Stochastic nonlinear system modelling and parametric oscillation response characteristics of gas turbines

Gas turbines, as highly complex thermal systems, exhibit significant nonlinearity and stochastic coupling in process control. Under closed-loop automatic speed regulation, persistent parametric oscillations may arise, posing serious threats to system reliability and safety. Aiming to reveal the stochastic response characteristics of parametric oscillations in gas turbines, this paper proposes a novel framework for analyzing the evolution law of parametric oscillation and multi-source stochastic excitations based on stochastic dynamics model, which is derived from thermodynamic equations and verified by measurement data. The internal stochastic excitation is determined by information entropy, while the form of the stochastic process of the external stochastic excitation is identified through data-driven reverse identification. The PDF evolution law of parametric oscillation is studied for different excitation forms, and the bifurcation behavior and sensitivity analysis of them are carried out. Under typical operating conditions, the synergistic effect of internal and external stochastic excitations reduces parametric oscillation amplitude by approximately 31 % compared to internal excitation alone. Moreover, the originally tri-modal distribution evolves into a unimodal pattern, revealing the transition trend of parametric oscillation behavior in gas turbines. These findings offer an effective approach to analyze parametric oscillation.