Abstract
Deep learning methods contain powerful tools for modelling nonlinear dynamic systems. However, these methods usually lack interpretability, so although they are useful for predicting outputs they tend to be less useful for giving insight into system characteristics. In this paper, we aim to demonstrate a method for interpreting and comparing deep learning models used in nonlinear system identification, using nonlinear output frequency response functions (NOFRFs). NOFRFs describe nonlinear dynamic system behaviour in the frequency domain, which is a classical way of interpreting and understanding system behaviour (via resonances, super and sub-harmonics, and energy transfer). We demonstrate the approach on a real system (a magneto-rheological damper), showing how different types of deep learning model, recurrent networks with gated recurrent units (GRUs) and long short term memory (LSTM), can be interpreted and compared in the frequency domain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Billings, S.A.: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Wiley, Hoboken (2013)
Billings, S.A., Tsang, K.M.: Spectral analysis for non-linear systems, part I: parametric non-linear spectral analysis. Mech. Syst. Signal Process. 3(4), 319–339 (1989)
Cho, K., van Merrienboer, B., Gulcehre, C., Bougares, F., Schwenk, H., Bengio, Y.: Learning phrase representations using RNN encoder-decoder for statistical machine translation. In: Conference on Empirical Methods in Natural Language Processing (EMNLP 2014) (2014)
Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9(8), 1735–1780 (1997)
Jacobs, W.R., Baldacchino, T., Dodd, T.J., Anderson, S.R.: Sparse Bayesian nonlinear system identification using variational inference. IEEE Trans. Autom. Control 63, 4172–4187 (2018)
Jacobs, W.R., Dodd, T.J., Anderson, S.R.: Frequency-domain analysis for nonlinear systems with time-domain model parameter uncertainty. IEEE Trans. Autom. Control 64(5), 1905–1915 (2019)
Lang, Z.Q., Billings, S.A.: Energy transfer properties of non-linear systems in the frequency domain. Int. J. Control 78(5), 345–362 (2005)
Ljung, L., Andersson, C., Tiels, K., Schön, T.B.: Deep learning and system identification. IFAC-PapersOnLine 53(2), 1175–1181 (2020). 21st IFAC World Congress
Ljung, L., Singh, R.: Version 8 of the Matlab system identification toolbox. IFAC Proc. Vol. 45(16), 1826–1831 (2012)
Sjöberg, J., et al.: Nonlinear black-box modeling in system identification: a unified overview. Automatica 31(12), 1691–1724 (1995)
Wang, J., Sano, A., Chen, T., Huang, B.: Identification of Hammerstein systems without explicit parameterisation of non-linearity. Int. J. Control 82(5), 937–952 (2009)
Zhao, B., Cheng, C., Peng, Z., Dong, X., Meng, G.: Detecting the early damages in structures with nonlinear output frequency response functions and the CNN-LSTM model. IEEE Trans. Instrum. Meas. 69(12), 9557–9567 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Jacobs, W., Anderson, S.R. (2024). Interpretable Deep Learning for System Identification Using Nonlinear Output Frequency Response Functions. In: Panoutsos, G., Mahfouf, M., Mihaylova, L.S. (eds) Advances in Computational Intelligence Systems. UKCI 2022. Advances in Intelligent Systems and Computing, vol 1454. Springer, Cham. https://doi.org/10.1007/978-3-031-55568-8_30
Download citation
DOI: https://doi.org/10.1007/978-3-031-55568-8_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-55567-1
Online ISBN: 978-3-031-55568-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)