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Abstract
A scheme is proposed for the identification of surface intrusion events, from signals detected by an ultra-weak fiber Bragg grating array in a subway tunnel. The spectral subtraction and the root mean square of the power spectral density are combined to extract event signals. The local characteristics-scale decomposition and the multi-scale permutation entropy are employed subsequently for feature extraction, which can improve the event recognition rate from the perspective of multi-scale analysis. Experimental demonstration verifies that the proposed scheme can identify four common events. Among the events, the discrete pulse construction and the continuous pulse construction on the ground surface are intrusion events, the subway train traveling in the tunnel and the lorry passing on the ground surface are non-intrusion events. The average recognition rate of 96.57% is achieved, which can satisfy actual application requirements.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With rapid urbanization in China, subway has been a popular transport-style in people’s daily life. However, accidents caused by unapproved construction actives which broken the safety boundary of subway often occur. Traditional monitoring methods widely use static health monitoring such as industrial cameras [1], non-destructive testing [2], etc., but these methods only give alerts after subway tunnel structures are damaged and are difficult to provide a large-scale monitoring. Recently, due to the superiority of high sensitivity, fast response and dynamic measurement, distributed vibration sensing based on ultra-weak fiber Bragg grating (UWFBG) array has attracted a close attention [3–8]. One study by Gan et al. verified that this method is viable to detect the vibration event signals near the subway tunnel [9], while they cannot distinguish the signals whether harmful to the subway tunnel. Therefore, the identification of the detected signals is the key to realize pre-warning of intrusion events.
Up to now, various methods have been proposed to identify intrusion events in perimeter security field. The feature vector was formed by the signal energies distributed over different frequency bands to recognize three kinds of intrusions, which was obtained by wavelet transform [10]. Whereas this method only considered frequency-domain characteristics, ignoring abundant time-domain information. Following this, a more accurate scheme took the kurtosis values of several intrinsic modal functions (IMFs) by empirical mode decomposition (EMD) as features [11]. Nevertheless, EMD had the problem of mode mixing and only kurtosis was considered. Another study reported a method based on hybrid feature vector (including bandwidth segmentation in frequency domain, kurtosis in statistics, the zero-crossing rate in time domain), and its recognition rate was high [12]. The selection of features is critical when there were many other features.
Although the above identification schemes are effective, the recognition rates are diverse due to the difference of features. Specifically, the information of more aspects the feature vector involves, the higher the accuracy is. Local characteristics-scale decomposition (LCD) is a new adaptive time-frequency analysis method, which can adaptively decompose complex signal into a series of intrinsic scale components (ISCs) [13]. Compared to EMD, LCD requires fewer iterations, and the ISCs contain more information than the IMFs. Hence, it is widely used to analyze non-stationary signals in mechanical fault diagnosis [14], EEG signal processing [15], and so on. In addition, multi-scale permutation entropy (MPE) can measure the complexity and randomness of signal at different scales [16], and has been extensively applied in various fields [17–20]. Thai, V et al. [21] utilized LCD-MPE to analyze the vibration signals detected by piezoelectric acceleration sensor for diagnosing the state of gears, and the accuracy was high.
By using the methods highlighted above, we propose a surface intrusion event identification scheme for subway tunnel based on a UWFBG array. Considering the efficiency, we only identify the event signals, so we preprocess the detected signals to extract event signals before feature extraction. Since the original signal acquired by the sensing system has a mixed noise composed of laser noise, optical device noise, detector noise and environmental noise, which would not only affect the subsequent processing effect of signals, but also affect the recognition rate of signals. Thus, the pre-processing including signal denoising and endpoint detection is indispensable in the proposed method. Among the noise reduction methods, spectral subtraction is an effective method to deal with wideband noise, which has the characteristics of direct physical meaning, simple realization and less computation complexity [22]. Moreover, the root mean square of power spectral density (PSD-RMS) has been widely used to analyze the vibration signal of a mechanical structure because it can accurately describe the vibration intensity [23,24]. Thus, the proposed scheme includes the following steps: First, the spectral subtraction method is used to enhance the signal noise ratio (SNR), after which the PSD-RMS of the signal is calculated for endpoint detection and event signal extraction. Second, the signal is decomposed into multiple ISCs based on LCD, and the MPEs of the ISCs are extracted to form a feature vector. Last, the feature vector is input to a support vector machine (SVM) for identifying signals. The experimental results verify that the scheme can identify four common events, which are two intrusion events and two non-intrusion events. The intrusion events are discrete pulse construction and continuous pulse construction on the ground surface, while the non-intrusion events are the subway train traveling in the tunnel and the lorry passing on the ground surface. The proposed scheme is also suitable for similar intrusion detection systems.
