Application of Artificial Neural Network (ANN) for the prediction of water treatment plant influent characteristics

madbrainedmudlickAI and Robotics

Oct 20, 2013 (3 years and 7 months ago)

70 views

1


Application of Artificial Neural Network (ANN)

f
or the prediction

of

water
treatment plant influent


characteristics




Mehri Solaimany Aminabad
1
,

Afshin Maleki
1
,

Mahdi Hadi
2
,

Behzad Shahmoradi
1


1

Kurdistan Environmental Health Research Center, Faculty
of Health, Kurdistan University of
Medical Sciences, Sanandaj, Iran.

2

Center for Water Quality Research (CWQR), Institute for Environmental Research (IER),
Tehran University of Medical Sciences, Tehran, Iran.


Correspondence

to:

Afshin Maleki
, Kurdistan
Environmental Health Research Center, Kurdistan University of
Medical S
ciences, Sanandaj, Iran. E
-
mail
:
maleki43@yahoo.com
, Tel.:
+988716626969.




Word count of abstract:
21
4

Word count of main text:
3737

Number of tables:

3

Number of figures:

5

Number of

references:

20

Dissertation code:

1391/56




Abstract
:


Application of reliable

forecasting

model for any
W
ater Treatment Plant
(
WTP
)
is essential in
order to

provide a tool for predicting
influent water quality

and to form a basis for controlling the
2


operation of

the process. This would minimize the operation

and analysis

costs and assess the
stability of
WTP

performance
s
.

This paper focuses on applying an Artificial Neural Network
(ANN) approach with a Feed
-
Forward Back
-
Propagation

non
-
linear autoregr
essive neural
network

to predict
the influent water quality

of
Sanandaj WTP.

Influent water quality

data
gathered

over a
2
-
year period

were used to building the prediction model
.

The study signifies that
the ANN can predict the

influent

water quality
parameters

with correlation coefficient (R)
between the observed and predicted output variables reached up to 0.9
3
.

The prediction models
developed in this work for Alk
alinity
, pH,
calcium
,
carbon dioxide
,
temperature
,
total hardness
,
t
ur
bidity
,
total diss
olved solids and

electrical conductivity

have an acceptable generalization
capability and accuracy with coefficient of determination

(R
2
)

ranged from 0.86

for alkalinity

to
0.54

for electrical conductivity
.

The predicting
ANN
models
provides an effective analyzing and
diagnosing tool to understand and simulate the non
-
linear behavior of the
influent water
characteristics
.

The developed predicting

models

can be used by

WTP

operators and decision
makers.

Key words
: Neural network,

time
series, influent water characteristics, forecasting







1. Introduction

To maintain stable performance in a

water
treatment plant (WTP), it is desirable to know in
advance the influent water characteristics to the WTP. Water characteristics such as turbidity,
3


total suspended solids, and pH are important water quality parameters and there is a significant
relationship
between these parameters and the amounts of coagulants and flocculants used in
treatme
n
t processes. Prediction of the influent water characteristics is helpful in the optimal
scheduling of coagulation and flocculation process. In practice, the influent
wat
er characteristics

are usually estimated by the operators based on experience and
or using online sensors
. Such
estimations, however, are not accurate enough to manage

WTPs, especially for
operators

that
want to manage the WTP performance for a next day.
T
he precipitation may cause large
variability of the influent
water characteristics
, thus reducing the efficiency of WTPs

moreover

h
eavy rainfall overwhelms the

water treatment system, causing spills and overflows.

Thus
building prediction models for water
quality characteristics based on their registered historical
data can be used by data mining
approach
.

Data
mining is a promising approach for building prediction models. It is the process of finding
patterns from data by algorithms versed on the
crossroads of statistics and computational
intelligence
.

