非自治湍流反应流系统中临界转变的早期预警：有效性、可靠性与预警时间
Early warnings of tipping in a non-autonomous turbulent reactive flow system: efficacy, reliability, and warning times
AI总结：
本文针对非自治湍流热声系统，系统评估多种早期预警信号对热声不稳定性（TAI）的预测效能与可靠性，发现Hurst指数和自相关系数方差能提前可靠预警，并揭示了声压模态振幅与Hurst指数间的标度律，为预测和控制TAI提供依据。
摘要：
现实世界中的复杂系统，如气候、生态系统、股票市场和燃烧发动机，容易发生从一个状态到另一个状态的动力学转变，并带来灾难性后果。这类系统的状态变量通常表现出非周期性波动，其本质既可能是混沌的，也可能是随机的。通常，描述系统的参数会随时间变化，表现出时间依赖性。受这些效应的制约，人们很难对即将到来的临界转变获得预警，因为这些效应会污染转变的前兆信号。因此，在此类复杂系统中，对高效且可靠的早期预警信号（EWS）的需求十分迫切。基于这一事实，在本工作中，我们在一个非自治湍流热声系统的背景下分析了各种早期预警信号。特别是，我们研究了不同早期预警信号在预测热声不稳定性（TAI）发生方面的有效性，以及它们相对于控制参数变化速率的可靠性。我们选取雷诺数（Re）作为控制参数，并以有限速率随时间线性变化。所考虑的早期预警信号来源于系统变量的临界慢化、谱特性和分形特征。热声不稳定性状态与大振幅声压振荡相关，这种振荡可能导致热声系统失效。我们的分析表明，无论控制参数的变化速率如何，Hurst指数和自相关系数的方差都能提前很久对即将到来的转变发出预警，并且比其他早期预警信号度量更为可靠。我们还研究了声压振荡中最显著模态的振幅随Hurst指数的变化。这种变化导致了标度律的出现，这些标度律在预测和制定控制措施以缓解热声不稳定性方面可能具有重要意义。
英文摘要：
Real-world complex systems such as the 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 (EWS) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWS 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. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWS 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. 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. We also investigate the variation of amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws which could be significant in prediction and devising control actions to mitigate TAI.
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