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A PINN approach for identifying governing parameters of noisy thermoacoustic systems

Published online by Cambridge University Press:  01 April 2024

Hwijae Son Open the ORCID record for Hwijae Son [Opens in a new window]  and
Minwoo Lee Open the ORCID record for Minwoo Lee [Opens in a new window]
Hwijae Son
Affiliation:
Department of Mathematics, Konkuk University, 120 Neungdongro, Gwangjin, Seoul 05029, South Korea
Minwoo Lee*
Affiliation:
Department of Mechanical Engineering, Hanbat National University, 125 Dongseodaero, Yuseong, Daejeon 34158, South Korea
*
†Email address for correspondence: mwlee@hanbat.ac.kr
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Abstract

Identifying the governing parameters of self-sustained oscillation is crucial for the diagnosis, prediction and control of thermoacoustic instabilities. In this paper, we propose and validate a novel method for computing the parameters of thermoacoustic oscillation in a stochastic environment, which exploits a physics-informed neural network (PINN). Specifically, we introduce a negative log-likelihood loss function that integrates the stochastic samples and the solution of the Fokker–Planck equation. The proposed framework is validated using the numerically generated signal and the experimental data obtained from an annular combustor, both before and after the supercritical Hopf bifurcation. The results of PINN-based system identification show good agreement with the actual system parameters and the original stochastic signal, with improved accuracy compared to established methods. To the best of our knowledge, this study constitutes the first demonstration of the PINN-inverse approach that uses the noise-induced dynamics of thermoacoustic systems, opening up new pathways for diagnosing and predicting the thermoacoustic behaviour of various combustion systems.

