static (one-shot design) and sequential settings. The second contribution is motivated by an agent-based model(ABM) of delta smelt conservation. The ABM is developed to assist in a study of delta smelt life cycles and to understand sensitivities to myriad natural variables and human interventions. However, the input space is high-dimensional, running the simulator is time-consuming, and its outputs change nonlinearly in both mean and variance. A batch sequential design scheme is proposed, generalizing one-at-a-time variance-based active learning, as a means of keeping multi-core cluster nodes fully engaged with expensive runs. The acquisition strategy is carefully engineered to favor selection of replicates which boost statistical and computational efficiencies. Design performance is illustrated on a range of toy examples before embarking on a smelt simulation campaign and downstream high-fidelity input sensitivity analysis.
Contributions to Data Reduction and Statistical Model of Data with Complex Structures
Wei, Yanran (Virginia Tech, 2022-08-30)
With advanced technology and information explosion, the data of interest often have complex structures, with the large size and dimensions in the form of continuous or discrete features. There is an emerging need for data reduction, efficient modeling, and model inference. For example, data can contain millions of observations with thousands of features. Traditional methods, such as linear regression or LASSO regression, cannot effectively deal with such a large dataset directly. This dissertation aims to develop several techniques to effectively analyze large datasets with complex structures in the observational, experimental and time series data. In Chapter 2, I focus on the data reduction for model estimation of sparse regression. The commonly-used subdata selection method often considers sampling or feature screening. Un- der the case of data with both large number of observation and predictors, we proposed a filtering approach for model estimation (FAME) to reduce both the size of data points and features. The proposed algorithm can be easily extended for data with discrete response or discrete predictors. Through simulations and case studies, the proposed method provides a good performance for parameter estimation with efficient computation. In Chapter 3, I focus on modeling the experimental data with quantitative-sequence (QS) factor. Here the QS factor concerns both quantities and sequence orders of several compo- nents in the experiment. Existing methods usually can only focus on the sequence orders or quantities of the multiple components. To fill this gap, we propose a QS transformation to transform the QS factor to a generalized permutation matrix, and consequently develop a simple Gaussian process approach to model the experimental data with QS factors. In Chapter 4, I focus on forecasting multivariate time series data by leveraging the au- toregression and clustering. Existing time series forecasting method treat each series data independently and ignore their inherent correlation. To fill this gap, I proposed a clustering based on autoregression and control the sparsity of the transition matrix estimation by adap- tive lasso and clustering coefficient. The clustering-based cross prediction can outperforms the conventional time series forecasting methods. Moreover, the the clustering result can also enhance the forecasting accuracy of other forecasting methods. The proposed method can be applied on practical data, such as stock forecasting, topic trend detection.
Deep Gaussian Process Surrogates for Computer Experiments
Sauer, Annie Elizabeth (Virginia Tech, 2023-04-27)
Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Recent applications in machine learning favor approximate, optimization-based inference for fast predictions, but applications to computer surrogate modeling - with an eye towards downstream tasks like Bayesian optimization and reliability analysis - demand broader uncertainty quantification (UQ). I prioritize UQ through full posterior integration in a Bayesian scheme, hinging on elliptical slice sampling of latent layers. I demonstrate how my DGP's non-stationary flexibility, combined with appropriate UQ, allows for active learning: a virtuous cycle of data acquisition and model updating that departs from traditional space-filling designs and yields more accurate surrogates for fixed simulation effort. I propose new sequential design schemes that rely on optimization of acquisition criteria through evaluation of strategically allocated candidates instead of numerical optimizations, with a motivating application to contour location in an aeronautics simulation. Alternatively, when simulation runs are cheap and readily available, large datasets present a challenge for full DGP posterior integration due to cubic scaling bottlenecks. For this case I introduce the Vecchia approximation, popular for ordinary GPs in spatial data settings. I show that Vecchia-induced sparsity of Cholesky factors allows for linear computational scaling without compromising DGP accuracy or UQ. I vet both active learning and Vecchia-approximated DGPs on numerous illustrative examples and real computer experiments. I provide open-source implementations in the "deepgp" package for R on CRAN.