1

Artificial neural networks (ANNs) are one of the most accurate and widely
used

data mining

process and
forecasting models
. It has been shown that a network can approximate any
continuous function to any desired accuracy.
ANNs are nonlinear and the tr
aditional approaches
to time series prediction, such as the Box

Jenkins or ARIMA, assume that the time series under
study are generated from linear processes.

However, they may be inappropriate if the underlying
mechanism is nonlinear. In fact,
real wor
ld

systems are often nonlinear
.
2

Artificial neural
networks have been found to be
a viable conte
nder
to various traditional time
series models
.
3
,
4

Lapedes and Farber
5
report

the first attempt to model n
onlinear time series with artificial neural
networks.
Imrie

6

reports the application of ANN for the
River

flow prediction.

Guan
-
De Wu
7

used the ANN to model the non
linear relationship
between accumulated input and output
4


numerical data for the coagulation processes in water treatment
.

Melesse
8

present
the application
of a
multilayer perceptron (MLP)

ANN

with

an error back propagation algorithm

for
the
prediction of
s
uspended sediment load of river s
ystems
.
A
n ANN data driven modeling approach
was used by Huo et al.

9

to

predict the water quality indicators of Lake Fuxian, the deepest lake of
southwest China
.

Kalpesh
et. al.

10

present a study of Predicting Sea Surface temperature with
Nonlinear Autoregressive Neural Networks
.

In this study, we use an ANN approach to predict daily influent water characteristic to Sanandaj
water tre
atment plant.

This paper presents a data
-
mining

approach to predict influent water
characteristic in a WTP for a short
-
term period (to one day ahead).
In this work, the proposed
approach is based on the classical
n
onlinear autoregressive time series using time
-
lagged feed
-
forward networks, in which the data from the daily time series are used to forecast the next one
day.
I
n this
study

t
he prediction models developed for Alkalinity

(Alk)
, pH, calcium

(Ca)
, carbon
di
oxide

(CO
2
)
, temperature

(T)
, total hardness

(TH)
, turbidity

(Tur)
, total dissolved solids

(TDS),
electrical conductivity

(EC) and chloride (Cl) as the influent water characteristics.

The model
s

output is evaluated using statistical indices and observed wa
ter quality data.



2.
M
aterials and Methods

2.1. Artificial Neural Network (ANN) theory

Artificial Neural Network

is an information processing
tool

that is inspired by the way such as
biological nervous systems. The objective of a neural network is to compute output values from
input values by some internal calculations
.

11

Neural network is trained
to perform a particular function
by adjusting the
values of the
connections

weights

between
elements

based on a comparison of the output and the target

until
5


the network output matches the target,
so that the network can predict the correct outputs for a
given set of inputs.

Fig
. 1 illustrates
neural network training Structure.

The

network

is trained to perform complex
functions

in various fields,
including pattern recognition, identification, classification, speech,
vision, and control systems. It is also trained to solve problems that are d
ifficult for conventional
computers or human beings
.

12

There are many different types of training algorithms. One of the
most common classes of training algorithms for Feed Forward Neural Networks
(
FFNNs
)

is
called Back Propagation
(
BP
)
.

13



Figure 1. Neural
network training Structure.


The basic component of a neural network is the neuron, also called ‘‘node’’.
Fig
. 2 illustrates a
single node of a neural network.
The i
nputs are represented by a
1
, a
2

and a
n
, and the output by O
j
.
Several signals can be
inserted into the node.

The node manipulates these inputs
in
such

a way
to
give a single output signal. The values W
1j
, W
2j
, and W
nj
, are weight factors associated with
each
of
the inputs to the node. Weights are adaptive coefficients within the network th
at determine the
intensity of the input signal. Every input (a
1
,

a
2
, . . . ,a
n
) is multiplied by its corresponding weight
factor (W
1j
,W
2j
, . . . ,W
nj
), and the node uses summation

of these weighted inputs (W
1j

×
a
1
,W
2j

×

a
2
, . . . ,W
nj

×
a
n
) to estimate an output signal using a transfer function. The other input to the
6


node, b
j
, is the node’s internal threshold, also called bias. This is a randomly chosen value that
governs the node’s net input through the following equation:


Node’s output is determined using a mathematical operation on the node’s net input. This
operation is called a transfer function. The transfer function can transform the node’s net input in
a linear or non
-
linear manner. Three types of commonly use
d transfer functions are as follows:



Sigmoid transfer function






Hyperbolic tangent transfer function






Linear transfer function




The neuron’s output O
j

is found by performing one of these functions on the neuron’s net input
u
j
.

