Genetic algorithm-based identification of transfer function parameters for a rectangular flexible plate system

doi:10.1016/j.engappai.2010.01.005

Engineering Applications of Artificial Intelligence

Volume 23, Issue 8, December 2010, Pages 1388-1397

https://doi.org/10.1016/j.engappai.2010.01.005 Get rights and content

Abstract

This paper focuses on an identification technique based on genetic algorithms (GAs) with application to rectangular flexible plate systems for active vibration control. A real coded GA with a new truncation-based selection strategy of individuals is developed, to allow fast convergence to the global optimum. A simulation environment characterizing the dynamic behavior of a flexible rectangular plate system is developed using the central finite difference (FD) techniques. The plate thus developed is excited by a uniformly distributed random disturbance and the input–output data of the system acquired is used for black-box modeling the system with the GA optimization using an autoregressive model structure. Model validity tests based on statistical measures and output prediction are carried out. The prediction capability of the model is further examined with unseen data. It is demonstrated that the GA gives faster convergence to an optimum solution and the model obtained characterizes the dynamic system behavior of the system well.

Introduction

In order to design and analyze a control system, a suitable model is often required to represent the relationship between the input and output of the system. System identification deals with the problem of building mathematical model of a dynamical system based on observed data. Conventionally, model identification requires the knowledge of the input and output data of the system of interest. Such data are typically obtained from tests or physical rules governing the system and later used to identify the system model.

In general, system identification involves two steps, namely, the selection of a suitable model structure and estimation of model parameters. In the first step, a priori knowledge is used to determine a class of models to which the target system may belong. If there is no a priori knowledge available, then the structure realization might be done by a trial-and-error method (Levine, 1995). The main focus in system identification is on the parameter identification process. Well-developed techniques such as least-square, instrumental variable and maximum likelihood exist for parameters estimation of models. However, these techniques often fail in search for the global optimum if the search space is not differentiable or linear in the parameters (Hossain et al., 1995).

To date, artificial intelligence (AI) techniques have become potential candidates to many control applications. One of the most powerful AI techniques is genetic algorithm, which has been widely used and applied to control systems (Bedwani and Ismail, 2001). Genetic algorithms are very good for optimization problems with several local minima where conventional search algorithms fail. GA techniques can be effectively applied to system identification problem to estimate the model parameters. A GA simultaneously evaluates many points in the parameters space and converges toward the global solution. It does not require the search space to be differentiable or continuous (Kargupta and Smith, 1991; Kristinsson and Dumont, 1992). Many researchers have applied the GA techniques to identify linear and non-linear systems.

Hossain and coworkers (Hossain et al., 1995) employed GA for identification of a flexible beam to design an active vibration controller. They used FD method to study the behavior of the beam and constructed a suitable simulation algorithm. Then, system identification was done using GA to find the system model parameters. They employed 30 individuals with a 20 bit string for each as initial population. Roulette wheel method was utilized as the selection strategy. Although the execution time of the GA-based algorithm was reported to be more than that of the conventional scheme, a more suitable solution for real-time application was found.

Li (1999) studied the application of GA to the identification of a Hammerstein model. He used piecewise linear and not a polynomial, to approximate the memoryless non-linear characterization. The effectiveness of GA to identify the corresponding system was shown. Doung and Stubberud (2002) presented a method for identifying systems through input–output behavior and application of GA. The GA identification method was compared to the least-square (LS) method and it was found that the GA method provided a more accurate solution than the LS method. However, because of the complexity (particularly for high order systems), it was reported that the GA identification method has computational advantages over the LS method. Puangdownreong (2006) investigated the identification of a cart-plus-pendulum system model via the GA. The results were compared with the Box–Jenkins (BJ) model obtained from the conventional identification method based on regression analysis. It was found that the GA provided superior performance in representing the system dynamics compared to the BJ model.