Detection of Latent Heteroscedasticity and Group-Based Regression Effects in Linear Models via Bayesian Model Selection
Metzger, Thomas Anthony (Virginia Tech, 2019-08-22)
Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way unreplicated layout has shown that hidden groupings among the levels of one categorical predictor frequently interact with the ungrouped factor. We extend the notion of a "latent grouping factor'' to linear models in general. The proposed work allows researchers to determine whether an apparent grouping of the levels of a categorical predictor reveals a plausible hidden structure given the observed data. Specifically, we offer Bayesian model selection-based approaches to reveal latent group-based heteroscedasticity, regression effects, and/or interactions. Failure to account for such structures can produce misleading conclusions. Since the presence of latent group structures is frequently unknown a priori to the researcher, we use fractional Bayes factor methods and mixture g-priors to overcome lack of prior information. We provide an R package, slgf, that implements our methodology in practice, and demonstrate its usage in practice.
Efficient computer experiment designs for Gaussian process surrogates
Cole, David Austin (Virginia Tech, 2021-06-28)
Due to advancements in supercomputing and algorithms for finite element analysis, today's computer simulation models often contain complex calculations that can result in a wealth of knowledge. Gaussian processes (GPs) are highly desirable models for computer experiments for their predictive accuracy and uncertainty quantification. This dissertation addresses GP modeling when data abounds as well as GP adaptive design when simulator expense severely limits the amount of collected data. For data-rich problems, I introduce a localized sparse covariance GP that preserves the flexibility and predictive accuracy of a GP's predictive surface while saving computational time. This locally induced Gaussian process (LIGP) incorporates latent design points, inducing points, with a local Gaussian process built from a subset of the data. Various methods are introduced for the design of the inducing points. LIGP is then extended to adapt to stochastic data with replicates, estimating noise while relying upon the unique design locations for computation. I also address the goal of identifying a contour when data collection resources are limited through entropy-based adaptive design. Unlike existing methods, the entropy-based contour locator (ECL) adaptive design promotes exploration in the design space, performing well in higher dimensions and when the contour corresponds to a high/low quantile. ECL adaptive design can join with importance sampling for the purpose of reducing uncertainty in reliability estimation.
Gradient-Based Sensitivity Analysis with Kernels
Wycoff, Nathan Benjamin (Virginia Tech, 2021-08-20)
Emulation of computer experiments via surrogate models can be difficult when the number of input parameters determining the simulation grows any greater than a few dozen. In this dissertation, we explore dimension reduction in the context of computer experiments. The active subspace method is a linear dimension reduction technique which uses the gradients of a function to determine important input directions. Unfortunately, we cannot expect to always have access to the gradients of our black-box functions. We thus begin by developing an estimator for the active subspace of a function using kernel methods to indirectly estimate the gradient. We then demonstrate how to deploy the learned input directions to improve the predictive performance of local regression models by ``undoing" the active subspace. Finally, we develop notions of sensitivities which are local to certain parts of the input space, which we then use to develop a Bayesian optimization algorithm which can exploit locally important directions.
hetGP: Heteroskedastic Gaussian Process Modeling and Sequential Design in R
Binois, Mickael; Gramacy, Robert B. (2021-07)
An increasing number of time-consuming simulators exhibit a complex noise structure that depends on the inputs. For conducting studies with limited budgets of evaluations, new surrogate methods are required in order to simultaneously model the mean and variance fields. To this end, we present the hetGP package, implementing many recent advances in Gaussian process modeling with input-dependent noise. First, we describe a simple, yet efficient, joint modeling framework that relies on replication for both speed and accuracy. Then we tackle the issue of data acquisition leveraging replication and exploration in a sequential manner for various goals, such as for obtaining a globally accurate model, for optimization, or for contour finding. Reproducible illustrations are provided throughout.
Hierarchical Gaussian Processes for Spatially Dependent Model Selection
Fry, James Thomas (Virginia Tech, 2018-07-18)
In this dissertation, we develop a model selection and estimation methodology for nonstationary spatial fields. Large, spatially correlated data often cover a vast geographical area. However, local spatial regions may have different mean and covariance structures. Our methodology accomplishes three goals: (1) cluster locations into small regions with distinct, stationary models, (2) perform Bayesian model selection within each cluster, and (3) correlate the model selection and estimation in nearby clusters. We utilize the Conditional Autoregressive (CAR) model and Ising distribution to provide intra-cluster correlation on the linear effects and model inclusion indicators, while modeling inter-cluster correlation with separate Gaussian processes. We apply our model selection methodology to a dataset involving the prediction of Brook trout presence in subwatersheds across Pennsylvania. We find that our methodology outperforms the stationary spatial model and that different regions in Pennsylvania are governed by separate Gaussian process regression models.