The presentation of this paper is organized as follows. In Section 2, we simply describe the distributed vibration sensing system based on the UWFBG array. In Section 3, we elaborate the principle of identification scheme, involving the preprocessing and the formation of feature vector based on the LCD and MPE methods. In Section 4, we compare the event identification experiments between the proposed scheme and the EMD based scheme. Finally, Section 5 comes to conclusions.
2. Distributed vibration sensing system based on UWFBG array
The sensor network is composed of UWFBGs with low reflectivity of about −50 dB, which can effectively reduce the crosstalk between multiple gratings and greatly increase the multiplexing capacity [5,6]. The sensing system adopts optical interferometry technology, which can obtain the frequency and the magnitude of the vibration from the phase of the optical signal [25]. Chirped fiber Bragg gratings (CFBG) are adopted to construct the sensor array, because they present much broader reflection bandwidths as compared to uniform fiber Bragg gratings. In this work, the sensor array is fabricated by the on-line writing technique based on an optical fiber drawing tower. In the writing system, the UV light emitted by a 248-nm excimer laser irradiates onto the optical fiber while it is drawn from the preform, through the phase mask plate with central wavelength of 1550 nm, chirp rate of 2 nm /cm and chirp length of 2.5 cm. With such a technique, the fabricated gratings generally present variation of the center wavelengths on the order of 0.1 nm, or reflectivities on the order of several decibels; and the transmission loss of the sensing network is extremely low because there are no splicing joints between the gratings [26].
The schematic of the distributed vibration sensing system based on the UWFBG array is shown in Fig. 1. The light source is a narrow linewidth laser (NLL) with central wavelength of 1550.12 nm and linewidth of 3 kHz. The continuous-wave (CW) light output from by NLL is modulated by a semiconductor optical amplifier (SOA) to obtain an optical pulse train with a repetition rate of 1 kHz and a pulse width of 20 ns. Then, the pulse light is amplified by an erbium-doped fiber amplifier (EDFA) and directed to the UWFBG array through a circulator (C1). Every two adjacent UWFBGs and the 5-m fiber in between constitute a sensor. The reflected pulse light from UWFBGs passes through the 3$\times$3 coupler phase demodulation unit which is essentially a Michelson interferometer. The outputs of the 3$\times$3 coupler are directed to three photodetectors (PD1, PD2, PD3) for optical-to-electrical conversion. The phase demodulation unit restores the time-domain vibration signal amplitude by demodulating the phase variation introduced to the light by the optical length variation in the 5-m optical fiber between two adjacent UWFBGs. In the meantime, the positions of the vibration events can be located based on the optical time domain reflection (OTDR) technology [27]. The serial data from three PDs are collected by a data acquisition (DAQ) device, and finally transmitted to a personal computer (PC) for processing and analysis.
Fig. 1. Schematic of the distributed vibration sensing system based on an UWFBG array. NLL: narrow linewidth laser; SOA: semiconductor optical amplifier; EDFA: erbium-doped fiber amplifier; C1/C2: circulator; 3$\times$3: symmetrical 3$\times$3 coupler; FRM: Faraday rotating mirror; PD: photodetector; DAQ: data acquisition; PC: personal computer.
