Research Article  Open Access
Jacek Wodecki, Justyna HebdaSobkowicz, Adam Mirek, Radosław Zimroz, Agnieszka Wyłomańska, "Combination of Principal Component Analysis and TimeFrequency Representation for PWave Arrival Detection", Shock and Vibration, vol. 2019, Article ID 5961073, 7 pages, 2019. https://doi.org/10.1155/2019/5961073
Combination of Principal Component Analysis and TimeFrequency Representation for PWave Arrival Detection
Abstract
Seismic events are phenomena which commonly occur in the mining industry. Due to their dangerous character, such information as the energy of the potential event, the location of hazardous regions with higher seismic activity is considered valuable. However, the acquisition of this information is almost impossible without the ability to detect the onset time of the seismic event. The main objectives of algorithms in finding Pwave are high accuracy, reasonable time of operation, and automatic detection of wave arrival. In this paper, an innovative method which incorporates principal component analysis (PCA) with timefrequency representation of the signal is proposed. Due to the significant difference between the spectra of recorded seismic wave and pure noise which precedes the event, timefrequency representation allows for better accuracy of signal change detection. However, with an additional domain, the complexity rises. Thus, the incorporation of PCA (which is known for high efficiency in lowering data dimensions while maintaining original information) seems to be recommended. In order to show the feasibility of the method, it will be tested on real data originating from monitoring system used in underground mine.
1. Introduction
Analysis of mininginduced seismic events, prediction of such events, their evaluation in sense of mechanism, location, and amplitude (energy) identification are crucial in the underground mining industry. One of the basic issues is the problem of Pwave indication. Pwave detection is essential in calculating the energy of the event, description of the event, focal mechanism [1], and so on. One might say that its calculation is fundamental in the evaluation of seismic hazard. The seismic hazard in Poland is relatively high in underground mines, and there are many studies on that topic [2–5]. However, this paper is focused on the Pwave detection techniques only.
The problem of Pwave detection might be solved in many ways. The time of seismic wave arrival can be acquired manually by specialists from seismic station in the mine or automatically by previously developed algorithms. Obviously, these two approaches differ in terms of time consumption and accuracy, as human work is slower but more precise. However, as the specialists may face hundreds of events daily, the utilization of algorithms seems indispensable. The preliminary usage of some algorithms followed by a manual improvement became a common habit in seismic stations.
In the era of Big Data, it seems to be more reasonable to have an automatic, quick, and robust detection algorithm. Indeed, there are plenty of such algorithms developed by various authors. However, their accuracy appears very similar to the manual result. The problem of Pwave detection is well known in scientific literature and in engineering practice. The STA/LTA algorithm [6] is probably the most broadly used algorithm due to its simpleness, fast processing, and the possibility of working online. Its main idea inspects the quotient of previously assumed characteristic function considered in shortterm (STA) and longterm (LTA) windows. Other classical methods include multiscale wavelet analysis [7], usage of neural network [8], and autoregressivebased techniques [9, 10] with usage of the AIC criterion [11]. In the literature, one can find also the acoustic emission (AE) based analysis [12–14]. Advanced analysis of the spectrogram allows detecting the decay of AE signal frequencies revealing the transition from microcracking to the macrocracking regime during laboratory fracture tests. However, in our application, it was not considered.
The automation of Pwave detection has been highlighted in many publications [7, 15–21]. The comparison of the classical methods can be found in [15, 22, 23]. In recent years, a couple of new algorithms were developed, e.g., [18–21, 24–29]. Further information about their accuracy and computational time can be found in [15, 23].
Due to the importance of onset time acquisition, the problem is still analyzed. Surprisingly, a couple of new solutions have been published in 2018 [19–21, 24–26]. It shows that there is still space for new solutions.
From the signal processing point of view, the problem of Pwave arrival can be considered, e.g., as a simplified segmentation issue, finding the time of regime switching, or rapid change of the value of some particular statistic. Thus, in order to acquire onset time, it seems to be reasonable to utilize tools used to solve the isometric problems. The exemplary algorithms solving these parallel issues have been included in the following articles [30–40]. As one might see, the segmentation problem is a fundamental task in the signal processing, and it might be applied to various types of signals.
