Train Obstacle Detection System Stabilization and Stochastic Vibrations Analysis Using the Moment Lyapunov Exponent Method

This paper analyzes stochastic vibrations of a specialised onboard railway obstacle detection system (ODS). The observed system consists of several vision-based sensors mounted in a special housing attached to the locomotive front profile via rubber metal springs and a mounting plate. In this study, the experimental measurements of acceleration were performed in the vertical, longitudinal, and lateral direction for two positions, on the mounting plate rigidly connected to the vehicle body and inside the sensor housing. The ODS stabilization is presented with the results obtained by the moment Lyapunov exponent (MLE) method. Analytical and numerical determination of MLE is firstly presented on a simply supported Euler-Bernoulli beam. Further, the stochastic vibration analysis was performed using the experimentally obtained data. According to these values, the appropriate system parameters essential for the application of the Lyapunov theory to stochastic stability problems were firstly numerically calculated. By means of the Monte Carlo simulation method, whose example was previously shown on a simple beam, the bounds of the almost sure stability of the observed system are given according to the measured accelerations in all of the observed directions.