Tomographic reconstruction of indoor spatial temperature distributions using room impulse responses

Abstract

Temperature can be estimated by acoustic travel time measurements along known sound paths. By using a multitude of known sound paths in combination with a tomographic reconstruction technique a spatial and temporal resolution of the temperature field can be achieved. Based on it, this article focuses on an experimental method in order to determine the spatially differentiated development of room temperature with only one loudspeaker and one microphone. The theory of geometrical room acoustics is being used to identify sound paths under consideration of reflections. The travel time along a specific sound path is derived from the room impulse response. Temporal variances in room impulse response can be attributed primarily to a change in air temperature and airflow. It is shown that in the absence of airflow a 3D acoustic monitoring of the room temperature can be realized with a fairly limited use of hardware.

Measurement of indoor air temperature distribution using acoustic travel-time tomography: Optimization of transducers location and sound-ray coverage of the room

“…where is the Laplace speed of sound for dry air, = 1.40 is the ratio of the specific heat at constant pressure and volume of the gas, = 287.058 −1 −1 is the specific gas constant, is the specific humidity which is the ratio of water vapor mass to the total mass of moist air, and is the temperature of the gas in [3,25,26]. Accordingly, (1) is used to determine the average air temperature along the propagation paths.…”

“…where ( ) is the spatially variable speed of sound, ( ) is the slowness which is a reciprocal value of the speed of sound, is the sound paths length, and describes the position inside the tomographic area as a vector of , and coordinates [11,3,4]. To extract the travel-time between the emitted and the received signal, the cross-correlating technique is used.…”

“…To reconstruct the air temperature and flow velocity distributions of a fluid in a volume (three-dimensional problem), the technique of Acoustic travel-time TOMography (ATOM) can be applied [1,2,3,4,5]. ATOM utilizes the dependency of the speed of sound on air temperature and flow velocity in the medium.…”

“…In this experiment, the same method of bidirectional soundray paths to calculate the influence of air temperature and flow properties was applied. More recent investigation was performed by [3] to determine spatially differentiated room air temperature with only one loudspeaker and one microphone with the intention to use as little hardware as possible. Although [3] utilized the visualization of the image source model (ISM) to find the proper location of transducers in terms of having homogeneous and distinguishable sound-ray paths, investigation of numerical estimation of optimal positions of the source and receiver is still required.…”

“…More recent investigation was performed by [3] to determine spatially differentiated room air temperature with only one loudspeaker and one microphone with the intention to use as little hardware as possible. Although [3] utilized the visualization of the image source model (ISM) to find the proper location of transducers in terms of having homogeneous and distinguishable sound-ray paths, investigation of numerical estimation of optimal positions of the source and receiver is still required. One primary factor, which has a major impact on the accuracy of the reconstructed temperatures, is the detection of the correct peaks in the room impulse response (RIR) reflectogram.…”