In this paper, we propose to use a combination of two wellknown techniques in signal processing and in data analysis. The seismic signal due to its impulsive nature is a nonstationary process. For that kind of signals, the most suitable way of analysis and processing is timefrequency representation. The shorttime Fourier transform (STFT) is used here as the simplest technique for the timefrequency transformation. It is possible to use more precise representations (Wigner–Ville, scalogram, or ARgram) but more complex, and anyway, the core of the procedure will be the same. The benefits of timefrequency representation are the possibilities to observe the behavior of the signal in the time (as in raw signal) and also in the frequency domain simultaneously. It brings additional opportunity for further signal processing and interpretation. The STFT timefrequency representation could be considered as a set of signals (we call them subsignals) for each frequency bin which is easier to process due to better signaltonoise ratio. In the case of very noisy signals, there is a possibility to use preprocessing techniques such as denoising [11] or mentioned segmentation, especially if the signal covers multiple events [31, 41].
Obviously, the idea of utilizing timefrequency domain in finding the Pwave arrival is not a new idea, e.g., [29, 32, 42]. The usage of shorttime Fourier transform has the ability to present the frequency structure changing over time. As the spectrum of a pure noise shall be flat and in terms of energy greatly differs from a spectrum of a signal containing registered seismic wave, the onset time detection shall be simple. However, timefrequency representation is a twodimensional map that from the mathematical point of view is just a matrix of data, usually in large sizes (depending on STFT parameters and length of the signal). Due to the high dimension of the timefrequency map, to avoid computational complexity during the detection phase, some data dimensionality reduction is recommended. Again, one of the most popular ways to reduce the dimensionality of highdimensional data is principal component analysis (PCA). The PCA algorithm seems to be a natural selection due to its high efficiency in lowering data dimensions while maintaining original information [43]. As a potential future development, one might consider other techniques of data dimension reduction, but at this stage, the combination of simplest techniques has been used. The PCA could be seen as weighted linear combination of input data that seem to be reasonable and intuitive for further analysis. It should be mentioned that the combination of a timefrequency approach and the PCA is not a novel idea. It was successfully applied, for instance, in mining machine condition monitoring [44]. According to our knowledge, there is no example of such procedure applied for a seismic signal, so we claim it is original. To summarize this section, we can say that we apply STFT timefrequency analysis to a raw seismic signal (single channel); for highdimensional data matrix (set of subsignals for each frequency bin ), we use the PCA to extract informative part of the map only; and for selected “subsignals,” we apply the Pwave detection technique based on a simple rule: find the maximum value on the differentiation function (with different window size) of principal component 1 (PC1). The method is very intuitive and provides automatically a result that could be compared to the decision of expert (and it is closer to expert’s opinion than the wellknown LTA/STA method).
2. Methodology
In this section, the detailed methodology of the proposed procedure has been described. A general outline of the algorithm is presented in Figure 1.
In the first step, the raw data are transformed into a timefrequency representation. A critical issue while using a spectrogram is establishing parameters of STFT. Due to Heisenberg’s uncertainty principle, the selection of window size and spectral resolution should be a compromise. It was found experimentally for these specific signals (will be discussed later).
After that, the spectrogram matrix is provided to the PCA algorithm to reduce the problem of high dimensionality. The PCA is applied to the spectrogram matrix with respect to the frequency dimension (principal components of time vectors for each frequency bin are derived). Values of the spectrogram matrix are describing the energy of frequency components with respect to time, so principal components are also informative in the energy context. Since the first principal component is the most informative one, it can be used as a time series indicator of the energy variability.
Finally, the differentiation function of the first principal component has been calculated, and its maximum value, obtained for the optimal order , is used as the Pwave arrival time indicator. One may expect that the simple derivatives (the differentiation function with order 1) could be calculated as the good enough to discover the sudden changes in PC1. Nevertheless, a more general approach for detection has been proposed to deal with the signal with very high frequency, where the simple derivative can fail and not always can give a unique solution.
