Vibration signal denoising using partial differential equations of arbitrary order

Abstract

In this paper, partial differential equations (PDE) denoising characteristics are investigated and a unified vibration denoising model is proposed based on arbitrary order PDE. The numerical solution for PDE filters with arbitrary order is demonstrated. The noise reduction features of the proposed model are analysed on Gaussian white noise, Pearson noise and Weibull noise. The realization of the PDE filter generally include the following steps: (1) Obtain the discretization equation according to the given order using the backward Euler scheme; (2) Compute the grid ratio according to the given order, the cut-off frequency and the sample frequency; (3) acquire the filter matrix. Numerical simulations are conducted and the results indicate that the proposed method exceeds relevant works in noise reduction and time-consuming performances. A shaft centreline orbit experiment has also been conducted to verify the efficacy of the proposed method in field application.