Authors

Judy Najnudel, Remy Muller, Thomas Helie, David Roze

Abstract

This paper addresses identification of nonlinear circuits for power-balanced virtual analog modeling and simulation. The proposed method combines a port-Hamiltonian system formulation with kernel-based methods to retrieve model laws from measurements. This combination allows for the estimated model to retain physical properties that are crucial for the accuracy of simulations, while representing a variety of nonlinear behaviors. As an illustration, the method is used to identify a nonlinear passive peaking EQ.

Citation

  • Journal: 2021 24th International Conference on Digital Audio Effects (DAFx)
  • Year: 2021
  • Volume:
  • Issue:
  • Pages: 1–8
  • Publisher: IEEE
  • DOI: 10.23919/dafx51585.2021.9768224

BibTeX

@inproceedings{Najnudel_2021,
  title={{Identification of Nonlinear Circuits as Port-Hamiltonian Systems}},
  DOI={10.23919/dafx51585.2021.9768224},
  booktitle={{2021 24th International Conference on Digital Audio Effects (DAFx)}},
  publisher={IEEE},
  author={Najnudel, Judy and Muller, Remy and Helie, Thomas and Roze, David},
  year={2021},
  pages={1--8}
}

Download the bib file

References

  • Wendland, H. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math 4, 389–396 (1995) – 10.1007/bf02123482
  • mongillo, Choosing basis functions and shape pa-rameters for radial basis function methods. SIAM under-graduate research online (2011)
  • higham, Analysis of the Cholesky Decomposition of A Semi-definite Matrix (1990)
  • Biolek, Z., Biolek, D., Kolka, Z. & Biolkova, V. Real-World Capacitor as a Memcapacitive Element. 2018 New Trends in Signal Processing (NTSP) 1–6 (2018) doi:10.23919/ntsp.2018.8524089 – 10.23919/ntsp.2018.8524089
  • najnudel, A power-balanced dynamic model of ferromagnetic coils. Proceedings of the 23rd International Conference on Digital Audio Effects (DAFx-20) (0)
  • Bigelow, T. A. Power and Energy in Electric Circuits. Electric Circuits, Systems, and Motors 105–121 (2020) doi:10.1007/978-3-030-31355-5_4 – 10.1007/978-3-030-31355-5_4
  • Fasshauer, G. E. & Zhang, J. G. On choosing “optimal” shape parameters for RBF approximation. Numer Algor 45, 345–368 (2007) – 10.1007/s11075-007-9072-8
  • nelles, Nonlinear System Identification (2002)
  • Schaback, R. Native Hilbert Spaces for Radial Basis Functions I. New Developments in Approximation Theory 255–282 (1999) doi:10.1007/978-3-0348-8696-3_16 – 10.1007/978-3-0348-8696-3_16
  • benoit, Note sur une méthode de resolution des équations normales provenant de 1’ application de la méthode des moindres carrés à un systéme d’ équations linéaires en nombre inférieur à celui des inconnues. Application de la méthode à la résolution d’un système défini d’équations linéaires (precédé du Commandant Cholesky). Bull Géodésique (1924)
  • Helie, T. Volterra Series and State Transformation for Real-Time Simulations of Audio Circuits Including Saturations: Application to the Moog Ladder Filter. IEEE Trans. Audio Speech Lang. Process. 18, 747–759 (2010) – 10.1109/tasl.2009.2035211
  • schaback, A practical guide to radial basis functions. Electronic Resource (2007)
  • Boyd, S., Tang, Y. & Chua, L. Measuring Volterra kernels. IEEE Trans. Circuits Syst. 30, 571–577 (1983) – 10.1109/tcs.1983.1085391
  • Orcioni, S., Terenzi, A., Cecchi, S., Piazza, F. & Carini, A. Identification of Volterra Models of Tube Audio Devices using Multiple-Variance Method. J. Audio Eng. Soc. 66, 823–838 (2018) – 10.17743/jaes.2018.0046
  • bouvier, Phase-based order separation for Volterra series identification. Ternational Journal of Control (2019)
  • sondhi, Lattice Wave Digital Filter based IIR system iden-tification with reduced coefficients. The International Symposium on Intelligent Systems Technologies and Applications (0)
  • Paduart, J. et al. Identification of nonlinear systems using Polynomial Nonlinear State Space models. Automatica 46, 647–656 (2010) – 10.1016/j.automatica.2010.01.001
  • parker, Mod-elling of nonlinear state-space systems using a deep neural network. Proceedings of the 22rd International Confer-ence on Digital Audio Effects (DAFx-19) (2019)
  • nercessian, Lightweight and interpretable neural modeling of an au-dio distortion effect using hyperconditioned differentiable bi-quads. ArXiv Preprint (2021)
