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.