7




Figure 2. Single node anatomy.



2.2. Data collection


ANN model was developed to
predict the characteristic parameters of influent water of Sanandaj
water treatment
plant. This plant is one of the oldest Iran’s water treatment plants in Sanandaj
city in the west of Iran.

It is located in the northeast of the city of Sanandaj at an altitude of 1510
meters above sea level and near Nanaleh

v
illage
r
oad.

Nominal
d
esign capacity of the treatment plant

is

0.7

cubic meters per second,
and can increased
upto1.5

cubic meter per
second

when is needed
.
T
he raw water is supplied from
Gheslagh
dam
.

The water is transferred through a
c
oncrete and steel

transmission line
with

the

length of

8
kilometers by gravity

force
.

Treated
water
after disinfection and storage is
pumping by
a steel
transmission
pipeline
with the length of 2.2

km to Faizabad

storage tank and then the distribution
network.

Registered
daily historical
data

of the
influent
water quality parameters including

carbon dioxide, total hardness, chloride, total calcium,

total dissolved solids, total alkalinity,
electrical conductivity, pH, turbidity and temperature

were used to conducting the study. The data
was provided by urban water and Wastewater Company of Kurdistan

and

collected over a
2
-
year
8


period.

This period wa
s satisfactory as it covers all probable seasonal variations in the studied
variables.

The number
s

of data points for plant data used for the training and

test data sets together are

707

points. The description of the variables, units of measure, range of the

data, together with the
mean and standard deviation of the plant
raw
data

are presented in Table

1
.

Table 1
.

Raw influent water characteristics data of Sanandaj WTP


N

Mean
(
µ
)

SD

Min

Max

µ
-
4SD

µ+4SD

CO
2

477

3.24

10.89

0.00

199.00

-
40.32

46.80

TH

507

153.51

11.79

9.00

205.00

106.35

200.66

Cl

531

9.40

7.63

0.04

160.40

-
21.12

39.92

Calcium

510

47.14

7.01

4.10

146.30

19.12

75.17

TDS

477

209.87

19.16

1.90

252.00

133.22

286.53

Alkalinity

540

157.95

16.57

0.00

193.00

91.68

224.23

EC

505

332.56

138.65

0.00

3337.00

-
222.03

887.15

pH

547

8.47

7.18

7.16

175.90

-
20.24

37.17

Turbidity

547

3.71

5.26

0.50

65.00

-
17.33

24.76

T

524

11.42

6.31

2.00

90.00

-
13.81

36.64



2.3
Data
preprocessing

Neural networks very rarely operate directly on the raw data, although this is possible. The
disadvantage of using raw data values is that the training time for the neural network would be
significantly longer as the various variables have

very different ranges. Data pre
-
processing can
have a significant effect on the generalization performance of a supervised neural network
14
.


2.3.1
Missing data

Plant data is most times not very reliable and many problems can occur which can affect the
reliability or integrity of the data. One
of the most common

problems is that of missing data
.
15

9


Tarassenko

16

proposes
some

strategies to deal with missing data.
One
method consists of
replacing the missing data value by its mean

17

or median across the training set. The other
method is to estimate the missing value for an n
-
dimensional input vector from knowledge of the
other n
-
1 input variables. The last method uses either a linear model or a NN network to predict
the nth value given the set (n
-
1)
-
dimensional vectors as inputs.

