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  • 1
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2022
    In:  Nonlinear Dynamics Vol. 108, No. 2 ( 2022-04), p. 1525-1545
    In: Nonlinear Dynamics, Springer Science and Business Media LLC, Vol. 108, No. 2 ( 2022-04), p. 1525-1545
    Abstract: A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz, the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot-based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. Finally, we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor.
    Type of Medium: Online Resource
    ISSN: 0924-090X , 1573-269X
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2022
    detail.hit.zdb_id: 2012600-1
    SSG: 11
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  • 2
    Online Resource
    Online Resource
    ASME International ; 2021
    In:  Journal of Engineering for Gas Turbines and Power Vol. 143, No. 12 ( 2021-12-01)
    In: Journal of Engineering for Gas Turbines and Power, ASME International, Vol. 143, No. 12 ( 2021-12-01)
    Abstract: The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibrational loads. Estimating the amplitude of the limit cycle oscillations that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the limit cycle oscillations. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using “spectral measures,” which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.
    Type of Medium: Online Resource
    ISSN: 0742-4795 , 1528-8919
    Language: English
    Publisher: ASME International
    Publication Date: 2021
    detail.hit.zdb_id: 2010437-6
    detail.hit.zdb_id: 165371-4
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  • 3
    Online Resource
    Online Resource
    AIP Publishing ; 2021
    In:  Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 31, No. 1 ( 2021-01-01)
    In: Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP Publishing, Vol. 31, No. 1 ( 2021-01-01)
    Abstract: Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of the control parameter greatly affects the performance of early warning signals (EWS) for such critical transitions. We study the impact of variation of the control parameter with a finite rate on the performance of EWS for critical transitions in a thermoacoustic system (a horizontal Rijke tube) exhibiting subcritical Hopf bifurcation. There is a growing interest in developing early warning signals for tipping in real systems. First, we explore the efficacy of early warning signals based on critical slowing down and fractal characteristics. From this study, lag-1 autocorrelation (AC) and Hurst exponent (H) are found to be good measures to predict the transition well before the tipping point. The warning time, obtained using AC and H, reduces with an increase in the rate of change of the control parameter following an inverse power law relation. Hence, for very fast rates, the warning time may be too short to perform any control action. Furthermore, we report the observation of a hyperexponential scaling relation between the AC and the variance of fluctuations during such a dynamic Hopf bifurcation. We construct a theoretical model for noisy Hopf bifurcation wherein the control parameter is continuously varied at different rates to study the effect of rate of change of the parameter on EWS. Similar results, including the hyperexponential scaling, are observed in the model as well.
    Type of Medium: Online Resource
    ISSN: 1054-1500 , 1089-7682
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2021
    detail.hit.zdb_id: 1472677-4
    SSG: 11
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  • 4
    Online Resource
    Online Resource
    AIP Publishing ; 2023
    In:  Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 33, No. 8 ( 2023-08-01)
    In: Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP Publishing, Vol. 33, No. 8 ( 2023-08-01)
    Abstract: Abrupt changes in the state of a system are often undesirable in natural and human-made systems. Such transitions occurring due to fast variations of system parameters are called rate-induced tipping (R-tipping). While a quasi-steady or sufficiently slow variation of a parameter does not result in tipping, a continuous variation of the parameter at a rate greater than a critical rate results in tipping. Such R-tipping would be catastrophic in real-world systems. We experimentally demonstrate R-tipping in a real-world complex system and decipher its mechanism. There is a critical rate of change of parameter above which the system undergoes tipping. We discover that there is another system variable varying simultaneously at a timescale different from that of the driver (control parameter). The competition between the effects of processes at these two timescales determines if and when tipping occurs. Motivated by the experiments, we use a nonlinear oscillator model, exhibiting Hopf bifurcation, to generalize such type of tipping to complex systems where multiple comparable timescales compete to determine the dynamics. We also explain the advanced onset of tipping, which reveals that the safe operating space of the system reduces with the increase in the rate of variations of parameters.
    Type of Medium: Online Resource
    ISSN: 1054-1500 , 1089-7682
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2023
    detail.hit.zdb_id: 1472677-4
    SSG: 11
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  • 5
    Online Resource
    Online Resource
    AIP Publishing ; 2019
    In:  Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 29, No. 10 ( 2019-10-01)
    In: Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP Publishing, Vol. 29, No. 10 ( 2019-10-01)
    Abstract: Liquid rockets are prone to large amplitude oscillations, commonly referred to as thermoacoustic instability. This phenomenon causes unavoidable developmental setbacks and poses a stern challenge to accomplish the mission objectives. Thermoacoustic instability arises due to the nonlinear interaction between the acoustic and the reactive flow subsystems in the combustion chamber. In this paper, we adopt tools from dynamical systems and complex systems theory to understand the dynamical transitions from a state of stable operation to thermoacoustic instability in a self-excited model multielement liquid rocket combustor based on an oxidizer rich staged combustion cycle. We observe that this transition to thermoacoustic instability occurs through a sequence of bursts of large amplitude periodic oscillations. Furthermore, we show that the acoustic pressure oscillations in the combustor pertain to different dynamical states. In contrast to a simple limit cycle oscillation, we show that the system dynamics switches between period-3 and period-4 oscillations during the state of thermoacoustic instability. We show several measures based on recurrence quantification analysis and multifractal theory, which can diagnose the dynamical transitions occurring in the system. We find that these measures are more robust than the existing measures in distinguishing the dynamical state of a rocket engine. Furthermore, these measures can be used to validate models and computational fluid dynamics simulations, aiming to characterize the performance and stability of rockets.
