A spectral evolution model for track geometric degradation in train–track long-term dynamics

Abstract

ABSTRACTIn this work, a new insight is put forward to characterise the evolution of track irregularities from viewpoint of spectral analysis. The main novelty lies in a proposal of regarding the geometric deterioration of track irregularities equivalently as the evolution of power spectral densities (PSD), and consequently, the stationarity of track irregularities and a robust dynamic assessment can be guaranteed. Besides a systematic framework integrating the train–track dynamic model, track irregularity PSD evolution model and the Pseudo-excitation method is developed to predict the uncertain responses of system components long-termly. In the PSD evolution method developed, we have departed from the conventional strategies trying to characterise the evolution of time-domain track irregularities from perspectives of physical-mechanical methods and elastic-plastic deformation. Instead, a statistical and mathematical model is proposed to randomly estimate the evolution of track irregularities with a guarantee of the stationarity of track geometries. In this model, the deterioration of time domain track irregularities is equivalently transformed as the evolution of PSD at frequency domain. A mathematical relationship between dynamic loads and PSD evolutions is constructed, in which the model parameters are defined by the statistical results and a Levenberg–Marquard iterative formula. Apart from predicting the long-term evolution of track irregularity amplitude and the track quality index, the PSD evolution model can be perfectly united with the train–track interaction model and a pseudo-excitation method to reveal the long-term evolution of system behaviours no matter on response amplitudes or on their characteristic frequencies against different confidence intervals.