# Analysis of Dynamic Parameters of a Railway Bridge
## 1 Introduction  
An analysis of the dispersion of vibration accelerations of the beams of the railway bridge overlay with a locomotive moving at 60 km/h and a freight train moving at 80 km/h was conducted in this study [1]. The theory of covariance functions was used in the analysis of vibration parameters. Graphical expressions of covariance functions illustrate the change of inter-dependence of vibration parameters over a given time scale [2]. The degree of the change of spatial dependences depends on technological and dynamic properties of the object being examined and the stability of the structure of the bridge trusses [3]. Many articles have been written on analyses of rail bridge vibrations. Such research has mainly focused on bridge conditions [4], such as a resonance mechanism explained by [PERSON] et al. [5], vibration mode-coupling and intermittent contact loss and vibration instability in a large motion bistable compliant mechanism by [PERSON] et al. [6, 7], the stability of dynamic response by [PERSON] et al. [8], the dependence of bridge vibration parameters on cross winds by [PERSON] et al. [9] and the use of bridge-track-vehicle element by [PERSON] et al. [10]. There are methods described in literature (1, 2 and 3 [11, 12, 13]) aimed at optimizing the number of metering points. Although there may be many different algorithms for the placement of sensors in order to optimize the number and locations of sensors on the structure, increasing the volume of available information is the key criterion identified in the examined sources of literature [14, 15]. The purpose of the information received is to identify structural defects or to provide information on structural changes (usually using modal analysis). Artificial Neural Networks (ANNs), Pattern Search (PS) and Evolutionary Strategies (ES), such as the Genetic Algorithms (GA) [5], the Particle Swarm Optimization (PSO) [6], and the Covariance-Matrix Adaptation Evolution Strategy (CMA-ES) are some of the countless examples available in the literature [7; 16; 17; 18]. This article focuses on analysing hard-to-reach significant points (because the examined object is an old-structure bridge that is not adapted for dynamic research) by performing dynamic load tests (with a train moving at different speeds). This article is aimed at determining the interdependencies of results of vibrations of bridge points rather than the impact that a train makes on a bridge without emphasizing the modal parameters of the bridge. The identification of the aforementioned interdependencies makes it possible to predict the results of hard-to-reach points. Methods of reversal analysis efficiently support studies of vibrations of railway bridges. Simplification of the measurement process and fewer sensors for determining vibration parameters make it possible to use the received compositional models. Diagnosing bridge condition status with the proposed methods is an important bridge resource forecasting tool for assessing the moving level of moving rolling stocks. The aim of this paper is to show that the proposed method can be used to assess the dependence of accelerometer points, and thus, that fewer sensors can be used in the experiment (because of a complicated bridge design, it is often impossible to physically measure significant acceleration of bridge points because of a difficult access to the bridge). There are many ways to diagnose bridge structures. The assessment of bridge structures is very important because of long service life, structural deformations, natural wear and tear and increasing need for axle load. A dynamic enhancement factor (DAF), which determines dynamic impact of moving trains on the bridge, is an important factor. The accurate assessment of DAF ensures sustainable management of existing bridges [1]. Assessing the main natural frequencies and mode forms of the bridge is of particular importance [19]. They can also be monitored using GAMMA Portable Radar Interferometer (GPRI) [20].