A Novel Sparse AR De-noising Algorithm of Vibration Signal

Abstract

The actual signal always contains noises produced by difierent surroundings and collected devices. So the signal de-noise algorithm is a signiflcant pre-processing. The paper proposes a new de-noise algorithm which is based on sparse optimization. The algorithm assumes that coe-cients of signal's AR model are sparse and the impact of noise efiect on coe-cients is equilibrium distribution. A sparse AR model and AR coe-cients matrix are built by noised signal. Take the matrix as the over-completed sparse basis. One under-determined equation set is obtained by cramping out some rows from the matrix randomly. Then the under-determined equation is solved by sparse optimization algorithm to get AR coe-cients. And the above process is repeated many times and obtain many sparse AR coe-cients. The de-noised signal is reconstructed by the average of those coe-cients. In this paper, Signal vectors are obtained by sparsely resample from one signal. For multi-frequency signals with lager noises, many simulation experiments are tested. It indicates that the de-noising efiect of the algorithm in this paper is superior to the classical wavelet de-noising algorithm. The algorithm in this paper is applied to de-noise for the vibration signal of the bridge cable, and practice shows that the algorithm has excellent efiect.