# Modal Identification of Train Passenger Seats Based on Dynamic Tests and Output-Only Techniques
## 1 Introduction  
Railways are one of the most widely used public transportation systems mainly due to their high safety levels and superior transportation capacity. Additionally, trains have been revealed to be the most sustainable transportation system, as a higher proportion of railway services are operated by electrified trains and, therefore, CO\({}_{2}\) emissions per passenger-kilometre are considerably reduced compared with air or car transportation [1; 2; 3]. Due to the low environmental impact, several governments worldwide are promoting rail use as the main mass transportation system, especially for connecting low and mid-range distances. Following this strategy, passengers have continuously increased since 2013 until the 2020 COVID pandemic. After a historic 4000 billion passenger-kilometres recorded worldwide between 2015 and 2019, the number drastically decreased due to the multiple lockdowns. Nowadays, those numbers are even higher than the pre-pandemic ones [4; 5]. To maintain this continuous rising trend, one must improve the trains' attractivity, which is usually achieved based on three main parameters: safety, comfort, and user conditions [6; 7; 8; 9]. Resulting from the rail motion and wheel-track interaction, seat vibration affects users' comfort and health, limiting the attractiveness performance. As passengers spend most of their time seated, vibration will be transmitted to the user through the interfaces between the human body and the seat structure and vehicle [8]. Thus, evaluating vibration transmission in a rail environment is crucial to assess the vibration frequencies and amplitudes transmitted to the user and evaluate passengers' comfort [9; 10; 11; 12; 13; 14]. Several reference standards and guidelines, such as EN 12299 [8], UIC 513 [15], and ISO 2631-1 [16], define methodologies for the assessment of passengers' comfort based on both simplified and complete measurements. The simplified measurements are exclusively based on the accelerations measured at the floor of the carbody. This approach has the advantage of using a simpler measurement layout. However, the transposition of the acceleration from the floor to the passenger seat level requires the application of dedicated weighting frequency-dependent filters [8; 15; 16]. Otherwise, the complete measurements are based on the acceleration recorded on the passenger-seat-carbody interfaces, such as headrest-neck, arm rest-upper arms, seat-hip, seatback, and floor-seat, as well as on the carbody floor, close to the seat. This approach requires a set of dedicated accelerometers installed on the several sites, which may be difficult. Inclusively, involuntary movements of the passengers can change the positioning of the accelerometers, compromising the quality of the measurements. Nevertheless, if performed adequately, it constitutes a more adequate approach to evaluate the passenger comfort as it considers more realistically the complexity of the seat structure dynamics [17; 18; 19; 20]. Seat dynamics is quantified regarding transmissibility, which verifies seat efficiency in handling vibration discomfort. Train seats are crucial to decrease vibration transmission from the floor to the user. Together, the seat and human body constitute a coupled complex dynamic system [14; 21; 22; 23]. A significant discrepancy can be observed when comparing the transmissibility of subjects with identical characteristics, including identical mass. Moreover, the human body has its own natural resonance frequencies that may lead to physiological responses when matched. The range between 5 and 10 Hz leads to resonance in the chest and abdominal region, and a higher frequency range, comprehended between 20 and 30 Hz, affects the head and neck muscles. Lastly, in the interval between 30 and 60 Hz, the ocular system perceives resonance [24; 25; 26; 27]. Therefore, seat transmissibility can be significantly influenced by the biodynamics of the human body and its pronounced nonlinearity [28].