  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.
