Skip to main content
Springer Nature Link
Log in

A new method for time series classification using multi-dimensional phase space and a statistical control chart

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Since large amounts of data were collected over time in many different areas, the classification of these data according to their similarities was an important problem. The methods used to classify time series are a combination of classifiers in different domains such as time, autocorrelation, frequency spectrum, and phase space. The weakest point of these methods is that they require high computational burden and the obtained features lead to misclassifications. When the phase space of the time series is modeled by the Gaussian mixture model, different conditions can be easily classified. However, this technique fails when the phase spaces of time series representing different conditions are similar. In this study, a new method for time series classification using multi-dimensional phase space is proposed using quality control charts that constructed from the phase space of a time series. It aims obtaining a new feature signal from the phase space, providing a faster method for classification of time series, and effectively detecting minor changes in time series. The method is consisted of six stages such as time series inputs, selecting an appropriate time delay and embedding dimension for each time series, construction of phase space, obtaining new time series from phase space using T2 control chart, alignment of time series with dynamic time warping, and classification with the nearest neighbor. The constructed time series is guaranteed to be a complete representation of a system where the phase space parameters are properly chosen. With the proposed new representation, the time series that belongs to different classes and whose phase spaces are similar can be easily distinguished. The k-nearest neighbor classifier is implemented for time series classification, and the datasets from two different domains are used for validation, including motor current signals and nine benchmark datasets from the UCR time series repository. The results show that the proposed method enhances the time series classification performance with new time series representation across these diverse domains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Povinelli RJ, Johnson MT, Lindgren AC, Ye J (2004) Time series classification using Gaussian mixture models of reconstructed phase spaces. IEEE Trans Knowl Data Eng 16:779–783

    Google Scholar 

  2. Firooz SG, Almasganj F, Shekofteh Y (2017) Improvement of automatic speech recognition systems via nonlinear dynamical features evaluated from the recurrence plot of speech signals. Comput Electr Eng 58:215–226

    Google Scholar 

  3. Mohapatra UM, Majhi B, Satapathy SC (2017) Financial time series prediction using distributed machine learning techniques. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3283-2

    Google Scholar 

  4. Rodriguez-Sotelo JL, Peluffo-Ordonez D, Cuesta-Frau D, Castellanos-Domínguez G (2012) Unsupervised feature relevance analysis applied to improve ECG heartbeat clustering. Comput Methods Programs Biomed 108:250–261

    Google Scholar 

  5. Yuan G, Sun P, Zhao J, Li D, Wang C (2017) A review of moving object trajectory clustering algorithms. Artif Intell Rev 47:123–144

    Google Scholar 

  6. Ferreira LN, Zhao L (2016) Time series clustering via community detection in networks. Inf Sci 326:227–242

    MathSciNet  MATH  Google Scholar 

  7. Ares J, Lara JA, Lizcano D, Suarez S (2016) A soft computing framework for classifying time series based on fuzzy sets of events. Inf Sci 330:125–144

    Google Scholar 

  8. Aydin I, Karakose M, Akin E (2010) Artificial immune classifier with swarm learning. Eng Appl Artif Intell 23:1291–1302

    Google Scholar 

  9. Fuchs E, Gruber T, Nitschke J, Sick B (2010) Online segmentation of time series based on polynomial least-squares approximations. IEEE Trans Pattern Anal Mach Intell 32:2232–2245

    Google Scholar 

  10. Xiao Q (2017) Time series prediction using Bayesian filtering model and fuzzy neural networks. Opt Int J Light Electron Opt 140:104–113

    Google Scholar 

  11. Li J, Pedrycz W, Jamal I (2017) Multivariate time series anomaly detection: a framework of hidden Markov models. Appl Soft Comput 60:229–240