For validation, the Pwave arrival time has been compared with the classical LTASTA method and time estimated manually by an expert. The main steps of the algorithm will be described in the following subsections.
2.1. TimeFrequency Representation
The shorttime Fourier transform of a discretetime signal with window in time point t and frequency point f is defined as follows [45]:where M is the length of (always an odd number), is the real sampling frequency of signal and j is the imaginary unit.
As a window function, the Hamming window is used [45]:
The spectrogram is a timefrequency map described as , where and , where c is the minimal desired difference between frequencies included in the spectrogram.
2.2. Principal Component Analysis
Principal component analysis is widely known in statistical analysis [43]. It assumes that dataset consisting of N observations, each spanned over K variables, can be interpreted as a point cloud in Kdimensional space. The goal of PCA is a rotation of local coordinate system towards variance maximization over a new set of dimensions such that the first dimension is characterized with the greatest variance, the second dimension with second greatest variance, and so on. Such a transformed system consists of new values of data over a new set of dimensions. Vectors of data over the new coordinate system are called principal components. Newly created feature space describes the original dataset mostly within several first principal components that carry most of the original information. Since for many types of analyses, the information contained in a small number of first principal components is sufficient, because their information content is very high, PCA is regarded to be a dimensionality reduction method.
Given n observations of mdimensional data stacked into a matrix , the principal components can be calculated using singular value decomposition (SVD) as follows:where and are unitary matrices and contains the nonnegative real singular values of nonincreasing magnitude (). Principal components are the orthonormal column vectors of the matrix V, and the variance of the ith component is equal to .
2.3. Detection Rule
After the PCA transformation, we use the first PC as the most informative component. We assume that due to the arrival of Pwave, a significant, rapid change in variance will appear. So, we propose to calculate the differentiation function with order from PC1, and a location of the maximum value will indicate sudden changes in PC1, so exactly the Pwave arrival time. However, in case of a highfrequency sampling, the first derivative not always gives a unique solution. In order to deal with that, we can calculate the ordinary differentiation for the given signal with bigger time interspace between given samples, what we called order (), namely,where t is the number of the observation, . Using this kind of approach, increasing the window, we allow to obtain the bigger peak in place of growth, and the detection can be much easier, but at the same time, we can lose some precision in time. It may happen that the maximum is not unique, and there are many local maximum values. However, application of different windows gives the possibility to localize the sudden changes more precisely. In our case, we select the differentiation order as small as possible, but such that it highlights the sudden change.
2.4. STA/LTA as a Verification Method
STA/LTA method is often used in the problem of Pwave arrival time detection [28]. The core idea is the evaluation of the characteristic function (CF) of the seismic signal using two sliding windows: one shorter and one longer. As a CF, various functions can be used, e.g., energy, absolute amplitude, and envelope. Regardless of the type of CF, the shorttime window (STA) is expected to represent the instantaneous amplitude of the seismic signal, while the longtime window (LTA) tracks the amplitude of seismic noise. When their ratio exceeds certain predefined value (the socalled activation threshold), the following portion of the signal is identified as the event until the described ratio decreases below a certain value (deactivation threshold). Inspection of such ratio called SLR (shorttolong ratio) can allow to identify the Pwave arrival time as the first time where SLR exceeded the value of .
3. Real Data Analysis
3.1. Seismic Data
In order to show the potential of the proposed method, it will be tested on real data originating from the ELOGORC seismic monitoring system, which is used for rock mass observation in the underground copper ore mine O/ZG “Rudna”. The system consists of 2 sets of differently located seismometers. Each of those seismometers collects velocity or acceleration with a sampling frequency equal to 500 Hz in the frequency band 0.5–150 Hz. Such a band is sufficient for locating and estimating seismic energy and indicating the focal mechanism by analyzing the first direction of motion, which is the primary goal of the monitoring system. The particular signal was registered in August 2015 (Figure 2).