JFM classification

Mathematical Foundations: Machine learning Nonlinear Dynamical Systems: Low-dimensional models Reacting Flows: Combustion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 984 , 10 April 2024 , A21
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Bonciolini, G., Boujo, E. & Noiray, N. 2017 Output-only parameter identification of a colored-noise-driven Van-der-Pol oscillator: thermoacoustic instabilities as an example. Phys. Rev. E 95 (6), 062217.CrossRefGoogle ScholarPubMed
Bonciolini, G., Faure-Beaulieu, A., Bourquard, C. & Noiray, N. 2021 Low order modelling of thermoacoustic instabilities and intermittency: flame response delay and nonlinearity. Combust. Flame 226, 396–411.CrossRefGoogle Scholar
Boujo, E. & Noiray, N. 2017 Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation. Proc. R. Soc. Lond. A 473 (2200), 20160894.Google ScholarPubMed
Chen, X., Yang, L., Duan, J. & Karniadakis, G.E. 2021 Solving inverse stochastic problems from discrete particle observations using the Fokker–Planck equation and physics-informed neural networks. SIAM J. Sci. Comput. 43 (3), B811–B830.CrossRefGoogle Scholar
Chen, Y., Lu, L., Karniadakis, G.E. & Dal Negro, L. 2020 Physics-informed neural networks for inverse problems in nano-optics and metamaterials. Opt. Express 28 (8), 11618–11633.CrossRefGoogle ScholarPubMed
Fraser, A.M. & Swinney, H.L. 1986 Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33 (2), 1134.CrossRefGoogle ScholarPubMed
Glorot, X. & Bengio, Y. 2010 Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, pp. 249–256. JMLR Workshop and Conference Proceedings.Google Scholar
Gopalakrishnan, E.A., Sharma, Y., John, T., Dutta, P.S. & Sujith, R.I. 2016 Early warning signals for critical transitions in a thermoacoustic system. Sci. Rep. 6 (1), 35310.CrossRefGoogle Scholar
Guk, S., Seo, S. & Lee, M. 2023 Thermoacoustic dynamics in an annular model gas-turbine combustor under transverse stochastic forcing. J. Korean Soc. Combust. 28 (3), 20–27.CrossRefGoogle Scholar
Han, E., Kim, D., Lee, J., Kim, Y., Yi, M. & Lee, M. 2023 Analysis of the Hall-effect thruster discharge instability using complexity-entropy causality plane. J. Korean Soc. Aeronaut. Space Sci. 51 (4), 263–271.Google Scholar
Indlekofer, T., Faure-Beaulieu, A., Dawson, J.R. & Noiray, N. 2022 Spontaneous and explicit symmetry breaking of thermoacoustic eigenmodes in imperfect annular geometries. J. Fluid Mech. 944, A15.CrossRefGoogle Scholar
Jaensch, S. & Polifke, W. 2017 Uncertainty encountered when modelling self-excited thermoacoustic oscillations with artificial neural networks. Intl J. Spray Combust. Dyn. 9 (4), 367–379.CrossRefGoogle Scholar
Jagtap, A.D., Mao, Z., Adams, N. & Karniadakis, G.E. 2022 Physics-informed neural networks for inverse problems in supersonic flows. J. Comput. Phys. 466, 111402.CrossRefGoogle Scholar
Juniper, M.P. & Sujith, R.I. 2018 Sensitivity and nonlinearity of thermoacoustic oscillations. Annu. Rev. Fluid Mech. 50, 661–689.CrossRefGoogle Scholar
Kabiraj, L., Steinert, R., Saurabh, A. & Paschereit, C.O. 2015 Coherence resonance in a thermoacoustic system. Phys. Rev. E 92, 042909.CrossRefGoogle Scholar
Kabiraj, L., Vishnoi, N. & Saurabh, A. 2020 A review on noise-induced dynamics of thermoacoustic systems. In Dynamics and Control of Energy Systems, pp. 265–281. Springer.CrossRefGoogle Scholar
Karniadakis, G.E., Kevrekidis, I.G., Lu, L., Perdikaris, P., Wang, S. & Yang, L. 2021 Physics-informed machine learning. Nat. Rev. Phys. 3 (6), 422–440.CrossRefGoogle Scholar
Kashinath, K., Li, L.K.B. & Juniper, M.P. 2018 Forced synchronization of periodic and aperiodic thermoacoustic oscillations: lock-in, bifurcations and open-loop control. J. Fluid Mech. 838, 690–714.CrossRefGoogle Scholar
Kingma, D.P. & Ba, J. 2014 Adam: a method for stochastic optimization. In Proceedings of International Conference on Learning Representations, 2015, pp. 1–15.Google Scholar
Krishnan, A., Sujith, R.I., Marwan, N. & Kurths, J. 2021 Suppression of thermoacoustic instability by targeting the hubs of the turbulent networks in a bluff body stabilized combustor. J. Fluid Mech. 916, A20.CrossRefGoogle Scholar
Lade, S.J. 2009 Finite sampling interval effects in Kramers–Moyal analysis. Phys. Lett. A 373 (41), 3705–3709.CrossRefGoogle Scholar
Lagaris, I.E., Likas, A. & Fotiadis, D.I. 1998 Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw. 9 (5), 987–1000.CrossRefGoogle ScholarPubMed
Landau, L.D. 1944 On the problem of turbulence. Dokl. Akad. Nauk SSSR 44 (8), 339–349.Google Scholar
Lee, M., Guan, Y., Gupta, V. & Li, L.K.B. 2020 Input–output system identification of a thermoacoustic oscillator near a Hopf bifurcation using only fixed-point data. Phys. Rev. E 101 (1), 013102.CrossRefGoogle Scholar
Lee, M., Kim, D., Lee, J., Kim, Y. & Yi, M. 2023 a A data-driven approach for analyzing Hall thruster discharge instability leading to plasma blowoff. Acta Astronaut. 206, 1–8.CrossRefGoogle Scholar
