## 2 State of the Art  
Rail corrugation has been studied extensively over the past decades, and the knowledge on its formation and characteristics has increased. However, the phenomenon of rail corrugation is still not fully understood and additional investigations are needed to address the open questions left in the literature. Some of these open questions are, for example: what determines the track sections where corrugation develops and what complex characteristics of the vehicle/track interaction determine its wavelength and amplitude. Since corrugation refers to a wide variety of defects caused by many different factors, a universal definition and classification have not been assigned yet. In [1; 2; 3; 4] the authors attempt a rail corrugation classification based on the root cause and define six categories: pinned-pinned resonance (or roaring rails), rutting, heavy load, light rails, special track form and other P2 resonance. [PERSON] was the first to describe rail corrugation as a wavelength-fixing mechanism that results from the vehicle/track dynamic interaction or as a damage mechanism that is caused by plastic deformation, rolling fatigue or wear. Another common classification of rail corrugation found in the literature is based on the wavelength range: short pitch (20-100 mm) and long pitch (>100 mm) [5]. In the German language rail corrugation occurring in a tangent track is called \"Riffel\" (translated as ripple) and in a curved track \"Schlupfwellen\" (translated as slip waves). These two definitions can be considered similar to roaring rails and rutting, respectively [6]. Although the literature is not uniform in its definition and classification, many publications can be found about the formation and development of rail corrugation. In [7], rail corrugation found on railway networks around the world is described with causes and treatments. The influencing track characteristics are also analysed: rail material, rail support, rail surface irregularities, track stiffness, etc. In [8], the formation of short pitch rail corrugation, found on a metro line, is analysed with experiments, and two mathematical models are formulated to evaluate the appropriate possible remedies. In [9], the causes of rail corrugation development and the corresponding control measures are analysed using a finite element model of the track structure and the dynamic model of the vehicle/track interaction. Based on these analyses and investigations, it is found that the formation and growth of rail corrugation are related to the characteristics of the interaction between the vehicle and the track. Metro lines and sharp curves are generally more prone to short pitch rail corrugation [10; 11; 12]. However, corrugation has also been widely observed on conventional and high-speed lines [13; 14]. The vehicle/track interaction is the main focus of the analysis of rail corrugation: in [15], the effect of rail corrugation on the dynamic behaviour of the vehicle is analysed with simulations. A [PERSON]'s non-Hertzian contact model is modified and used to calculate the frictional work density on the contact area and the rail surface wear depth is determined. In [16], an extended Hertzian contact model is used to generate a numerical wear profile history and to study the influence of contact-induced wear filtering on short pitch corrugation growth. A modified [PERSON]'s non-Hertzian non-steady three-dimensional wheel/rail contact model is also used in [17] to calculate wear for various rail corrugation wavelengths and amplitudes. In addition to the formation, evolution and countermeasure of rail corrugation, and besides the influence of the dynamic interaction of wheels and rails, another important topic in the literature is how to detect rail corrugation based on the dynamic response of the vehicle.