As the result of vibration emission in air, machine sound signal carries affluent information about the working condition of machine and it can be used to make mechanical fault diagnosis. The fundamental problems with fault diagnosis are the estimation of the number of sound sources and the localization of sound sources. The wave superposition can be employed to identify and locate sound sources, which is based on the idea that an acoustic radiator can be approximated and represented by the sum of the fields due to a finite number of interior point sources. But, in practice, a large number of measurements must be used in order to achieve a desired resolution, which makes the reconstruction process very time-consuming and expensive. In this paper, a combined wave superposition method has been developed reconstruct to acoustic radiation from machine acoustical signals. This method combines the advantages of both the wave superposition and Helmholtz equationleast squares methods, and it allows for reconstruction of the acoustic field from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. After sound source localization, the blind source separation (BSS) is proposed to extract acoustical feature from the mixed measuring sound signals. In a semi-anechoic chamber, a cross-planar microphone array, which consists of 29 microphones, was successfully applied to obtain the two-dimensional mapping of the sound sources. The location, the sound pressure, and the properties in frequency domain of the sound sources can be found through this method precisely. The experimental results demonstrate that the methods presented can potentially become an acoustical diagnosis tool.

In order to reconstruct the sound field, the fast Fourier transform (FFT)-based near-field acoustical holography (NAH) demands that the measurement surface must extend to a region where the sound pressure decreases to a low level. This method is unfit for reconstructing the partial sound field in which the measurement aperture size is limited either by physical necessity or as a way of reducing the measurement cost. Statistically optimal NAH (SONAH) performs plane-to-plane calculations directly in the spatial domain, avoids all errors occurred in the FFT-based NAH and significantly increases the accuracy of the reconstruction of the partial sound field. In the present work, combined with the different regularization methods, SONAH is performed for reconstructing the partial sound field. The errors over the central and the peripheral sections of the reconstruction area are researched separately. Simulations and experiments show that SONAH is successful in reconstructing the partial sound field and the errors over the central sections are smaller than that over the peripheral sections. Experiments demonstrate that Tikhonov regularization in conjunction with Engl's criterion is suitable for the reconstruction of the practical sound field.

Sound field visualization is a helpful design and analysis tool for the study of sound radiation and dispersion problems. It can help to comprehend deeply about noise transmission mechanism, monitor environment noise, evaluate sound quality, and even diagnose the machinery faults based on mechanical noise. The well-known near-field acoustic holography is an accurate sound field visualization technique. However, this technique has disadvantages such as strict measurement requirements and the need of an enormous number of microphones, which limits its extended applications. In order to visualize the sound field with a small number of microphones for measurements, the regeneration method of the radiated field by using the wave superposition algorithm is attempted in this study. It is based on the principle of equivalent source: the sound field radiated by an arbitrarily shaped radiator is substituted by the distributed point sources (monopole or dipole) constrained inside the actual source surface. For suppressing the adverse effect of measurement noise, the Tikhonov regularization strategy is adopted to work together with the wave superposition algorithm to give an accurate solution. Numerical simulations were performed based on a two-pulse-ball model to evaluate the accuracy of the combined algorithm of the wave superposition and the Tikhonov regularization strategy. In addition, an integrated sound field visualization system is designed and implemented. The functions include acoustic signal acquisition and processing, sound field reconstruction, and results visualization. The performance of the presented system was tested by experiments in a semi-anechoic chamber by using two sound boxes to simulate the sound sources. As concerning practical measurement microphones, there exist phase mismatches between the channels. Results will go wrong if the sound field reconstruction is performed directly with these uncalibrated measurement data. Therefore, a calibration procedure is applied to eliminate them. Experimental results indicate that the phase mismatches between the channels after calibration decay to 0.1 • . Both the numerical simulations and experimental results accurately reconstructed the exterior sound field of the models. It is shown that the wave superposition algorithm together with the Tikhonov regularization strategy can exactly reconstruct the exterior sound field of radiators, which makes a base to its applications in practice. This sound field visualization system will make an operator's experimental work much easier.