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

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Abstract

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.

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Funding

This research was supported by the National Natural Science Foundation of China (Grant NOs. 12372034, 12072261).

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, **’an, 710072, Shaanxi, People’s Republic of China

    Yuanyuan Bai, Wei Xu & Wenting Zhang

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  1. Yuanyuan Bai
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  2. Wei Xu
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  3. Wenting Zhang
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Correspondence to Wei Xu.

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Bai, Y., Xu, W. & Zhang, W. Reliability analysis of iced transmission lines under Poisson white noise excitation via path integration method. Nonlinear Dyn 112, 12019–12033 (2024). https://doi.org/10.1007/s11071-024-09662-0

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