Fast Fourier transform (FFT) has mainly been designed to analyze stationary data. Yet, the FFT under non stationary conditions is quite difficult to apply with accuracy due to problems such as frequency resolution, magnitude accuracy at steady state, and more generally, due to data processing. To overcome this drawback, the multiple-signal-classification method with an algorithm with zooming in a specific frequency range can be used to extract the meaningful frequencies from the signal.

Working with different signal processing different solutions can be attempted: The first one is based on short-time Fourier transform (STFT) and the second one on wavelet decompositions.

TFA Spectograma 2
TFA Spectograma

The STFT is a Fourier-related transform that is used to determine the sinusoidal frequency and the phase content of the local sections of a signal as it changes over time. In other words, it is the time-dependent Fourier transform for a sequence, and it is computed using a sliding window. The magnitude squared of the STFT yields the spectrogram of the function, which is usually represented like color plots. The spectrogram is used to estimate the frequency content of a signal. Moreover, these kinds of images provide graphical information of the evolution of the power spectrum of a signal, as this signal is swept through time. Spectrograms are widely used by voice and audio engineers. They help to develop a visual understanding of the frequency content of one speech signal while a particular sound is being vocalized. The spectrograms are also used in industrial environments to analyze the frequency content and variation of a nonconstantfrequency signal. In the case of nonconstant load torque of an induction motor, either the STFT or the spectrogram could be used to show the changes in harmonic-current amplitudes.

In fact, in recent years Wavelet transforms have been successfully applied to motor fault detection problems.  Continuous wavelet transform (CWT) has been used in to propose a detection method of faulted rotor bars based on ridges of a CWT.  Also, CWT is used in to process both waveforms of electromagnetic torque and phase voltage summation in order to detect windings short circuits in a Brushless DC Motor.

On the other hand, Discrete Wavelet Transform (DWT) is commonly used in electric engineering to detect and diagnose disturbances occurring in three-phase induction motors. In the amplitude of relevant coefficients of DWT is used as proper feature coefficients to represent the mechanical faults of the induction motor. This proposal is based on the analysis of the wavelet packet transform coefficients, and a useful implementation is presented, though discrimination between faults is not possible and faults harmonics under main harmonic is lost, because only two levels are considered in wavelet decomposition. DWT has been also used for the diagnosis of rotor bar failures in induction machines by means of analysis of the stator current during the machine startup.