The Short-Time Fourier transform is widely applied in the condition monitoring of rotating machinery. Even so, selecting the optimal window length for the Short-Time Fourier Transform remains a challenge. This work presents a procedure for adapting the Short Time Fourier Transform algorithm to be differentiable with respect to window length by using continuous window functions defined over the entire input signal duration. Thanks to this modification, a differentiable loss criterion can be defined to measure the Short-Time Fourier quality, and the gradient of the loss criterion with respect to window length can be computed. The optimal window length for a given loss criterion can then be efficiently solved for using a gradient-based optimization algorithm. Results from a simulated bearing dataset and three experimental bearing datasets are used to compare the optimal spectrograms obtained using different loss criteria. Specifically, a sparsity-based loss criterion is compared with two loss criteria inspired by the characteristic cyclo-stationarity machine of faults in rotating machinery. The results demonstrate the effectiveness of the differentiable window length selection method and highlight the importance of selecting appropriate loss criteria for defining STFT quality. Loss criteria that account for the cyclo-stationary nature of the signals are shown to be less likely to target single high-amplitude impulsive events compared to the sparsity-based loss criterion.
How to Cite
bearing, condition monitoring, differentiable, short-time Fourier Transform, cyclo-stationary
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