High-dimensional Multimodal Bayesian Learning
Salem, Mohamed Mahmoud (Virginia Tech, 2024-12-12)
High-dimensional datasets are fast becoming a cornerstone across diverse domains, fueled by advancements in data-capturing technology like DNA sequencing, medical imaging techniques, and social media. This dissertation delves into the inherent opportunities and challenges posed by these types of datasets. We develop three Bayesian methods: (1) Multilevel Network Recovery for Genomics, (2) Network Recovery for Functional data, and (3) Bayesian Inference in Transformer-based Models. Chapter 2 in our work examines a two-tiered data structure; to simultaneously explore the variable selection and identify dependency structures among both higher and lower-level variables, we propose a multi-level nonparametric kernel machine approach, utilizing variational inference to jointly identify multi-level variables as well as build the network. Chapter 3 addresses the development of a simultaneous selection of functional domain subsets, selection of functional graphical nodes, and continuous response modeling given both scalar and functional covariates under semiparametric, nonadditive models, which allow us to capture unknown, possibly nonlinear, interaction terms among high dimensional functional variables. In Chapter 4, we extend our investigation of leveraging structure in high dimensional datasets to the relatively new transformer architecture; we introduce a new penalty structure to the Bayesian classification transformer, leveraging the multi-tiered structure of the transformer-based model. This allows for increased, likelihood-based regularization, which is needed given the high dimensional nature of our motivating dataset. This new regularization approach allows us to integrate Bayesian inference via variational approximations into our transformer-based model and improves the calibration of probability estimates.
Linear Parameter Uncertainty Quantification using Surrogate Gaussian Processes
Macatula, Romcholo Yulo (Virginia Tech, 2020-07-21)
We consider uncertainty quantification using surrogate Gaussian processes. We take a previous sampling algorithm and provide a closed form expression of the resulting posterior distribution. We extend the method to weighted least squares and a Bayesian approach both with closed form expressions of the resulting posterior distributions. We test methods on 1D deconvolution and 2D tomography. Our new methods improve on the previous algorithm, however fall short in some aspects to a typical Bayesian inference method.
An open challenge to advance probabilistic forecasting for dengue epidemics
Johansson, Michael A.; Apfeldorf, Karyn M.; Dobson, Scott; Devita, Jason; Buczak, Anna L.; Baugher, Benjamin; Moniz, Linda J.; Bagley, Thomas; Babin, Steven M.; Guven, Erhan; Yamana, Teresa K.; Shaman, Jeffrey; Moschou, Terry; Lothian, Nick; Lane, Aaron; Osborne, Grant; Jiang, Gao; Brooks, Logan C.; Farrow, David C.; Hyun, Sangwon; Tibshirani, Ryan J.; Rosenfeld, Roni; Lessler, Justin; Reich, Nicholas G.; Cummings, Derek AT T.; Lauer, Stephen A.; Moore, Sean M.; Clapham, Hannah E.; Lowe, Rachel; Bailey, Trevor C.; Garcia-Diez, Markel; Carvalho, Marilia Sa; Rodo, Xavier; Sardar, Tridip; Paul, Richard; Ray, Evan L.; Sakrejda, Krzysztof; Brown, Alexandria C.; Meng, Xi; Osoba, Osonde; Vardavas, Raffaele; Manheim, David; Moore, Melinda; Rao, Dhananjai M.; Porco, Travis C.; Ackley, Sarah; Liu, Fengchen; Worden, Lee; Convertino, Matteo; Liu, Yang; Reddy, Abraham; Ortiz, Eloy; Rivero, Jorge; Brito, Humberto; Juarrero, Alicia; Johnson, Leah R.; Gramacy, Robert B.; Cohen, Jeremy M.; Mordecai, Erin A.; Murdock, Courtney C.; Rohr, Jason R.; Ryan, Sadie J.; Stewart-Ibarra, Anna M.; Weikel, Daniel P.; Jutla, Antarpreet; Khan, Rakibul; Poultney, Marissa; Colwell, Rita R.; Rivera-Garcia, Brenda; Barker, Christopher M.; Bell, Jesse E.; Biggerstaff, Matthew; Swerdlow, David; Mier-y-Teran-Romero, Luis; Forshey, Brett M.; Trtanj, Juli; Asher, Jason; Clay, Matt; Margolis, Harold S.; Hebbeler, Andrew M.; George, Dylan; Chretien, Jean-Paul (National Academy of Sciences, 2019-11-26)
A wide range of research has promised new tools for forecasting infectious disease dynamics, but little of that research is currently being applied in practice, because tools do not address key public health needs, do not produce probabilistic forecasts, have not been evaluated on external data, or do not provide sufficient forecast skill to be useful. We developed an open collaborative forecasting challenge to assess probabilistic forecasts for seasonal epidemics of dengue, a major global public health problem. Sixteen teams used a variety of methods and data to generate forecasts for 3 epidemiological targets (peak incidence, the week of the peak, and total incidence) over 8 dengue seasons in Iquitos, Peru and San Juan, Puerto Rico. Forecast skill was highly variable across teams and targets. While numerous forecasts showed high skill for midseason situational awareness, early season skill was low, and skill was generally lowest for high incidence seasons, those for which forecasts would be most valuable. A comparison of modeling approaches revealed that average forecast skill was lower for models including biologically meaningful data and mechanisms and that both multimodel and multiteam ensemble forecasts consistently outperformed individual model forecasts. Leveraging these insights, data, and the forecasting framework will be critical to improve forecast skill and the application of forecasts in real time for epidemic preparedness and response. Moreover, key components of this project-integration with public health needs, a common forecasting framework, shared and standardized data, and open participation-can help advance infectious disease forecasting beyond dengue.
