Method for the extraction of shock signal features based on the upper limit of density integral

Haikun Yang1 , Hongxia Pan2

1School of Mechatronics Engineering, North University of China, Taiyuan, China

2School of Mechanical and Power Engineering, North University of China, Taiyuan, China

1Corresponding author

Journal of Vibroengineering, Vol. 21, Issue 6, 2019, p. 1751-1760.
Received 10 September 2018; received in revised form 13 January 2019; accepted 26 January 2019; published 30 September 2019

Copyright © 2019 Haikun Yang, 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.
Creative Commons License

Shock signal features must be extracted for use in pattern recognition or fault diagnosis. In this work, we proposed a method for the feature extraction of shock signals, which are vibration signals that change faster and have larger amplitude ranges than general signals. First, we proposed the concepts of amplitude density for monotonic functions and piecewise monotonic functions. On the basis of these concepts, we then proposed the concept of the upper limit of density integral (ULDI), which was adopted to obtain signal features. Then, we introduced two types of serious fault cracks to the latch sheet of an automatic gun mechanism that is used on warships. Next, we applied the proposed method to extract the features of shock signals from data acquired when the automatic gun mechanism fired with normal and two fault patterns. Finally, we verified the effectiveness of our proposed method by applying the features that it extracted to a support vector machine (SVM). Our proposed method provided good results and was superior to the traditional statistics-based feature extraction method when applied to a SVM for classification. In addition, the former method demonstrated better generalisation than the latter. Thus, our method is an efficient approach for extracting shock signal features in pattern recognition and fault diagnosis.

Graphical Abstract

  • We proposed the concept of upper limit of density integral to obtain signal features.
  • The proposed method was applied to extract the features about an automatic gun mechanism.
  • The proposed method was superior to the traditional statistics-based feature extraction method.

Keywords: signal processing, feature extraction, pattern recognition, fault diagnosis.


The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Grants 51675491 and 51175480).


  1. Zhao M. Y., Xu G. Feature extraction of power transformer vibration signals based on empirical wavelet transform and multiscale entropy. IET Science, Measurement and Technology, Vol. 12, Issue 1, 2018, p. 63-71. [Publisher]
  2. Kumar M., Pachori R. B., Acharya U. R. An efficient automated technique for CAD diagnosis using flexible analytic wavelet transform and entropy features extracted from HRV signals. Expert Systems with Applications, Vol. 63, Issue 30, 2016, p. 165-172. [Publisher]
  3. Das A. B., Bhuiyan M. I. H. Discrimination and classification of focal and non-focal EEG signals using entropy-based features in the EMD-DWT domain. Biomedical Signal Processing and Control, Vol. 29, 2016, p. 11-21. [Publisher]
  4. Sun J., Li H. R., Xu B. H. Degradation feature extraction of the hydraulic pump based on high-frequency harmonic local characteristic-scale decomposition sub-signal separation and discrete cosine transform high-order singular entropy. Advances in Mechanical Engineering, Vol. 11, Issue 1, 2009, p. 17-26. [CrossRef]
  5. Huang E., Shen Z., Long S. R., et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings Mathematical Physical and Engineering Sciences, Vol. 454, Issue 1974, 1998, p. 903-995. [Publisher]
  6. Veltcheva A. D., Guedes Soares C. Identification of the components of wave spectra by the Hilbert Huang transform method. Applied Ocean Research, Vol. 26, Issues 1-2, 2004, p. 1-12. [Publisher]
  7. Alvanitopoulos P. F., Papavasileiou M., Andreadis I., Elenas A. Identification of the components of wave spectra by the Hilbert Huang transform method. IEEE Transactions on Instrumentation and Measurement, Vol. 61, Issue 2, 2012, p. 326-337. [Publisher]
  8. Roy A., Wen C. H., Doherty J. F. Signal feature extraction from microbarograph observations using the Hilbert-Huang transform. IEEE Transactions on Geoscience and Remote Sensing, Vol. 46, Issue 5, 2008, p. 1442-1447. [Publisher]
  9. Ghasemzadeh A., Demirel H. 3D discrete wavelet transform-based feature extraction for hyperspectral face recognition. IET Biometrics, Vol. 7, Issue 1,2018, p. 49-55. [Publisher]
  10. Wang T., Li L., Huang Y. A., et al. Prediction of protein-protein interactions from amino acid sequences based on continuous and discrete wavelet transform features. Molecules, Vol. 23, Issue 4, 2018, p. E823. [Publisher]
  11. Gauthama Raman M. R., Somu N., Kirthivasan K., Liscano R., Shankar Sriram V. S. An efficient intrusion detection system based on hypergraph-genetic algorithm for parameter optimization and feature selection in support vector machine. Knowledge-Based Systems, Vol. 134, Issue 15, 2017, p. 1-12. [Publisher]
  12. Ma B. T., Xia Y. A tribe competition-based genetic algorithm for feature selection in pattern classification. Applied Soft Computing, Vol. 58, 2017, p. 328-338. [Publisher]
  13. Li H. Q., Yuan D. Y., Ma X. D., Cui D. Y., Cao L. Genetic algorithm for the optimization of features and neural networks in ECG signals classification. Scientific Reports, Vol. 7, 2017, p. 41011. [Publisher]
  14. Lei L., Yan J. H., de Silva C. W. Feature selection for ECG signal processing using improved genetic algorithm and empirical mode decomposition. Measurement, Vol. 94, 2016, p. 374-381. [CrossRef]
  15. Shah S. M. S., Batool S., Khan I., et al. Feature extraction through parallel probabilistic principal component analysis for heart disease diagnosis. Physica A: Statistical Mechanics and its Applications, Vol. 482, 2017, p. 796-807. [Publisher]
  16. Luss R., D’Aspremont A. Clustering and feature selection using sparse principal component analysis. Optimization and Engineering, Vol. 11, Issue 1, 2010, p. 145-157. [Publisher]
  17. Sahu A., Apley D. W., Runger G. C. Feature selection for noisy variation patterns using kernel principal component analysis. Knowledge-Based Systems, Vol. 72, 2014, p. 37-47. [Publisher]
  18. Schölkopf B., Smola A., Müller K. R. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, Vol. 10, Issue 5, 1998, p. 1299-1319. [Publisher]
  19. Yang M. S., Nataliani Y. A Feature-reduction fuzzy clustering algorithm based on feature-weighted entropy. IEEE Transactions on Fuzzy Systems, Vol. 26, Issue 2, 2018, p. 817-835. [Publisher]
  20. Saif N., Amalin P., Anita A. Entropy-based feature extraction and classification of vibroarthographic signal using complete ensemble empirical mode decomposition with adaptive noise. IET Science, Measurement and Technology, Vol. 12, Issue 3, 2018, p. 350-359. [Publisher]
  21. Deng W., Yao R., Zhao H., et al. A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm. Soft Computing, 2017, [Publisher]
  22. Zhao H., Zuo S., Hou M., et al. A novel adaptive signal processing method based on enhanced empirical wavelet transform technology. Sensors, Vol. 18, Issue 10, 2018, p. 3323. [Publisher]
  23. Cristianini N., Shawe-Taylor J. An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. Cambridge University, London, 2000. [Publisher]
  24. Theodoridis S., Koutroumbas K. Pattern Recognition. Linear Classifiers. 4th Edition, Elsevier, Burlington, MA, USA, 2009. [Publisher]
  25. Russell S. J., Norvig P. Artificial Intelligence: a Modern Approach. Learning from Examples. 3rd Edition, Pearson Education, Upper Saddle River, NJ, USA, 2010. [CrossRef]