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NEURAL NETWORK BASED HAMMERSTEIN
SYSTEM IDENTIFICATION
USING PARTICLE SWARM SUBSPACE ALGORITHM
S. Z. Rizvi and H. N. Al-Duwaish
Department of Electrical Engineering, King Fahd Univ. of Petroleum & Minerals, Dhahran, Saudi Arabia
Keywords:
Particle swarm optimization, Neural network training, Subspace identification, Static nonlinearity, Dynamic
linearity, Radial basis function (RBF) neural networks.
Abstract:
This paper presents a new method for modeling of Hammerstein systems. The developed identification method
uses state-space model in cascade with radial basis function (RBF) neural network. A recursive algorithm
is developed for estimating neural network synaptic weights and parameters of the state-space model. No
assumption on the structure of nonlinearity is made. The proposed algorithm works under the weak assumption
of richness of inputs. The problem of modeling is solved as an optimization problem and Particle Swarm
Optimization (PSO) is used for neural network training. Performance of the algorithm is evaluated in the
presence of noisy data and Monte-Carlo simulations are performed to ensure reliability and repeatability of
the identification technique.
1 INTRODUCTION
The Hammerstein Model belongs to the family of
block oriented models and is made up of a memory-
less nonlinear part followed by a linear dynamic part
as shown in Figure 1. It has been known to effectively
represent and approximate several nonlinear dynamic
industrial processes, for example pH neutralization
process (Fruzzetti, K. P., Palazoglu A., McDonald,
K. A., 1997), heat exchanger (Eskinat, E., Johnson,
S. H., Luyben, W. L., 1991), nonlinear filters (Had-
dad, A. H., Thomas, J. B., 1968), and water heater
(Abonyi, I., Nagy, L., Szeifert, E., 2000).
Figure 1: Block diagram of a Hammerstein model.
A lot of research has been carried out on identi-
fication of Hammerstein models. Hammerstein Sys-
tems can be modeled by employing either nonpara-
metric or parametric models. Nonparametric mod-
els represent the system in terms of curves result-
ing from expansion of series such as the Volterra se-
ries or kernel regression. Parametric representations
are more compact having fewer parameters. Notable
parametric identification techniques can be found in
(Narendra, K. S., Gallman, P., 1966), (Billings, S.,
1980), (Al-Duwaish, H., 2001), (V¨or¨os, J., 2002),
(Wenxiao, Z., 2007) and in references therein. Non-
parametric identification techniques can be found in
several papers including, but not limited to those of
(Greblicki, W., 1989), (Al-Duwaish, H., Nazmulka-
rim, M., Chandrasekar, V., 1997), (Zhao, W., Chen,
H., 2006).
Recently, subspace identification has emerged as
a well known method for identification of linear
systems. It is computationally less complicated as
compared to conventional prediction error methods
(PEM), does not require initial estimate of a canon-
ical model like PEM and, is easily extendable to sys-
tems having multiple inputs and outputs (Katayama,
T., 2005). However, its use is restricted mostly to lin-
ear systems. To make use of this, attempts have been
made to extend subspace linear identification to non-
linear systems such as Wiener and Hammerstein sys-
tems including use of static nonlinearity in the feed-
back path (Luo, D., Leonessa, A., 2002), assuming
known nonlinearity structures (Verhaegen, M., West-
wick, D., 1996), and using least squares support vec-
tor machines (Goethals, I., Pelckmans, K., Suykens,
J. A. K., Moor, B. D., 2005).
In this paper, a new subspace based method is pro-
182
Z. Rizvi S. and N. Al-Duwaish H..
NEURAL NETWORK BASED HAMMERSTEIN SYSTEM IDENTIFICATION USING PARTICLE SWARM SUBSPACE ALGORITHM.
DOI: 10.5220/0003072401820189
In Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation (ICNC-2010), pages
182-189
ISBN: 978-989-8425-32-4
Copyright
c
2010 SCITEPRESS (Science and Technology Publications, Lda.)