## 1 Introduction  
During train travel, the passengers's comfort can be affected by several factors, some due to the movement of the railway vehicle, such as vibrations and noise, while others come from the environment conditions inside the vehicle, e.g., temperature, humidity and air speed, lighting, or the interior fittings and decor (for instance, the shape and placement of chairs) [1, 2, 3, 4]. All of these fall under the category of physical factors, to which social factors (interaction with the other passengers, management of services inside the vehicle, general organization of the transport service) and time factors (integration time, travel time) can be added [5]. It is a difficult task to establish an assessment method for the passengers' comfort to include all these factors simultaneously because it would involve a great amount of test data, which incurs a very high cost [1, 2]. Moreover, more preliminary stages would be required, as in associating one or more criteria with each factor, defining a comfort index for each criterion and partnering these indices with a comfort scale and combining these comfort indices to define a global indicator [5]. Among all factors affecting the passengers' comfort, vibrations are paid a special attention because their effect upon the human body is very important [6, 7, 8]. As a function of vibrations' intensity, direction and frequency value they occur at, as well as the exposure time, vibrations can perturb the comfort and the ability of passengers to conduct certain sedentary activities and can even affect their health condition. Generally, the vibrations of the railway vehicle are considered to be the main factor in determining the ride comfort [1; 2; 3; 9; 10]. Ride comfort counts as one of the criteria for evaluating the dynamic behavior of railway vehicles [1; 11]. It is used to describe the degree of the passengers' comfort from the perspective of mechanical vibrations, taking into account the physiological characteristics of the human body [12]. In practice, it is necessary to have a method to assess the passengers' comfort state over vibrations during running of the railway vehicle. A difficult situation happens in this case--different circumstances claim different assessment methods, and therefore, it is impossible to set up a universally applicable method [13]. One of the explanations is that each country has variable characteristics of the vibrations of railway vehicles, due to the conditions in vehicles and tracks or exploitation conditions [1]. Different assessment methods for the ride comfort have been independently developed in time, with a selective applicability depending on the traffic type, namely urban, suburban, underground, long distance, etc. To evaluate the ride comfort of the railway vehicles, methods based on ISO 2631 [14; 15; 16; 17; 18; 19] and [PERSON]'s [20; 21], known as [PERSON]'s method or _Wz_ ride index method are frequently used. The ride index _Wz_ method was brought in Germany by [PERSON] [20; 21] in the mid-20 th century, and it represents the most known assessment method for the ride comfort and ride quality of the railway vehicles [22]. The method advanced by [PERSON] introduces the concept of ride comfort index (_Wz_ ride comfort index). The International Union of Railways (UIC) and the European Committee for Standardization (CEN), along with ISO, have established through the European Rail Research Institute (ERRI) [23; 24] standards of ride comfort assessment of the railway vehicles, based on ISO 2631, respectively, the UIC 513R [25] leaflet, the standards EN 12299 [26] and ISO 10056 [27]. As seen earlier, it is rather difficult to establish a universally applicable method to assess the ride comfort, so it would be quite useful to set up a relation among the ride comfort indices derived from different methods in order to convert one index to another immediately, as well as to be aware of the strengths and limitations of each assessment method.