publications

2024

1. Chaos

   

   Model adaptive phase space reconstruction

   Jayesh M. Dhadphale, K. Hauke Kraemer, Maximilian Gelbrecht, and 3 more authors

   Chaos: An Interdisciplinary Journal of Nonlinear Science, Jul 2024

   Featured Article Abs DOI Bib

   

   The Editors felt that this article was one of the journal’s best, and have chosen to promote it as a Featured Article.

   Phase space reconstruction (PSR) methods allow for the analysis of low-dimensional data with methods from dynamical systems theory, but their application to prediction models, such as those from machine learning (ML), is limited. Therefore, we here present a model adaptive phase space reconstruction (MAPSR) method that unifies the process of PSR with the modeling of the dynamical system. MAPSR is a differentiable PSR based on time-delay embedding and enables ML methods for modeling. The quality of the reconstruction is evaluated by the prediction loss. The discrete-time signal is converted into a continuous-time signal to achieve a loss function, which is differentiable with respect to the embedding delays. The delay vector, which stores all potential embedding delays, is updated along with the trainable parameters of the model to minimize prediction loss. Thus, MAPSR does not rely on any threshold or statistical criterion for determining the dimension and the set of delay values for the embedding process. We apply the MAPSR method to uni- and multivariate time series stemming from chaotic dynamical systems and a turbulent combustor. We find that for the Lorenz system, the model trained with the MAPSR method is able to predict chaotic time series for nearly seven to eight Lyapunov time scales, which is found to be much better compared to other PSR methods [AMI-FNN (average mutual information-false nearest neighbor) and PECUZAL (Pecora-Uzal) methods]. For the univariate time series from the turbulent combustor, the long-term cumulative prediction error of the MAPSR method for the regime of chaos stays between other methods, and for the regime of intermittency, MAPSR outperforms other PSR methods.

   @article{10.1063/5.0194330,
     author = {Dhadphale, Jayesh M. and Hauke Kraemer, K. and Gelbrecht, Maximilian and Kurths, Jürgen and Marwan, Norbert and Sujith, R. I.},
     title = {Model adaptive phase space reconstruction},
     journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
     volume = {34},
     number = {7},
     pages = {073125},
     year = {2024},
     month = jul,
     issn = {1054-1500},
     doi = {10.1063/5.0194330},
     url = {https://doi.org/10.1063/5.0194330},
     eprint = {https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0194330/20039420/073125_1_5.0194330.pdf},
   }

2. AIP Adv.

   

   Continuous and explosive synchronization transition in turbulent combustors

   Samarjeet Singh, Amitesh Roy, Jayesh M. Dhadphale, and 2 more authors

   AIP Advances, Jun 2024

   Abs DOI Bib

   

   Thermoacoustic instabilities in turbulent combustors have disastrous consequences and present notorious challenges in their modeling, prediction, and control. Such instabilities are characterized by self-excited periodic oscillations, arising from a positive feedback between the acoustic pressure and heat release rate fluctuations. We present a mean-field approach to model thermoacoustic transitions. The nonlinear flame response is modeled using an ensemble of phase oscillators constrained to collectively evolve at the rhythm of acoustic fluctuations. Starting from the acoustic wave equation coupled with the phase oscillators, we derive the evolution equations for the amplitude and phase for acoustic oscillations. The model captures abrupt and continuous transitions to thermoacoustic instability observed in disparate combustors. We also discover that continuous and abrupt transitions happen through paradigmatic continuous and explosive synchronization, respectively. Importantly, our approach explains spatiotemporal synchronization and pattern formation underlying the transition to thermoacoustic instability. The versatility of the model in capturing different types of transitions suggests promising prospects for its extension to encompass a wide range of fluid dynamics phenomena.

