Banerjee Ankan, Pavithran Induja, Sujith R I
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Center of Excellence for Studying Critical Transitions in Complex Systems, Indian Institute of Technology Madras, Chennai 600036, India.
Chaos. 2024 Jan 1;34(1). doi: 10.1063/5.0160918.
Real-world complex systems such as the earth's climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWSs) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWSs in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. This is the first experimental study of tipping points in a non-autonomous turbulent thermoacoustic system. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWSs are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. We consider acoustic pressure fluctuations as a potential system variable to perform the analysis. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. Additionally, we show the variation in the warning time to an impending TAI with rates of change of the control parameter. We also investigate the variation in amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws that could be significant in prediction and devising control actions to mitigate TAI.
诸如地球气候、生态系统、股票市场和内燃机等现实世界中的复杂系统容易发生从一种状态到另一种状态的动态转变，并带来灾难性后果。此类系统的状态变量通常呈现非周期性波动，本质上要么是混沌的，要么是随机的。通常，描述系统的参数会随时间变化，呈现出时间依赖性。受这些影响的制约，很难对即将发生的临界转变发出预警，因为这些影响会干扰转变的前兆信号。因此，在这类复杂系统中迫切需要高效且可靠的早期预警信号（EWS）。基于这一事实，在本工作中，我们在非自治湍流热声系统的背景下分析各种EWS。特别是，我们研究不同EWS在预测热声不稳定性（TAI） onset方面的功效及其相对于控制参数变化率的可靠性。这是对非自治湍流热声系统中临界点的首次实验研究。我们将雷诺数（Re）视为控制参数，它以有限速率随时间线性变化。所考虑的EWS源自系统变量的临界减速、频谱特性和分形特征。TAI状态与大幅声压振荡相关，这可能导致热声系统崩溃。我们将声压波动视为一个潜在的系统变量来进行分析。我们的分析表明，无论控制参数的变化率如何，赫斯特指数和自相关系数的方差都能提前很好地预警即将发生的转变，并且比其他EWS度量更可靠。此外，我们展示了随着控制参数变化率，对即将发生的TAI的预警时间的变化。我们还研究了声压振荡最显著模式的振幅随赫斯特指数的变化。这种变化导致了标度律，这在预测和设计控制行动以减轻TAI方面可能具有重要意义。
