Artículo

Recognition of system behaviours based on temporal series similarity

D. Llanos¹, F.J. Cuberos², J. Meléndez¹, Fco. I. Gamero¹, J. Colomer¹ and J.A. Ortega³

¹ Grupo eXiT, University of Girona. Av. Lluis Santalo s/n E–17071–Girona (Spain) dllanosr@eia.udg.es ; quimmel@eia.udg.es ; gamero@eia.udg.es ; colomer@eia.udg.es

² Departamento de Planificación. Radio Televisión de Andalucía. Crta. San Juan–Tomare km. 1,3. S.J. Aznalfarache–Sevilla (Spain) fcuberos@rtva.es

³ Departamento de Lenguajes y Sistemas Informáticos. University of Seville. Avda Reina Mercedes S/n. Sevilla (Spain) ortega@lsi.us.es

Resumen

Existen multitud de aproximaciones al estudio de los sistemas que evolucionan en el tiempo. Este artículo revisa trabajos previos relacionados con series temporales y evalúa tres aproximaciones enfocadas a la comparación de dicho tipo de series. Dos aproximaciones están basadas en los principios del algoritmo Dynamic Time Warping (DTW) y una de ellas usa representación cualitativa basada en sodios. Ambas estrategias son discutidas y aplicadas en la diagnosis de un sistema de tanques y en la recuperación de registros de perturbaciones obtenidos en una subestación de distribución eléctrica. La tercera aproximación usa un índice de similitud definido por etiquetas cualitativas. Cada etiqueta representa un rango de valores que, desde una perspectiva cualitativa, podemos considerar similares. Esta aproximación se prueba con dos conjuntos de datos. Este estudio se completa con un estudio del ruido y de otros posibles etiquetados.

Palabras clave: Series Temporales, Análisis de series temporales, Análisis Cualitativo, Programación Dinámica, Formas, Conocimiento Cualitativo, Ruido.

Abstract

There are different approaches to the temporal study of time evolving systems. This paper reviews previous works related to time series and it evaluates three approaches focused to the comparison of these type of series. Two approaches are based on the principles of Dynamic Time Warping algorithm (DTW) and one of them uses qualitative representation based on episodes. Both strategies are discussed and applied to a tank system diagnosis and retrieval of registers of perturbations gathered in a electric distribution substation. The third approach uses a similarity index defined by qualitative labels. Each label represents a range of values that, from a qualitative perspective, we may consider similar. This approach is tested with two datasets. This study is completed with a evaluation of noise and other possible labellings.

Keywords: Temporal series, Time–series Analysis, Qualitative Analysis, Dynamic Programming, Shapes, Qualitative Knowledge, Noise.

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Acknowledgement

This work is partially supported by the projects "Desarrollo de un sistema de control y supervisión aplicado a un reactor secuencial por cargas para la eliminación de materia orgánica, nitrógeno y Fósforo" (DPI2002–04579–C02–01) and DPI SECSE – "Supervisión Experta de la Calidad de Servicio Eléctrico" (DPI2001–2198) within the CICYT program from the Spanish government and FEDER funds.

Bibliography

1. Aamodt A. and Plaza E., Case–based Reasoning: Foundational Issues, Methodological Variations, and system approaches. Artif. Intell. Communications, IOS Press, Vol. 1, 1994, pp. 39–59.        [ Links ]

2. Agrawal R., Faloutsos C. and Swami A., Efficient similarity search in sequence databases. In Proc. of the Fourth Intl. Conf. on Foundations of Data Organization and Algorithms (FODO '93), Chicago,1993.        [ Links ]

3. Agrawal R., Lin K.I., Sawhney H.S. and Shim K., Fast similarity search in the presence of noise, scaling, and translation in time series databases. The 21^st VLDB Conference Switzerland, 1995.        [ Links ]

4. Agrawal R., Psaila G., Wimmers E.L. and Zaït M., Querying shapes of Histories. The 21^st VLDB Conference Switzerland, 1995b, pp. 502–514.        [ Links ]

5. Arrillaga J., Bollen M.H.J. and Watson N.R., Power quality following deregulation IEEE Trans. Vol. 88, No. 2, 2000, pp. 246 –261.        [ Links ]

6. Bay S., UCI Repository of KDD databases http://kdd.ics.uci.edu/ . Irvine, CA: University of California, Departamet of Information and Computer Science, 1999.        [ Links ]

7. Beckmann N., Kriegel H.–P., Schneider R. and Seeger B., "The r*–tree: an eficient and robust access method for points and rectangles", ACM SIG–MOD, 1990, pp. 322–331.        [ Links ]