The approach adopted eventually
is to use a linear interpolation method to replace the missing data va
lues in the Sanandaj WTP
plant data set
. In a few instances the missing data points were consecutive, but this did not extend
to more than 5 consecutive missing points.


2.3.2
Outliers and data rejection

Data that appear to be very far away from the normal data distribution may be classified as being
outliers. In certain instances however, this outlying value may be correct and is a natural product
of the variables distribution
18
.
One

approach for data rejection
is

to plot the histogram of the

data
distribution and then carefully scrutinize the data which appeared as outliers.
The s
tandard
deviation based outlier analysis
is also

as a mechanism for revealing values that are numerically
distant from the rest of the data.

In this study we take a normal distribution with cutoff 4 standard
deviations from the mean

to detect the outliers
.

Thus the data that were
more extreme than

µ±4SD

were considered as
outliers
.



2.3.3
Normalization

Neural networks can be trained by using raw data as inputs, but the training time will be
considerably longer.

But if scaled data is presented to the ne
twork, the weights can remain in
small, similar predictable ranges. Box
-
cox

transforms non
-
normally distributed data to a set of
data that has approximately normal distribution. The Box
-
Cox transformation is a family of
10


power transformations.

The

values of λ parameter for studied variables are shown in
T
able
2
.

These values are different to zero for all water characteristic parameters and the transformation of
data was performed according to the following relationships:

If λ is not =
0
, then



If λ is =
0
, then


Table 2
.

Pre
-
processed influent water characteristics data
of and

number of
Feedback delays


Description and unit of
measure

Min.

Median

Mean

Max.

SD

λ
=
䙥敤扡捫
=
摥d慹s
=

2

Carbon dioxide (mg/l)

0.1

2.3

2.6

8.2

1.5

0.41

6

TH

Total Hardness(mg/l)

122.0

155.3

154.0

197.2

10.1

1.86

4

Cl

Chloride (mg/l)

0.0

9.0

8.9

12.5

1.2

-
0.2

8

Ca

Calcium (mg/l)

25.9

48.0

47.2

59.8

4.0

2.43

5

TDS

Total dissolved
solids(mg/l)

143.0

214.0

211.0

252.0

12.6

5.05

7

Alk

Total alkalinity(mg/li)

120.6

160.2

158.2

193.0

14.0

1.76

5

EC

Electrical conductivity

(μ.mohs/cm)
=
㈵〮O
=
㌳㌮3
=
㌳〮3
=
㌹㌮3
=
ㄸ⸵
=
㐮㔹
=
N
=

=
-
=
㜮T
=
㠮U
=
㠮U
=
㠮U
=
〮0
=
-
〮〲
=
5
=
qur
=
qur扩dity(kqr)
=
〮0
=
㈮O
=
㌮3
=
㈴⸰
=
㌮3
=
-
〮㈰
=
S
=
q
=
q敭灥pat畲攨C°)
=
㈮O
=
㘮S
=
ㄱ⸰
=
ㄱ⸴
=
㔮5
=
〮㜲
=
4
=

2.
4
. Network properties

After
pre
-
processing the raw data
, the neural network model was created in
MATLAB
software
that offers a platform for the simulation application.
MATLAB Toolbox
opens the Network/Data
Manager window, which allows the user to import, create, use, and export neural networks and
data.

A nonlinear autoregressive (
NAR
) time series

neural networks
was used and
trained to
predict
the variable for the next day
from
that series past values.

The NAR is a recurrent network
with feedback arrangement as shown in
f
ig 3
.

In NAR network, there is only one series involved.
11


The future values of a time series y(t) are predicted only from past values of that series. This form
of

prediction is called nonlinear autoregressive and can be written as follows:


The networks were trained using the common algorithm of Levenberg
-
Marquardt. The

network
had
non
-
linear
sigmoid
transfer

function for the hidden layer and a linear
transfer

function for the
output layer neurons.
The number of
feedback delays
was
determined by depicting partial
autocorrelation function

(PACF)
.
The numbers of delays in PACF chart with a significant
correlatio
n coefficient were considered as the numbers of feedback delays
.