   @article{10.1063/5.0187980,
     author = {Singh, Samarjeet and Roy, Amitesh and Dhadphale, Jayesh M. and Chaudhuri, Swetaprovo and Sujith, R. I.},
     title = {Continuous and explosive synchronization transition in turbulent combustors},
     journal = {AIP Advances},
     volume = {14},
     number = {6},
     pages = {065106},
     year = {2024},
     month = jun,
     issn = {2158-3226},
     doi = {10.1063/5.0187980},
     url = {https://doi.org/10.1063/5.0187980},
     eprint = {https://pubs.aip.org/aip/adv/article-pdf/doi/10.1063/5.0187980/19977626/065106_1_5.0187980.pdf},
   }

3. US patent

   

   Device and method to predict the onset of oscillatory instabilities in systems with turbulent flow

   Dhadphale Jayesh, Aguilar Ruiz Eustaquio, Rajasekharan Unni Vishnu, and 2 more authors

   Jul 2024

   Abs Bib

   Disclosed are devices and methods of detecting and mitigating oscillatory instabilities in systems with turbulent flow, such as thermoacoustic, aeroacoustic or aeroelastic equipment. The system includes a sensor array for measuring one or more parameters of an operating equipment S, and an analysis and prediction unit. The analysis and prediction unit is configured to estimate a state tensor to identify a state of the equipment indicating stable operation or impending oscillatory instability. The system further includes an actuator array configured to implement a control action to promote stable operation of the equipment. Methods for robust prediction of the state of stability are also disclosed. A neural ordinary differential equation (ODE) method of predicting stability or instability is disclosed, involving forming a neural network that incorporates an equation characteristic of the operational state. The invention further discloses a hybrid convolutional neural network based prediction method for stability.

   @patent{US12025528B2,
     author = {Jayesh, Dhadphale and Eustaquio, Aguilar Ruiz and Vishnu, Rajasekharan Unni and Abhishek, Saha and Nair, Sujith Indusekharan},
     title = {Device and method to predict the onset of oscillatory instabilities in systems with turbulent flow},
     journal = {USPTO},
     year = {2024},
     month = jul,
     url = {https://patents.google.com/patent/US12025528B2/en},
     eprint = {https://patentimages.storage.googleapis.com/98/e7/5c/cccfd7d892e967/US12025528.pdf},
   }

2023

1. Chaos

   

   Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system

   Samarjeet Singh, Ankit Kumar Dutta, Jayesh M. Dhadphale, and 3 more authors

   Chaos: An Interdisciplinary Journal of Nonlinear Science, Apr 2023

   Abs DOI Bib

   

   Open-loop control is known to be an effective strategy for controlling self-excited periodic oscillations, known as thermoacoustic instability, in turbulent combustors. Here, we present experimental observations and a synchronization model for the suppression of thermoacoustic instability achieved by rotating the otherwise static swirler in a lab-scale turbulent combustor. Starting with the state of thermoacoustic instability in the combustor, we find that a progressive increase in the swirler rotation rate leads to a transition from the state of limit cycle oscillations to the low-amplitude aperiodic oscillations through a state of intermittency. To model such a transition while also quantifying the underlying synchronization characteristics, we extend the model of Dutta et al. [Phys. Rev. E 99, 032215 (2019)] by introducing a feedback between the ensemble of phase oscillators and the acoustic. The coupling strength in the model is determined by considering the effect of the acoustic and swirl frequencies. The link between the model and experimental results is quantitatively established by implementing an optimization algorithm for model parameter estimation. We show that the model is capable of replicating the bifurcation characteristics, nonlinear features of time series, probability density function, and amplitude spectrum of acoustic pressure and heat release rate fluctuations at various dynamical states observed during the transition to the state of suppression. Most importantly, we discuss the flame dynamics and demonstrate that the model without any spatial inputs qualitatively captures the characteristics of the spatiotemporal synchronization between the local heat release rate fluctuations and the acoustic pressure that underpins a transition to the state of suppression. As a result, the model emerges as a powerful tool for explaining and controlling instabilities in thermoacoustic and other extended fluid dynamical systems, where spatiotemporal interactions lead to rich dynamical phenomena.

   @article{10.1063/5.0136385,
     author = {Singh, Samarjeet and Kumar Dutta, Ankit and Dhadphale, Jayesh M. and Roy, Amitesh and Sujith, R. I. and Chaudhuri, Swetaprovo},
     title = {Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system},
     journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
     volume = {33},
     number = {4},
     pages = {043104},
     year = {2023},
     month = apr,
     issn = {1054-1500},
     doi = {10.1063/5.0136385},
     url = {https://doi.org/10.1063/5.0136385},
     eprint = {https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0136385/16825559/043104_1_5.0136385.pdf},
   }

2. Chaos

   

   Mitigation of limit cycle oscillations in a turbulent thermoacoustic system via delayed acoustic self-feedback