    Type of Medium: Online Resource
    ISSN: 1054-1500 , 1089-7682
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2019
    detail.hit.zdb_id: 1472677-4
    SSG: 11
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  • 6
    Online Resource
    Online Resource
    AIP Publishing ; 2020
    In:  Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 30, No. 6 ( 2020-06-01)
    In: Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP Publishing, Vol. 30, No. 6 ( 2020-06-01)
    Abstract: Many complex systems exhibit periodic oscillations comprising slow–fast timescales. In such slow–fast systems, the slow and fast timescales compete to determine the dynamics. In this study, we perform a recurrence analysis on simulated signals from paradigmatic model systems as well as signals obtained from experiments, each of which exhibit slow–fast oscillations. We find that slow–fast systems exhibit characteristic patterns along the diagonal lines in the corresponding recurrence plot (RP). We discern that the hairpin trajectories in the phase space lead to the formation of line segments perpendicular to the diagonal line in the RP for a periodic signal. Next, we compute the recurrence networks (RNs) of these slow–fast systems and uncover that they contain additional features such as clustering and protrusions on top of the closed-ring structure. We show that slow–fast systems and single timescale systems can be distinguished by computing the distance between consecutive state points on the phase space trajectory and the degree of the nodes in the RNs. Such a recurrence analysis substantially strengthens our understanding of slow–fast systems, which do not have any accepted functional forms.
    Type of Medium: Online Resource
    ISSN: 1054-1500 , 1089-7682
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2020
    detail.hit.zdb_id: 1472677-4
    SSG: 11
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  • 7
    Online Resource
    Online Resource
    Proceedings of the National Academy of Sciences ; 2021
    In:  Proceedings of the National Academy of Sciences Vol. 118, No. 39 ( 2021-09-28)
    In: Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, Vol. 118, No. 39 ( 2021-09-28)
    Abstract: Many natural systems exhibit tipping points where slowly changing environmental conditions spark a sudden shift to a new and sometimes very different state. As the tipping point is approached, the dynamics of complex and varied systems simplify down to a limited number of possible “normal forms” that determine qualitative aspects of the new state that lies beyond the tipping point, such as whether it will oscillate or be stable. In several of those forms, indicators like increasing lag-1 autocorrelation and variance provide generic early warning signals (EWS) of the tipping point by detecting how dynamics slow down near the transition. But they do not predict the nature of the new state. Here we develop a deep learning algorithm that provides EWS in systems it was not explicitly trained on, by exploiting information about normal forms and scaling behavior of dynamics near tipping points that are common to many dynamical systems. The algorithm provides EWS in 268 empirical and model time series from ecology, thermoacoustics, climatology, and epidemiology with much greater sensitivity and specificity than generic EWS. It can also predict the normal form that characterizes the oncoming tipping point, thus providing qualitative information on certain aspects of the new state. Such approaches can help humans better prepare for, or avoid, undesirable state transitions. The algorithm also illustrates how a universe of possible models can be mined to recognize naturally occurring tipping points.
    Type of Medium: Online Resource
    ISSN: 0027-8424 , 1091-6490
    RVK:
    RVK:
    Language: English
    Publisher: Proceedings of the National Academy of Sciences
    Publication Date: 2021
    detail.hit.zdb_id: 209104-5
    detail.hit.zdb_id: 1461794-8
    SSG: 11
    SSG: 12
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  • 8
    Online Resource
    Online Resource
    American Physical Society (APS) ; 2023
    In:  Physical Review E Vol. 107, No. 2 ( 2023-2-28)
    In: Physical Review E, American Physical Society (APS), Vol. 107, No. 2 ( 2023-2-28)
    Type of Medium: Online Resource
    ISSN: 2470-0045 , 2470-0053
    RVK:
    Language: English
    Publisher: American Physical Society (APS)
    Publication Date: 2023
    detail.hit.zdb_id: 2844562-4
    SSG: 12
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  • 9
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2021
    In:  The European Physical Journal Special Topics Vol. 230, No. 16-17 ( 2021-10), p. 3411-3432
    In: The European Physical Journal Special Topics, Springer Science and Business Media LLC, Vol. 230, No. 16-17 ( 2021-10), p. 3411-3432
    Type of Medium: Online Resource
    ISSN: 1951-6355 , 1951-6401
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2021
    detail.hit.zdb_id: 2267176-6
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  • 10
    Online Resource
    Online Resource
    AIP Publishing ; 2021
    In:  Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 31, No. 9 ( 2021-09-01)
    In: Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP Publishing, Vol. 31, No. 9 ( 2021-09-01)
    Abstract: Many fluid dynamic systems exhibit undesirable oscillatory instabilities due to positive feedback between fluctuations in their different subsystems. Thermoacoustic instability, aeroacoustic instability, and aeroelastic instability are some examples. When the fluid flow in the system is turbulent, the approach to such oscillatory instabilities occurs through a universal route characterized by a dynamical regime known as intermittency. In this paper, we extract the peculiar pattern of phase space attractors during the regime of intermittency by constructing recurrence networks corresponding to the phase space topology. We further train a convolutional neural network to classify the periodic and aperiodic structures in the recurrence networks and define a measure that indicates the proximity of the dynamical state to the onset of oscillatory instability. We show that this measure can predict the onset of oscillatory instabilities in three different fluid dynamic systems governed by different physical phenomena.
    Type of Medium: Online Resource
    ISSN: 1054-1500 , 1089-7682
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2021
    detail.hit.zdb_id: 1472677-4
    SSG: 11
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