Numbers

of feedback
delays are shown in Table
2
.
The other Network properties are as follows:



Network type: Feed
-
Forward Back
-
Propagation.



Training function: TRAINLM.



Performance function:

MSE.



Number of hidden layers:
1
.



H
idden
layer size:
A single hidden layer with different count of neurons (i.e. 1 to 20) has
been assessed for this study
.
The hidden layer with the size near ten neurons was provided
the best performance for all studied

parameters. Thus 10 neurons in the hidden layer were
considered for all models.

12




Figure 3. Neural network predicting structure with a hidden layer.


The

MATLAB routine trainlm

with memory reduction was used for the optimization
.

this
algorithm
attains fast learning speed and high performance relative to other optimization
algorithms

and t
he details of this algorithm are reported by Hagan et al
.
19

The performance
function used for training is based on the mean square errors (MSE) between actual
WTP

influent
water characteristics

and network predictions. Based on the selected network structure, the
training process was activated to achieve a performance target of 1×10
-
3

for a maximum training
epochs of 1000. The learning rate was chosen to be 0.01. The value of this parameter was
obtained after performing several trial and error runs. It was found that this value insures stable
fast learning.

In order to study the relative performance of the network
,
the

error statistics of correlation
coefficient (
R
) and mean square error (MSE)

were worked out. The underlying expressions as
well as the strengths and weaknesses of these parameters are given as below

10
.

Correlation coefficient (
R
):


13



where
= observed y
t
,

= mean of

,
= predicted
y
t
,

=

mean of
, and
𝑛

= number of observations.

The correlation coefficient,
R
, shows the extent of the

linear association and similarity of trends
between the target

and the realized outcome. It is a number
between 0 and 1

such that the higher
the correlation coefficients the better the

model fit is. It however gets heavily affected by the
extreme

values.

Mean square error (MSE):


The mean square error is suited to iterative algorithms
and is a better measure for high values. It
offers a general picture of the errors involved in the prediction but is also sensitive to

high values.


3. Results and discussion

The most common training algorithm used

in the ANN literature is called Back Propagation
(BP). Back propagation was developed and popularized by Rumelhart

et al.
20

and it is widely
implemented of all neural network

algorithms.

It is based on a multi
-
layered feed forward
topology

with supervised learning.
The network uses the defaul
t Levenberg

Marquardt algorithm
for training.
The

input vectors and target vectors
randomly divide
d

into three sets as follows:
70
% are used for
training;
15
% are used to validate that the network is generalizing and to stop
training before over
-
fitting; the last
15
%

are used as a completely independent test of network
generalization.

14


F
ig.
4

shows
the results

of regression between network outputs and
data sets of validation,
training and test targets.
It is observed that the
output tracks the targets

very well
.

Data from
Table
3

shows
R

and MSE

of each ANN
for validation, training and test steps.

The

correlation
coefficient
R

measure

the correlation between outputs and targets.

An R value of 1 means a close
relationship, 0 a random relationship while
the MSE

is the
mean
squared difference between
outputs and targets, the lower values are the better.

The coefficient
R

for the validation phase upon application of the test set, ranges from
0.
61

for Cl

till
0.93

for Alk and t
he coefficient of determination
R
2

ranges from 0.
37

for Cl to
0.
86


for Alk
.
These figures indicate that
thirty seven percent of the variation in
the Cl variable can be
explained by the variable time delays. The remaining sixty four percent can be attributed to
unknown, lurking variables or inherent variability.

Neural network model for Cl may

therefore
not able to solve this particular input
-
output

mapping problem

well
.


