The article does a research on the order selection of the autoregressive (AR) model for the rolling element bearings. First, the model of the signal that matches the one introduced by McFadden is considered. To clearly describe it, here it is called the resonance damping model. It is shown that the impulses generated by a fault will cause structure resonance and soon decay with a periodic mode. As the AR process based on the prediction theory has an ability to recognize the periodic (quasi-periodic) part, it is possible to pick out the damping part that is a quasi-periodic component. Because of the background noise, the damping part cannot be recognized if the component decays to be buried into noise absolutely. Hence the optimal order should be the number of points contained by the process, which is the maximum length of the periodic damping part that the AR model can recognize. That is to say, the process should last until the resonance damping part is buried into noise completely. Then an experiment to validate the method is carried out and success is achieved in the fault diagnosis of real rolling bearings. In the end, it is concluded that the optimal order has a high ability for noise cancellation for rolling element bearing diagnosis.

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.