Recursive Compressive Sensing for Vibration Analysis

Vibration analysis is an effective method of rotating machinery diagnostics, where order tracking is a common tool. In most applications, the rotational speed changes only slightly between two adjacent rotation periods, and thus, similar order spectra are expected. This article presents how this similarity can be exploited to use recursive compressive sensing for order tracking. Compressive sensing allows reduced computational burden, which is especially useful in the case of multiple-channel measurements. Given synchronous tachometer impulses, first the signal is even-angle resampled. The compressive measurements from each period are transmitted for processing, where recursive compressive reconstruction methods are used to obtain the order spectra. For reconstruction of the vibration signal, the continuity-modified basis pursuit denoising (BPDN) algorithm is proposed. The procedure is demonstrated by simulation and measurement examples.