Figure 2 shows how the intrusion events are detected by the UWFBG array. The sensing optical cable is deployed in the tunnel between the Hugong and the Yezhihu Stations of the Wuhan Metro Line 7, which has a total length of about 3 km and a grating spacing of 5 m. The sensor network transmits the real-time vibration response with a sampling rate of 1 kHz back to the monitoring center, where demodulation of the sensing signal is realized. As shown in Fig. 2, for the subway tunnel, its perceptible vibration events, in addition to the intrusion incident such as unapproved drilling, also include interferences from the subway and ground traffic. Therefore, this paper mainly studies the identification of two common intrusion signals and two common non-intrusion signals: discrete pulse construction, continuous pulse construction on the ground surface, the subway train traveling in the tunnel, and the lorry passing on the ground surface.
3. Principle of identification scheme
Figure 3 shows the flow chart of the identification scheme, which mainly includes signal denoising by spectral subtraction, endpoint detection by PSD-RMS, event signal extraction, feature extraction by LCD-MPE, and event identification by SVM.
3.1 Signal preprocessing
3.1.1 Signal denoising by spectral subtraction
Spectral subtraction is based on the assumption that additive noise and effective signal are independent of each other. Hence, the original signal is assumed to be the sum of the noise signal and the effective signal in the frequency-domain. The power spectrum of stationary noise is considered unchanged before and during the disturbance. Thus, the noise power spectrum can be estimated by the "quiet section" before the disturbance occurs. Then the power spectrum of the effective signal can be acquired by subtracting the noise power spectrum from the original signal power spectrum. Finally, the denoised time-domain signal is obtained by the inverse Fourier transform.
First, the vibration signals were divided into signal frames by Hamming windows with 128 points and a 50% inter-frame overlap rate. Second, the power spectrum of each signal frame was calculated by Welch’s method, and the power spectrum of noise was estimated according to the power spectrum of the signals in 5 quiet frames. Third, the denoised signals’ power spectrum were obtained by subtracting the noise’s power spectrum from the signals’. The average SNR gain of 1000 vibrational data samples was 13.40 dB. Figures 4(a) and 4(b) are the time-domain waveform and power spectrum of the vibration signal, which contains a subway train traveling signal and a discrete pulse construction signal. Figures 4(c) and 4(d) are the corresponding results after spectral subtraction denoising. As shown in Fig. 4(c), the signal quality is significantly improved after denoising. Furthermore, the signal strength and time-domain characteristics of the effective signal are not weakened. From Fig. 4(d), it is observed that the broadband noise in the original signal is significantly suppressed, and the frequency-domain characteristics of the effective signal are not affected.
Fig. 4. Signal denoising by spectral subtraction. (a) Time-domain waveform and (b) Power spectrum of the vibration signal before denoising. (c) Time-domain waveform and (d) Power spectrum of the vibration signal after denoising.
3.1.2 Endpoint detection based on PSD-RMS
The energy distribution of the vibration signal is always acquired by calculating the PSD-RMS of the frequency range of interest. As shown in Fig. 4, the energy of the subway train traveling signal is mainly distributed in the range of 0$\sim$200 Hz, and that of the construction signal is mainly distributed in the range of 0$\sim$100 Hz. Therefore, after spectral subtraction, the energy distribution of the vibration signal can be obtained by calculating the amplitude of PSD-RMS of the denoised signals’ power spectrum in 0$\sim$100 Hz. Through the threshold judgment, the start and the end points of the disturbance signal are detected, and the disturbance signal can be intercepted. Figure 5 shows the PSD-RMS distribution of the signal analyzed in Fig. 4. It is found that the amplitude of PSD-RMS jumps about 97 dB when the events happen. According to the distribution of vibration signal energy before and after the occurrence of the events, −125 dB is chosen as the threshold for endpoint detection because it is the median of the amplitude fluctuation range (−200 dB $\sim$ −50 dB) of PSD-RMS. The result shows that this method can intercept the events’ signals well.
