Abstract
Cyber-physical systems (CPS) and the Internet-of-Things (IoT) result in a tremendous amount of generated, measured and recorded time-series data. Extracting temporal segments that encode patterns with useful information out of these huge amounts of data is an extremely difficult problem. We propose shape expressions as a declarative formalism for specifying, querying and extracting sophisticated temporal patterns from possibly noisy data. Shape expressions are regular expressions with arbitrary (linear, exponential, sinusoidal, etc.) shapes with parameters as atomic predicates and additional constraints on these parameters. We equip shape expressions with a novel noisy semantics that combines regular expression matching semantics with statistical regression. We characterize essential properties of the formalism and propose an efficient approximate shape expression matching procedure. We demonstrate the wide applicability of this technique on two case studies.
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Notes
- 1.
The signal with the empty time domain is equivalent to the empty word in the classical language theory.
- 2.
We use \(\underline{l}\) instead of \(\underline{l}_{\sigma ,x}\) whenever its association to \(\sigma _{x}\) is clear from the context, and omit \(\underline{l}_{\sigma ,x}\) altogether when not interested in the duration of the shape.
- 3.
We omit the duration variable \(\underline{l}\) whenever we are not interested in the duration of a shape - for instance we then use the notation \(\textsf {sin}(a,b,c,d)\).
- 4.
We abuse the notation and replace a parameter variable by a constant, for instance \(\textsf {lin}_x(0,b)\), as a shortcut for \(\textsf {lin}_x(a_1,b)~:~a_1 = 0\).
- 5.
We also assume that the SMA \(\hat{\mathcal {A}}\), the signal w, the noise tolerance threshold \(\nu \) and the minimum match length \(\lambda \) are given as global parameters to the main procedure \(\textsf {policy\_scheduler}\) and are implicitly propagated to all the other methods.
- 6.
Recall that we require atomic matches of minimum length \(\lambda \).
- 7.
The figure is under copyright by A. Rad.
- 8.
We recall that \(\nu = 0\) denotes zero noise tolerance and \(\nu = 1\) allows arbitrary level of noise.
References
IEEE standard on pulse Measurement and analysis by objective techniques. IEEE Std. 181–1977 (1977)
Abbas, H., Rodionova, A., Bartocci, E., Smolka, S.A., Grosu, R.: Quantitative regular expressions for arrhythmia detection algorithms. In: Feret, J., Koeppl, H. (eds.) CMSB 2017. LNCS, vol. 10545, pp. 23–39. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67471-1_2
Alur, R., Fisman, D., Raghothaman, M.: Regular programming for quantitative properties of data streams. In: Thiemann, P. (ed.) ESOP 2016. LNCS, vol. 9632, pp. 15–40. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49498-1_2
Alur, R., Mamouras, K., Stanford, C.: Modular quantitative monitoring. In: Proceedings of the ACM on Programming Languages, vol. 3(POPL), p. 50 (2019)
André, É., Hasuo, I., Masaki, W.: Offline timed pattern matching under uncertainty. In: 23rd International Conference on Engineering of Complex Computer Systems, ICECCS 2018, Melbourne, Australia, 12–14 December 2018, pp. 10–20 (2018)
Asarin, E., Caspi, P., Maler, O.: A Kleene theorem for timed automata. In: Logic in Computer Science (LICS), pp. 160–171 (1997)
Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. J. ACM 49(2), 172–206 (2002)
Bakhirkin, A., Ferrère, T., Maler, O., Ulus, D.: On the quantitative semantics of regular expressions over real-valued signals. In: Abate, A., Geeraerts, G. (eds.) FORMATS 2017. LNCS, vol. 10419, pp. 189–206. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65765-3_11
Bakhirkin, A., Ferrère, T., Nickovic, D., Maler, O., Asarin, E.: Online timed pattern matching using automata. In: Jansen, D.N., Prabhakar, P. (eds.) FORMATS 2018. LNCS, vol. 11022, pp. 215–232. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00151-3_13
D’Angelo, B., et al.: LOLA: runtime monitoring of synchronous systems. In: 12th International Symposium on Temporal Representation and Reasoning (TIME 2005), 23–25 June 2005, Burlington, Vermont, USA, pp. 166–174 (2005)
Faymonville, P., Finkbeiner, B., Schirmer, S., Torfah, H.: A stream-based specification language for network monitoring. In: Falcone, Y., Sánchez, C. (eds.) RV 2016. LNCS, vol. 10012, pp. 152–168. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46982-9_10
