Effects of Reduced-Order-Model in Reproducibility of Cars’ Displacement of High-Speed-Moving Vehicle subjected to Sinusoidal Waves

Abstract

In this paper, we study reproducibilities of response behavior of high-speed-moving vehicle when using the reduced-order-model. The vehicle model is made up of 10 cars and has 210 degrees of freedom in total. It is considered 9 cases of sinusoidal waves (3 patterns of frequency: 1.0, 2.0, 3.0Hz, and 3 patterns of direction: East-West, Up-Down, North-South) as input waves, and analyze cars’ displacements. Then we make reduced-order-models by sparse estimation for each case and investigate the reproducibility which is estimated by correlation coefficient between original-model and reduced-order-model. Moreover, in order to reveal which modes are important to express movements of the vehicle, 210 vibration modes are divided into 8 groups, based on natural frequency of the vehicle. As a result, from the perspective of correlation coefficient, around 20 modes were necessary to reproduce the response behavior and these modes were chosen from specific groups. Furthermore, it turned out that correlation coefficient was not enough to estimate the accuracy of the reduced-order-model because the correlation coefficient was high when ‘phases’ of response behaviors of original model and reduced-order-model were match though their ‘amplitudes’ were not match. So we use another indicator, normalized mean square error (NMSE) to estimate the accuracy of ‘amplitude.’ As a result, 30-50 modes were necessary, that was nearly double modes when using correlation coefficient. Moreover, it needed more modes to express horizontal direction (y), yawing direction (ψ), and it needed less modes to express displacements of truck and wheel set than body.