3.2 Feature extraction
3.2.1 Local characteristics-scale decomposition
LCD is an adaptive signal decomposition method, which can decompose any complex signal $x(t)$ into a series of ISC components and a residue [13], expressed by
where $c_{i}(t)$ is the $i$-th ISC and $r_{n}(t)$ is the residue. The LCD method supposes that any two ISCs are independent of each other, and each ISC must meet the follow two conditions: (1) any two adjacent extreme points are monotone and opposite in sign; (2) the local waveform fit the sine curve. According to the definition of ISC, the LCD decomposition process of $x(t)$ is as follows [21]:(1) Determine all maximum (minimum) points of the signal, and calculate the function value $A_{k+1}$ at the corresponding time $\tau _{k+1}$ of minimum (maximum) between two adjacent maxima (minimum),
where $X_{k}$ is extreme point and $\tau _{k}$ is the corresponding time.(2) Calculate the baseline value $L_{k+1}$ corresponding to $A_{k+1}$:
where $a$ is a proportional coefficient, which is generally set as 0.5.(3) The cubic spline function was used to fit all the $L_{k+1}$ to get the baseline $BL_{1}$. Then the $BL_{1}$ is separated from the original signal $x(t)$,
If $h_{1}(t)$ meets the ISC’s conditions, output $h_{1}(t)$ as the first ISC $c_{1}(t)$. Otherwise, perform the above operations on $h_{1}(t)$ until the conditions are met.(4) Separate $c_{1}(t)$ from $x(t)$, and process the residue $r_{1}(t)$ like $x(t)$. Repeat the above process until $r_{n}(t)$ is a constant or monotonic function or a function with no more than three extrema. Similarly, we obtain $c_{2}(t)$, $\cdots$, $c_{n}(t)$.
(5) Finish the decomposition of $x(t)$, $n$ ISCs and a residue $r_{n}(t)$ are obtained as Eq. (1).
To compare the performance of LCD and EMD, we decompose the discrete pulse construction signal using EMD and LCD, respectively. Figure 6 shows the decomposition results of the signal. In Fig. 6(a), IMF 1 is the original signal, IMF 2 $\sim$ IMF 5 can exhibit multiple pulses corresponding to the discrete pulse construction signals, but IMF 6 $\sim$ IMF 14 reveal no significant information due to the phenomenon of mode mixing. However, in Fig. 6(b), ISC 1 is the noise signal, ISC 2 $\sim$ ISC 11 clearly present the multiple pulse, only ISC 12 $\sim$ ISC 14 display no significant information because the decomposition is about to end. Therefore, the LCD method can decompose a signal into more components close to the original signal. As shown in Fig. 7, the correlations of the ISC 7 $\sim$ ISC 14 with the original signal are higher than that of IMF 7 $\sim$ IMF 14, which means that the ISCs contain more information than the IMFs. Hence, ISCs better reflect the intrinsic characteristics of the signal, and LCD is superior to EMD in the application scenario considered here.
Fig. 6. The decomposition results of the discrete pulse construction signal using (a) EMD and (b) LCD.
