Identification of the power spectral density of vertical track irregularities based on inverse pseudo-excitation method and symplectic mathematical method

A new method is proposed to identify the power spectral density (PSD) of vertical track irregularities. A vertical coupled vehicle-track dynamic model is established. In this model, a vehicle is simplified as a multi-rigid-body model with 10 degrees of freedom, and a track is treated as a three-layer discrete elastic support model in which the rail, which is supported discretely by the sleepers, is described by Bernoulli-Euler beam theory. The vehicle and track models are coupled by a linearized Hertzian spring. The axle box acceleration is selected as the measurement data, and the stationary PSD of the axle box acceleration is simply transformed into its displacement PSD. The PSD of the vertical track irregularities is identified using a combination of the inverse pseudo-excitation method and the symplectic mathematical method. The accuracy of the proposed method is investigated for the different measurement noise levels, vehicle speeds, primary suspension parameters and PSD classes. The numerical results indicate that the proposed method can accurately identify the PSD of the vertical track irregularities.