Jia et al 2020b - Revision history

Rimni at 13:26, 20 May 2021

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Rimni: table

2020-11-03T09:44:50Z

table

Rimni at 09:33, 3 November 2020

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Rimni at 13:52, 30 October 2020

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Rimni at 13:51, 30 October 2020

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@@ Line 36: / Line 36: @@
 ===2.1 Noisy signal BSS model===
-Source signals  <math display="inline">{s_{i} (t)}</math> come from different signal sources (assuming that the signal is a continuous signal), so  <math display="inline">{s_{i} (t)}</math> can be regarded as mutual statistical independence, <math display="inline">{x_{i} (t)}</math> is the mixed signals or observation signals ( [[#img-1|Figure 1]]).
+Source signals  <math display="inline">{s_{i} (t)}</math> come from different signal sources (assuming that the signal is a continuous signal), so  <math display="inline">{s_{i} (t)}</math> can be regarded as mutual statistical independence, <math display="inline">{x_{i} (t)}</math> is the mixed signals or observation signals ([[#img-1|Figure 1]]).
 <div id='img-1'></div>

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 During the operation of the engine rotor, the vibration signal measured by the sensor is the mixed signal of each vibration source, and contains strong noise at the same time. In this paper, a new separation method for mixed vibration signals in strong noise environment (such as SNR=-5dB) is proposed. Firstly, the time-delay autocorrelation de-noising method is used to de-noise the mixed signals. Secondly, one common algorithm (the MSNR algorithm is used here) is adopted to separate the mixed vibration signals, which can improve the separation performance. The simulation results verify the validity of the method. The proposed method provides a new idea for health monitoring and fault diagnosis of engine rotor vibration signals.
-'''Keywords''': blind source separation, rotor, vibration signals, auto-correlation de-noising, high-noise environments
+'''Keywords''': Blind source separation, rotor, vibration signals, auto-correlation de-noising, high-noise environments
 ==1. Introduction==

@@ Line 8: / Line 8: @@
 <sup></sup>College of Computer and Information, Hohai University, Nanjing, Jiangsu 210098, China
 <!--'''*'''Corresponding author: Pengfei Xu ([mailto:xpf@hhu.edu.cn])-->
 ==Abstract==

@@ Line 5: / Line 5: @@
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-'''Yinjie Jia<sup>1,2</sup>,Pengfei Xu<sup>2,*</sup>,Zhijian Wang<sup>2</sup>,Ping Zong<sup>2</sup>'''</div>
+'''Yinjie Jia<sup></sup>,Pengfei Xu<sup></sup>,Zhijian Wang<sup></sup>,Ping Zong<sup></sup>'''</div>
 <sup></sup>College of Computer and Information, Hohai University, Nanjing, Jiangsu 210098, China
-<sup>1</sup>Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huaian, Jiangsu 223003, China
-<sup>2</sup>College of Computer and Information, Hohai University, Nanjing, Jiangsu 210098, China
 <!--'''*'''Corresponding author: Pengfei Xu ([mailto:xpf@hhu.edu.cn])-->

@@ Line 9: / Line 9: @@
 <sup>1</sup>Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huaian, Jiangsu 223003, China
 <sup>2</sup>College of Computer and Information, Hohai University, Nanjing, Jiangsu 210098, China
-<!--'''*'''Corresponding author: Pengfei Xu ([mailto:xpf@hhu.edu.cn xpf@hhu.edu.cn])-->
+<!--'''*'''Corresponding author: Pengfei Xu ([mailto:xpf@hhu.edu.cn])-->
 ==Abstract==

@@ Line 306: / Line 306: @@
 ==Acknowledgments==
-This work was partially supported by the project of industrial-academic-research cooperation of Jiangsu province (No.2019320802000301)
+This work was partially supported by the project of industrial-academic-research cooperation of Jiangsu province (No.BY2020241)
 ==Disclosures==

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 The improved MSNR algorithm based on autocorrelation de-noising can be summarized as: (1) Finding the autocorrelation function of the noisy mixed signals <math display="inline">{x(t)}</math>. (2) Removing the data near the condition  <math display="inline">{\tau =0}</math> and using the remaining data  <math display="inline">{\hat{x}(t)}</math> as the data of blind separation. (3) Blind separation of the de-noised mixed signals  <math display="inline">{\hat{x}(t)}</math> by means of the MSNR algorithm. The improved MSNR algorithm with four lines of Matlab code are listed in [[#tab-1|Table 1]].
 <div class="center" style="font-size: 75%;">'''Table 1'''. The improved MSNR algorithm </div>
-<div id='tab-1'></div>
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:left"