3.2.2 Multi-scale permutation entropy
MPE was proposed based on the multi-scale entropy analysis to measure the complexity and randomness of time series at different scales [16]. After processing the original time series by coarse-graining to construct a multi-scale time series, the permutation entropy at each scale is calculated. To obtain the MPE of a time series is $X = x(i)$, ($i=1$, $2$, $3$,$\cdots$, $n$), the specific steps are as follows [16]:
(1) For a given discrete time series $x(i)$, multiple coarse-grained time series are constructed using coarse-grained processing given by
where $s$ is scale factor, and $y^{s}(j)$ is the time series with different scale factors.(2) Refactor $y^{s}(j)$ in time using
where $m$ is embedding dimension and $\tau$ is the delay time.(3) Calculate the permutation entropy of the time series with different scale factors $s$ using
where $P_{j}$ is the probability of occurrence of the $j$-th symbol sequence.(4) Normalize the permutation entropy at multiple scales
where $H_{p}^{s}$ should meet $0\le H_{p}^{s}\le 1$. The larger the value of $H_{p}^{s}$, the more random and irregular the signal is, and the more complex the signal is.Before calculating the MPE of the signal, we must select the appropriate embedding dimension $m$ and scale factor $s$. Figure 8 uses the discrete pulse construction signal as an example to show how $m$ and $s$ are determined. Bandt et al. recommended $m$ = 3$\sim$7 for practical purposes [28]. As shown in Fig. 8(a), when $m$ = 3$\sim$4 and $m$ = 6$\sim$7, the values of PE are high but vary within a small range. The PE line presents the largest slope when $m$ = 5, which is chosen as the embedding dimension. Figure 8(b) is the distribution of PE values at different scales for four common vibration events detected by subway tunnels when $m$ = 5. If $s$ is too small, it cannot fully reflect the characteristic information of the signal. However, if $s$ is too large, it may lead to information redundancy and increase the time of identification and training. It is found that when $s$ = 5, the PE values of the four signals are obviously different and the value of $s$ is not very large. Therefore, we choose the scale factor $s$ = 5.
4. Experimental result
In order to verify the effectiveness of the proposed identification scheme, field experiments are carried out in an actual subway (Wuhan Metro Line 7) tunnel. The vibration signals are obtained by using the experimental platform shown in Fig. 2 and the demodulation system shown in Fig. 1. The sampling rate of the system is 1 kHz, which is determined by the repetition rate of the optical pulse train. Figure 9 shows four kinds of vibration events obtained in the field experiments, which are the common events detected by subway tunnels. They are subway train traveling in the tunnel, lorry passing, discrete pulse construction, and continuous pulse construction on the ground surface. The signals corresponding to the four events are acquired in the following ways: the signals of the subway train traveling in the tunnel and the lorry passing on the ground surface are acquired during the daily operation of the tunnel; and the signals of discrete pulse construction and continuous pulse construction are acquired while a small hydraulic excavator is working in two different modes on the ground surface. The average buried depth of the tunnels under the pavement observation area is about 22.6 m.
Fig. 9. Four common vibration events detected by subway tunnels: (a) Subway train traveling; (b) Lorry passing (c) Discrete pulse construction; (d) Continuous pulse construction.
Four kinds of common vibration event signals are successfully intercepted based on PSD-RMS of STFT spectrum, as shown in Fig. 10. The intercepted signals are decomposed into 14 ISCs by LCD, after which the MPE of each ISC is calculated. Based on the previous analysis, the embedding dimension and the scale factor of MPE are both set to 5. A two-dimensional matrix of 14$\times$5 is thus obtained for each intercepted signal. To create an input to a SVM for classification, the two-dimensional matrix is transformed into a one-dimensional matrix to form the feature vectors. Figure 11 is the feature vectors of the four events. Obvious differences are observed among the feature vectors.
Fig. 10. Signals of four common subway tunnel vibration events: (a) Subway train traveling; (b) Lorry passing (c) Discrete pulse construction; (d) Continuous pulse construction.
Fig. 11. Feature vectors of four common events (1 - the subway train traveling, 2 - the lorry passing, 3 - discrete pulse construction, 4 - continuous pulse construction).
Finally, the SVM is used to identify and classify the extracted feature vectors. The kernel function of the SVM selects the radial basis function (RBF) with better effect, and the kernel parameter is set to $g$ = 1. We select 350 groups of samples for each event and randomly divide them into two groups, 300 groups as training samples and 50 groups as test samples. Table 1 shows the identification results of four events using LCD-MPE. As a comparison, the experiments based on the EMD-PE identification method are also carried out, and the recognition results are also listed in Table 1. The average recognition rate of EMD-PE is 90.70%, while the recognition rates of four common events are 96.67%, 94.29%, 87.03%, and 82.29%, respectively. However, the average recognition rate of LCD-MPE is 96.57%, and the recognition rates of four common events are 100%, 99.58%, 99.07%, and 90.10%, respectively. The recognition rates are higher when LCD-MPE is adopted, for all four events considered.