3.2. Results: Spectrogram
First, the spectrogram of the input signal (Figure 3) has been calculated with the parameters presented in Table 1.

Practically, it means that frequency map, presented graphically in Figure 3, is a matrix size of MN ().
So, we have N subsignals, and for each subsignal, Pwave arrival time should be estimated. Instead of doing this, we will subject this matrix for dimensionality reduction via PCA. Instead of Msamplelong N signals, we expect to receive Msamplelong several PCs that will maximize information spread along frequencies.
3.3. Results: PCA
After performed PCA on the spectrogram matrix, we receive N vectors, but only some of them should contain the information. As one can see in Figure 4, the distribution of information is uneven. Most of the information is focused on PC1. It means that the spectrogram is redundant, and there is no need to detect Pwave arrival time for each subsignal of the spectrogram; there is only need to analyse the first PCs which handle the most significant information.
In the further analysis, we focus on the first three principal components, presented in Figure 5. As one can see, only the first component carries useful information about energy variability. Hence, it is selected for further analysis.
3.4. Results: Detection
In the next step, the differentiation function for orders has been calculated for PC1, and its maximum value locations have been investigated (Figure 6).
As one can see, the maximum values of for each order indicate the same place of rapid change in values of PC1, therefore, we take the location obtained from the differentiation with order , which maximizes the ability to precise detection and location. In Figure 7, the distances between the points indicated by the proposed method and indicated by the expert for each differentiation order have been presented. Then, the detection can be much easier. However, we lose some precision in time. Consequently, the result can be shifted by several samples (depending on the size of the order ). Finally, according to the description in Section 2, the optimal value for detection and location has been considered as the time of the Pwave arrival (Figures 6 and 8). In our case, we take the optimal value of differentiation order as , which gives the easy detection (the maximum value has a bigger amplitude easier to detect automatically) without loosing precision in the localization. The zooming of Figure 8 with the arrival time matched has been presented in Figure 9. As one might see, indeed, it pointed out the beginning of seismic impulse.
3.5. Results: Verification
As presented in Figure 9, the proposed method returned the timestamp of 1.526 seconds after the beginning of the signal. In comparison, the STA/LTA algorithm, regarded as the classical method, returned the timestamp of 1.534 seconds, and an expert from the mine indicated the point 1.524 seconds from the beginning (Figure 9). One might conclude that all techniques provided similar results. Indeed, all arrival times are similar; however, LTASTA and the technique proposed in the paper are automatic (expert provided result manually based on experience), and what is more, our result is closer to the expert’s decision, so we might state that results are better than the classical LTASTAbased method.
It is important to notice that the presented method has a few limitations. Due to properties of the spectrogram, there is a reduction of precision in comparison with methods that operate purely in time domain. Considering a comparison of our method with the classical STA/LTA approach, one can see that the proposed technique provides better result. The benefit is related to better signaltonoise ratio for the narrow band signal (for the given frequency band).
4. Conclusion
In this paper, the concept of a new method for determining Pwave onset time is described. The method uses a spectrogram altogether with principal component analysis. The spectrogram gives the visible difference between the frequency spectrum of registered seismic wave and pure seismic noise which precedes this wave. The resulting timefrequency map is used as a multidimensional input for PCA, which extracts the information required to identify the Pwave arrival time. The usefulness of the method was proved on real seismic data originating from the underground mine. Obtained results have been compared with the STA/LTA method as well as with the arrival time indicated by the mine expert. The comparison shows that the described method shows greater accuracy than the STA/LTA approach by indicating the point diverging from the point indicated by the expert only by 0.002 s, while STA/LTA shows point distant by 0.01 s.
Data Availability
The data used to support the findings of this study have not been made available because of NDA statements.