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 ==References==
-[1] J. H´erault, C. Jutten, B. Ans. D´etection de grandeurs primitives dans un message composite par une architecture de calcul neuromim´etique en apprentissage non supervis´e, Proc. SSIP, Nice, France, pp. 1017–1022, 1985.
+[1]  H´erault J., Jutten C.,  Ans B. D´etection de grandeurs primitives dans un message composite par une architecture de calcul neuromimétique en apprentissage non supervisé. Proc. SSIP, Nice, France, pp. 1017–1022, 1985.
-[2] P. Xu, Y. Jia, Z. Wang, M. Jiang. Underdetermined Blind Source Separation for Sparse Signals based on the Law of Large Numbers and Minimum Intersection Angle Rule. Circuits Systems and Signal Processing, 39(5), 2442–2458, 2020.
+[2]  Xu P.,  Jia Y.,  Wang Z.,  Jiang M. Underdetermined blind source separation for sparse signals based on the law of large numbers and minimum intersection angle rule. Circuits Systems and Signal Processing, 39(5):2442–2458, 2020.
-[3] Y. Jia, P. Xu. Convolutive Blind Source Separation for Communication Signals Based on the Sliding Z-Transform. IEEE Access, 8, 41213–41219, 2020.
+[3]  Jia Y.,  Xu P. Convolutive blind source separation for communication signals based on the sliding Z-transform. IEEE Access, 8:41213–41219, 2020.
-[4] Y. Cheng, Z. Li, Y. Jin, et al. Blind Source Separation of Multi Mixed Vibration Signal Based on Parallel Factor Analysis. Proc. Prognostics and System Health Management Conference, PHM, Harbin, China, pp. 1–8, 2017.
+[4]  Cheng Y.,  Li Z.,  Jin Y., et al. Blind source separation of multi mixed vibration signal based on parallel factor analysis. Proc. Prognostics and System Health Management Conference, PHM, Harbin, China, pp. 1–8, 2017.
-[5] P. Xu, Y. Jia. Blind source separation based on source number estimation and fast-ICA with a novel non-linear function. Proceedings of the romanian academy series a-mathematics physics technical sciences information science, 21(2), pp. 93–194, 2020.
+[5]  Xu P.,  Jia Y. Blind source separation based on source number estimation and fast-ICA with a novel non-linear function. Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, 21(2):93–194, 2020.
-[6] J. Ma, X. Zhang, X. Blind Source Separation Algorithm Based on Maximum Signal Noise Ratio. Proc. First International Conference on Intelligent Networks and Intelligent Systems,Wuhan, China, pp. 625–628, 2008.
+[6]  Ma J.,  Zhang X.  Blind source separation algorithm based on maximum signal noise ratio. Proc. First International Conference on Intelligent Networks and Intelligent Systems,Wuhan, China, pp. 625–628, 2008.
-[7] M. Borga. Learning multidimensional signal processing." Ph.D. dissertation, Linkoping University, Sweden, 1998.
+[7]  Borga M. Learning multidimensional signal processing. Ph.D. Dissertation, Linkoping University, Sweden, 1998.
-[8] Y. Jia, P. Xu. Noise Cancellation in Vibration Signals Using an Oversampling and Two-Stage Autocorrelation Model. Results in Engineering, 6, p. 100136, 2020.
+[8]  Jia Y.,  Xu P. Noise cancellation in vibration signals using an oversampling and two-stage autocorrelation model. Results in Engineering, 6:100136, 2020.
-[9] D. Huang, J. Yang, D. Zhou, et al. Recovering an unknown signal completely submerged in strong noise by a new stochastic resonance method. Communications in Nonlinear Science and Numerical Simulation, 66, 156–166, 2019.
+[9]  Huang D.,  Yang J.,  Zhou D., et al. Recovering an unknown signal completely submerged in strong noise by a new stochastic resonance method. Communications in Nonlinear Science and Numerical Simulation, 66:156–166, 2019.

@@ Line 297: / Line 297: @@
 |  '''0.9988'''
 |}
 By comparing the two experiments, it is fully demonstrated that time-delay correlation de-noising can effectively remove noise and improve the signal-to-noise ratio, which provides the precondition for the accurate realization of BSS of noisy mixed signals.

@@ Line 284: / Line 284: @@
 Many repeated tests can reduce the randomness and improve the reliability of results. Therefore, in order to evaluate the stability of these algorithms, total number of iterations in the present study is set to 50. The two algorithms are compared with each other from the separation accuracy (average correlation coefficient). [[#tab-2|Table 2]] presents obtained values after 50 iterations.
-<div class="center" style="font-size: 75%;">'''Table 2'''. Average correlation coefficient for different algorithms after 50 iterations (SNR=-5dB)
+<div class="center" style="font-size: 75%;">'''Table 2'''. Average correlation coefficient for different algorithms after 50 iterations (SNR=-5dB)</div>
 <div id='tab-2'></div>