Stochastic dynamics and first passage analysis of iced transmission lines via path integration method

The mechanism of stochastic factors in wind load on iced transmission line galloping has attracted widespread attention. In this paper, the random part of wind load is simulated by Gaussian white noise, and a galloping model of the iced transmission line excited by stochastic wind is established. The path integration method based on the Gauss–Legendre formula and short-time approximation is used to solve the steady-state probability density function of the system and the evolution of the transient probability density. The resonance response of the system is considered when the fluctuating wind acts. Meanwhile, through path integration, the stability of galloping motion is evaluated based on the first passage theory. Comparing with the Monte Carlo simulation, the effectiveness of the proposed method is verified. It turns out that the large external excitation intensity and the small natural frequency are not conducive to the stability of iced transmission line galloping.