Non-negative matrix underapproximation as optimal frequency band selector

Time-frequency representation (TFR) is often used for non-stationary signal analysis. The most intuitive and interpretable TFR is the spectrogram. Recently, a concept of non-negative matrix factorization (NMF) has been successfully applied to local damage detection in rolling elements of bearings via spectrogram factorization. NMF applied to the spectrogram allows one to find an informative frequency band, which could be further used as a filter characteristic. However, the obtained filter characteristics mostly detect the informative frequency band, which also encompasses a lot of noise. In the case where noise is more problematic, as is the case for acoustic signals from industrial machines, the NMF hardly detects the damage. To solve this problem and obtain more selective filters, which are more robust to noise, we propose the non-negative matrix under-approximation (NMU) as an informative frequency band selector. Due to the more sparse parts-based representation of the NMU compared to NMF, NMU provides more selective filter characteristics, which neglect the non-informative frequency bands related to the noise. In practice, it means that NMU gives a better signal-to-noise ratio for the filtered signal. The efficiency of the proposed approach has been validated on the vibration signal from the test rig and the acoustic signal from an idler.