Variable cosine windowing of intrinsic mode functions: Application to gear fault diagnosis

Abstract

Gear pair is used for speed reduction or increasing torque and/or to change the direction of rotation. Gears are considered critical element in various mechanical systems. When gears are in use, the multi component vibration signals are generated. These vibration signals can be captured by mounting accelerometers at suitable locations. Vibration signal analysis is very effective tool in finding gear fault at early stage. The methods based on empirical mode decomposition (EMD) have been used for gear fault diagnosis in mechanical systems. The EMD method decomposes an original signal into different frequency-bands in time domain, known as intrinsic mode functions (IMFs). A serious problem in application of EMD is boundary distortion of IMFs. While doing statistical analysis of IMFs, boundary distortion may provide high values of statistical indicator (e.g. kurtosis, Sr, Sα), even if fault is not present. Several extension-based methods are employed to eliminate the boundary distortion problem. Extension-based methods cannot completely eliminate the boundary distortion, especially when the low-frequency component of the analyzed signal is weak. Recently, cosine window-based method has been proposed by which the boundary distortion can be controlled in boundaries of the signal and the middle component of it can be exactly decomposed into IMFs. The cosine window-based method works only for a particular IMF depending on the size of window. Since, in EMD process, the boundary distortion of successive IMFs increases, a variable cosine window is proposed in this paper to address the increasing boundary distortion problem. In the proposed method boundary distortion problem is minimized by using variable cosine window for all IMFs. The simulation and experimental results for three statistical indicators viz. kurtosis, Sr, Sα show that the proposed method based on variable cosine window is a powerful and reliable technique for fault diagnosis.