Details
| Original language | English |
|---|---|
| Journal | PAMM - Proceedings in Applied Mathematics and Mechanics |
| Volume | 4 |
| Issue number | 1 |
| Publication status | Published - 22 Dec 2004 |
| Externally published | Yes |
Abstract
One important step during the product development of railway vehicles is the analysis of the dynamic properties of the system. Like in all real life systems, the behaviour of railway vehicles exhibits certain nonlinear properties, which have to be analysed and controlled. Unfortunately the system complexity of railway vehicles is so high that there exist no universal and powerful methods which can be directly applied to the analysis of the nonlinear dynamic behaviour. Set-oriented methods, however, provide an encouraging alternative. In the present paper, the application of these methods to the active guidance of railway vehicles will be presented. The main idea of set-oriented methods is to discretise the state space into subsets. Transition probabilities for each of these boxes are computed by integrating a large number of trajectories over small time intervals. In this way a transition matrix is obtained, which can be used to compute stationary probability distributions (also known as observation probability) and absorption probability distributions by solving an eigenvalue problem and identifying right and left eigenvectors of the transition matrix.
Keywords
- Absorption probability, Bifurcation analysis, Nonlinear dynamical system, Observation probability, Railway vehicle analysis, Set-oriented numerical methods
ASJC Scopus subject areas
- Computer Science(all)
- Artificial Intelligence
- Mathematics(all)
- Applied Mathematics
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In: PAMM - Proceedings in Applied Mathematics and Mechanics, Vol. 4, No. 1, 22.12.2004.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the application of set-oriented numerical methods in the analysis of railway vehicle dynamics
AU - Neumann, Nicolai
AU - Goldschmidt, Stefan
AU - Wallaschek, Jörg
N1 - Copyright: Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2004/12/22
Y1 - 2004/12/22
N2 - One important step during the product development of railway vehicles is the analysis of the dynamic properties of the system. Like in all real life systems, the behaviour of railway vehicles exhibits certain nonlinear properties, which have to be analysed and controlled. Unfortunately the system complexity of railway vehicles is so high that there exist no universal and powerful methods which can be directly applied to the analysis of the nonlinear dynamic behaviour. Set-oriented methods, however, provide an encouraging alternative. In the present paper, the application of these methods to the active guidance of railway vehicles will be presented. The main idea of set-oriented methods is to discretise the state space into subsets. Transition probabilities for each of these boxes are computed by integrating a large number of trajectories over small time intervals. In this way a transition matrix is obtained, which can be used to compute stationary probability distributions (also known as observation probability) and absorption probability distributions by solving an eigenvalue problem and identifying right and left eigenvectors of the transition matrix.
AB - One important step during the product development of railway vehicles is the analysis of the dynamic properties of the system. Like in all real life systems, the behaviour of railway vehicles exhibits certain nonlinear properties, which have to be analysed and controlled. Unfortunately the system complexity of railway vehicles is so high that there exist no universal and powerful methods which can be directly applied to the analysis of the nonlinear dynamic behaviour. Set-oriented methods, however, provide an encouraging alternative. In the present paper, the application of these methods to the active guidance of railway vehicles will be presented. The main idea of set-oriented methods is to discretise the state space into subsets. Transition probabilities for each of these boxes are computed by integrating a large number of trajectories over small time intervals. In this way a transition matrix is obtained, which can be used to compute stationary probability distributions (also known as observation probability) and absorption probability distributions by solving an eigenvalue problem and identifying right and left eigenvectors of the transition matrix.
KW - Absorption probability
KW - Bifurcation analysis
KW - Nonlinear dynamical system
KW - Observation probability
KW - Railway vehicle analysis
KW - Set-oriented numerical methods
UR - http://www.scopus.com/inward/record.url?scp=84893496868&partnerID=8YFLogxK
U2 - 10.1002/pamm.200410270
DO - 10.1002/pamm.200410270
M3 - Article
VL - 4
JO - PAMM - Proceedings in Applied Mathematics and Mechanics
JF - PAMM - Proceedings in Applied Mathematics and Mechanics
SN - 1617-7061
IS - 1
ER -