The Journal of the Acoustical Society of Korea (한국음향학회지)

The Acoustical Society of Korea (한국음향학회)
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Regeneration of the Retarded Time Vector for Enhancing the Precision of Acoustic Pyrometry

온도장 측정 정밀도 향상을 위한 시간 지연 벡터의 재형성

  • 김태균 (한국과학기술원 기계공학과 소음 및 진동제어 연구센터) ;
  • 이정권 (한국과학기술원 기계공학과 소음 및 진동제어 연구센터)
  • Received : 2013.12.19
  • Accepted : 2014.02.03
  • Published : 2014.03.31
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Abstract

An approximation of speed of sound in the measurement plane is essential for the inverse estimation of temperature. To this end, an inverse problem relating the measured retarded time data in between set of sensors and actuators array located on the wall is formulated. The involved transfer matrix and its coefficient vectors approximate speed of sound of the measurement plane by using the radial basis function with finite number of interpolation points deployed inside the target field. Then, the temperature field can be reconstructed by using spatial interpolation technique, which can achieve high spatial resolution with proper number of interpolation points. A large number of retarded time data of acoustic paths in between sensors and arrays are needed to obtain accurate reconstruction result. However, the shortage of interpolation points due to practical limitations can cause the decrease of spatial resolution and deterioration of the reconstruction result. In this works, a regeneration for obtaining the additional retarded time data for an arbitrary acoustic path is suggested to overcome the shortage of interpolation points. By applying the regeneration technique, many interpolation points can be deployed inside the field by increasing the number of retarded time data. As a simulation example, two rectangular duct sections having arbitrary temperature distribution are reconstructed by two different data set: measured data only, combination of measured and regenerated data. The result shows a decrease in reconstruction error by 15 % by combining the original and regenerated retarded time data.

역문제에 기반한 음향 온도 측정법에서는 단면의 음속 분포 계산이 필수적이며, 이를 위하여 단면 외곽에 위치한 센서들 간의 지연시간을 계측하고, 이를 입력으로 하는 전달행렬과 계수 벡터를 이용한 역문제를 이용하여 음속 분포를 예측한다. 그러나, 센서 개수의 부족으로 인하여 충분한 수의 음향 경로가 확보되지 못하면, 지연시간 벡터의 개수가 한정될 수 있다. 지연시간 벡터의 개수는 공간 해상도와 관련 있으며, 부족한 지연시간 벡터의 개수는 공간 해상도의 저하를 초래하여 정확한 온도 재구성 결과를 얻지 못할 수 있다. 본 연구에서는 이 문제를 해결하기 위하여, 실제 측정된 지연시간으로부터 온도장을 재구성 한 뒤, 임의의 경로에 해당하는 지연시간을 재구성 된 온도장으로부터 재형성하여 지연시간 벡터의 개수를 증가시켰다. 측정된 지연시간 벡터와 재형성 된 지연시간 벡터를 함께 사용할 경우, 음향 경로의 개수가 증가하므로 공간 분해능의 향상을 기대할 수 있다. 임의의 온도 분포를 가지는 2차원 단면을 수치 예제로서 채택하였고, 측정된 지연시간만을 이용한 결과와 재형성 된 지연시간을 함께 사용한 재구성 결과를 비교하였다. 그 결과, 재형성 된 지연시간과 측정된 지연시간을 함께 사용한 경우의 온도 재구성 오차가 측정된 지연시간만을 사용한 온도 재구성 오차보다 최대 15 % 감소하였다.

Keywords

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