8. Bollen M. H. J., "Understanding Power Quality problems" IEEE Press., New York, 2000, pp. 139–251.        [ Links ]

9. Caiani E.G., Porta A., Baselli G., Turiel M., Muzzupappa S., Pieruzzi F., Crema C., Malliani A. and Cerutti S., Warped–average template technique to track on a cycle–bycycle basis the cardiac filling phases on left ventricular volume. IEEE Computers in Cardiology, vol. 25, 1998, pp. 73–76.        [ Links ]

10. Chan K. and Wai–chee F.A., Efficient time series matching by wavelets Proc. 15^th International Conference on Data Engineering, 1999.        [ Links ]

11. Cheung J.T. and Stephanopoulos G., Representation of process trend – Part II. The problem of scale and qualitative scaling, Computers and Chemical Engineering 14(4/5), 1990, pp. 511–539.        [ Links ]

12. Cochran W.G. Técnicas de muestreo. Edit. Continental, Mexico, 6 edition.        [ Links ]

13. Colomer J. and Meléndez J., A family of FIR differentiators based on a polynomial least squares estimation. Proc. Of the European Control Conference, 2001, pp. 2802–2807.        [ Links ]

14. Colomer J., Representado qualitative assíncrona de senyals per la supervisó de sistemes dinámics, Thesis Universitat de Girona, 1998.        [ Links ]

15. Colomer J., Meléndez J., De la Rosa J.L. and Aguilar J., A qualitative/quantitative representation of signals for supervision of continuous systems., Proc. European Control Conference–ECC97, Brussels, 1997.        [ Links ]

16. Cuberos F.J., Ortega J.A., Gasca R.M. and Toro M. QSI – Qualitative Similarity Index. QR–2002.  Sitges. Barcelona (Spain), (2002), pp. 45–51.        [ Links ]

17. Das G., Gunopulos D. and Mannila H., Finding similar Time Series, In Proceedings of Principles of Data Mining and Knowledge Discovery, 1^st European Symposium. Trondheim, Norway, 1997, pp. 88–100.        [ Links ]

18. Faloutsos C., Ranganathan M., and Manolopoulos Y., Fast subsequence matching in time–series databases. The ACM SIGMOD Conference on Management of Data, 1994, pp. 419–429        [ Links ]

19. Goldin D.Q. and Kanellakis P.C., On similarity queries for time–series data: constraint specification and implementation. In 1st Intl. Conf. on the Principles and Practive of Constraint Prog., Minneapolis, 1994, pages 419–429.        [ Links ]

20. González L. and Gavilan J.M. Una metodología para la construcción de histogramas. Aplicación a los ingresos de los hogares andaluces, XIV Reunión ASEPELT España Oviedo (Spain), 2000.        [ Links ]

21. Jagadish H., Mendelzon A.O. and Milo T., Similarity–based queries. In Proc. of the 14th ACM SIGACT–SIGMOD–SIGART Symposium on Principles of Database Systems (PODS'95), San Jose, California, USA, 1995,pp. 36–45.        [ Links ]

22. Kahveci T., Singh A. and Gurel A., Shift and scale invariant search of multi–attribute time sequence. 2001.        [ Links ]

23. Kahveci T., Singh A. and Gurel A., Similarity Searching for Multi–Attribute Sequences, SSDBM 2002, Edinburgh, Scotland, 2002.        [ Links ]

24. Kassidas A., MacGregor J.F. and Taylor P.A., Synchronization of Batch Trajectories Using Dynamic Time Warping. Proc. AIChE Journal vol. 44, No. 4, 1998, pp. 864–875.        [ Links ]

25. Keogh E.J. and Smyth P., A probabilistic approach to fast pattern matching in time series databases, Proceedings of the 9^th International Conference on Tools with Artifial Inteligence, IEEE Press, 1998, pp. 578–584.        [ Links ]

26. Keogh E.J. and Pazzani M.J., An enhaced representation of time series wich allows fast and accurate classification, clustering and relevance feedback, Proc. 4^th International Conference of Knowledge Discovery and Data Mining , AAAI Press, 1998,pp. 239–241,.        [ Links ]

27. Keogh E.J. and Pazzani M.J., Scaling up Dynamic Time Warping to massive datasets, Proc. Principles and Practice of Knowledge Discovery in Databases, 1999.        [ Links ]

