**Abstract**

This chapter presents a method for identifying the dynamic response of vehicles (railcars) running on a rail track. The method is based on the recurrence plots developed from the phase diagram (phase plane). The phase plane is constructed using Hamilton's principle for a single-mass system. The state variables are estimated from acceleration measurements registered in an experimental test rig. The measurements were recorded with accelerometers and gyroscopes mounted on the railcar that circulated on a closed-loop track. The acceleration data were integrated using the empirical mode decomposition method and the time delay principle. The acceleration data were separated into two data vectors: rigid body motion and vibration modes. The recurrence plots were built for both data vectors, and it was found that the vibration modes were more sensitive to track defects and curvature changes. The recurrence plots were analyzed with the recurrence quantification analysis, and it was found that the Recurrence Plots can determine the location and type of defects.

**Keywords:** recurrence plots, recurrence quantification analysis, vehicle dynamic measurements, empirical mode decomposition, phase plane