Ghaffari et al. (2007) utilized GA to identify and control a power plant. Their results indicated a successful identification of the high order de-superheating process as well as improvements in the performance of the steam temperature controller. Abdelhafid (2008) presented a new technique based on GA to obtain the best series of parameters for the identification of the ZnO surge arrester models. The validity of the predicted parameters was then checked by comparing the predicted results with the experimental results available in the literature. Ebrahimzadeh and Ranjbar (2008) employed GA to optimize the number of nodes in the hidden layer of a neural network for digital signal-type identification.

In this research, a real coded GA together with a novel truncation-based selection algorithm is employed for the model identification of a rectangular flexible plate system. Accordingly, this study is conducted to highlight the effectiveness of the proposed GA for system identification of flexible structures in which a fast convergence to global optimum is often required. The first step would be to simulate the flexible thin plate using the FD approach. Then, GA-based system identification is carried out using the input–output data of the system acquired from simulation and the proposed GA. The performance of the proposed selection algorithm for system identification of the plate system is compared with another conventional selection strategy through which the superiority of the proposed scheme is demonstrated. Finally, the validity of the obtained model is investigated.

Section snippets

Dynamic equation of the thin plate

The governing equation of a flexible thin plate can be formulated as a differential equation together with corresponding boundary conditions. The plate is assumed to undergo a small lateral deflection. Using Kirchhoff’s plate theory, this yields (Timoshenko and Woinowsky-Krieger, 1959) $\frac{\partial^{4} w (x, y, t)}{\partial x^{4}} + 2 \frac{\partial^{4} w (x, y, t)}{\partial x^{2} \partial y^{2}} + \frac{\partial^{4} w (x, y, t)}{\partial y^{4}} + \frac{ρ h}{D} \frac{\partial^{2} w (x, y, t)}{\partial t^{2}} = \frac{q (x, y, t)}{D}$ where w is the lateral deflection in z direction, ρ the density of plate with dimension mass per unit volume, h the thickness, D=(Eh³)/(12(1−υ

Model structure

The most basic relationship between the input and output of a system is the linear difference equation (Ljung, 1999) given by $y (t) + a_{1} y (t - 1) + \dots + a_{n} y (t - n) = b_{1} u (t - 1) + \dots + b_{m} u (t - m)$ where y(t) is the model output at time t and [y(t−1),….,y(t−n), u(t−1),…,u(t−m)] are past observed data. Since the observed data would be collected by the sampling process from the simulation procedure of Section 2, it is more straightforward to relate the observed data to a discrete time model as expressed in Eq. (12). A useful

Model validation

Once a model of the system has been obtained, it is required to validate whether the model is good enough to represent the system. There are basically two ways to investigate the validity of a model (Soderstrom and Stoica, 1984)

•
Use of plots and common sense;
•
Use of statistical tests on the prediction error.

It is often useful to plot the measured data and the model output. For a good model, the predicted output should resemble the measured output. Such plots and the numerical fits associated with

Conclusion

A GA optimization strategy has been developed for black-box modeling of dynamic systems and this has been tested within a simulation environment of a flexible plate system subjected to external disturbances. A FD simulation algorithm characterizing the dynamic behavior of the plate has been utilized as a platform for test and evaluation of the GA modeling approach. A new truncation-based selection strategy of fittest individuals has been developed, which allows the GA to converge relatively

Acknowledgments

The authors wish to thank the Ministry of Science, Technology and Innovation (MOSTI) and the Universiti Teknologi Malaysia (UTM) for providing the research grant and facilities. This research is supported using a research Grant, Vote no. 79297.

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Genetic algorithm-based identification of transfer function parameters for a rectangular flexible plate system

Abstract

Introduction

Section snippets

Dynamic equation of the thin plate

Model structure

Model validation

Conclusion

Acknowledgments

Journal of Engineering Applications of Artificial Intelligence

Journal of Engineering Applications of Artificial Intelligence

Parameter identification of ZnO surge arrester models based on genetic algorithms

Journal of Electric Power Systems Research

An Introduction to Genetic Algorithm for Scientists and Engineers

Genetic Algorithms in search

Optimization and Machine Learning

Adaptation in Natural and Artificial Systems

System identification with evolving polynomial networks

Proceeding of the 4th International Conference on Genetic Algorithm