   Ankit Sahay, Abhishek Kushwaha, Samadhan A. Pawar, and 3 more authors

   Chaos: An Interdisciplinary Journal of Nonlinear Science, Apr 2023

   Abs DOI Bib

   

   We report the occurrence of amplitude death (AD) of limit cycle oscillations in a bluff body stabilized turbulent combustor through delayed acoustic self-feedback. Such feedback control is achieved by coupling the acoustic field of the combustor to itself through a single coupling tube attached near the anti-node position of the acoustic standing wave. We observe that the amplitude and dominant frequency of the limit cycle oscillations gradually decrease as the length of the coupling tube is increased. Complete suppression (AD) of these oscillations is observed when the length of the coupling tube is nearly 3 / 8 times the wavelength of the fundamental acoustic mode of the combustor. Meanwhile, as we approach this state of amplitude death, the dynamical behavior of acoustic pressure changes from the state of limit cycle oscillations to low-amplitude chaotic oscillations via intermittency. We also study the change in the nature of the coupling between the unsteady flame dynamics and the acoustic field as the length of the coupling tube is increased. We find that the temporal synchrony between these oscillations changes from the state of synchronized periodicity to desynchronized aperiodicity through intermittent synchronization. Furthermore, we reveal that the application of delayed acoustic self-feedback with optimum feedback parameters completely disrupts the positive feedback loop between hydrodynamic, acoustic, and heat release rate fluctuations present in the combustor during thermoacoustic instability, thus mitigating instability. We anticipate this method to be a viable and cost-effective option to mitigate thermoacoustic oscillations in turbulent combustion systems used in practical propulsion and power systems.

   @article{10.1063/5.0129512,
     author = {Sahay, Ankit and Kushwaha, Abhishek and Pawar, Samadhan A. and P. R., Midhun and Dhadphale, Jayesh M. and Sujith, R. I.},
     title = {Mitigation of limit cycle oscillations in a turbulent thermoacoustic system via delayed acoustic self-feedback},
     journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
     volume = {33},
     number = {4},
     pages = {043118},
     year = {2023},
     month = apr,
     issn = {1054-1500},
     doi = {10.1063/5.0129512},
     url = {https://doi.org/10.1063/5.0129512},
     eprint = {https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0129512/16822914/043118_1_5.0129512.pdf},
   }

2022

1. Chaos

   

   Neural ODE to model and prognose thermoacoustic instability

   Jayesh M. Dhadphale, Vishnu R. Unni, Abhishek Saha, and 1 more author

   Chaos: An Interdisciplinary Journal of Nonlinear Science, Jan 2022

   Abs DOI Bib

   

   Thermoacoustic instability in a reacting flow field is characterized by high amplitude pressure fluctuations driven by a positive coupling between the unsteady heat release rate and the acoustic field of the combustor. In a turbulent flow, the transition of a thermoacoustic system from a state of chaos to periodic oscillations occurs via a state of intermittency. During the transition to periodic oscillations, the unsteady heat release rate synchronizes with the acoustic pressure fluctuations. Thermoacoustic systems are traditionally modeled by coupling the model for the heat source and the acoustic subsystem, each estimated independently. The response of the unsteady heat source, i.e., the flame, to acoustic fluctuations is characterized by introducing unsteady external forcing. The forced response of the flame need not be the same in the presence of an acoustic field due to their nonlinear coupling. Instead of characterizing individual subsystems, we introduce a neural ordinary differential equation (neural ODE) framework to model the thermoacoustic system as a whole. The neural ODE model for the thermoacoustic system uses time series of the heat release rate and the pressure fluctuations, measured simultaneously without introducing any external perturbations, to model their coupled interaction. Furthermore, we use the parameters of neural ODE to define an anomaly measure that represents the proximity of system dynamics to limit cycle oscillations and thus provide an early warning signal for the onset of thermoacoustic instability.

   @article{10.1063/5.0064215,
     author = {Dhadphale, Jayesh M. and Unni, Vishnu R. and Saha, Abhishek and Sujith, R. I.},
     title = {Neural ODE to model and prognose thermoacoustic instability},
     journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
     volume = {32},
     number = {1},
     pages = {013131},
     year = {2022},
     month = jan,
     issn = {1054-1500},
     doi = {10.1063/5.0064215},
     url = {https://doi.org/10.1063/5.0064215},
     eprint = {https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0064215/16453188/013131_1_online.pdf},
   }