Table 1. Comparison of recognition effects between LCD-MPE and EMD-PE
5. Conclusion
In this paper, a surface intrusion event identification scheme is proposed for subway tunnel, from signals detected by an UWFBG array. The spectral subtraction method is used to enhance the SNR, and the PSD-RMS of the frequency range of interest is used to evaluate the vibration intensity of the signal, thereby intercept the event signal. Then, the event signal is decomposed into a series of ISCs by LCD, and the MPEs of the ISCs are extracted to form a feature vector, which is the input of the SVM for identifying. The experimental results show that the proposed scheme can identify two common intrusion signals from two common non-intrusion events. The average recognition rate reaches 96.57%, which is better than the EMD-PE method. The proposed scheme can not only detect and identify the subway surface intrusion event, but also provides reference for perimeter security, pipeline leakage and other similar research using vibration signals for intrusion detection.
Funding
Natural Science Foundation of Hubei Province (2018CFA056); National Natural Science Foundation of China (61575149, 61735013).
Disclosures
The authors declare no conflicts of interest.
References
1. W. Zhang, Z. Zhang, D. Qi, and Y. Liu, “Automatic crack detection and classification method for subway tunnel safety monitoring,” Sensors 14(10), 19307–19328 (2014). [CrossRef]
2. L. Feng, X. Yi, D. Zhu, X. Xie, and Y. Wang, “Damage detection of metro tunnel structure through transmissibility function and cross correlation analysis using local excitation and measurement,” Mech. Syst. Signal Process. 60-61, 59–74 (2015). [CrossRef]
3. X. Liang, N. Xiang, Z. Li, L. Zhou, T. Zhao, Q. Liu, and X. Bao, “Precision dynamic sensing with ultra-weak fiber bragg grating arrays by wavelength to frequency transform,” J. Lightwave Technol. 37(14), 3526–3531 (2019). [CrossRef]
4. C. Wang, Y. Shang, X. Liu, C. Wang, H. Yu, D. Jiang, and G. Peng, “Distributed otdr-interferometric sensing network with identical ultra-weak fiber bragg gratings,” Opt. Express 23(22), 29038–29046 (2015). [CrossRef]
5. X. Gui, Z. Li, F. Wang, Y. Wang, C. Wang, S. Zeng, and H. Yu, “Distributed sensing technology of high-spatial resolution based on dense ultra-short fbg array with large multiplexing capacity,” Opt. Express 25(23), 28112–28122 (2017). [CrossRef]
6. P. Han, Z. Li, L. Chen, and X. Bao, “A high-speed distributed ultra-weak fbg sensing system with high resolution,” IEEE Photonics Technol. Lett. 29(15), 1249–1252 (2017). [CrossRef]
7. Z. Li, Y. Tong, X. Fu, J. Wang, Q. Guo, H. Yu, and X. Bao, “Simultaneous distributed static and dynamic sensing based on ultra-short fiber bragg gratings,” Opt. Express 26(13), 17437–17446 (2018). [CrossRef]
8. X. Fu, W. Yang, J. Wang, and Z. Li, “Noise resilient quasi-distributed sensing with an interferometric-noise-suppressing golay coded optical source,” Opt. Express 27(18), 25330–25341 (2019). [CrossRef]
9. W. Gan, S. Li, Z. Li, and L. Sun, “Identification of ground intrusion in underground structures based on distributed structural vibration detected by ultra-weak fbg sensing technology,” Sensors 19(9), 2160 (2019). [CrossRef]
10. L. Liu, W. Sun, Y. Zhou, Y. Li, J. Zheng, and B. Ren, “Security event classification method for fiber-optic perimeter security system based on optimized incremental support vector machine,” in Pattern Recognition, (2014).
