Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment

Abstract

Thermoacoustic instability has been an important challenge in the development of highperformance combustion systems, as it can have catastrophic consequences. The process of a sudden change in the dynamical behaviour of a thermoacoustic system from a low to a high amplitude thermoacoustic instability, actually entails as a tipping point phenomenon.It has been found that when rate-dependent parameters are considered, a tipping-delay phenomenon may arise, which helps in the control of undesirable states that give rise to thermoacoustic instabilities. This work aims at understanding rate-dependent tipping dynamics of the thermoacoustic system with both time-varying parameters and a non-Gaussian Lévy noise. The latter better describes the severe operating environment of such systems than simpler types of noise. Through numerical simulations, the tipping dynamical behaviour is analysed by considering the rate-dependent parameters coupled with the main parameters of the Lévy noise, including the stability and skewness indices, and the noise intensity. In addition, we investigate the effectiveness of early warning indicators in rate-dependent systems under Lévy noise excitation, and uncover a relationship between warning measures and the rate of change in the parameters. These results inform and enlighten the development and design of power combustion devices, and also provide researchers and engineers with effective ideas to control thermoacoustic instability and the associated tipping dynamics.

Early Warning Signals for Critical Transitions in Sandpile Cellular Automata

“…These results are consistent with our results for the facilitated model. Similar results are presented in [37][38][39], but obtained using fractal analysis methods. The results we obtained for facilitated models are also fully confirmed by the results presented in the papers [40][41][42][43].…”

Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview

“…[61][62][63][64][65][66][67][68][69][70] Stochasticity has several remarkable impacts on the dynamical behaviors of nonlinear systems due to the coupling between random fluctuations and nonlinear factors. In particular, for the nonlinear systems with bistable or multistable characteristics, random fluctuation can cause rich and interesting behaviors, including critical transition, [71][72][73][74] stochastic bifurcation, 75,76 stochastic resonance, [77][78][79] etc. For the deterministic airfoil systems, if random inputs are considered, the nonlinear airfoil systems will exhibit more complex dynamical behaviors and even induce the occurrence of extreme events, which can cause huge deformation or catastrophic damage to the wing structure and seriously affect the reliability and service life of the wing structure.…”

Dynamical analysis of an SDOF quasi‐linear system with jump noises and multitime‐delayed feedback forces

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“…However, excitations in practical applications are not always continuous, and random discontinuous excitations have been observed in practice. [19][20][21][22][23] The existence of stochastic jumps causes discontinuous changes in system states, which cannot be characterized by continuous excitations. In recent years, dynamical systems governed by stochastic discontinuous processes have been the subject of investigations.…”