Reliability analysis of iced transmission lines under Poisson white noise excitation via path integration method

• Published in: Nonlinear dynamics Vol. 112; no. 14; pp. 12019 - 12033
• Main Authors: Bai, Yuanyuan, Xu, Wei, Zhang, Wenting
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.07.2024; Springer Nature B.V
• Subjects: Approximation; Automotive Engineering; Classical Mechanics; Control; Dynamical Systems; Engineering; Excitation; Mechanical Engineering; Monte Carlo simulation; Original Paper; Probability density functions; Probability theory; Random vibration; Randomness; Reliability analysis; Runge-Kutta method; System reliability; Transition probabilities; Transmission lines; Vibration; White noise; Wind effects; Probability density; Path integration method; Reliability; Poisson white noise; Iced transmission line; Mean first passage time
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-09662-0

The stochastic fluctuating factors caused by wind gust can change the dynamic behavior of iced transmission lines, which has been widely concerned by scholars. The stochastic impulsive disturbance in nature is simulated as Poisson white noise in this paper. For the path integration method under Poisson white noise excitation, a function that considers the randomness of pulses occurring at each time interval is used as an approximation of the short-time transition probability density. The Chapman–Kolmogorov equation with variable substitution is numerically solved using the backward Runge–Kutta method and the linear interpolation. Thus the evolution of probability density function of the system is worked out. After that, based on the results obtained by the path integration method, three indexes are got to measure the reliability of the system through the reliability theory. The effects of pulse sparsity, wind gust intensity and security domain scope on system reliability are revealed by analyzing the reliability function, first passage probability density, and mean first passage time. The accuracy of the path integration method is verified by comparing the results with the Monte Carlo results.