Heat Exchanger Data Driven Model Using GMDH Methodology
Iraci Martinez Pereira Gonçalves and Daniel Kao Sun Ting
Ipen – Instituto de Pesquisas Energéticas e Nucleares
São Paulo SP CEP 05508-970 Travessa R, 400, Brasil
martinez@ipen.br
Abstract - This paper presents a heat exchanger model
developed in the Matlab platform. The model was
used to investigate the use of the GMDH (Group
Method for Data Handling) methodology to predict
system variables, generating analytical redundancy.
This work is a part of a Monitoring and Diagnosis
System for Fault Detection using the GMDH datadriven
model to be applied to the IEA-R1 Ipen nuclear
research reactor. The GMDH is an algebraic model
for system characterization. It provides a general
framework for characterizing the relationship among
a set of state variables of a process and is used for
generating estimates of critical variables in an optimal
data-driven model form.
In this work we studied the following aspects:
normalization, number of input data points and noise
level. The GMDH methodology implemented is
working properly since the magnitude of the
regularity criterion is controlled by the magnitude of
the machine rounding error, indicating that the
method is not introducing additional errors and, most
of all, the error propagation is stable. The main results
are: data normalization is fundamental to obtain
better precision, the larger the number of data points,
the lesser the error, the error decreases with the
decreasing of noise level.
I. INTRODUCTION
Modern science and engineering are based on using firstprinciple
models to describe physical, biological, and
social systems. Such an approach starts with a basic
scientific model and then builds upon them various
applications in mechanical engineering or electrical
engineering. Under this approach experimental data are
used to verify the underlying first-principle models and to
estimate some of the model parameters that are difficult to
measure directly. However, in many applications the
underlying first principles are unknown or the systems
under study are too complex to be mathematically
described. With the growing use of computers and lowcost
sensors for data collection, there is a great amount of
data being generated by such systems. In the absence of
first-principle models, such readily available data can be
used to derive models by estimating useful relationships
between a system's variables. Thus there is currently a
paradigm shift from the classical modeling based on first
principles to developing models from data.
This paper presents a heat exchanger model developed in
the Matlab platform. The model was used to investigate
the use of the GMDH (Group Method of Data Handling)
methodology to predict system variables, generating
analytical redundancy. This work is a part of a Monitoring
and Diagnosis System for Fault Detection using the
GMDH data-driven model to be applied to the IEA-R1
Ipen nuclear research reactor [Gonçalves et al., 2001] and
[Upadhyaya et al., 2000].
II. GMDH – GROUP METHOD OF DATA
HANDLING
The Group Method of Data Handling (GMDH) is an
algebraic method for predicting system states, controller
and actuator functions [Farlow, 1984] and [Ferreira,
1999]. The GMDH constructs a model, of a desired
output as a function of a set of related inputs from a
subsystem, by a successive polynomial approximation.
The general relationship has the form shown in (1) where
{x1, x2,…,xm} is a vector of input variables and y is the
variable to be predicted. This formulation can be extended
to the prediction of multiple outputs {y1, y2, … , yn}.
?? ?
= = =
+ + + =
m
1 i
m
1 j
j i ij
m
1 i
i i x x c x b a y
???
= = =
+
m
1 i
m
1 j
m
1 k
k j i ijk x x x d L (1)
Fig. 1 shows a typical node of a GMDH modeling layer
with the basic quadratic predictor. The model parameters
such as {A,B,C,D,E,F}, are estimated from a leastsquares
fit using N observations of the input and output
variables. Fig. 2 illustrates that the predicted values of Y
are propagated successively to higher layers of the
algorithm, with the approximation of Ypred improving at
successive stages. At each stage of the approximation,
Ypred is formed from pairs of input signals (to that layer),
and new values of the predicted variable are propagated
pairwise to the next layer.
The iteration is continued until the mean-squared error
between the predicted and the measured values of the
output variable attains a desired value.
Parsimony in model fitting is achieved by comparing the
fractional prediction errors from one generation to the
next, and by terminating the algorithm when the error is a
minimum or when the errors from successive
approximation stages is less than a preset limit.
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