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为了进行轨道电路暂态分析,采用同伦分析法对轨道电路传输线方程求解。将Caputo分数阶导数作为线性算子,建立轨道电路传输线方程的高阶形变方程,求解得轨道电路传输线方程三阶近似解。根据不同的道床电阻确定其收敛区域,对轨道电路电压波暂态响应进行仿真分析。仿真结果表明,将分数阶导数作为线性算子的同伦分析法可以准确分析轨道电路传输线电压波传输特征和过程,为轨道电路暂态分析提供了一种新的方法。
For the transient analysis of the track circuit, the homotopy analysis method is used to solve the transmission line equation of the track circuit. Using Caputo fractional derivative as a linear operator, a higher-order deformation equation of the transmission line equation of the track circuit is established, and a third-order approximate solution of the transmission line equation of the tracking circuit is solved. According to the different resistance of the ballast bed, the convergence area is determined, and the transient response of the track voltage wave is simulated and analyzed. The simulation results show that the homotopy analysis method using fractional derivative as a linear operator can accurately analyze the transmission characteristics and process of the voltage wave in the transmission line of the track circuit and provide a new method for the transient analysis of the track circuit.