聲學斷層掃描（Acoustic Tomography）是一種以非侵入性方式獲取目標區域的訊息的技術。在監控系統中目標區域的溫度訊息常常是監控中不可或缺的部分。而使用聲學斷層掃描的方式可以在不影響目標區域的狀況下重建出目標區域的二維溫度分佈圖。其中關鍵的挑戰是如何提高相對空間分佈和絕對溫度值的匹配準確性。
利用超音波測溫的方式，可以藉由聲波傳遞速度與介質溫度之關係，計算目標區域內的介質溫度。使用超音波陣列在目標區域內產生數十條超音波傳遞路徑，並根據所測得之各路徑的聲波速度，推算出二維平面上各點氣體的溫度。
本研究通過分析在二維平面上不同的網格形狀和超音波路徑的影響，提出了一種根據多個聲波傳導路徑重建溫度分佈的演算法並在MATLAB中實現。此演算法主要使用了空間之移動平均技術並使用六角網格進行溫度分佈之重建。對網格形狀與大小之選擇，本研究進行了數個模擬測試，共使用三種網格形狀（六角形分佈，正方形分佈和極座標分佈）分析重建溫度分佈的準確性。根據研究結果，發現六角形網格可以最準確地追蹤熱點的峰值溫度以及移動。在理想模型上可達所有聲速路徑上之平均溫度誤差小於1%，並可在熱點於正中心往外移動之情況下，感測到相對區域直徑3%之熱點移動，同時最高溫誤差小於10%。

Acoustic tomography (AT) is a non-invasive method to acquire specific information of the target region. Recently, the 2D temperature distribution of the region of interest (RoI) becomes an indispensable part for sensor network of internet of things (IoT). With AT, it is possible to reconstruct 2D temperature distribution of ROI without physically places temperature sensors inside it. However, the challenge is to improve the accuracy of the relative spatial distribution and the absolute temperature value.
Theoretically, the time of flight (ToF) of an ultrasonic pulse travels in RoI would be affected by the temperature of the medium. Consequently, if the traveling distance is fixed, the variation of acoustic speed could be calculated by ToF. With an ultrasonic transducer array surrounding the RoI, a matrix of ultrasonic transmission paths could be created. Based on the measured velocity of each path, an adequate reconstruction algorithm should be able to rebuild the 2D temperature distribution of RoI.
In this study, a novel reconstructed algorithm for 2D temperature distribution is proposed and implemented in MATLAB. Through analyzing the influence of shape and size of grid structures and applying the technique of spatial moving average, hexagon grid is selected to reconstruct the temperature distribution with best sensitivity and accuracy of tracking the shift of hot spot and the peak temperature respectively. In theoretical model, the reconstruction algorithm proposed in this work could reproduce the average velocity of each acoustic path with error less than 1%. Besides, the algorithm could successfully detects the movement of hotspot when it moves away from the center of RoI more than 3% of the diameter. Moreover, the error of peak temperature is less than 10%.

[1] Y. Yu et al., "A method for ultrasound thermal image distribution reconstruction," Measurement Science and Technology, vol. 30, no. 9, p. 095007, 2019.
[2] M. Gonzalez, B. Kelly, Y. Hayashi, and Y. J. Kim, "Heat transfer mechanisms in pulsating heat-pipes with nanofluid," Applied Physics Letters, vol. 106, no. 1, p. 013906, 2015.
[3] H. Xie, L. Chen, W. Yu, and B. Wang, "Temperature dependent thermal conductivity of a free-standing graphene nanoribbon," Applied Physics Letters, vol. 102, no. 11, p. 111911, 2013.
[4] T. Durka, G. D. Stefanidis, T. Van Gerven, and A. Stankiewicz, "On the accuracy and reproducibility of fiber optic (FO) and infrared (IR) temperature measurements of solid materials in microwave applications," Measurement Science and Technology, vol. 21, no. 4, p. 045108, 2010.
[5] M. Barth and A. Raabe, "Acoustic tomographic imaging of temperature and flow fields in air," Measurement Science and Technology, vol. 22, no. 3, p. 035102, 2011.
[6] H. Yan, Z. Ma, and Y. G. Zhou, "Acoustic tomography system for online monitoring of temperature fields," IET Science, Measurement & Technology, vol. 11, no. 5, pp. 623-630, 2017.
[7] M. Bramanti, E. A. Salerno, A. Tonazzini, S. Pasini, and A. Gray, "An acoustic pyrometer system for tomographic thermal imaging in power plant boilers," IEEE Transactions on instrumentation and measurement, vol. 45, no. 1, pp. 159-167, 1996.
[8] S. Liu, S. Liu, and T. Ren, "Acoustic tomography reconstruction method for the temperature distribution measurement," IEEE Transactions on Instrumentation and Measurement, vol. 66, no. 8, pp. 1936-1945, 2017.
[9] R. Jia, Q. Xiong, G. Xu, K. Wang, and S. Liang, "A method for two-dimensional temperature field distribution reconstruction," Applied Thermal Engineering, vol. 111, pp. 961-967, 2017.
[10] X. Shen, Q. Xiong, W. Shi, K. Wang, and G. Lai, "Temperature distribution monitoring using ultrasonic thermometry based on markov radial basis function approximation and singular values decomposition," Mathematical Problems in Engineering, vol. 2014, 2014.
[11] S. Liu, S. Liu, and T. Ren, "Ultrasonic tomography based temperature distribution measurement method," Measurement, vol. 94, pp. 671-679, 2016.
[12] X. Shen, H. Chen, T.-M. Shih, Q. Xiong, and H. Zhang, "Construction of three-dimensional temperature distribution using a network of ultrasonic transducers," Scientific reports, vol. 9, no. 1, pp. 1-10, 2019.
[13] S. Ren, J. Lei, and Z. Jia, "Reconstruction method for temperature field measurement using ultrasonic tomography," Chemical Engineering Science, vol. 183, pp. 177-189, 2018.
[14] R. J. Steriti and M. A. Fiddy, "Regularized image reconstruction using SVD and a neural network method for matrix inversion," IEEE Transactions on Signal Processing, vol. 41, no. 10, pp. 3074-3077, 1993.
[15] X. Shen, Q. Xiong, X. Shi, K. Wang, S. Liang, and M. Gao, "Ultrasonic temperature distribution reconstruction for circular area based on Markov radial basis approximation and singular value decomposition," Ultrasonics, vol. 62, pp. 174-185, 2015.
[16] R. Jia, Q. Xiong, and S. Liang, "Acoustic imaging for temperature distribution reconstruction," AIP Advances, vol. 6, no. 12, p. 125018, 2016.
[17] R. Jia and Q. Xiong, "Two-Dimensional Temperature Field Distribution Reconstruction Based on Least Square Method and Radial Basis Function Approximation," Mathematical Problems in Engineering, vol. 2017, 2017.
[18] E. P. Gleeson and F. Han, "Systems and methods for measuring temperature in a gas turbine using acoustic interference," ed: Google Patents, 2018.
[19] R. Jia, Q. Xiong, K. Wang, L. Wang, G. Xu, and S. Liang, "The study of three-dimensional temperature field distribution reconstruction using ultrasonic thermometry," AIP Advances, vol. 6, no. 7, p. 075007, 2016.
[20] U. P. Desilva, H. Claussen, M. X. Yan, J. Rosca, and N. H. Ulerich, "Non-intrusive measurement of hot gas temperature in a gas turbine engine," ed: Google Patents, 2016.
[21] S. Richards, A. Heathershaw, and P. Thorne, "The effect of suspended particulate matter on sound attenuation in seawater," The Journal of the Acoustical Society of America, vol. 100, no. 3, pp. 1447-1450, 1996.
[22] J. Allegra and S. Hawley, "Attenuation of sound in suspensions and emulsions: Theory and experiments," The Journal of the Acoustical Society of America, vol. 51, no. 5B, pp. 1545-1564, 1972.
[23] W. H. Thorp, "Analytic description of the low‐frequency attenuation coefficient," The Journal of the Acoustical Society of America, vol. 42, no. 1, pp. 270-270, 1967.
[24] C. M. Harris, "Absorption of sound in air versus humidity and temperature," The Journal of the Acoustical Society of America, vol. 40, no. 1, pp. 148-159, 1966.
[25] R. Lin, H. Rausch, W. Hartig, and L. Wu, "Development and Implementation of New Measuring and Monitoring Systems to Support BF Control," BHM Berg-und Hüttenmännische Monatshefte, vol. 162, no. 1, pp. 41-49, 2017.
[26] M. Tonteling, M. Brodeck, and H. Rausch, "2D Blast Furnace Top Gas Temperature Measurement System—TMT SOMA," Iron & Steel Technology, vol. 10, no. 12, pp. 45-55, 2013.
[27] https://tmt.com/en/measuring/measuring-technology/.
[28] D. Nabagło and P. Madejski, "Combustion process analysis in boiler OP-650k based on acoustic gas temperature measuring system," in Proc. 3rd Int. Conference on Contemporary Problems of Thermal Engineering, 2012.
[29] https://www.budi.de/en/agam-2d-gas-temperature-measurement.html.
[30] https://powerupgs.com/site/sciengr/boilerwatch-mmp-ii-ssx/#1535228058480-927f5ae5-e2315426-2a926f74-1460988e-f413.