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One-Shot Learning of Ensembles of Temporal Logic Formulas for Anomaly Detection in Cyber-Physical Systems

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Genetic Programming (EuroGP 2022)

Abstract

Cyber-Physical Systems (CPS) are prevalent in critical infrastructures and a prime target for cyber-attacks. Multivariate time series data generated by sensors and actuators of a CPS can be monitored for detecting cyber-attacks that introduce anomalies in those data. We use Signal Temporal Logic (STL) formulas to tightly describe the normal behavior of a CPS, identifying data instances that do not satisfy the formulas as anomalies. We learn an ensemble of STL formulas based on observed data, without any specific knowledge of the CPS being monitored. We propose an algorithm based on Grammar-Guided Genetic Programming (G3P) that learns the ensemble automatically in a single evolutionary run. We test the effectiveness of our data-driven proposal on two real-world datasets, finding that the proposed one-shot algorithm provides good detection performance.

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Notes

  1. 1.

    The code is publicly available at https://github.com/pindri/OneShot-ensemble-learning-anomaly-detection-MTS.

  2. 2.

    For the SWaT testbed, different versions of the dataset exist. Thus, no direct quantitative comparison can be made.

References

  1. Bartocci, E., Bortolussi, L., Loreti, M., Nenzi, L., Silvetti, S.: MoonLight: a lightweight tool for monitoring spatio-temporal properties. In: Deshmukh, J., Ničković, D. (eds.) RV 2020. LNCS, vol. 12399, pp. 417–428. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-60508-7_23

    Chapter  Google Scholar 

  2. Bartocci, E., Bortolussi, L., Sanguinetti, G.: Data-driven statistical learning of temporal logic properties. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 23–37. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10512-3_3

    Chapter  MATH  Google Scholar 

  3. Bartoli, A., De Lorenzo, A., Medvet, E., Tarlao, F.: Learning text patterns using separate-and-conquer genetic programming. In: Machado, P., et al. (eds.) EuroGP 2015. LNCS, vol. 9025, pp. 16–27. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16501-1_2

    Chapter  Google Scholar 

  4. Deshmukh, J.V., Donzé, A., Ghosh, S., Jin, X., Juniwal, G., Seshia, S.A.: Robust online monitoring of signal temporal logic. Form. Methods Syst. Des. 51(1), 5–30 (2017). https://doi.org/10.1007/s10703-017-0286-7

    Article  MATH  Google Scholar 

  5. Donzé, A., Ferrère, T., Maler, O.: Efficient robust monitoring for STL. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 264–279. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_19

    Chapter  Google Scholar 

  6. Ergurtuna, M., Gol, E.A.: An efficient formula synthesis method with past signal temporal logic. IFAC-PapersOnLine 52(11), 43–48 (2019)

    Article  Google Scholar 

  7. Feng, C., Palleti, V.R., Mathur, A., Chana, D.: A systematic framework to generate invariants for anomaly detection in industrial control systems. In: NDSS (2019)

    Google Scholar 

  8. Goh, J., Adepu, S., Junejo, K.N., Mathur, A.: A dataset to support research in the design of secure water treatment systems. In: Havarneanu, G., Setola, R., Nassopoulos, H., Wolthusen, S. (eds.) CRITIS 2016. LNCS, vol. 10242, pp. 88–99. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71368-7_8

    Chapter  Google Scholar 

  9. Goh, J., Adepu, S., Tan, M., Lee, Z.S.: Anomaly detection in cyber physical systems using recurrent neural networks. In: 2017 IEEE 18th International Symposium on High Assurance Systems Engineering (HASE), pp. 140–145. IEEE (2017)

    Google Scholar 

  10. Wayne, H.: Temporal logic. In: Practical TLA+, pp. 97–110. Apress, Berkeley (2018). https://doi.org/10.1007/978-1-4842-3829-5_6

  11. Inoue, J., Yamagata, Y., Chen, Y., Poskitt, C.M., Sun, J.: Anomaly detection for a water treatment system using unsupervised machine learning. In: 2017 IEEE International Conference on Data Mining Workshops (ICDMW), pp. 1058–1065. IEEE (2017)

    Google Scholar 

  12. Jha, S., Tiwari, A., Seshia, S.A., Sahai, T., Shankar, N.: TeLEx: learning signal temporal logic from positive examples using tightness metric. Form. Methods Syst. Des. 54(3), 364–387 (2019). https://doi.org/10.1007/s10703-019-00332-1