Precision Aggregated Local Models
Edwards, Adam Michael (Virginia Tech, 2021-01-28)
Large scale Gaussian process (GP) regression is infeasible for larger data sets due to cubic scaling of flops and quadratic storage involved in working with covariance matrices. Remedies in recent literature focus on divide-and-conquer, e.g., partitioning into sub-problems and inducing functional (and thus computational) independence. Such approximations can speedy, accurate, and sometimes even more flexible than an ordinary GPs. However, a big downside is loss of continuity at partition boundaries. Modern methods like local approximate GPs (LAGPs) imply effectively infinite partitioning and are thus pathologically good and bad in this regard. Model averaging, an alternative to divide-and-conquer, can maintain absolute continuity but often over-smooth, diminishing accuracy. Here I propose putting LAGP-like methods into a local experts-like framework, blending partition-based speed with model-averaging continuity, as a flagship example of what I call precision aggregated local models (PALM). Using N_C LAGPs, each selecting n from N data pairs, I illustrate a scheme that is at most cubic in n, quadratic in N_C, and linear in N, drastically reducing computational and storage demands. Extensive empirical illustration shows how PALM is at least as accurate as LAGP, can be much faster in terms of speed, and furnishes continuous predictive surfaces. Finally, I propose sequential updating scheme which greedily refines a PALM predictor up to a computational budget, and several variations on the basic PALM that may provide predictive improvements.
Semi-Supervised Anomaly Detection and Heterogeneous Covariance Estimation for Gaussian Processes
Crandell, Ian C. (Virginia Tech, 2017-12-12)
In this thesis, we propose a statistical framework for estimating correlation between sensor systems measuring diverse physical phenomenon. We consider systems that measure at different temporal frequencies and measure responses with different dimensionalities. Our goal is to provide estimates of correlation between all pairs of sensors and use this information to flag potentially anomalous readings. Our anomaly detection method consists of two primary components: dimensionality reduction through projection and Gaussian process (GP) regression. We use non-metric multidimensional scaling to project a partially observed and potentially non-definite covariance matrix into a low dimensional manifold. The projection is estimated in such a way that positively correlated sensors are close to each other and negatively correlated sensors are distant. We then fit a Gaussian process given these positions and use it to make predictions at our observed locations. Because of the large amount of data we wish to consider, we develop methods to scale GP estimation by taking advantage of the replication structure in the data. Finally, we introduce a semi-supervised method to incorporate expert input into a GP model. We are able to learn a probability surface defined over locations and responses based on sets of points labeled by an analyst as either anomalous or nominal. This allows us to discount the influence of points resembling anomalies without removing them based on a threshold.
Sequential learning, large-scale calibration, and uncertainty quantification
Huang, Jiangeng (Virginia Tech, 2019-07-23)
With remarkable advances in computing power, computer experiments continue to expand the boundaries and drive down the cost of various scientific discoveries. New challenges keep arising from designing, analyzing, modeling, calibrating, optimizing, and predicting in computer experiments. This dissertation consists of six chapters, exploring statistical methodologies in sequential learning, model calibration, and uncertainty quantification for heteroskedastic computer experiments and large-scale computer experiments. For heteroskedastic computer experiments, an optimal lookahead based sequential learning strategy is presented, balancing replication and exploration to facilitate separating signal from input-dependent noise. Motivated by challenges in both large data size and model fidelity arising from ever larger modern computer experiments, highly accurate and computationally efficient divide-and-conquer calibration methods based on on-site experimental design and surrogate modeling for large-scale computer models are developed in this dissertation. The proposed methodology is applied to calibrate a real computer experiment from the gas and oil industry. This on-site surrogate calibration method is further extended to multiple output calibration problems.