Lee, M., Kim, K.T., Gupta, V. & Li, L.K.B. 2021 System identification and early warning detection of thermoacoustic oscillations in a turbulent combustor using its noise-induced dynamics. Proc. Combust. Inst. 38 (4), 6025–6033.CrossRefGoogle Scholar
Lee, M., Kim, K.T. & Park, J. 2023 b A numerically efficient output-only system-identification framework for stochastically forced self-sustained oscillators. Probab. Engng Mech. 74, 103516.CrossRefGoogle Scholar
Lee, M., Zhu, Y., Li, L.K.B. & Gupta, V. 2019 System identification of a low-density jet via its noise-induced dynamics. J. Fluid Mech. 862, 200–215.CrossRefGoogle Scholar
Lieuwen, T. & Yang, V. 2005 Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms and Modeling. AIAA.Google Scholar
Lu, L., Pestourie, R., Yao, W., Wang, Z., Verdugo, F. & Johnson, S.G. 2021 Physics-informed neural networks with hard constraints for inverse design. SIAM J. Sci. Comput. 43 (6), B1105–B1132.CrossRefGoogle Scholar
Magri, L., Juniper, M.P. & Moeck, J.P. 2020 Sensitivity of the Rayleigh criterion in thermoacoustics. J. Fluid Mech. 882, R1.CrossRefGoogle Scholar
Mishra, S. & Molinaro, R. 2022 Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs. IMA J. Numer. 42 (2), 981–1022.CrossRefGoogle Scholar
Nair, V., Thampi, G. & Sujith, R.I. 2014 Intermittency route to thermoacoustic instability in turbulent combustors. J. Fluid Mech. 756, 470–487.CrossRefGoogle Scholar
Nayfeh, A.H. 1981 Introduction to Perturbation Techniques. John Wiley.Google Scholar
Noiray, N. & Denisov, A. 2017 A method to identify thermoacoustic growth rates in combustion chambers from dynamic pressure time series. Proc. Combust. Inst. 36 (3), 3843–3850.CrossRefGoogle Scholar
Noiray, N. & Schuermans, B. 2013 Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors. Intl J. Non-Linear Mech. 50, 152–163.CrossRefGoogle Scholar
Nóvoa, A. & Magri, L. 2022 Real-time thermoacoustic data assimilation. J. Fluid Mech. 948, A35.CrossRefGoogle Scholar
Nóvoa, A., Racca, A. & Magri, L. 2024 Inferring unknown unknowns: regularized bias-aware ensemble Kalman filter. Comput. Meth. Appl. Mech. Engng 418, 116502.CrossRefGoogle Scholar
Ozan, D.E. & Magri, L. 2023 Hard-constrained neural networks for modeling nonlinear acoustics. Phys. Rev. Fluids 8, 103201.CrossRefGoogle Scholar
Park, S. & Lee, M. 2024 A semi-supervised framework for analyzing the potential core of a low-density jet. Flow Meas. Instrum. 95, 102516.CrossRefGoogle Scholar
Pikovsky, A.S. & Kurths, J. 1997 Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 78, 775–778.CrossRefGoogle Scholar
Raghu, S. & Monkewitz, P.A. 1991 The bifurcation of a hot round jet to limit-cycle oscillations. Phys. Fluids A 3, 501.CrossRefGoogle Scholar
Selimefendigil, F. & Polifke, W. 2011 A nonlinear frequency domain model for limit cycles in thermoacoustic systems with modal coupling. Intl J. Spray Combust. Dyn. 3 (4), 303–330.CrossRefGoogle Scholar
Shin, H. & Choi, M. 2023 Physics-informed variational inference for uncertainty quantification of stochastic differential equations. J. Comput. Phys. 487, 112183.CrossRefGoogle Scholar
Siegert, S., Friedrich, R. & Peinke, J. 1998 Analysis of data sets of stochastic systems. Phys. Lett. A 243 (5–6), 275–280.CrossRefGoogle Scholar
Son, H. & Lee, M. 2023 Continuous probabilistic solution to the transient self-oscillation under stochastic forcing: a PINN approach. J. Mech. Sci. Technol. 37 (8), 3911–3918.CrossRefGoogle Scholar
Stuart, J.T. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows – part 1. The basic behaviour in plane Poiseuille flow. J. Fluid Mech. 9, 353–370.CrossRefGoogle Scholar
Subramanian, P., Mariappan, S., Sujith, R.I. & Wahi, P. 2010 Bifurcation analysis of thermoacoustic instability in a horizontal Rijke tube. Intl J. Spray Combust. Dyn. 2 (4), 325–355.CrossRefGoogle Scholar
Subramanian, P., Sujith, R.I. & Wahi, P. 2013 Subcritical bifurcation and bistability in thermoacoustic systems. J. Fluid Mech. 715, 210–238.CrossRefGoogle Scholar
Takens, F. 1981 Detecting strange attractors in turbulence. Lect. Notes Math. 898, 366–381.CrossRefGoogle Scholar
Tathawadekar, N., Doan, N.A.K., Silva, C.F. & Thuerey, N. 2021 Modeling of the nonlinear flame response of a Bunsen-type flame via multi-layer perceptron. Proc. Combust. Inst. 38 (4), 6261–6269.CrossRefGoogle Scholar
Ushakov, O.V., Wünsche, H.J., Henneberger, F., Khovanov, I.A., Schimansky-Geier, L. & Zaks, M.A. 2005 Coherence resonance near a Hopf bifurcation. Phys. Rev. Lett. 95, 123903.CrossRefGoogle Scholar
Xu, K. & Darve, E. 2021 Solving inverse problems in stochastic models using deep neural networks and adversarial training. Comput. Meth. Appl. Mech. Engng 384, 113976.CrossRefGoogle Scholar
Zhang, M., Li, Q. & Liu, J. 2023 On stability and regularization for data-driven solution of parabolic inverse source problems. J. Comput. Phys. 474, 111769.CrossRefGoogle Scholar
Zhu, W.Q. & Yu, J.S. 1987 On the response of the Van der Pol oscillator to white noise excitation. J. Sound Vib. 117 (3), 421–431.CrossRefGoogle Scholar
Zhu, Y., Gupta, V. & Li, L.K.B. 2017 Onset of global instability in low-density jets. J. Fluid Mech. 828, R1.CrossRefGoogle Scholar