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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 916741, 10 pages
Research Article

A New Algorithm for Reconstructing Two-Dimensional Temperature Distribution by Ultrasonic Thermometry

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 8 August 2014; Accepted 29 January 2015

Academic Editor: Muhammad N. Akram

Copyright © 2015 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.


Temperature, especially temperature distribution, is one of the most fundamental and vital parameters for theoretical study and control of various industrial applications. In this paper, ultrasonic thermometry to reconstruct temperature distribution is investigated, referring to the dependence of ultrasound velocity on temperature. In practical applications of this ultrasonic technique, reconstruction algorithm based on least square method is commonly used. However, it has a limitation that the amount of divided blocks of measure area cannot exceed the amount of effective travel paths, which eventually leads to its inability to offer sufficient temperature information. To make up for this defect, an improved reconstruction algorithm based on least square method and multiquadric interpolation is presented. And then, its reconstruction performance is validated via numerical studies using four temperature distribution models with different complexity and is compared with that of algorithm based on least square method. Comparison and analysis indicate that the algorithm presented in this paper has more excellent reconstruction performance, as the reconstructed temperature distributions will not lose information near the edge of area while with small errors, and its mean reconstruction time is short enough that can meet the real-time demand.