    Google Scholar 

  12. Serra J, Arcos JL (2016) Particle swarm optimization for time series motif discovery. Knowl Based Syst 92:127–137

    Google Scholar 

  13. Pappachan BK, Caesarendra W, Tjahjowidodo T, Wijaya T (2017) Frequency domain analysis of sensor data for event classification in real-time robot assisted deburring. Sensors 17:1247

    Google Scholar 

  14. Li D, Bissyande TF, Klein J, Traon YL (2016) Time series classification with discrete wavelet transformed data. Int J Softw Eng Knowl Eng 26:1361–1377

    Google Scholar 

  15. Lei Y, Lin J, He Z, Zuo MJ (2013) A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mech Syst Signal Process 35:108–126

    Google Scholar 

  16. Thirumalaisamy MR, Ansell PJ (2018) Fast and adaptive empirical mode decomposition for multidimensional, multivariate signals. IEEE Signal Process Lett 25:1550–1554

    Google Scholar 

  17. Moussa MA, Boucherma M, Khezzar A (2017) A detection method for induction motor bar fault using sidelobes leakage phenomenon of the sliding discrete Fourier transform. IEEE Trans Power Electron 32:5560–5572

    Google Scholar 

  18. Rahman MM, Uddin MN (2017) Online unbalanced rotor fault detection of an IM drive based on both time and frequency domain analyses. IEEE Trans Ind Appl 53:4087–4096

    Google Scholar 

  19. Dias CG, Pereira FH (2018) Broken rotor bars detection in induction motors running at very low slip using a hall effect sensor. IEEE Sens J 18:4602–4613

    Google Scholar 

  20. Aydin I (2018) Fuzzy integral and cuckoo search based classifier fusion for human action recognition. Adv Electr Comput Eng 18:3–11

    Google Scholar 

  21. Wang A, Chen G, Yang J, Zhao S, Chang CY (2016) A comparative study on human activity recognition using inertial sensors in a smartphone. IEEE Sens J 16:4566–4578

    Google Scholar 

  22. Riera-Guasp M, Antonino-Daviu JA, Capolino GA (2015) Advances in electrical machine, power electronic, and drive condition monitoring and fault detection: state of the art. IEEE Trans Ind Electron 62:1746–1759

    Google Scholar 

  23. Aydin I, Karakose M, Akin E (2015) Combined intelligent methods based on wireless sensor networks for condition monitoring and fault diagnosis. J Intell Manuf 26:717–729

    Google Scholar 

  24. Goyal D, Pabla BS, Dhami SS, Lachhwani K (2017) Optimization of condition-based maintenance using soft computing. Neural Comput Appl 28:829–844

    Google Scholar 

  25. Nejadgholi I, Moradi MH, Abdolali F (2011) Using phase space reconstruction for patient independent heartbeat classification in comparison with some benchmark methods. Comput Biol Med 41:411–419

    Google Scholar 

  26. Xu B, Jacquir S, Laurent G, Bilbault JM, Binczak S (2014) Analysis of an experimental model of in vitro cardiac tissue using phase space reconstruction. Biomed Signal Process Control 30:313–326

    Google Scholar 

  27. Lopez-Mendez A, Casas JR (2012) Model-based recognition of human actions by trajectory matching in phase spaces. Image Vis Comput 30:808–816

    Google Scholar 

  28. Guo Y, Liu Q, Wang A, Sun C, Tian W, Naik GR, Abraham A (2017) Optimized phase-space reconstruction for accurate musical-instrument signal classification. Multimed Tools Appl 76:20719–20737

    Google Scholar 

  29. Aydin İ, Karaköse M, Akin E (2014) An approach for automated fault diagnosis based on a fuzzy decision tree and boundary analysis of a reconstructed phase space. ISA Trans 53:220–229

    Google Scholar 

  30. da Silva AM, Povinelli RJ, Demerdash NAO (2008) Induction machine broken bar and stator short-circuit fault diagnostics based on three phase stator current envelopes. IEEE Trans Ind Electron 55:1310–1318

