A parametric dynamic study on hunting stability of full dual-bogie railway vehicle

Abstract

Analysis is performed on the hunting stability of a full railway vehicle system composed of a vehicle body, two bogie frames, and two wheelsets for each bogie frame. Incorporated into this analysis are the nonlinear heuristic creep and flange-rail contact models. The results show that the hunting speed is most sensitive to the primary longitudinal and lateral stiffnesses, and the nonlinear heuristic creep model plays a key role in confining the hunting speed within a physically reasonable range. Eigenanalysis is performed to investigate the dynamic behavior of the vehicle in the vicinity of the hunting speed. The results reveal that there exists not only the most dominant pair of complex conjugate roots, but also its shadowed roots. The roles of these two principal pairs of eigensolutions in the hunting motion are thoroughly explored via numerical studies using bifurcation analysis and an orbital representation. It is shown that the nonlinear hunting motions before the modal transition speed mainly refer to the principal mode, and those after the critical speed refer not only to the principal mode, but also to its shadowed mode, which supports the necessity of the dual-bogie railway vehicle model in the hunting analysis. Parameters Values Vehicle body, bogie frame, and wheelset masses [kg] m c =34,000, m t =3,000, m w =1,400 Roll, pitch, and yaw moments of inertia of the vehicle body [kg m 2 ] I cx =75.06×10 3 , I cy , I cz =2.086×10 6 Roll, pitch, and yaw moments of inertia of the bogie frame [kg m 2 ] I tx =2,260, I ty =2,710, I tz =3,160 Roll, pitch, and yaw moments of inertia of the wheelset [kg m 2 ] I wx =915, I wy =140, I wz =915 Primary longitudinal, lateral, and vertical stiffnesses [kN/m] K px =10,000, K py =5,000, K pz =750 Secondary longitudinal, lateral, and vertical stiffnesses [kN/m] K sx =150, K sy =150, K sz =400 Primary longitudinal, lateral, and vertical damping coefficients [kNs/m] C px =12, C py =12, C pz =15 (450)

Efficient Approximation of the Labeled Multi‐Bernoulli Filter for Online Multitarget Tracking

“…in which {( ( ) , ( ) )} ∈L is a given finite parameter set, with ( ) representing the existence probability of target and ( ) denoting the probability density of the kinematic state of target given its existence [12]. Remark that the LMB family is a special case of the GLMB family with only one term for each target.…”

“…In the following, we briefly recall the prediction and update process for the LMB filter which was proposed in [12].…”

“…The LMB filter recursion described in Section 2.3 is an approximation of the Bayes multitarget tracking filter by only preserving the unlabeled intensity of the multitarget posterior density [15]. Due to its simplification, the LMB filter can be parallelized by grouping and gating [12] and runs much faster than the -GLMB filter, especially for tracking large number of targets. However, in every update step, the component number to represent target posterior state, that is, Gaussian component number or particle number, would increase linearly with the number of measurements caused by the association mapping Θ + .…”

“…Here, we refer the readers to Section IV of [12] for detailed description and equations and present the ELMB filter in the following.…”

“…Then, the Marginalized -Generalized Labeled Multi-Bernoulli (M -GLMB) [11] and the Labeled Multi-Bernoulli (LMB) filter [12] were proposed to perform multitarget tracking more efficiently, respectively, under different approximations and update paradigms. However, the efficiency issue of multitarget tracking method still remains challenging for online applications, especially for multisensor scenarios [13,14].…”