A hybrid kernel function approach for acoustic reconstruction of temperature distribution

•An improved hybrid kernel method is proposed to reconstruct the temperature field.•Travel times can be collected and then used as input data after pre-processing.•Effectiveness of the proposed method is experimentally validated.•The proposed method provides more detailed temperature information. This paper utilizes a hybrid kernel method based on a cubic + exponential kernel to reconstruct the temperature field in a measurement area. In the experiments, we simulate the internal circumstance of a furnace in the measurement area with a heat source. It is based on measuring the acoustic travel time (ATT) between several pairs of ultrasonic transducers placed around the entire probed area. These ATT data, in turn, are related to temperature along the sound paths between any two transducers. The ATT data can then be used as input data after pre-processing by means of mean filtering, correction, and calibration. On this basis, three other different kernel functions are presented, and then a thermal map can be reconstructed with one of these kernel-based methods. Experimental results indicate that the hybrid kernel method (our proposed method) has a lower condition number and provides more detailed temperature information on the probed area, compared with the cubic kernel method, the Gaussian + cubic method, and the exponential kernel method.