    Article  MATH  Google Scholar 

  13. Jin, X., Donzé, A., Deshmukh, J.V., Seshia, S.A.: Mining requirements from closed-loop control models. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 34(11), 1704–1717 (2015)

    Article  Google Scholar 

  14. Li, D., Chen, D., Goh, J., Ng, S.K.: Anomaly detection with generative adversarial networks for multivariate time series. arXiv preprint arXiv:1809.04758 (2018)

  15. Li, D., Chen, D., Jin, B., Shi, L., Goh, J., Ng, S.-K.: MAD-GAN: multivariate anomaly detection for time series data with generative adversarial networks. In: Tetko, I.V., Kůrková, V., Karpov, P., Theis, F. (eds.) ICANN 2019. LNCS, vol. 11730, pp. 703–716. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30490-4_56

    Chapter  Google Scholar 

  16. 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

    Chapter  MATH  Google Scholar 

  17. Maler, O., Ničković, D.: Monitoring properties of analog and mixed-signal circuits. Int. J. Softw. Tools Technol. Transfer 15(3), 247–268 (2013)

    Article  Google Scholar 

  18. Manzoni, L., Bartoli, A., Castelli, M., Gonçalves, I., Medvet, E.: Specializing context-free grammars with a (1+1)-EA. IEEE Trans. Evol. Comput. 24(5), 960–973 (2020)

    Article  Google Scholar 

  19. Medvet, E., Bartoli, A., Carminati, B., Ferrari, E.: Evolutionary inference of attribute-based access control policies. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) EMO 2015. LNCS, vol. 9018, pp. 351–365. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-15934-8_24

    Chapter  Google Scholar 

  20. Meidan, Y., et al.: N-BaIoT-network-based detection of IoT botnet attacks using deep autoencoders. IEEE Pervasive Comput. 17(3), 12–22 (2018)

    Article  Google Scholar 

  21. Nenzi, L., Silvetti, S., Bartocci, E., Bortolussi, L.: A robust genetic algorithm for learning temporal specifications from data. In: McIver, A., Horvath, A. (eds.) QEST 2018. LNCS, vol. 11024, pp. 323–338. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99154-2_20

    Chapter  Google Scholar 

  22. Nicolau, M.: Understanding grammatical evolution: initialisation. Genet. Program Evolvable Mach. 18(4), 467–507 (2017). https://doi.org/10.1007/s10710-017-9309-9

    Article  Google Scholar 

  23. Pappa, G.L., Freitas, A.A.: Evolving rule induction algorithms with multi-objective grammar-based genetic programming. Knowl. Inf. Syst. 19(3), 283–309 (2009)

    Article  Google Scholar 

  24. Pigozzi, F., Medvet, E., Nenzi, L.: Mining road traffic rules with signal temporal logic and grammar-based genetic programming. Appl. Sci. 11(22), 10573 (2021)

    Article  Google Scholar 

  25. Squillero, G., Tonda, A.: Divergence of character and premature convergence: a survey of methodologies for promoting diversity in evolutionary optimization. Inf. Sci. 329, 782–799 (2016)

    Article  Google Scholar 

  26. Umer, M.A., Mathur, A., Junejo, K.N., Adepu, S.: Generating invariants using design and data-centric approaches for distributed attack detection. Int. J. Crit. Infrastruct. Prot. 28, 100341 (2020)

    Google Scholar 

  27. Virgolin, M.: Genetic programming is naturally suited to evolve bagging ensembles. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 830–839 (2021)

    Google Scholar 

  28. Whigham, P.A., et al.: Grammatically-based genetic programming. In: Proceedings of the Workshop on Genetic Programming: From Theory to Real-World Applications, vol. 16, pp. 33–41. Citeseer (1995)

    Google Scholar 

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Indri, P., Bartoli, A., Medvet, E., Nenzi, L. (2022). One-Shot Learning of Ensembles of Temporal Logic Formulas for Anomaly Detection in Cyber-Physical Systems. In: Medvet, E., Pappa, G., Xue, B. (eds) Genetic Programming. EuroGP 2022. Lecture Notes in Computer Science, vol 13223. Springer, Cham. https://doi.org/10.1007/978-3-031-02056-8_3

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  • DOI: https://doi.org/10.1007/978-3-031-02056-8_3

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