Gaussian Process Regression Analysis for Functional Data

Shi, Jianghong; Choi, Tae-Yong

doi:10.1201/b11038

Cited by 218 publications

(209 citation statements)

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“…GP is by now common in nonparametric Bayes literature as prior for regression functions (Neal 1999;Shi and Choi 2011) and in geostatistics to model the response correlated over space (Banerjee, Carlin, and Gelfand 2004). The model is specified as…”

Section: Choice Of Functions With Interpretationmentioning

confidence: 99%

Spline-Based Emulators for Radiative Shock Experiments With Measurement Error

Chakraborty

Mallick

McClarren

et al. 2013

Journal of the American Statistical Association

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Radiation hydrodynamics and radiative shocks are of fundamental interest in the high-energy-density physics research due to their importance in understanding astrophysical phenomena such as supernovae. In the laboratory, experiments can produce shocks with fundamentally similar physics on reduced scales. However, the cost and time constraints of the experiment necessitate use of a computer algorithm to generate a reasonable number of outputs for making valid inference. We focus on modeling emulators that can efficiently assimilate these two sources of information accounting for their intrinsic differences. The goal is to learn how to predict the breakout time of the shock given the information on associated parameters such as pressure and energy. Under the framework of the Kennedy-O'Hagan model, we introduce an emulator based on adaptive splines. Depending on the preference of having an interpolator for the computer code output or a computationally fast model, a couple of different variants are proposed. Those choices are shown to perform better than the conventional Gaussian-process-based emulator and a few other choices of nonstationary models. For the shock experiment dataset, a number of features related to computer model validation such as using interpolator, necessity of discrepancy function, or accounting for experimental heterogeneity are discussed, implemented, and validated for the current dataset. In addition to the typical Gaussian measurement error for real data, we consider alternative specifications suitable to incorporate noninformativeness in error distributions, more in agreement with the current experiment. Comparative diagnostics, to highlight the effect of measurement error model on predictive uncertainty, are also presented. Supplementary materials for this article are available online.

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Section: Choice Of Functions With Interpretationmentioning

confidence: 99%

Spline-Based Emulators for Radiative Shock Experiments With Measurement Error

Chakraborty

Mallick

McClarren

et al. 2013

Journal of the American Statistical Association

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“…In most cases where there is no enough prior knowledge, the mean function is assumed to be zero. This leaves model developers with the selection of the covariance function and its associated hyperparameters [9].…”

Section: Model Selection Of Gaussian Process-based Soft Sensormentioning

confidence: 99%

Selection of covariance functions in Gaussian process-based soft sensors

Abusnina

Kudenko

Roth

2014

2014 IEEE International Conference on Industrial Technology (ICIT)

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Gaussian processes are emerging as a new option in soft sensor building techniques. They can provide predictions with associated uncertainty measure that can be of great importance in open and closed loop control applications. Most importantly, they have a relatively simple model structure as they are totally determined by their mean and covariance functions. The selection of the covariance function determines the overall performance of the soft sensor. This paper conducts an empirical comparison using 8 different data sets from various industrial applications between the squared exponential covariance function -used in all previously published Gaussian process-based soft sensors -and the Matérn class covariance function. The contribution of the paper is to recommend the use of the Matérn class covariance function for soft sensors, since in our experiments its accuracy is at least that of the squared exponential covariance function, and in some cases higher. In addition, results on condition numbers indicate that the Matérn class covariance function results in a prediction model that is less sensitive to numerical errors.

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“…The authors have encountered various problems performing multidimensional regression analyses for p, v, and, T when all three regression coefficients l, m, and n for the friction model by Filzek and Ludwig [6] are to be determined simultaneously. According to the literature, this might be caused by the fact that the convergence of the algorithm is higher when less independent coefficients are defined [11,12]. Therefore, the authors suggest to summarize all scalars in one single coefficient c which is then determined by the regression algorithm.…”

Section: Modification Of a Friction Model To Be Used With Multidimensmentioning

confidence: 99%

FE-analysis and in situ visualization of pressure-, slip-rate-, and temperature-dependent coefficients of friction for advanced sheet metal forming: development of a novel coupled user subroutine for shell and continuum discretization

Klocke

Trauth

Shirobokov

et al. 2015

Int J Adv Manuf Technol

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In sheet metal forming simulations using finite element method, the coefficient of friction according to Coulomb is normally assumed to be constant for the whole tool region. Recent research has demonstrated that under contact conditions typical for sheet metal forming, the coefficient of friction is strongly dependent on the contact pressure and the slip-rate between the interacting partners as well as on the contact temperature. A friction law based on the approach of Filzek is proposed in this research paper and implemented as a user subroutine in ABAQUS. Moreover, a novel user subroutine coupling is developed which enables the visualization of local coefficients of friction for every contact node. For the very first time, this enables the in situ visualization of local coefficients of friction in sheet metal forming simulations using the FE system ABAQUS. Multiple evaluation algorithms are presented as well. The presented friction model and the user subroutine coupling are validated using experimental data of an industrial deep drawing process. The proposed combination of the friction modeling and the in situ visualization of coefficients of friction enables the identification of friction hot spots. Based on such analysis, the tool and die making industry can realize tribologically optimized tools either by applying special coatings in areas of low or high friction, or by choosing different materials for tooling inserts, or by changing the type as well as the amount of the lubricant. Whereas the presented friction model is tailored to sheet metal forming and developed using the commercial code of ABAQUS, the visualization coupling methodology is transferable to any manufacturing process and various FE systems supporting FORTRAN programming language.

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Gaussian Process Regression Analysis for Functional Data

Cited by 218 publications

References 0 publications

Spline-Based Emulators for Radiative Shock Experiments With Measurement Error

Spline-Based Emulators for Radiative Shock Experiments With Measurement Error

Selection of covariance functions in Gaussian process-based soft sensors

FE-analysis and in situ visualization of pressure-, slip-rate-, and temperature-dependent coefficients of friction for advanced sheet metal forming: development of a novel coupled user subroutine for shell and continuum discretization

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