A multivariate statistical representation of railway track irregularities using ARMA models

Railway track irregularities occur naturally from service operations and are characterised by deviations of the track relative to its nominal geometry. Since the dynamic behaviour of a rail vehicle depends on the geometry of the track, studying irregularities is essential for safety, comfort, and maintenance. Conventionally, an irregularity is synthesised from a univariate stochastic process, which is a suitable way to represent excitations occurring in one dimension. However, most three-dimensional analyses of rail vehicles require a multivariate description of the irregularities. Therefore, synthesising multiple variables using univariate processes neglects possible relationships among them. This work addresses track irregularities from a multivariate series perspective to model the spatial autocorrelation of each irregularity and their spatial correlation with other types of irregularities. Several multivariate models with different complexity levels are estimated from the irregularities of a 3.6-km long straight track segment. A comparison among models shows that they should be selected based on not only statistical information criteria, but also their ability to reproduce relevant physical characteristics. Finally, a case study shows that the vehicle response to irregularities that are synthesised using the proposed multivariate process matches the response to measured data better than irregularities synthesised using independent univariate processes.