Why Mel-frequency Cepstrum Analysis Is Not Always The Ideal Solution For Vibration Analysis

The Mel-frequency Cepstrum (MFC) and it's associated outputs, the Mel-frequency Cepstral Coefficients (MFCCs), are commonly used for speech applications such as speaker and speech recognition, using neural networks. Unfortunately, the nature of the MFC means that it is not always ideally suited to applications such as vibration analysis and predictive maintenance

The MFC uses logarithmicaly spaced frequency banks to replicate how the human ear hears sound. This approach can lead to very large savings in the number of MIPS required for the recognition part of speaker and speech recognition. Unfortunately, this logarithmic frequency space hides frequencies that are closely spaced meaning that this approach is sub-optimal for applications such as machine vibration analysis, where small variations in vibrational frequency can indicate problems with the machine, particularly the bearings.

The following diagram shows a simple Mel-spaced filterbank, with 12 separate filters:

As can be seen from the diagram, resolution of close by frequencies is a particular problem for higher frequency harmonics, where the filters have a wider bandwidth.

The problem can also be seen in the following two images, which are sampled from identical machines running with two different error modes. It can be seen that it is the higher frequency peaks (1 kHz to 2 kHz) that vary the most and this is just the region, for this Mel-spaced filterbank, where the filter bandwidths start to get exessively wide.

Vibration Mode #1

Vibration Mode #2

The solution to this problem is to use a regular Fast Fourier Transform (FFT) for the front-end processing of these types of applications and use spectral analysis of the anticpated vibration modes to observe the frequency resolution required and this will then define the FFT size required for the application.

The SigLib Digital Signal Processing and Machine Learning library includes examples for machine vibration monitoring. These can be found here.

Copyright © 2024 Delta Numerix