The results for
Alk

in Table
3

are interesting as the
R correlation coefficient

is
0.93(R
2
=0.86)

for
the
validation
phase. Th
is

indicate
s
that this model has the best result throughout. However all
other results are not too far
off. The regression coefficient ranges from 0.
74 for EC (R
2
=0.54)

up
to 0.
89 (R
2
=0.79) for pH
.

Thus for these variables more than fifty percent
of the variation in
them

can be explained by their time delays.
Time series model for these variables therefo
re are able to
solve input
-
output mapping problem well.

For all studied water influent characteristics
t
he simulation results of influent parameters are
presented in
f
ig.
5

by plotting the measured and predicted output variables.

The

network response
is satisfactory, and simulation can be used for entering new inputs.

15




CO2

TH



Cl

Ca



TDS

Alk



EC

pH

Figure 4. Network regressions.


16




Tur

T

Figure 4. (continued)


The
test
ing

step

of the models

were also
provides similar results to
validation step

results
.

The
correlation
coefficient
ranges from

0.
65 (R
2
=0.42) for Cl to 0.8
8 (R
2
=0.77)

for
TH and T
.

for
Alkalinity the test phase R is 0.85(R
2
=0.72).

Thus t
h
ese

result
s

confirm the validation step
.



Table 3. Performance of MLP networks

parameter


training phase

validation phase

all phase

Testing phase

MSE

R

MSE

R

MSE

R

MSE

R

Cl

0.46

0.77

0.80

0.61

0.55

0.73

0.76

0.65

EC

164.12

0.74

153.97

0.74

161.16

0.73

154.59

0.70

TDS

44.92

0.85

48.45

0.78

51.77

0.82

87.24

0.74

Tur

3.11

0.85

3.88

0.83

3.63

0.84

5.81

0.83

TH

13.01

0.93

22.73

0.84

16.55

0.91

26.98

0.88

T

1.43

0.93

4.80

0.84

2.33

0.91

4.03

0.88

CO
2

0.52

0.87

0.59

0.84

0.58

0.85

0.85

0.80

Ca

5.17

0.84

4.12

0.85

4.76

0.84

3.48

0.86

pH

0.02

0.87

0.02

0.89

0.02

0.86

0.03

0.79

Alk

22.94

0.94

22.55

0.93

28.40

0.93

59.87

0.85



17



(CO
2
)


(Cl)


(TDS)


Figure 5. Simulation results.


18



(TH)


(Ca)


(Alk)

Figure 5. (continued)



19



(pH)


(EC)


(Tur)

Figure 5. (continued)



20



(T)

Figure 5. (continued)


Given the above, it can be conclude that a feed
-
forward neural network based nonlinear
autoregressive (NAR) model can be used for forecasting time series

values well.

The results of
this study indicated high
correlation coefficient between
the measured and predicted output
variables, reaching up to 0.93.
Therefore, the prediction models developed in this work for Alk,
pH, Ca, CO
2
, T, TH, Tur, TDS and

EC have an acceptable generalization capability and accuracy
with coefficient of determination ranged from 0.86 for Alk to 0.54 for EC. As a result, the neural
network modeling could effectively simulate and predict these influent water quality parameter
s
of Sanandaj WTP.

Finally it is concluded that

nonlinear autoregressive or NAR neural network provides an effective
analyzing and diagnosing tool to understand and simulate the non
-
linear behavior of influent
water characteristics of the plant, and is
a valuable predicting tool for plant operators and
decision
makers
.


4
. Acknowledgement

21


The authors thank the Kurdistan University of Medical Sciences for financial support. The
authors also would like to thank Kurdistan
U
rban Water and Wastewater
Company for

the
provision of
the two years period results of chemical analyzing
of
the influent water of Sanandaj
WTP
.


5
. References

1.

Witten IH
,

Frank

E.

Data Mining: Practical machine learning tools and techniques.
Second
Edition.
Morgan Kaufmann

Publishers Inc.

San Francisco, CA, USA
;

2005.

2.

