A Robust Data-Driven Identification Algorithm for Nonlinear Dynamical Systems With Time Delay

2021 ◽  
Author(s):  
Ghazaale Leylaz Mehrabadi ◽  
Jian-Qiao Sun ◽  
Shuo Wang
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Identification Algorithm ◽  
Nonlinear Dynamical

scholarly journals Multidimensional Approximation of Nonlinear Dynamical Systems

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Patrick Gelß ◽  
Stefan Klus ◽  
Jens Eisert ◽  
Christof Schütte
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Measurement Data ◽  
Data Driven ◽  
High Dimensional ◽  
Data Sets ◽  
Nonlinear Dynamical ◽  
Tensor Network ◽  
Wide Range ◽  
Multidimensional Approximation

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.

A data-driven approach to model calibration for nonlinear dynamical systems

2019 ◽  
Vol 125 (24) ◽  
pp. 244901 ◽  
Author(s):  
C. M. Greve ◽  
K. Hara ◽  
R. S. Martin ◽  
D. Q. Eckhardt ◽  
J. W. Koo
Keyword(s):  
Dynamical Systems ◽  
Model Calibration ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Nonlinear Dynamical ◽  
Data Driven Approach

scholarly journals Identification of nonlinear dynamical systems with time delay

2021 ◽  
Author(s):  
Ghazaale Leylaz ◽  
Shuo Wang ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Duffing Oscillator ◽  
Algebraic Operation ◽  
Computationally Efficient ◽  
Nonlinear Dynamical ◽  
Automatic Model Selection ◽  
Robust To Noise

AbstractThis paper proposes a technique to identify nonlinear dynamical systems with time delay. The sparse optimization algorithm is extended to nonlinear systems with time delay. The proposed algorithm combines cross-validation techniques from machine learning for automatic model selection and an algebraic operation for preprocessing signals to filter the noise and for removing the dependence on initial conditions. We further integrate the bootstrapping resampling technique with the sparse regression to obtain the statistical properties of estimation. We use Taylor expansion to parameterize time delay. The proposed algorithm in this paper is computationally efficient and robust to noise. A nonlinear Duffing oscillator is simulated to demonstrate the efficiency and accuracy of the proposed technique. An experimental example of a nonlinear rotary flexible joint is presented to further validate the proposed method.

scholarly journals Data-driven Evolution Equation Reconstruction for Parameter-Dependent Nonlinear Dynamical Systems

2018 ◽  
Vol 58 (6-7) ◽  
pp. 787-794 ◽  
Author(s):  
David W. Sroczynski ◽  
Or Yair ◽  
Ronen Talmon ◽  
Ioannis G. Kevrekidis
Keyword(s):  
Dynamical Systems ◽  
Evolution Equation ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Nonlinear Dynamical ◽  
Parameter Dependent
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