222
G.J. Bowden . G.C. Dandy . R.R. Maier
The disadvantages of this procedure are that it is computationally intensive and the
synergistic effect of certain combinations of variables may be overlooked.
11.3
ease Study
The ANN models were developed to forecast (4 weeks in advance) a particular
species group of cyanobacteria (Anabaena spp.) in the River Murray at Morgan,
South Australia. In this research, the available data include weekly values of
concentrations of the cyanobacterium Anabaena spp., total phosphorus, soluble
phosphorus, total kjedahl nitrogen (TKN) and silica as weIl as turbidity, colour,
pR, temperature, river levels at Morgan and weekly flows at Lock 7 (for locations
see Maier et al. (2000». All data were available from 1980/1981 to 1995/1996. A
full description of the case study is provided in Maier et al. (1998) and Maier et al.
(2000). Three additional variables were used in this study, namely, pR, silica
concentrations and river levels. pR was included as pR variations can alter
phytoplankton community composition Le. low pR « 6.0) favours eukaryotes,
and high pR (> 8.0) favours cyanobacteria. Silica itself is not a direct requirement
for cyanobacterial growth, however, silica is an important nutrient for the growth
of diatoms and therefore, it is a key nutrient that determines phytoplankton
succession. River levels were also included as they are highly correlated to flow
data but exhibit less noise.
11.4
Model Development
Backpropagation networks were developed using the commercially available
software package NeuroGenetic Optimizer (NGO) (BioComp Systems 1998). The
NGO evolves ANN structures whilst simultaneously searching for combinations
of significant input variables. The following features can be optimised by the
NGO:
1. the inputs used,
2. the number of hidden layers,
3. the number of hidden layer neurons in each layer, and
4. the transfer functions at each of the hidden and output layer nodes (logistic,
hyperbolic tangent or linear).
It has been shown that only one hidden layer is required to approximate any
continuous function, given that sufficient degrees of freedom (Le. connection
weights) are provided (Cybenko 1989). Rence, one hidden layer was utilised in
this study and this feature was not varied. The number of hidden layer neurons by
layer was optimised by the NGO and the maximum limit was set at 64 neurons.
The test set data were used to choose the optimal network architecture and inputs.
The GA-ANN process was conducted in an iterative manner until the maximum
G.J. Bowden . G.C. Dandy . R.R. Maier
The disadvantages of this procedure are that it is computationally intensive and the
synergistic effect of certain combinations of variables may be overlooked.
11.3
ease Study
The ANN models were developed to forecast (4 weeks in advance) a particular
species group of cyanobacteria (Anabaena spp.) in the River Murray at Morgan,
South Australia. In this research, the available data include weekly values of
concentrations of the cyanobacterium Anabaena spp., total phosphorus, soluble
phosphorus, total kjedahl nitrogen (TKN) and silica as weIl as turbidity, colour,
pR, temperature, river levels at Morgan and weekly flows at Lock 7 (for locations
see Maier et al. (2000». All data were available from 1980/1981 to 1995/1996. A
full description of the case study is provided in Maier et al. (1998) and Maier et al.
(2000). Three additional variables were used in this study, namely, pR, silica
concentrations and river levels. pR was included as pR variations can alter
phytoplankton community composition Le. low pR « 6.0) favours eukaryotes,
and high pR (> 8.0) favours cyanobacteria. Silica itself is not a direct requirement
for cyanobacterial growth, however, silica is an important nutrient for the growth
of diatoms and therefore, it is a key nutrient that determines phytoplankton
succession. River levels were also included as they are highly correlated to flow
data but exhibit less noise.
11.4
Model Development
Backpropagation networks were developed using the commercially available
software package NeuroGenetic Optimizer (NGO) (BioComp Systems 1998). The
NGO evolves ANN structures whilst simultaneously searching for combinations
of significant input variables. The following features can be optimised by the
NGO:
1. the inputs used,
2. the number of hidden layers,
3. the number of hidden layer neurons in each layer, and
4. the transfer functions at each of the hidden and output layer nodes (logistic,
hyperbolic tangent or linear).
It has been shown that only one hidden layer is required to approximate any
continuous function, given that sufficient degrees of freedom (Le. connection
weights) are provided (Cybenko 1989). Rence, one hidden layer was utilised in
this study and this feature was not varied. The number of hidden layer neurons by
layer was optimised by the NGO and the maximum limit was set at 64 neurons.
The test set data were used to choose the optimal network architecture and inputs.
The GA-ANN process was conducted in an iterative manner until the maximum