Disclosure
Our work was prepared as part of the employment of the authors at the Wroclaw University of Science and Technology.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
References
 G. Kwiatek and Y. BenZion, “Assessment of P and S wave energy radiated from very small sheartensile seismic events in a deep South African mine,” Journal of Geophysical Research: Solid Earth, vol. 118, no. 7, pp. 3630–3641, 2013. View at: Publisher Site  Google Scholar
 A. Tajduś, M. Cała, and K. Tajduś, “Seismicity and rock burst hazard assessment in fault zones: a case study,” Archives of Mining Sciences, vol. 63, no. 3, pp. 747–765, 2018. View at: Google Scholar
 G. Mutke, J. Dubiński, and A. Lurka, “New criteria to assess seismic and rock burst hazard in coal mines/nowe kryteria dla oceny zagrożenia sejsmicznego I tąpaniami W kopalniach węgla kamiennego,” Archives of Mining Sciences, vol. 60, no. 3, pp. 743–760, 2015. View at: Publisher Site  Google Scholar
 D. Chlebowski, Z. Burtan, and A. Zorychta, “Evaluation of rockburst hazard under abandoned mine workings,” Archives of Mining Sciences, vol. 63, no. 3, pp. 687–699, 2018. View at: Google Scholar
 A. Gogolewska and P. Junik, “Seismic hazard related to rate of face advance in lubin copper ore mine,” Mining Science, vol. 20, no. 1, pp. 87–99, 2013. View at: Google Scholar
 R. V. Allen, “Automatic earthquake recognition and timing from single traces,” Bulletin of the Seismological Society of America, vol. 68, no. 5, pp. 1521–1532, 1978. View at: Google Scholar
 H. Zhang, C. Thurber, and C. Rowe, “Automatic Pwave arrival detection and picking with multiscale wavelet analysis for singlecomponent recordings,” Bulletin of the Seismological Society of America, vol. 93, no. 5, pp. 1904–1912, 2003. View at: Publisher Site  Google Scholar
 J. Wang and T.L. Teng, “Artificial neural networkbased seismic detector,” Bulletin of the Seismological Society of America, vol. 85, no. 1, pp. 308–319, 1995. View at: Google Scholar
 R. Sleeman and T. van Eck, “Robust automatic Pphase picking: an online implementation in the analysis of broadband seismogram recordings,” Physics of the Earth and Planetary Interiors, vol. 113, no. 1–4, pp. 265–275, 1999. View at: Publisher Site  Google Scholar
 M. Leonard and B. L. N. Kennett, “Multicomponent autoregressive techniques for the analysis of seismograms,” Physics of the Earth and Planetary Interiors, vol. 113, no. 1–4, pp. 247–263, 1999. View at: Publisher Site  Google Scholar
 M. Polak, J. Obuchowski, A. Wyłomańska, and R. Zimroz, “Seismic signal enhancement via ar filtering and spatial timefrequency denoising,” in Cyclostationarity: Theory and Methods III, pp. 51–68, Springer, Berlin, Germany, 2017. View at: Google Scholar
 A. BenaventCliment, A. Gallego, and J. M. Vico, “An acoustic emission energy index for damage evaluation of reinforced concrete slabs under seismic loads,” Structural Health Monitoring: An International Journal, vol. 11, no. 1, pp. 69–81, 2012. View at: Publisher Site  Google Scholar
 T. H. W. Goebel, D. Schorlemmer, T. W. Becker, G. Dresen, and C. G. Sammis, “Acoustic emissions document stress changes over many seismic cycles in stickslip experiments,” Geophysical Research Letters, vol. 40, no. 10, pp. 2049–2054, 2013. View at: Publisher Site  Google Scholar
 L. M. Bogomolov, P. V. Il’ichev, V. A. Novikov et al., “Acoustic emission responseof rocks to electric power actionas seismicelectric effect manifestation,” Annals of Geophysics, vol. 47, no. 1, 2004. View at: Google Scholar
 M. Leonard, “Comparison of manual and automatic onset time picking,” Bulletin of the Seismological Society of America, vol. 90, no. 6, pp. 1384–1390, 2000. View at: Publisher Site  Google Scholar
