Nonlinear System Analysis with Karhunen–Loève Transform

Glösmann, Philipp; Kreuzer, Edwin

doi:10.1007/s11071-005-2794-z

Cited by 20 publications

(10 citation statements)

References 16 publications

(15 reference statements)

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“…Thus, provided that the ellipse is flat enough, we may represent the system motion by just the first coordinate α 1 without significant loss of information, e.g. [27]. In this section we briefly introduce the mathematical background of the KLT procedure and refer to e.g.…”

Section: Basics Of Kltmentioning

confidence: 99%

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Reduction of discrete element models by Karhunen–Loève transform: a hybrid model approach

Glösmann

2009

Comput Mech

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The term "discrete element method" (DEM) in engineering science comprises various approaches to model physical systems by agglomerates of free particles. While shapes, sizes and properties of particles may vary, in most DEM models, particles are not confined by constraints, but subject to applied forces derived from potential fields and/or contact laws. This general approach allows for widespread use of DEM models for physical phenomena including gas dynamics, granular flow, fracture and impact analysis. However, its characteristic feature, combining particle restraints and forces into applied forces, does not only provide for flexible adaption of DEM to different physics, but also creates the most limiting restriction: Evaluation of the applied forces for each particle is computational expensive restraining the time sequence and sample size for numerical analyses. As an ansatz to circumvent this obstacle for a class of DEM models, we propose a model order reduction method based on coherency in the dynamics of particles. While initial flexibility of DEM is conserved, computational effort can be reduced significantly.

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Section: Basics Of Kltmentioning

confidence: 99%

“…We choose cluster particles p i to comply with kinetic energy criterion of Eq. (27), where µ = 1.5. Finally, we simulate the hybrid DEM/KLT model and compare the results.…”

Section: An Exemplary Study: Dynamics Of a Cantilever Beammentioning

confidence: 99%

Reduction of discrete element models by Karhunen–Loève transform: a hybrid model approach

Glösmann

2009

Comput Mech

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“…After several trials (e.g. wavelet analysis among others) the Karhunen Loève transformation (also known as Proper Orthogonal Decomposition POD or Principle Component Analysis PCA, [4]), using signal-dependent characteristic functions, proved to be the adequate for this purpose. …”

Section: Evaluation Of the Wheel Set Rolling Qualitymentioning

confidence: 99%

On the evaluation of wheel sets and railway track quality

Bogacz¹,

Meinke²,

Zajac³

2008

WIT Transactions on the Built Environment

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The cost of maintenance and the safety of railway operation depend (among other things) on the quality of the wheel sets interaction with the rails. There is the necessity to monitor the rolling behaviour of regular vehicles. Of most importance is the time behaviour of the travelling contact forces between the wheel sets and the trucks. The rolling wheel set obtains a very different position relative to the track, which creates restraints in the wheel set and the track panel structure, and which will discharge continuously by friction induced vibration. Those vibrations cause corrugation, ballast deterioration, wear, squealing noise and other environmental impacts.

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“…Solving the eigenvalue problem (1) we derive sets of Weighing Factors, eigenvalues and Characteristic Functions. Assuming structural consistency of the bogie/wheelset motion during time intervals ∆T , we characterize the dynamics by KLT ([GK04] and [GK05]):…”

Section: Concept Of Karhunen-loève Transformmentioning

confidence: 99%

Track–Monitoring of Wheel–Rail–Systems

Glösmann

Kreuzer

2006

Proc Appl Math and Mech

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Inspection and maintenance of railway networks is a complex and expensive task. Special measurement vehicles are used to record the geometrical properties of railway lines within required time intervals. Due to the extent of measurement data the quality of railway track is evaluated considering only a few parameters. Although safety and comfort of wheel-rail-systems depend on the dynamical behavior, current inspection vehicles are not equipped to measure dynamic properties.In this paper, we will discuss a novel approach to evaluate the quality of railway tracks based on wheel-rail dynamics: Wheelset dynamics of subway trains are analyzed by Karhunen-Loève Transformation to extract the principal dynamics from the collected measurement data.

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Nonlinear System Analysis with Karhunen–Loève Transform

Cited by 20 publications

References 16 publications

Reduction of discrete element models by Karhunen–Loève transform: a hybrid model approach

Reduction of discrete element models by Karhunen–Loève transform: a hybrid model approach

On the evaluation of wheel sets and railway track quality

Track–Monitoring of Wheel–Rail–Systems

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