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Mathematical Problems in Engineering
Volume 2017, Article ID 2147935, 12 pages
Research Article

Temperature Distribution Measurement Using the Gaussian Process Regression Method

1School of Energy, Power and Mechanical Engineering, North China Electric Power University, Changping District, Beijing 102206, China
2Institute of Engineering Thermophysics, Chinese Academy of Sciences, Haidian District, Beijing 100190, China

Correspondence should be addressed to Huaiping Mu; moc.621@rdgnipiauhum

Received 28 February 2017; Accepted 31 July 2017; Published 29 August 2017

Academic Editor: Carmen Castillo

Copyright © 2017 Huaiping Mu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The temperature distribution in real-world industrial environments is often in a three-dimensional space, and developing a reliable method to predict such volumetric information is beneficial for the combustion diagnosis, the understandings of the complicated physical and chemical mechanisms behind the combustion process, the increase of the system efficiency, and the reduction of the pollutant emission. In accordance with the machine learning theory, in this paper, a new methodology is proposed to predict three-dimensional temperature distribution from the limited number of the scattered measurement data. The proposed prediction method includes two key phases. In the first phase, traditional technologies are employed to measure the scattered temperature data in a large-scale three-dimensional area. In the second phase, the Gaussian process regression method, with obvious superiorities, including satisfactory generalization ability, high robustness, and low computational complexity, is developed to predict three-dimensional temperature distributions. Numerical simulations and experimental results from a real-world three-dimensional combustion process indicate that the proposed prediction method is effective and robust, holds a good adaptability to cope with complicated, nonlinear, and high-dimensional problems, and can accurately predict three-dimensional temperature distributions under a relatively low sampling ratio. As a result, a practicable and effective method is introduced for three-dimensional temperature distribution.