scholarly journals Motion of a falling card in a fluid: Finite-dimensional models, complex phenomena, and nonlinear dynamics

2015 ◽  
pp. 3-49 ◽  
Author(s):  
Sergey Kuzntetsov ◽  
Keyword(s):  
Nonlinear Dynamics ◽  
Finite Dimensional ◽  
Dimensional Models ◽  
Complex Phenomena

scholarly journals Finite-dimensional models of diffusion chaos

2010 ◽  
Vol 50 (5) ◽  
pp. 816-830 ◽  
Author(s):  
S. D. Glyzin ◽  
A. Yu. Kolesov ◽  
N. Kh. Rozov
Keyword(s):  
Finite Dimensional ◽  
Diffusion Chaos ◽  
Dimensional Models

Hamiltonian finite-dimensional models of baroclinic instability

1997 ◽  
Vol 229 (5) ◽  
pp. 299-305 ◽  
Author(s):  
R.I. McLachlan ◽  
I. Szunyogh ◽  
V. Zeitlin
Keyword(s):  
Baroclinic Instability ◽  
Finite Dimensional ◽  
Dimensional Models

scholarly journals Embedding variables in finite dimensional models

2001 ◽  
Vol 63 (10) ◽  
Author(s):  
M. Ambrus ◽  
P. Hájíček
Keyword(s):  
Finite Dimensional ◽  
Dimensional Models

A neural network-based distributed parameter model identification approach for microcantilever

2016 ◽  
Vol 230 (20) ◽  
pp. 3663-3676
Author(s):  
Chenkun Qi ◽  
Feng Gao ◽  
Han-Xiong Li ◽  
Xianchao Zhao ◽  
Liming Deng
Keyword(s):  
Neural Network ◽  
Nonlinear Dynamics ◽  
Model Identification ◽  
Equation Model ◽  
Distributed Parameter ◽  
Differential Equation Model ◽  
Finite Dimensional ◽  
Distributed Parameter Model ◽  
Identification Approach ◽  
Unknown Nonlinear Dynamics

The microcantilever used in micro–nanomanipulator is a spatially distributed and flexible mechanical system. An accurate model of the microcantilever is essential for the accurate tip positioning and force sensing. Traditional lumped parameter model will lose the spatial dynamics. Though the nominal Euler–Bernoulli model is a distributed parameter model, in practice there are still some unknown nonlinear dynamics. In this study, a neural network-based distributed parameter model identification approach is proposed for modelling the microcantilever. First, a nominal Euler–Bernoulli beam model is derived. To compensate unknown nonlinear dynamics, a nonlinear term that needs to be estimated is added in the nominal model. For finite-dimensional implementation, the infinite-dimensional partial differential equation model is reduced into a finite-dimensional ordinary differential equation model using the Galerkin method. Next, a neural network-based intelligent learning approach is developed to learn the unknown nonlinearities from the input–output data. A radial basis function recurrent neural network observer is designed to estimate the finite-dimensional states from a few sensors of measurements. After that, a general regression neural network model is identified to establish the nonlinear spatiotemporal dynamic model between the inputs and outputs. The effectiveness of the proposed neural network-based distributed parameter modelling approach is verified by the simulations on a typical microcantilever.

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