11. K. Liu, M. Tian, T. Liu, J. Jiang, Z. Ding, Q. Chen, C. Ma, C. He, H. Hu, and X. Zhang, “A high-efficiency multiple events discrimination method in optical fiber perimeter security system,” J. Lightwave Technol. 33(23), 4885–4890 (2015). [CrossRef]
12. X. Huang, H. Zhang, K. Liu, T. Liu, Y. Wang, and C. Ma, “Hybrid feature extraction based intrusion discrimination in optical fiber perimeter security system,” IEEE Photonics J. 9(1), 1–12 (2017). [CrossRef]
13. J. Zheng, J. Cheng, and Y. Yang, “A rolling bearing fault diagnosis approach based on lcd and fuzzy entropy,” Mech. Mach. Theory 70, 441–453 (2013). [CrossRef]
14. H. Pan, Y. Yang, X. Li, J. Zheng, and J. Cheng, “Symplectic geometry mode decomposition and its application to rotating machinery compound fault diagnosis,” Mech. Syst. Signal Process. 114, 189–211 (2019). [CrossRef]
15. Q. Ai, A. Chen, K. Chen, Q. Liu, T. Zhou, S. Xin, and Z. Ji, “Feature extraction of four-class motor imagery eeg signals based on functional brain network,” J. Neural Eng. 16(2), 026032 (2019). [CrossRef]
16. W. Aziz and M. Arif, “Multiscale permutation entropy of physiological time series,” in 2005 Pakistan Section Multitopic Conference, (2005).
17. P. Ma, K. Liu, J. Jiang, Z. Li, P. Li, and T. Liu, “Probabilistic event discrimination algorithm for fiber optic perimeter security systems,” J. Lightwave Technol. 36(11), 2069–2075 (2018). [CrossRef]
18. M. N. Yasir and B.-H. Koh, “Data decomposition techniques with multi-scale permutation entropy calculations for bearing fault diagnosis,” Sensors 18(4), 1278 (2018). [CrossRef]
19. H. Niu, J. Wang, and C. Liu, “Analysis of crude oil markets with improved multiscale weighted permutation entropy,” Phys. A 494, 389–402 (2018). [CrossRef]
20. R. Jia, H. Sun, Y. Peng, Y. Liang, and X. Lu, “Automatic event detection in low snr microseismic signals based on multi-scale permutation entropy and a support vector machine,” J. Seismol. 21(4), 735–748 (2017). [CrossRef]
21. V. Thai, J. Cheng, V. Nguyen, and P. Daothi, “Optimizing svm’s parameters based on backtracking search optimization algorithm for gear fault diagnosis,” J. Vibroengineering 21(1), 66–81 (2019). [CrossRef]
22. S. F. Boll, “Suppression of acoustic noise in speech using spectral subtraction,” IEEE Trans. Acoust., Speech, Signal Process. 27(2), 113–120 (1979). [CrossRef]
23. S. Wang, L. Zhao, Y. Hu, and F. Yang, “Vibration characteristics analysis of convalescent-wheelchair robots equipped with dynamic absorbers,” Shock. Vib. 2018, 1–16 (2018). [CrossRef]
24. V. Nguyen, J. Zhang, V. Le, and R. Jiao, “Vibration analysis and modeling of an off-road vibratory roller equipped with three different cab’s isolation mounts,” Shock. Vib. 2018, 1–17 (2018). [CrossRef]
25. X. Fu, J. Wu, Z. Li, Y. Tong, X. Gui, and H. Wang, “Fiber-based large dynamic range vibration sensing with dual-wavelength phase unwrapping,” J. Lightwave Technol. 37(24), 6090–6096 (2019). [CrossRef]
26. H. Guo, F. Liu, Y. Yuan, H. Yu, and M. Yang, “Ultra-weak fbg and its refractive index distribution in the drawing optical fiber,” Opt. Express 23(4), 4829–4838 (2015). [CrossRef]
27. Y. Tong, Z. Li, J. Wang, H. Wang, and H. Yu, “High-speed mach-zehnder-otdr distributed optical fiber vibration sensor using medium-coherence laser,” Photonic Sens. 8(3), 203–212 (2018). [CrossRef]
28. C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002). [CrossRef]