  • Maschke, B. M., Van Der Schaft, A. J. & Breedveld, P. C. An intrinsic hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators. Journal of the Franklin Institute 329, 923–966 (1992) – 10.1016/s0016-0032(92)90049-m
  • van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. FnT in Systems and Control 1, 173–378 (2014) – 10.1561/2600000002
  • lutter, Deep la-grangian networks: Using physics as model prior for deep learning. ArXiv Preprint (2019)
  • cohen, Real-time simulation of a guitar power amplifier. Proceedings of the 13th International Conference on Digital Audio Effects (DAFx-10) (0)
  • gillespie, Modeling non-linear circuits with linearized dynamical models via kernel regression. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (0)
  • alberto, Wave digital modeling of nonlinear 3-terminal devices for virtual analog applications. Circuits Systems and Signal Processing (2020)
  • Holters, M. & Zolzer, U. A generalized method for the derivation of non-linear state-space models from circuit schematics. 2015 23rd European Signal Processing Conference (EUSIPCO) 1073–1077 (2015) doi:10.1109/eusipco.2015.7362548 – 10.1109/eusipco.2015.7362548
  • Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
  • macak, Simu-lation of Fender type guitar preamp using approximation and state space model. Proceedings of the 15th International Conference on Digital Audio Effects (DAFx-12) (0)
  • Martínez Ramírez, M. A., Benetos, E. & Reiss, J. D. Deep Learning for Black-Box Modeling of Audio Effects. Applied Sciences 10, 638 (2020) – 10.3390/app10020638
  • damskägg, Real-time modeling of audio distortion circuits with deep learning. Proceedings of the International Sound and Mu-sic Computing Conference (SMC-19) (2019)
  • Werner, K. J., Bernardini, A., Smith, J. O. & Sarti, A. Modeling Circuits With Arbitrary Topologies and Active Linear Multiports Using Wave Digital Filters. IEEE Trans. Circuits Syst. I 65, 4233–4246 (2018) – 10.1109/tcsi.2018.2837912
  • Hélie, T. & Roze, D. Sound synthesis of a nonlinear string using Volterra series. Journal of Sound and Vibration 314, 275–306 (2008) – 10.1016/j.jsv.2008.01.038
  • Fettweis, A. Wave digital filters: Theory and practice. Proc. IEEE 74, 270–327 (1986) – 10.1109/proc.1986.13458
  • Najnudel, J., Helie, T., Roze, D. & Boutin, H. Simulation of an Ondes Martenot Circuit. IEEE/ACM Trans. Audio Speech Lang. Process. 28, 2651–2660 (2020) – 10.1109/taslp.2020.3019643
  • Park, J. & Sandberg, I. W. Universal Approximation Using Radial-Basis-Function Networks. Neural Computation 3, 246–257 (1991) – 10.1162/neco.1991.3.2.246
  • bohn, Operator adjustable equalizers: An overview. Audio Engineering Society Conference 6th International Conference Sound Reinforcement (0)
  • Falaize, A. & Hélie, T. Passive Guaranteed Simulation of Analog Audio Circuits: A Port-Hamiltonian Approach. Applied Sciences 6, 273 (2016) – 10.3390/app6100273
  • Matsuda, T. & Miyatake, Y. Estimation of Ordinary Differential Equation Models with Discretization Error Quantification. SIAM/ASA J. Uncertainty Quantification 9, 302–331 (2021) – 10.1137/19m1278405
  • vapnik, Support vector method for function approximation, regression estimation, and signal processing. Advances in neural information processing systems (1997)
  • Cieśliński, J. L. & Ratkiewicz, B. Discrete gradient algorithms of high order for one-dimensional systems. Computer Physics Communications 183, 617–627 (2012) – 10.1016/j.cpc.2011.12.008
  • Benner, P., Goyal, P. & Van Dooren, P. Identification of port-Hamiltonian systems from frequency response data. Systems & Control Letters 143, 104741 (2020) – 10.1016/j.sysconle.2020.104741
  • mclachlan, Discrete gra-dient methods have an energy conservation law. ArXiv Preprint (2013)
  • medianu, Identification for port-controlled Hamilto-nian systems (2017)
  • Deuflhard, P. Newton Methods for Nonlinear Problems. Springer Series in Computational Mathematics (Springer Berlin Heidelberg, 2011). doi:10.1007/978-3-642-23899-4 – 10.1007/978-3-642-23899-4
  • Schaback, R. & Wendland, H. Kernel techniques: From machine learning to meshless methods. Acta Numerica 15, 543–639 (2006) – 10.1017/s0962492906270016
  • Boyd, S. & Vandenberghe, L. Convex Optimization. (2004) doi:10.1017/cbo9780511804441 – 10.1017/cbo9780511804441
  • Cherifi, K. An overview on recent machine learning techniques for Port Hamiltonian systems. Physica D: Nonlinear Phenomena 411, 132620 (2020) – 10.1016/j.physd.2020.132620