Fast partial differential equation de‐noising filter for mechanical vibration signal

A novel approach for mechanical vibration signal de‐noising filter using PDE and its numerical solution were presented. The proposed method is computationally fast compared with other conventional PDE‐based de‐noising methods. It enables: (i) by incorporating unconditional stable finite difference backward Euler scheme, the de‐noising process has no requirements of grid ratio; (ii) developing variational matrix‐based fast filter while the de‐noising process can be completed instantly, which will be accomplished by only one iteration; and (iii) effective de‐noising method for mechanical vibration signal interfered by Gauss white noise. The method is performed efficiently, and the de‐noising tests on different artificial Gauss white noise as well as natural mechanical noise are conducted. Experimental tests have been rigorously compared with different de‐noising methods to verify the efficacy of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.