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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 835619, 12 pages
Research Article

Temperature Distribution Monitoring Using Ultrasonic Thermometry Based on Markov Radial Basis Function Approximation and Singular Values Decomposition

1School of Automation, Chongqing University, Chongqing 400044, China
2Key Laboratory of Dependable Service Computing in Cyber Physical Society, MOE, Chongqing 400044, China
3School of Software Engineering, Chongqing University, Chongqing 400044, China

Received 26 December 2013; Revised 24 March 2014; Accepted 2 April 2014; Published 28 April 2014

Academic Editor: Ping-Lang Yen

Copyright © 2014 Xuehua Shen 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.


Information about temperature distribution is complex but of critical importance for the control of various microwave applications. In this paper, an innovative way of temperature distribution monitoring using ultrasonic thermometry in microwave field is investigated. The principle of ultrasonic thermometry in the situation of ideal gas is elaborated, and reconstruction algorithm based on Markov radial basis function approximation and singular values decomposition is presented and described in detail. In order to validate the performance of temperature distribution reconstruction of our presented algorithm, four two-dimensional temperature distribution models with different complexities are utilized in simulation experiments. Especially, simulation experiments taking error of measurement into account are studied to verify the robustness. Figure profiles show remarkable correspondence between the reconstructed ones and their models, while quantitative analysis, including the overall temperature error analysis and the hotspot positioning analysis, shows that different kinds of errors calculated are all within the limit ranges. In addition, the time analysis of simulation experiments also demonstrates its well real-time capability.