Modeling of a Flexible Beam System using NARMAX Model integrated with Multi-Objective optimization Differential Evolution

Modeling a dynamic system such as a flexible beam system without knowing the physical equations involved is a challenging task. An accurate model representing the system is needed for more efficient controller design. This paper presents the identification of a flexible beam system using Nonlinear Auto- Regressive Moving Average with eXogenous input (NARMAX) model integrating with Multi-Objective optimization Differential Evolution (MOODE) algorithm. This proposed algorithm called MOODE-NARMAX is applied to minimize two objective functions; the model complexity and the mean square error between actual and predicted outputs. The system identification procedures were followed for identifying the flexible beam system. Model validity tests were applied to the set of solutions called the Pareto-optimal set that was generated from the proposed algorithm to select an optimal model. Using the input and output experimental data of the rig, the simulation results show that the MOODE-NARMAX algorithm is able to produce an adequate and optimal model for the flexible beam system and therefore could be used as an alternative to identify an adequate and parsimonious model for the system.

[1]  Radhi M'hiri,et al.  An approach to polynomial NARX/NARMAX systems identification in a closed-loop with variable structure control , 2008, Int. J. Autom. Comput..

[2]  P. K. Palani,et al.  Active Vibration Control in Smart Structures , 2014 .

[3]  Stephen A. Billings,et al.  An application of Lyapunov stability analysis to improve the performance of NARMAX models , 2010, Robotics Auton. Syst..

[4]  Peter J. Fleming,et al.  Time and frequency domain identification and analysis of a gas turbine engine , 2002 .

[5]  Sheng Chen,et al.  Representations of non-linear systems: the NARMAX model , 1989 .

[6]  T. Martin McGinnity,et al.  Robot control code generation by task demonstration in a dynamic environment , 2012, Robotics Auton. Syst..

[7]  S. Billings.  Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains , 2013 .

[8]  Hong Wang,et al.  Optimal probability density function control for NARMAX stochastic systems , 2008, Autom..

[9]  S. Billings,et al.  Correlation based model validity tests for non-linear models , 1986 .

[10]  Nitesh P. Yelve,et al.  Active vibration control of cantilever beam by using PID based output feedback controller , 2012 .

[11]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[12]  Gianluca Gatti,et al.  Active vibration control of a beam using piezoelectric actuators , 2005 .

[13]  Peter J. Fleming,et al.  Application of system identification techniques to aircraft gas turbine engines , 2001 .

[14]  MOHD ZAKIMI ZAKARIA,et al.  Multi-Objective Optimization Using Differential Evolution for Modeling Automotive Palm Oil Biodiesel Engine , 2014 .

[15]  Wei He,et al.  Vibration Control of a Flexible Beam , 2018, Active Vibration Control and Stability Analysis of Flexible Beam Systems.

[16]  Deepak Chhabra,et al.  Design and Analysis of Piezoelectric Smart Beam for Active Vibration Control , 2012 .

[17]  Sayed Mohammad Reza Loghmanian,et al.  Multi-Objective Optimization of NARX Model for System Identification Using Genetic Algorithm , 2009, 2009 First International Conference on Computational Intelligence, Communication Systems and Networks.

[18]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[19]  I. J. Leontaritis,et al.  Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .