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*Materials Transactions*, Vol.53 No.02 (2012) pp.316-320

© 2012 The Japanese Society for Non-Destructive Inspection

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Temperature Distribution Estimated by Optimization and Near-Field Acoustical Holography

Takeshi Ohbuchi^{1}, Kojiro Nishimiya^{1}, Koichi Mizutani^{1}, Naoto Wakatsuki^{1} and Hiroyuki Masuyama^{2}

^{1}Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba 305-8573, Japan

^{2}Toba National College of Maritime Technology, Toba 517-8501, Japan

We propose a method to estimate temperature distribution non-destructively using combination of near-field acoustical holography (NAH) method and optimization method. NAH method is valid to calculate forward and back propagations of ultrasonic wave in a uniform medium. To estimate of temperature distribution, we proposed a modified method of NAH, called sectional NAH (SNAH), for using NAH in an inhomogeneous medium. In SNAH, a calculation space is discretized into a number of sections, so that the temperature in each section becomes nearly uniform, and NAH calculation is performed in each section. Calculation results using SNAH in the inhomogeneous medium well agreed with the calculation result using finite element method (FEM). By using SNAH, the temperature distribution is estimated as bellows. Firstly, sound fields, which are complex amplitude of harmonic oscillation, in three planes are measured. Next, sound field at one of measured plane is calculated from the other measured sound fields, which are calculated from other measurement planes using SNAH, with an initial sound velocity distribution. Then, difference between calculated and measured sound fields is minimized by optimizing the sound velocity distribution using multi-start downhill simplex method. In this method, a temperature distribution is obtained as the sound velocity distribution. In simulations, temperature distributions given as linear and Gaussian distributions were estimated. Validity of our proposal methods is confirmed by simulations.

(Received 2009/11/12; Accepted 2011/03/11; Published 2012/01/25)

**Keywords:** non-destructive measurement, optimization, near-field acoustical holography, multi-start downhill simplex method

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