# Model Updating of a Freight Wagon Based on Dynamic Tests under Different Loading Scenarios
## 1 Introduction
Typically, the contribution of the local dynamic response is relevant in studies regarding the assessment of passenger comfort [27; 33], fatigue-life prediction [29] and cargo stability [26; 28]. One specificity on the dynamic analysis of rail freight vehicles is related to the adequate modelling of the different types of suspension systems (leaf, coil, etc.) which, in most situations, presents a nonlinear dynamic behaviour [15; 34; 35; 36; 37; 38]. Another issue is the correct modelling of the overload, because in these wagons, the cargo load usually represents a significant portion of the total weight of the vehicle [28]. The high overload/tare mass ratio influences the dynamic behaviour of the wagon, forcing designers to include loaded and unloaded scenarios in their analysis [35]. Furthermore, the overload distribution requires special attention since it can change the position of the gravity centre of the vehicle [39]. Several works report the use of dedicated dynamic tests to experimentally evaluate the dynamic properties of the railway vehicles, particularly the natural frequencies, mode shapes and damping coefficients [25; 30; 40; 41]. These tests can be executed when the vehicle is at its rest position or in motion, during its normal operation. When in rest position, an external excitation is usually applied to the structure by means of special equipment, such as an electrodynamic exciter, impact hammer, or even by people moving randomly over the vehicle [24; 42; 43]. Most of the authors perform the modal identification with the application of output-only techniques, also known as operational modal analysis [41]. Typically, the calibration of the numerical models of railway vehicles are based on experimental modal parameters derived from dynamic tests [24]. Model calibration strategies usually resort to iterative methodologies grounded in optimization algorithms, in which successive modifications of numerical parameters are performed, aiming to minimize an objective function [24]. In these type of problems, the objective function typically comprises weighted residuals derived from the natural frequencies and modal configurations [24]. The objective function must be properly constructed and the weights well selected in order to avoid ill-conditioned optimization problems [44]. Most algorithms used to solve these problems are the gradient-based algorithms, response surface methods and nature-inspired algorithms, such as the genetic algorithm and particle swarm optimization [31]. Several recent studies on damage identification problems based on modal parameters [45; 46; 47] demonstrated the great potential of recently developed nature-inspired algorithms, namely the Whale and the Moth-Flame optimization algorithms. There is still a scarce number of studies regarding the experimental model calibration of freight vehicles [31; 43], and most of the published works are focused on passenger vehicles [12; 24; 33]. Regarding the latter, [PERSON] et al. [33] proposed an automatic calibration methodology based on a particle swarm optimization algorithm, aiming to reduce the maximum difference between numerical and experimental vibration frequencies. The experimental setup performed on a Shinkansen-type wagon involved 42 acceleration measurement points and an external excitation provided by an electrodynamic shaker. Six operational mode shapes were extracted using classical modal analysis based on frequency response functions. The model updating process involved 14 numerical parameters and resulted in a maximum difference of only 0.86% between numerical and experimental frequencies. [PERSON] [12] proposed a simplified multibody single-level suspension model for the EN57 vehicle that was manually calibrated based on the stiffnesses and damping values of the suspensions. The calibration was based on the natural frequencies' values, as well as the damping coefficients' values, of the rolling and bouncing rigid-body modes of the car body.