Geurts, P.: Pattern extraction for time series classification. In: De Raedt, L., Siebes, A. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, pp. 115–127. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44794-6_10
Ghidella, J., Mosterman, P.: Requirements-based testing in aircraft control design. In: AIAA Modeling and Simulation Technologies Conference and Exhibit, p. 5886 (2005)
Goldberger, A.L., et al.: Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals. Circulation 101(23), e215–e220 (2000)
Gorostiaga, F., Sánchez, C.: Striver: stream runtime verification for real-time event-streams. In: Colombo, C., Leucker, M. (eds.) RV 2018. LNCS, vol. 11237, pp. 282–298. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03769-7_16
Hallé, S., Khoury, R.: Event stream processing with beepbeep 3. In: RV-CuBES 2017. An International Workshop on Competitions, Usability, Benchmarks, Evaluation, and Standardisation for Runtime Verification Tools, 15 September 2017, Seattle, WA, USA, pp. 81–88 (2017)
Leucker, M., Sánchez, C., Scheffel, T., Schmitz, M., Schramm, A.: TeSSLa: runtime verification of non-synchronized real-time streams. In: Proceedings of the 33rd Annual ACM Symposium on Applied Computing, SAC 2018, Pau, France, 09–13 April 2018, pp. 1925–1933 (2018)
Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30206-3_12
Mamouras, K., Raghothaman, M., Alur, R., Ives, Z.G., Khanna, S.: StreamQRE: modular specification and efficient evaluation of quantitative queries over streaming data. In: ACM SIGPLAN Notices, vol. 52, pp. 693–708. ACM (2017)
Olszewski, R.T.: Generalized feature extraction for structural pattern recognition in time-series data. Technical report, Carnegie-Mellon Univ. School of Computer Science (2001)
Rakthanmanon, T., et al.: Searching and mining trillions of time series subsequences under dynamic time warping. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 262–270. ACM (2012)
Ulus, D.: Montre: a tool for monitoring timed regular expressions. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 329–335. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_16
Ulus, D., Ferrère, T., Asarin, E., Maler, O.: Timed pattern matching. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 222–236. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10512-3_16
Ulus, D., Ferrère, T., Asarin, E., Maler, O.: Online timed pattern matching using derivatives. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 736–751. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49674-9_47
Waga, M., Hasuo, I.: Moore-machine filtering for timed and untimed pattern matching. IEEE Trans. CAD Integr. Circ. Syst. 37(11), 2649–2660 (2018)
Waga, M., Hasuo, I., Suenaga, K.: Efficient online timed pattern matching by automata-based skipping. In: Abate, A., Geeraerts, G. (eds.) FORMATS 2017. LNCS, vol. 10419, pp. 224–243. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65765-3_13
Waga, M., Hasuo, I., Suenaga, K.: MONAA: a tool for timed pattern matching with automata-based acceleration. In: 3rd Workshop on Monitoring and Testing of Cyber-Physical Systems, MT@CPSWeek 2018, Porto, Portugal, 10 April, pp. 14–15 (2018)
Wenig, F., Klanatsky, P., Heschl, C., Mateis, C., Dejan, N.: Exponential pattern recognition for deriving air change rates from CO2 data. In: 26th IEEE International Symposium on Industrial Electronics, ISIE 2017, Edinburgh, United Kingdom, 19–21 June 2017, pp. 1507–1512 (2017)
Ye, L., Keogh, E.J.: Time series shapelets: a new primitive for data mining. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Paris, France, 28 June–1 July 2009, pp. 947–956 (2009)
Acknowledgments
This research was supported in part by the Austrian Science Fund (FWF) under grants 27 S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award), and by the Productive 4.0 project (ECSEL 737459).
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Ničković, D., Qin, X., Ferrère, T., Mateis, C., Deshmukh, J. (2019). Shape Expressions for Specifying and Extracting Signal Features. In: Finkbeiner, B., Mariani, L. (eds) Runtime Verification. RV 2019. Lecture Notes in Computer Science(), vol 11757. Springer, Cham. https://doi.org/10.1007/978-3-030-32079-9_17
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DOI: https://doi.org/10.1007/978-3-030-32079-9_17
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