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Online System Identification in a Duffing Oscillator by Free Energy Minimisation

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1326))

Abstract

Online system identification is the estimation of parameters of a dynamical system, such as mass or friction coefficients, for each measurement of the input and output signals. Here, the nonlinear stochastic differential equation of a Duffing oscillator is cast to a generative model and dynamical parameters are inferred using variational message passing on a factor graph of the model. The approach is validated with an experiment on data from an electronic implementation of a Duffing oscillator. The proposed inference procedure performs as well as offline prediction error minimisation in a state-of-the-art nonlinear model.

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Notes

  1. 1.

    http://nonlinearbenchmark.org/.

  2. 2.

    Derivations at https://github.com/biaslab/IWAI2020-onlinesysid.

  3. 3.

    Experiment notebooks at https://github.com/biaslab/IWAI2020-onlinesysid.

References

  1. Abdessalem, A.B., Dervilis, N., Wagg, D., Worden, K.: Identification of nonlinear dynamical systems using approximate Bayesian computation based on a sequential Monte Carlo sampler. In: International Conference on Noise and Vibration Engineering (2016)

    Google Scholar 

  2. Aguirre, L.A., Letellier, C.: Modeling nonlinear dynamics and chaos: a review. Math. Problems Eng. 2009 (2009)

    Google Scholar 

  3. Buckley, C.L., Kim, C.S., McGregor, S., Seth, A.K.: The free energy principle for action and perception: a mathematical review. J. Math. Psychol. 81, 55–79 (2017)

    Article  MathSciNet  Google Scholar 

  4. Cox, M., van de Laar, T., de Vries, B.: Forneylab.jl: Fast and flexible automated inference through message passing in Julia. In: International Conference on Probabilistic Programming (2018)

    Google Scholar 

  5. Dauwels, J.: On variational message passing on factor graphs. In: IEEE International Symposium on Information Theory, pp. 2546–2550 (2007)

    Google Scholar 

  6. Dauwels, J., Eckford, A., Korl, S., Loeliger, H.A.: Expectation maximization as message passing - Part I: Principles and Gaussian messages (2009). arXiv:0910.2832

  7. Engel, Y., Mannor, S., Meir, R.: The kernel recursive least-squares algorithm. IEEE Trans. Signal Process. 52(8), 2275–2285 (2004)

    Article  MathSciNet  Google Scholar 

  8. Friston, K., Kilner, J., Harrison, L.: A free energy principle for the brain. J. Physiol. 100(1–3), 70–87 (2006)

    Google Scholar 

  9. Fujimoto, K., Satoh, A., Fukunaga, S.: System identification based on variational Bayes method and the invariance under coordinate transformations. In: IEEE Conference on Decision and Control and European Control Conference, pp. 3882–3888 (2011)

    Google Scholar 

  10. Green, P.L.: Bayesian system identification of a nonlinear dynamical system using a novel variant of simulated annealing. Mech. Syst. Signal Process. 52, 133–146 (2015)

    Article  Google Scholar 

  11. de Klerk, C.C., Johnson, M.H., Heyes, C.M., Southgate, V.: Baby steps: Investigating the development of perceptual-motor couplings in infancy. Develop. Sci. 18(2), 270–280 (2015)

    Article  Google Scholar 

  12. Korl, S.: A factor graph approach to signal modelling, system identification and filtering. Ph.D. thesis, ETH Zurich (2005)

    Google Scholar 

  13. van de Laar, T., Cox, M., Senoz, I., Bocharov, I., de Vries, B.: ForneyLab: a toolbox for biologically plausible free energy minimization in dynamic neural models. In: Conference on Complex Systems (2018)

    Google Scholar 

  14. Loeliger, H.A., Dauwels, J., Hu, J., Korl, S., Ping, L., Kschischang, F.R.: The factor graph approach to model-based signal processing. Proc. IEEE 95(6), 1295–1322 (2007)

    Article  Google Scholar 

  15. Moon, F., Holmes, P.J.: A magnetoelastic strange attractor. J. Sound Vibration 65(2), 275–296 (1979)

    Article  Google Scholar 

  16. Paleologu, C., Benesty, J., Ciochina, S.: A robust variable forgetting factor recursive least-squares algorithm for system identification. IEEE Signal Process. Lett. 15, 597–600 (2008)

    Article  Google Scholar 

  17. Parr, T., Friston, K.J.: Generalised free energy and active inference. Biol. Cybern. 113(5–6), 495–513 (2019)

    Article  MathSciNet  Google Scholar 

  18. Parr, T., Markovic, D., Kiebel, S.J., Friston, K.J.: Neuronal message passing using mean-field, Bethe, and marginal approximations. Sci. Rep. 9(1), 1–18 (2019)

    Article  Google Scholar 

  19. Podusenko, A., Kouw, W.M., de Vries, B.: Online variational message passing in hierarchical autoregressive models. In: IEEE International Symposium on Information Theory, pp. 1343–1348 (2020)

    Google Scholar 

  20. Särkkä, S.: Bayesian Filtering And Smoothing. Cambridge University Press, Cambridge (2013). Vol. 3

    Book  Google Scholar 

  21. Schoukens, M., Noël, J.P.: Three benchmarks addressing open challenges in nonlinear system identification. IFAC-PapersOnline 50(1), 446–451 (2017)

    Article  Google Scholar 

  22. Senoz, I., Podusenko, A., Kouw, W.M., de Vries, B.: Bayesian joint state and parameter tracking in autoregressive models. In: Conference on Learning for Dynamics and Control, pp. 1–10 (2020)

    Google Scholar 

  23. Tangirala, A.K.: Principles of System Identification: Theory And Practice. CRC Press, Boca Raton (2018)

    Book  Google Scholar 

  24. Tin, C., Poon, C.S.: Internal models in sensorimotor integration: perspectives from adaptive control theory. J. Neural Eng. 2(3), S147 (2005)

    Article  Google Scholar 

  25. Wigren, T., Schoukens, J.: Three free data sets for development and benchmarking in nonlinear system identification. In: European Control Conference (ECC), pp. 2933–2938 (2013)

    Google Scholar 

  26. Yoshimoto, J., Ishii, S., Sato, M.: System identification based on online variational Bayes method and its application to reinforcement learning. In: Artificial Neural Networks and Neural Information Processing, pp. 123–131. Springer (2003)

    Google Scholar 

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Acknowledgements

The author thanks Magnus Koudahl, Albert Podusenko and Thijs van de Laar for insightful discussions and the reviewers for their constructive feedback.

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Correspondence to Wouter M. Kouw .

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Kouw, W.M. (2020). Online System Identification in a Duffing Oscillator by Free Energy Minimisation. In: Verbelen, T., Lanillos, P., Buckley, C.L., De Boom, C. (eds) Active Inference. IWAI 2020. Communications in Computer and Information Science, vol 1326. Springer, Cham. https://doi.org/10.1007/978-3-030-64919-7_6

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  • DOI: https://doi.org/10.1007/978-3-030-64919-7_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-64918-0

  • Online ISBN: 978-3-030-64919-7

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