 S. Gentili and A. Michelini, “Automatic picking of P and S phases using a neural tree,” Journal of Seismology, vol. 10, no. 1, pp. 39–63, 2006. View at: Publisher Site  Google Scholar
 C. Panagiotakis, E. Kokinou, and F. Vallianatos, “Automatic $P$phase picking based on localmaxima distribution,” IEEE Transactions on Geoscience and Remote Sensing, vol. 46, no. 8, pp. 2280–2287, 2008. View at: Publisher Site  Google Scholar
 E.S. Akhouayri, D. Agliz, A. Atmani et al., “Automatic detection and picking of Pwave arrival in locally stationary noise using crosscorrelation,” Digital Signal Processing, vol. 26, no. 1, pp. 87–100, 2014. View at: Google Scholar
 X. Wang, J. Fu, C. Tang, Z. Li, and J. Wang, “A P waves’ automatic picking by detecting the changes of seismic signals’ stationary random process through similarity analysis,” Soil Dynamics and Earthquake Engineering, vol. 115, pp. 225–231, 2018. View at: Publisher Site  Google Scholar
 Y. Zhang, Q. Chen, X. Liu et al., “Adaptive and automatic Pand Sphase pickers based on frequency spectrum variation of sliding time windows,” Geophysical Journal International, vol. 215, no. 3, pp. 2172–2182, 2018. View at: Publisher Site  Google Scholar
 C. Hun, “Automatic seismic Pwave detection algorithm using variations of impact momentum,” The Transactions of the Korean Institute of Electrical Engineers, vol. 67, no. 7, pp. 884–891, 2018. View at: Google Scholar
 M. Withers, R. Aster, C. Young et al., “A comparison of select trigger algorithms for automated global seismic phase and event detection,” Bulletin of the Seismological Society of America, vol. 88, no. 1, pp. 95–106, 1998. View at: Google Scholar
 J. Sokołowski, J. Obuchowski, R. Zimroz, and A. Wyłomańska, “Comparison of recent Pwave arrival picking methods,” in Proceedings of the 16th International Multidisciplinary Scientific GeoConference SGEM, vol. 2, no. 1, pp. 133–140, Curran Associates, Red Hook, NY, USA, June 2016. View at: Publisher Site  Google Scholar
 J. Zhang, Y. Tang, and H. Li, “STA/LTA fractal dimension algorithm of detecting the Pwave arrival,” Bulletin of the Seismological Society of America, vol. 108, no. 1, pp. 230–237, 2018. View at: Publisher Site  Google Scholar
 J. Kwon, T. Heo, J. K. Kim, and H. S. Oh, “A new Pwave detector via moving empirical cumulative distribution function,” Bulletin of the Seismological Society of America, vol. 108, no. 4, pp. 2080–2089, 2018. View at: Publisher Site  Google Scholar
 M. Li, H. Li, G. Tao, M. Ali, and Y. Guo, “Microseismic event location using multiscale time reversed imaging,” Journal of Petroleum Science and Engineering, vol. 174, pp. 144–160, 2019. View at: Publisher Site  Google Scholar
 Nurhaida, A. Subanar, and A. M. Abadi, “Detecting p and swave of mt. rinjani seismic based on a locally stationary autoregressive (lsar) model,” in Proceedings of the AIP Conference Proceedings, vol. 1868, no. 1, AIP Publishing, Yogyakarta, Indonesiavol, August 2017. View at: Google Scholar
 J. Sokołowski, J. Obuchowski, R. Zimroz, A. Wyłomańska, and E. Koziarz, “Algorithm indicating moment of Pwave arrival based on secondmoment characteristic,” Shock and Vibration, vol. 2016, Article ID 4051701, 6 pages, 2016. View at: Publisher Site  Google Scholar
 G. Xiantai, L. Zhimin, Q. Na, and J. Weidong, “Adaptive picking of microseismic event arrival using a power spectrum envelope,” Computers & Geosciences, vol. 37, no. 2, pp. 158–164, 2011. View at: Publisher Site  Google Scholar
 C. H. Chen, “On a segmentation algorithm for seismic signal analysis,” Geoexploration, vol. 23, no. 1, pp. 35–40, 1984. View at: Publisher Site  Google Scholar