    Google Scholar 

  31. Bagnall A, Janacek G (2014) A run length transformation for discriminating between autoregressive time series. J Classif 31:274–295

    MATH  Google Scholar 

  32. Smyth P (1997) Clustering sequences with hidden Markov models. Adv Neural Inf Process Adv in Neural Inf Process Syst 9:648–654

    Google Scholar 

  33. Senin P (2008) Dynamic time warping algorithm review. Information and Computer Science Department University of Hawaii at Manoa Honolulu, USA, vol 855, pp 1–23

  34. Karabiber F (2013) An automated signal alignment algorithm based on dynamic time warping for capillary electrophoresis data. Turk J Electr Eng Comput Sci 21:851–863

    Google Scholar 

  35. Kaya H, Gündüz-Öğüdücü S (2015) A distance based time series classification framework. Inf Syst 51:27–42

    Google Scholar 

  36. Abanda A, Mori U, Lozano JA (2018) A review on distance based time series classification. Data Min Knowl Discov 1:2. https://doi.org/10.1007/s10618-018-0596-4

    Google Scholar 

  37. Zabihi M, Kiranyaz S, Rad AB, Katsaggelos AK, Gabbouj M, Ince T (2015) Analysis of high-dimensional phase space via Poincaré section for patient-specific seizure detection. IEEE Trans Neural Syst Rehabil Eng 24(3):386–398

    Google Scholar 

  38. Kumar SS, Kasthuri N (2017) EEG seizure classification based on exploiting phase space reconstruction and extreme learning. Cluster Comput. https://doi.org/10.1007/s10586-017-1409-z

    Google Scholar 

  39. Johnson MT, Povinelli RJ, Lindgren AC, Ye J, Liu X, Indrebo KM (2005) Time-domain isolated phoneme classification using reconstructed phase spaces. IEEE Trans Speech Audio Process 13:458–466

    Google Scholar 

  40. Ishola B, Povinelli RJ, Corliss GF, Brown RH (2016) Identifying extreme cold events using phase space reconstruction. Int J Appl Pattern Recognit 3:1–21

    Google Scholar 

  41. Abarbanel HDI (1996) Analysis of observed chaotic data. Springer, New York

    MATH  Google Scholar 

  42. Takens F (1980) Detecting strange attractors in turbulence. In: Proceedings of dynamical systems and turbulence, pp 366–381

    Google Scholar 

  43. Montgomery DC (2009) Statistical quality control, vol 7. Wiley, New York

    MATH  Google Scholar 

  44. Bangura JF, Povinelli RJ, Demerdash NA, Brown RH (2003) Diagnostics of eccentricities and bar/end-ring connector breakages in polyphase induction motors through a combination of time-series data mining and time-stepping coupled FE-state-space techniques. IEEE Trans Ind Appl 39:1005–1013

    Google Scholar 

  45. Chen Y, Keogh E, Hu B, Begum N, Bagnall A, Mueen A, Batista G (2015) The ucr time series classification archive. https://www.cs.ucr.edu/~eamonn/time_series_data/

Download references

Acknowledgements

This work was supported by TUBITAK (The Scientific and Technological Research Council of Turkey) under Grant No: 5160043.

Author information

Authors and Affiliations

  1. Computer Engineering Department, Firat University, 23119, Elazig, Turkey

    İlhan Aydin, Mehmet Karakose & Erhan Akin

Authors
  1. İlhan Aydin
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Mehmet Karakose
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Erhan Akin
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to İlhan Aydin.

Ethics declarations

Conflict of interest

The author(s) declared no potential conflict of interest with respect to the research, authorship, and/or publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aydin, İ., Karakose, M. & Akin, E. A new method for time series classification using multi-dimensional phase space and a statistical control chart. Neural Comput & Applic 32, 7439–7453 (2020). https://doi.org/10.1007/s00521-019-04270-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-019-04270-1

Keywords