Zhang

G
, Eddy Patuwo

B
, Hu

MY
.

Forecasting
with artificial neural networks
: The state of
the art. Int
J

F
orecasting 1998; 14(1): 35
-
62.

3.

Chen

Y
,
Yang B
,

Dong J, Abraham A.

Time
-
series forecasting using flexible neural tree
model. Inform sciences 2005; 174(3
-
4
): 219
-
35.

4.

Giordano

F
, La Rocca

M
, Perna

C.

Forecasting nonlinear time series with neural network
sieve bootstrap. Comput Stat Data An 2007; 51(8): 3871
-
84.

5.

Lapedes A
,

Farber

R.

Nonlinear signal processing using neural networks: Prediction and
system modelling.

IEEE international conference on neural networks, San Diego, CA, USA
;
1987.

6.

Imrie

C
, Durucan

S
, Korre

A.

River flow prediction using artificial neural networks:
generalisation beyond the calibration range. J
Hydrol

2000; 233(1): 138
-
53.

7.

Wu G
-
D
,

Lo

S
-
L
.

Effects of data normalization and inherent
-
factor on decision of optimal
coagulant dosage in water treat
ment by artificial neural network. Expert Syst Appl 2010;
37(7): 4974
-
83.

22


8.

Melesse

A
,
Ahmad S, McClain ME, Wang X, Lim YH.

Suspended sediment load prediction
of river systems: An artificial neural network approach. Agr Water Manage 2011; 98(5):
855
-
66.

9
.

Huo

S
,
He Z
,

Su J, Xi B, Zhu C.

Using Artificial Neural Network Models for Eutrophication
Prediction. Procedia Environ Sci 2013;
(
18
)
: 310
-
6.

10.

Patil K,
Deo MC
,

Ghosh S, Ravichandran M.

Predicting Sea Surface Temperatures in the
North Indian Ocean with Nonlinear Autoregressive Neural Networks. Int J Oceanogr 2013;
2013
: 1
-
11.

11.

Delgrange N,
Cabassud C
,

Cabassud M, Durand
-
Bourlier L, Laine JM.

Neural networks for
prediction of ultrafilt
ration transmembrane pressure

application to drinking water
production. J membrane sci 1998; 150(1): 111
-
23.

12.

Looney CG, Pattern recognition using neural networks: theory and algorithms for engineers
and scientists. Oxford University Press Inc
, NY/Oxfor
d; 1997.

13.

Demuth

H
, Beale

M
, Hagan

M.

Neural
n
etwork
t
oolbox™ 6. User Guide,
Copyright
, 1992;
2008.

14.

Teng CM. Correcting
n
oisy
d
ata. Proceedings of 16
th

International Conference on Machine
Learning.
Morgan Kaufmann Publishers Inc
,

San Francisco,
CA, USA
;
1999.

15.

Arthur RM. Application of
o
n
-
line
a
nalytical
i
nstrumentation to
p
rocess
c
ontrol. Proceedings
of the
f
irst
a
nnual
c
onference on
a
ctivated
s
ludge
p
rocess
c
ontrol. Michigan: Ann Arbor
Science Publishers
; 1982.

16.

Tarassenko

L
, A Guide To
Neural Computing Applications. John Wiley and Sons
, New
York; 1998.

17.

Olssen G
,

Newell

B.

Wastewater
t
reatment
s
ystems,
m
odelling,
d
iagnosis and
c
ontrol. IWA
Publishing
, London, UK; 1999.

23


18.

Masters

T.

Practical
n
eural
n
etwork
r
ecipes in C++. Academic P
ress
, San Diego;1993
.

19.

Hagan MT
, Demuth

HB
, Beale

MH.

Neural network design. Thomson Learning Stamford,
CT
;1996.

20.

Rumelhart DE
, Hinton

GE
, Williams

RJ.

Learning internal representations by error
propagation.

MIT Press

Cambridge, MA, USA
; 1986.