Power estimation of sound sources on low-speed electric trains using a deconvolution approach

The traditional delay and sum beamforming method has been widely used over the past two decades to locate and characterize sound sources on moving trains. However, when the total number of major and minor sources is uncertain, this method tends to overestimate the sound powers for multiple sources. The overestimation of sound powers becomes significant when the separation of the sources is very 'small' for a microphone array with fixed configuration for avoiding spatial aliasing at high frequencies for broadband noise. The separation of the sources is 'small' because the resulting resolution of the delay and sum beamforming method is 'low' at low frequencies. For train noise characterization, the contribution from some other parts of the train would be masked due to this low resolution power at low frequencies. This paper describes a deconvolution approach which is developed to give estimates of the sound powers on a moving line source. Simulation results illustrate that sound powers can be accurately estimated by using the proposed deconvolution method at both low- and high-frequency regions. Both the delay and sum beamforming method and the deconvolution method were applied to the measured data using an array of 15 microphones.