 R. Hossa, R. Makowski, and R. Zimroz, “Automatic segmentation of seismic signal with support of innovative filtering,” International Journal of Rock Mechanics and Mining Sciences, vol. 91, pp. 29–39, 2017. View at: Publisher Site  Google Scholar
 R. Zimroz, M. Madziarz, G. Żak, A. Wyłomańska, and J. Obuchowski, “Seismic signal segmentation procedure using timefrequency decomposition and statistical modelling,” Journal of Vibroengineering, vol. 17, no. 6, pp. 3111–3121, 2015. View at: Google Scholar
 D. Kucharczyk, A. Wyłomańska, J. Obuchowski, R. Zimroz, and M. Madziarz, “Stochastic modelling as a tool for seismic signals segmentation,” Shock and Vibration, vol. 2016, Article ID 8453426, 13 pages, 2016. View at: Publisher Site  Google Scholar
 T. D. Popescu, “Signal segmentation using changing regression models with application in seismic engineering,” Digital Signal Processing, vol. 24, pp. 14–26, 2014. View at: Publisher Site  Google Scholar
 T. D. Popescu and D. Aiordachioaie, “Signal segmentation in timefrequency plane using renyi entropyapplication in seismic signal processing,” in Proceedings of the 2013 Conference on Control and FaultTolerant Systems (SysTol), pp. 312–317, IEEE, Nice, France, October 2013. View at: Publisher Site  Google Scholar
 E.V. Pikoulis and E. Z. Psarakis, “A new automatic method for seismic signals segmentation,” in Proceedings of the 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3973–3976, IEEE, Kyoto, Japan, March 2012. View at: Publisher Site  Google Scholar
 D. Kucharczyk, A. Wyłomańska, and R. Zimroz, “Structural break detection method based on the adaptive regression splines technique,” Physica A: Statistical Mechanics and Its Applications, vol. 471, pp. 499–511, 2017. View at: Publisher Site  Google Scholar
 H. Azami, S. Sanei, K. Mohammadi, and H. Hassanpour, “A hybrid evolutionary approach to segmentation of nonstationary signals,” Digital Signal Processing, vol. 23, no. 4, pp. 1103–1114, 2013. View at: Publisher Site  Google Scholar
 J. Gajda, G. Sikora, and A. Wyłomańska, “Regime variance testing  a quantile approach,” Acta Physica Polonica B, vol. 44, no. 5, pp. 1015–1035, 2013. View at: Publisher Site  Google Scholar
 A. Wyłomańska and R. Zimroz, “Signal segmentation for operational regimes detection of heavy duty mining mobile machinesa statistical approach,” Diagnostyka, vol. 15, no. 2, pp. 33–42, 2014. View at: Google Scholar
 J. Obuchowski, M. Madziarz, and R. Zimroz, “Seismic multiple events–a study on signals separation,” Vibroengineering PROCEDIA, vol. 6, pp. 212–216, 2015. View at: Google Scholar
 A. G. Hafez, T. A. Khan, and T. Kohda, “Earthquake onset detection using spectroratio on multithreshold timefrequency subband,” Digital Signal Processing, vol. 19, no. 1, pp. 118–126, 2009. View at: Publisher Site  Google Scholar
 B. Moore, “Principal component analysis in linear systems: controllability, observability, and model reduction,” IEEE Transactions on Automatic Control, vol. 26, no. 1, pp. 17–32, 1981. View at: Publisher Site  Google Scholar
 R. Zimroz, J. Wodecki, P. Stefaniak, J. Obuchowski, and A. Wyłomańska, “Combination of principal component analysis and timefrequency representations of multichannel vibration data for gearbox fault detection,” Journal of Vibroengineering, vol. 18, no. 4, pp. 2167–2175, 2016. View at: Publisher Site  Google Scholar
 B. Boashash, Timefrequency Signal Analysis and Processing: A Comprehensive reference, Academic Press, Cambridge, Massachusetts, USA, 2015.
Copyright
Copyright © 2019 Jacek Wodecki et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.