28. Keogh E.J. and Pazzani M.J., A simple dimensionality reduction technique for fast similarity search in large time series databases, In Proc. of the Pacific–Asia Conference on Knowledge Discovery and Data Mining, 2000.        [ Links ]

29. Keogh E.J., Chakrabarti K., Mehrotra S. and Pazzani M.J., Locally adaptative dimensionality reduction for indexing large time series databases, SIG–MOD, 2001.        [ Links ]

30. Keogh E.J. and Pazzani M.J. Derivative Dynamic Time Warping, In Proc. Firts SIAM International Conference on Data Mining (SDM'2001), Chicago, USA, 2001.        [ Links ]

31. Lenz M., Bartsch–Spörl B., Burkhard H.–D. and Wess S., Case–Based Reasoning Technology from Foundations to Applications. Lecture Notes in Artificial Intelligence, State–of–the–Art–Survey, LNAI 1400, Springer–Verlag, 1998.        [ Links ]

32. Meléndez J. and Colomer J., Episodes representation for supervision. Application to diagnosis of a level control system. Proc. Workshop on Principles of Diagnosis DX'01, Sansicario, Italy, 2001.        [ Links ]

33. Oppenheim V. and Schafer R.W., Digital Signal Processing, Prentice Hall, Englewood Cliffs, N.J., 1975.        [ Links ]

34. Ortega J.A., Cuberos F.J., Gasca R.M., and Toro M., Comparación Cualitativa de Series Temporales. Indice Cualitativo de Similitud – QSI. Computación y Sistemas, Vol. 5 No. 2, 2001, pp. 96–108.        [ Links ]

35. Paterson M. and Dancík V. Longest Common Subsequences. Mathematical Foundations of Computer Science vol. 841 de LNCS, 1994, pp.127–142.        [ Links ]

36. Perng C.S., Wang H., Zhang S.R. and Parker D.S., Landmarks: a New Model for Similarity–based Pattern Querying in Time Series Databases. Proc. IEEE ICDE, 2000, pp. 33–42.        [ Links ]

37. Raifei D. and Mendelzon A., Similarity–based queries for time data series. In Proc. of the ACM SIG–MOD Intl. Conf. of Management of Data(SIGMOD '97), Tucson, 1998, pp. 13–24.        [ Links ]

38. Raifei D. and Mendelzon A., Efficient Retreival of similar time sequences using DFT. In Proc. of the 5^th Intl. Conf. on Foundations of Data Organization and Algorithms (FODO '98). Kobe, 1998.        [ Links ]

39. Raifei D., On Similarity–based queries for time series data. In Proc. of the 15^th International Conference on Data Engineering., Sydney, 1999.        [ Links ]

40. Sakoe H. and Chiba S., Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. Acoustics, Speech, and Signal., vol. ASSP–26(1), 1978, pp. 43–49.        [ Links ]

41. Shatkay H. and Zdonic S., Approximate queries and representation for large data sequences. In Proc. of the 12^th International Conference on Data Engineering., 1996, pp. 546–553.        [ Links ]

42. Silverman H.F., Morgan D.P., The application of dynamic programming to connected speech recognition. IEEE ASSP Magazine. vol. 7, 1990, pp. 6–25.        [ Links ]

43. Struss P., Automated Abstraction of Numerical Simulation Models–Theory and Practical Experience, Proc. of the 16^th International workshop on Qualitative Reasoning, Barcelona–Spain, 2002, pp. 161–168.        [ Links ]

44. Vlachos M., Gunopoulos D. and Kollios G., Discovering Similar Multidimensional Trajectories. 18^th International Conference on Data Engineering (ICDE'02). San Jose, California (USA), 2002, pp. 673–684.        [ Links ]

45. Vullings H.J.L.M., Verhaegen M.H.G. and Ver–bruggen H.B., Automated ECG segmentation with dynamic time warping. IEEE Intl. Conf. on Engineering in Medicine and Biology Society, vol.20, No.1, 1998, pp.163–166.        [ Links ]

46. Williams B.C., Doing Time: Putting qualitative reasoning on firmer ground. Proc. National Conf. on Artif. Intel. AAAI–86, 1986, pp. 105–112.        [ Links ]

47. Wu D., Agrawal D. and Abbadi A., A comparison of DFT and DWT based Similarity Search in Time–Series Databases. Proc. of the 9^th International Conference on Information and Knowledge Management, 2000.        [ Links ]

48. Yi B.K. and Faloutsos C., Fast time sequence indexing for arbitrary L_p norms. Proceedings of the 26^th Intl. Conf. on Very Large Databases, Cairo, 2000.        [ Links ]