Parametric estimation of the Duffing system by using a modified gradient algorithm

2008 ◽  
Vol 372 (3) ◽  
pp. 210-214 ◽  
Author(s):  
Carlos Aguilar-Ibáñez ◽  
Jorge Sanchez Herrera ◽  
Ruben Garrido-Moctezuma
Keyword(s):  
Parametric Estimation ◽  
Gradient Algorithm ◽  
Duffing System

scholarly journals An Improved Method for Stochastic Nonlinear System’s Identification Using Fuzzy-Type Output-Error Autoregressive Hammerstein–Wiener Model Based on Gradient Algorithm, Multi-Innovation, and Data Filtering Techniques

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-29
Author(s):  
Donia Ben Halima Abid ◽  
Saif Eddine Abouda ◽  
Hanane Medhaffar ◽  
Mohamed Chtourou
Keyword(s):  
Stochastic Systems ◽  
Parametric Estimation ◽  
Gradient Algorithm ◽  
Data Filtering ◽  
Estimation Algorithms ◽  
Output Error ◽  
Proposed Model ◽  
Identification Approach ◽  
Identification Techniques ◽  
Intermediate Variables

This paper proposes an innovative identification approach of nonlinear stochastic systems using Hammerstein–Wiener (HW) model with output-error autoregressive (OEA) noise. Two fuzzy systems are suggested for the identification of the input and output nonlinear blocks of a proposed model from given input-output data measurements. In this work, the need for the commonly used assumptions including well-known structure of input and/or output nonlinearities and/or reversible nonlinear output is eliminated by replacing the intermediate variables and noise with their estimates. Four parametric estimation algorithms to identify the proposed fuzzy-type stochastic output-error autoregressive HW (FSOEAHW) model are derived based on backpropagation algorithm and multi-innovation and data filtering identification techniques. The proposed algorithms are improved backpropagation gradient (IBPG) algorithm, multi-innovation IBPG (MIIBPG) algorithm, a data filtering IBPG (FIBPG) algorithm, and a multi-innovation-based FIBPG (MIFIBPG) algorithm. The convergence of the parameter estimation algorithms is studied. The effectiveness of the proposed algorithms is shown by a given simulation example.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

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