Some Advances in Local Approximate Gaussian Processes
Sun, Furong (Virginia Tech, 2019-10-03)
Nowadays, Gaussian Process (GP) has been recognized as an indispensable statistical tool in computer experiments. Due to its computational complexity and storage demand, its application in real-world problems, especially in "big data" settings, is quite limited. Among many strategies to tailor GP to such settings, Gramacy and Apley (2015) proposed local approximate GP (laGP), which constructs approximate predictive equations by constructing small local designs around the predictive location under certain criterion. In this dissertation, several methodological extensions based upon laGP are proposed. One methodological contribution is the multilevel global/local modeling, which deploys global hyper-parameter estimates to perform local prediction. The second contribution comes from extending the laGP notion of "locale" to a set of predictive locations, along paths in the input space. These two contributions have been applied in the satellite drag emulation, which is illustrated in Chapter 3. Furthermore, the multilevel GP modeling strategy has also been applied to synthesize field data and computer model outputs of solar irradiance across the continental United States, combined with inverse-variance weighting, which is detailed in Chapter 4. Last but not least, in Chapter 5, laGP's performance has been tested on emulating daytime land surface temperatures estimated via satellites, in the settings of irregular grid locations.
A Statistical Approach to Modeling Wheel-Rail Contact Dynamics
Hosseini, SayedMohammad (Virginia Tech, 2021-01-12)
The wheel-rail contact mechanics and dynamics that are of great importance to the railroad industry are evaluated by applying statistical methods to the large volume of data that is collected on the VT-FRA state-of-the-art roller rig. The intent is to use the statistical principles to highlight the relative importance of various factors that exist in practice to longitudinal and lateral tractions and to develop parametric models that can be used for predicting traction in conditions beyond those tested on the rig. The experiment-based models are intended to be an alternative to the classical traction-creepage models that have been available for decades. Various experiments are conducted in different settings on the VT-FRA Roller Rig at the Center for Vehicle Systems and Safety at Virginia Tech to study the relationship between the traction forces and the wheel-rail contact variables. The experimental data is used to entertain parametric and non-parametric statistical models that efficiently capture this relationship. The study starts with single regression models and investigates the main effects of wheel load, creepage, and the angle of attack on the longitudinal and lateral traction forces. The assumptions of the classical linear regression model are carefully assessed and, in the case of non-linearities, different transformations are applied to the explanatory variables to find the closest functional form that captures the relationship between the response and the explanatory variables. The analysis is then extended to multiple models in which interaction among the explanatory variables is evaluated using model selection approaches. The developed models are then compared with their non-parametric counterparts, such as support vector regression, in terms of "goodness of fit," out-of-sample performance, and the distribution of predictions.
A statistical evaluation of multiple regression models for contact dynamics in rail vehicles using roller rig data
Hosseini, Sayed Mohammad; Radmehr, Ahmad; Ahangarnejad, Arash Hosseinian; Gramacy, Robert B.; Ahmadian, Mehdi (Taylor & Francis, 2022-01-06)
A statistical analysis of a large amount of data from experiments conducted on the Virginia Tech-Federal Railroad Administration (VT-FRA) roller rig under various field-emulated conditions is performed to develop multiple regression models for longitudinal and lateral tractions. The experiment-based models are intended to be an alternative to the classical wheel-rail contact models that have been available for decades. The VT-FRA roller rig data is used to develop parametric regression models that efficiently capture the relationship between traction and the combined effects of the influential variables. Single regression models for representing the individual effect of wheel load, creepage, and angle of attack on longitudinal and lateral traction were investigated by the authors in an earlier study. This study extends single regression models to multiple regression models and assesses the interaction among the variables using model selection approaches. The multiple-regression models are then compared with CONTACT, a well-known modelling tool for contact dynamics, in terms of prediction accuracy. The predictions made by both CONTACT and multiple regression models for longitudinal and lateral tractions are in close agreement with the measured data on the VT-FRA roller rig. The multiple regression model, however, offers an algebraic expression that can be solved far more efficiently than a simulation run in CONTACT for a new dynamic condition. The results of the study further indicate that the established multiple regression models are an effective means for studying the effect of multiple parameters such as wheel load, creepage, and angle of attack on longitudinal and lateral tractions. Such data-driven parametric models provide an essential analysis and engineering tool in contact dynamics, just as they have in many other areas of science and engineering.

Browsing by Author "Gramacy, Robert B."

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