Benchmarking of Gaussian Process Regression with Multiple Random Fields for Spatial Variability Estimation

Tomizawa, Yukihisa; Yoshida, Ikumasa

doi:10.1061/ajrua6.0001277

Cited by 7 publications

(2 citation statements)

References 18 publications

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“…Tomizawa and Yoshida [13] applied Gaussian Process regression with various Gaussian random fields to data with problems of spatial variability. The maximum likelihood method was used to estimate the random and fluctuating fields' scale.…”

Section: Survey Of Related Literaturementioning

confidence: 99%

Spatio-Temporal Forecasting of Global Horizontal Irradiance Using Bayesian Inference

2022

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Accurate global horizontal irradiance (GHI) forecasting promotes power grid stability. Most of the research on solar irradiance forecasting has been based on a single-site analysis. It is crucial to explore multisite modeling to capture variations in weather conditions between various sites, thereby producing a more robust model. In this research, we propose the use of spatial regression coupled with Gaussian Process Regression (GP Spatial) and the GP Autoregressive Spatial model (GP-AR Spatial) for the prediction of GHI using data from seven radiometric stations from South Africa and one from Namibia. The results of the proposed methods were compared with a benchmark model, the Linear Spatial Temporal Regression (LSTR) model. Five validation sets each comprised of three stations were chosen. For each validation set, the remaining five stations were used for training. Based on root mean square error, the GP model gave the most accurate forecasts across the validation sets. These results were confirmed by the statistical significance tests using the Giacommini–White test. In terms of coverage probability, there was a 100% coverage on three validation sets and the other two had 97% and 99%. The GP model dominated the other two models. One of the study’s contributions is using standardized forecasts and including a nonlinear trend covariate, which improved the accuracy of the forecasts. The forecasts were combined using a monotone composite quantile regression neural network and a quantile generalized additive model. This modeling framework could be useful to power utility companies in making informed decisions when planning power grid management, including large-scale solar power integration onto the power grid.

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Section: Survey Of Related Literaturementioning

confidence: 99%

Spatio-Temporal Forecasting of Global Horizontal Irradiance Using Bayesian Inference

2022

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“…geosciences), but such a large number of measurements is not practical and unfeasible when considering measurements from destructive tests on concrete structures. Moreover, the requirements found for soil properties might differ from those for concrete, due to the differences in spatial variation (Cami et al, 2020;Yu et al, 2020;Tomizawa & Yoshida, 2022). Hence, in this work, it is investigated for what ratio of the correlation length to the structural length and for what sampling distances an appropriate estimate of the actual correlation model can be found.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Investigation of a Correlation Model to Describe Spatial Variability of Concrete Properties

Botte

Vereecken

Caspeele

2023

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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The heterogeneous character of concrete results in spatial variation of its material properties. Random field models are often used to account for this effect. Due to the large scatter on the correlation lengths suggested in literature, tests could be performed to determine the most appropriate correlation model and corresponding correlation length. Subsequently, different techniques can be employed to fit an analytical model to the experimental semivariogram resulting in the most appropriate correlation model and corresponding correlation length. However, the resulting correlation lengths can largely depend on the experimental design. In this work, the effect of several parameters and choices to be made by an engineer in deriving the correlation model based on experimental data from destructive tests has been investigated. It was found that the curve fitting method generally leads to better estimates of the scale of fluctuation compared to the maximum likelihood method. Moreover, there is a clear benefit of applying a bootstrapping procedure to the experimental data to estimate the covariance matrix adopted in the fitting procedures as well as to estimate the uncertainty related to the estimated parameters. When a measurement error is suspected to be present and cannot be neglected, the nugget should be estimated together with the variance and the scale of fluctuation. Furthermore, the Gaussian correlation model was found to be the most robust choice, even if the actual correlation model is not Gaussian. the latter was confirmed for actual experimental data on the material properties of concrete, where a linear model was found to fit the data best but the Gaussian model provided comparable results.

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Probabilistic classification of surrounding rock mass of tunnels based on fully Bayesian Gaussian process classification (fB‐GPC) with consideration of influencing factors selection

Song,

Zhao,

2024

Geological Journal

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Rock mass classification is of great significance in guiding the design and construction of tunnels, which is often determined through single‐factor or multi‐factor classification methods based on some readily available rock indices, for example, dynamic elastic modulus, degree of tectonization, and so forth. Although these methods work reasonably well in some cases, they tend to lead to inaccurate classification results due to the pre‐selected main factor or function forms, especially for tunnels with complex geological conditions. Alternatively, the classification may be achieved with the aid of some machine learning (ML) methods, which are data‐driven, hence bypassing pre‐determination of the mathematical function forms of the main factor(s). Note although these ML methods perform well in the classification of surrounding rock mass, they generally employ all measurements of readily available rock indices as input variables, which might lead to excessive model complexity and a potential decrease in generalization performance. In this paper, a fully Bayesian Gaussian process classification (fB‐GPC) approach is proposed for probabilistic classification of surrounding rock mass, which is data‐driven and can select the optimal combination of main factors that affect rock mass classification. A real‐life example is used to illustrate and validate the proposed approach. Results show that the proposed fB‐GPC method performs very well in determination of the most important factor for classification of surrounding rock mass, with an area under the receiver operating characteristic curve (AUC) of around 0.98. A sensitivity study is also performed to systematically examine the accuracy and robustness of the proposed approach in this study.

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Benchmarking of Gaussian Process Regression with Multiple Random Fields for Spatial Variability Estimation

Cited by 7 publications

References 18 publications

Spatio-Temporal Forecasting of Global Horizontal Irradiance Using Bayesian Inference

Spatio-Temporal Forecasting of Global Horizontal Irradiance Using Bayesian Inference

Numerical and Experimental Investigation of a Correlation Model to Describe Spatial Variability of Concrete Properties

Probabilistic classification of surrounding rock mass of tunnels based on fully Bayesian Gaussian process classification (fB‐GPC) with consideration of influencing factors selection

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