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Improvement of spectral representation by using single channel independent component analysis

!"""#$%&'()%*#+,-. Industrial and Medical Measurement and Sensor Technology Vehicle Sensor Technology | June, 6th - 7th 2019, Mülheim an der Ruhr
Improvement of spectral representation by using single
channel independent component analysis
Rubens Rossi(1,2), Norbert Gomolla(1)
(1) DMT GmbH & Co. KG, Industrial Engineering Dept. D-45307 Essen, Germany
(2) Faculty of Technology and Bionics, Rhein-Waal University of Applied Sciences, D-47533 Kleve, Germany
E-Mail: Web:
Early damaged components produce weak and irregular impacts, whose frequencies are smoothed in a simple
spectrum. Moreover, it is not always possible to place sensors to the desired locations and in the desired
amount, in particular for retrofitting applications and in underground mining machines. As a result, the reduced
availability of data increases the complexity of its processing to detect fault patterns.
The independent component analysis (ICA) belongs to the blind source separation methods and it is an unsu-
pervised learning algorithm. Its goal is to find non-Gaussian hidden factors that are as much as possible statis-
tically independent. Given that a source signal x is the sum of several components s, the goal of the ICA is to
determine the mixing matrix A or the separating matrix W for the inverse transformation:
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The ICA method has been used for condition monitoring purposes [1], [2] and also in single-channel analysis
of vibrational data [3], [4].
In this abstract we examine the signal of a single sensor placed on a gearbox of a hard rock cutting machine.
Fault frequencies in this environment are difficult to detect because the signal contains several components
and it is highly contaminated by the vibration of the cutting process and by other equipment. Moreover, fault
impulses do not always come out since the cutting process itself is discontinuous and the gearbox is thus
irregularly loaded.
We use the independent component analysis (ICA) to process the signal of a one-dimensional time series. It is
assumed that the components of the signal have non-Gaussian distribution and have disjointed spectra.
Artificial signals are created from overlapping blocks of the source signal and are then organised into a matrix
which is then processed with ICA. This novel method is applied to a simulated signal and validated with
experimental data, with and without damages.
According to the analysed machine, it is necessary to select one or more ICA components. In our case two
components were sufficient to describe the phenomena, additional components would include less information
and also make it more difficult to comprehend the results.
The Fig.1 compares the results of a traditional envelope spectrum with our proposed method. The graphs depict
the analysis of a gearbox with damages. The frequencies, identified with a,b,c,d, correspond with the real
characteristic frequencies of the shafts and bearings.
!"""#$%&'()%*#+,-. Industrial and Medical Measurement and Sensor Technology Vehicle Sensor Technology | June, 6th - 7th 2019, Mülheim an der Ruhr
Fig.1: Comparison between envelope spectrum and the results of the analysis with ICA of a gearbox with defects. Letters a,b,c,d
denote the characteristic frequencies of the investigated gearbox.
By using our new algorithm, the frequencies of the impacts are more distinguishable and the peak dynamic is
Results demonstrate that the proposed method is able to reveal fault frequencies, which were not visible with
a traditional method, in particular when the machine is under load.
In conclusion, the onset of the damage is clearly visible with the proposed algorithm. As a result, it is possible
to detect the damage much earlier, which eventually reduces the maintenance cost.
R.Rossi is supported by EIT RawMaterials and by the program “Karrierewege FH-Professur” of NRW. N. Gomolla is supported by
EIT RawMaterials.
[1] J. Wodecki, P. Stefaniak, J. Obuchowski, A. Wylomanska, and R. Zimroz, “Combination of ICA and time-frequency
representations of multichannel vibration data for gearbox fault detection,” J. Vibroengineering, vol. 18, no. 4, pp. 2167–2175,
[2] G. Yu, “Fault feature extraction using independent component analysis with reference and its application on fault diagnosis of
rotating machinery,” Neural Comput. Appl., vol. 26, no. 1, pp. 187–198, 2014.
[3] M. E. Davies and C. J. James, “Source separation using single channel ICA,” Signal Processing, vol. 87, no. 8, pp. 1819–1832,
[4] P. He, T. She, W. Li, and W. Yuan, “Single channel blind source separation on the instantaneous mixed signal of multiple dynamic
sources,” Mech. Syst. Signal Process., vol. 113, pp. 22–35, 2018.
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Full-text available
A multichannel vibration data processing method in the context of local damage detection in gearboxes is presented in this paper. The purpose of the approach is to achieve more reliable information about local damage by using several channels in comparison to results obtained by single channel vibration analysis. The method is a combination of time-frequency representation and Principal Component Analysis (PCA) applied not to the raw time series but to each slice (along the time) from its spectrogram. Finally, we create a new time-frequency map which aggregated clearly indicates presence of the damage. Details and properties of this procedure are described in this paper, along with comparison to single-channel results. We refer to autocorrelation function of the new aggregated time frequency map (1D signal) or simple spectrum (that might be somehow linked to classical envelope analysis). The results are very convincing – cyclic impulses associated with local damage might be clearly detected. In order to validate our method, we used a model of vibration data from heavy duty gearbox exploited in mining industry.
Single Channel Blind Source Separation (SCBSS) has had many algorithms for artificial mixed signal, where the number of mixing sources is assumed to be known, and mixed signal used in validation algorithm only contains two signal sources. However, in real-world application, the mixed number of sources is unknown and is usually more than two. This paper presents a new single-channel blind source separation algorithm based on the multi-channel mapping and Independent Component Analysis (ICA), which supposes that mixed signal comes from a dynamic system in which any component depends on the interaction of other components and signals are linear instantaneous mixture. The mathematical model demonstrates the single channel signal of linear instantaneous mixture. In order to map single channel signals into multi-channel signals, Takens theory and C-C method are used to estimate the time delay and the embedding dimension in the time series of the dynamic system. FastICA for multi-channel blind source separation is improved by using FSS-Kernel (Finite Support Samples Kernel), where the nonlinear function of FastICA is replaced by PDF (probability density function) and estimated by FSS-Kernel. The experiments are conducted to evaluate the proposed algorithm of single channel blind source separation, in which the synthetic signals and speech signals are used respectively. The experiment results show that the proposed method is very effective to estimate the number of independent components and is practical to separate two or more mixed signals.
In practical situations, the vibration collected from rotating machinery is often a mixture of many vibration components and noise; therefore, it is very necessary to extract fault features from the mixture first in order to achieve effective rotating machinery fault diagnosis. In this paper, independent component analysis with reference method is proposed to extract the fault features using reference signals established based on the a priori knowledge of machine faults; experimental studies based on both simulated and actual fault signals of rotating machinery have been performed; and the results show that the proposed approach can effectively extract fault features under the situation of interferences and coexistence of multiple faults.
Many researchers have recently used independent component analysis (ICA) to generate codebooks or features for a single channel of data. We examine the nature of these codebooks and identify when such features can be used to extract independent components from a stationary scalar time series. This question is motivated by empirical work that suggests that single channel ICA can sometimes be used to separate out important components from a time series. Here we show that as long as the sources are reasonably spectrally disjoint then we can identify and approximately separate out individual sources. However, the linear nature of the separation equations means that when the sources have substantially overlapping spectra both identification using standard ICA and linear separation are no longer possible.