Biomedical Engineering Reference
In-Depth Information
to stream geometry or flow dynamics. ANNs are
systems that are deliberately constructed to make
use of some organizational principles resembling
those of the human brain (Lin & Lee, 1996).
They offer an effective approach for handling
large amounts of dynamic, non-linear and noisy
data, especially when the underlying physical
relationships are not fully understood (Cannas,
Fanni, See, & Sias, 2006; Hagan, Demuth, &
Beale, 1996; Haykin, 1994).
In specific terms, several authors (Kashefipour,
Falconer, & Lin, 2002; Piotrowski, Rowinski, &
Napiorkowski, 2006; Rowinski et al., 2005; Tay-
fur, 2006; Tayfur & Singh, 2005) have reported
successful applications of ANNs to the prediction
of dispersion coefficient. For example, in the case
of Tayfur and Singh (2005) the ANN was trained
and tested using 71 data samples of hydraulic and
geometric variables and dispersion coefficients
measured on 29 streams and rivers in the United
States, with the result that 90% of the dispersion
coefficient was explained. However, there is
always a lack of a suitable input determination
methodology for ANN models in these applica-
tions. Moreover, without further interpretation of
the trained network, their results are not easily
transferable.
The aim of the present work is to present and
demonstrate a data driven method (hereafter
called GNMM, the Genetic Neural Mathemati-
cal Method) based on a Multi-Layer Perceptron
(MLP) neural network, for the prediction of
longitudinal dispersion coefficient. By utilizing
a Genetic Algorithm (GA), GNMM is able to
optimise the number of inputs to the ANN. As
we will show this simplifies the network structure
and also accelerates the training process. Employ-
ing a Mathematical Programming (MP) method
(Tsaih & Chih-Chung, 2004), GNMM is also
capable of identifying regression rules extracted
from the trained MLP.
(5)
These equations are easy to use, assuming
measurements or estimates of the bulk flow
parameters are available. However, they may be
unable to capture the complexity of the interac-
tions of the fundamental transport and mixing
mechanisms, particularly those created by non-
uniformities, across the wide range of channels
encountered in nature. In addition, the advantage
of one expression over another is often just a
matter of the selection of data and the manner of
their presentation. Regardless of the expression
applied, one may easily find an outlier in the data,
which definitely does not support the applicabil-
ity of a particular formula. An expectation that,
in spite of the complexity of the river reach, the
dispersion coefficient may be represented by one
of the empirical formulae seems exaggerated
(Rowinski et al., 2005).
Furthermore, most of the studies have been
carried out based on specific assumptions and
channel conditions and therefore the performance
of the equations varies widely for the same stream
and flow conditions. For instance, Seo and Cheong
(1998) used 35 of the 59 measured data sets for
establishing equation (3) and the remaining 24 for
verifying their model. While the model of Deng et
al. (equation (4) - (5)) (2001) is limited to straight
and uniform rivers. They also assume that the
river is straight and uniform with a width-to-depth
ratio greater than 10. Therefore, a model that has
greater general applicability is desirable.
Recently Artificial Neural Network (ANN)
modelling approaches have been embraced en-
thusiastically by practitioners in water resources,
as they are perceived to overcome some of the
difficulties associated with traditional statistical
approaches, e.g. making assumptions with regard
Search WWH ::
Custom Search