Computational Feasibility Study for Time-Frequency Analysis of Non-Stationary Vibration Signals based on Wigner-Ville Distribution

The time-frequency analysis has been gaining a significant amount of attention for research purposes as its applications in the study of non-stationary signals offers meaningful information that is usually suppressed by the conventional analysis in the time or frequency domains. In this context, the smoothed pseudo Wigner-Ville distribution (WVD) for analytic signals arises as a reliable time-frequency tool that is used in the study of various different signal data. Due to the extensive computational operations involved in generating the WVD, the objective of this study is to explore approaches that reduce the computational cost associated with analyzing large datasets using the mentioned tool. The dataset used comprised a 9000-sample acoustic signal obtained from a milling machine run, with a sampling rate of 100 kHz captured by a sensor and filtered in its 1kHz to 8kHz band by a pass-band butterworth filter of 5th order. Two approaches were, then, pursued, the first involved calculating the average WVD of three time-frequency transformations obtained from equidistant time windows of the signal. The second involved reducing the sampling rate of the analyzed signal by a factor of k by creating an array where each nth element corresponded to the k*nth element of the original signal. The mean WVD method distorted the signal’s time-frequency diagram by adding middle range frequencies throughout its entire time axis regardless of the time window taken, while the second approach showed an identical WVD to the one of the original signal even for big k factors, decreasing the analysis time greatly. This leads to the conclusion that diminishing the sample frequency of the signal is a viable way to overcome the computational cost of the WVD calculation for the study of the behavior of the signal’s low-frequency components.