Journal of Environmental Protection, 2010, 1, 438-447
doi:10.4236/jep.2010.14051 Published Online December 2010 (http://www.SciRP.org/journal/jep)
A Fast Predicting Neural Fuzzy Model for Suspended Solid
Removal Efficiency in Multimedia Filter
Rusul Naseer1, Alaa' Abdulrazaq Jassim1, Saad AbuAlhail2
1Department of Chemical Engineering, Faculty of Engineering, Basrah University, Basrah, Iraq; 2Department of Civil Engineering,
Faculty of Engineering, Basrah University, Basrah, Iraq.
Received August 4th, 2010; revised September 6th, 2010; accepted September 10th, 2010.
ABSTRACT
Modeling of filter performance is very difficult because of complexity of the defining physical and chemical events in
the filtration system whereas the knowledge of functionality of filter coefficient. The main objective of this study is to
predict the performance of multimedia filter and to evaluate both the initial and transient stage of suspended solid re-
moval efficiency depending on experimental data. Fuzzy logic has been used to build a model of multi input and one
output (MISO) for the removal efficiency of multimedia filter which it consists from sand and granular activa ted carbon
(GAC) mediums. The control parameters of (FLC) of Sugeno model are seven parameters which are media depths, me-
dia grains size for both sand and GAC, filtration rate, diameter of susp ension particle, feed conc entration, and opera-
tion time. The output parameter is removal efficiency of media filter wh ereas these data are collo cated from pilot scale
deep bed filter, thus, the removal efficiency of filter was modeled by 575 rules as a function of different control pa-
rameters. An adaptive of neuron fuzzy inference system (ANFIS) had used to simulate the experimental data. The simu-
lation results were evaluated using mean absolute percentage error (MAPE), whereas the results showed that the pre-
diction of ANFIS model has a good agreement with experimental data when the MAPE is equal to 7.0458 and fuzzy rule
-based modeling proved a reliable and flexible tool to study the performance of multimedia filter. The conclusion
showed that there is a relationship between flow rate, effective size and optimum bed depth for all filter media, the in-
crement of effective size generates a higher value of optimum filter bed depth fo r a lower value of filtration rate. It was
concluded that th e optima l remova l efficiency (95-100) achieved by (0.5-0.7 mm) grain size of sand, (1.5-1.9) mm grain
size of granular activated carbon (GAC), with media depths should range from 0.3 to 0.6 m.
Keywords: Multimedia Filter, Sand Filtration, Removal Efficiency, Fuzzy Logic, Suspended Solid
1. Introduction
Deep bed filtration is an effective process in removing
particles from range 0.01 (µm) to 100 (µm) in size [1]
Removal of these particles by deep bed filtration in-
volves co mplex mechan isms .First; p articles in susp en-
sion are transported near filter grains by mechanisms
such as sedimentation, interception, diffusion, inertia
and hydrodynamic effect. The effective removal of
these particles depends on the attachment mechanism,
which depends on the surface forces acting between
particles and filter grains. The factors, which affect
these forces eventually, it will affect of the perform-
ance of deep bed filtration. Generally, several mathe-
matical filtration models have been proposed to de-
scribe Dispersed particles removal by filter whereas
macroscopic and microscopic theories are widely ac-
cepted. In the macroscopic approach, first order kinet-
ics in the removal of particulate is assumed, whereas
the microscopic approach takes into account single
collector efficiencies. Filtration equations describing
the deep bed filtration was proposed by [2]. Similarly,
there are many other models available in the literature
including in [3-5]. These models require data for char-
acteristics of filter media, type of flow and liquid. In
last decade, fuzzy logic and neural network has been
employed to model in some complex environmental
processes such as water and wastewater treatment.
Fuzzy logic provides a language with a syntax and se-
mantics to translate qualitative knowledge into a Nu-
merical reasoning. The term computing with words has
been introduced by [6] to explain the notion of reason-
ing linguistically rather than with numerical quantities.
Such reasoning has central importance for many emer-

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 439
ging technologies related to engineering and the sci-
ences. Fuzzy and neural models have shown great ad-
vantages in the simulation, prediction and controlling
of the medical diagnosis, information technology, wa-
ter quality, reliability analysis and many other indus-
trial applications, [7] Fuzzy modeling was used to pre-
dict estuary quality in [8], prediction of evaporation [9],
prediction of Consumption Istanbul city using fuzzy
logic approach [10], prediction of water level in reser-
voir [11], modeling of anaerobic digestion of primary
sedimentation sludge [12]. In this study, the perform-
ance of multimedia filter (sand and GAC) filters was
investigated and predicated as a function of media
characteristics, operation condition and the quality of
row water by a neural fuzzy model based on adaptive
neuron-fuzzy inference system (ANFIS) model which
is proposed in this work.
2. Material and Methods
2.1. Experimental Set up
Filtration Process was carried out by a pilot laboratory
filter which is used to collect the data in this work. The
laboratory scale Deep bed filter column has been de-
signed to operate identically to full scale granular fil-
ters. Using deferent filter media with different bed
depth tests on this unit to provide operational data
which was scaled up to full size. The media in each
filter was supported on a PVC orifice plate drilled with
5 mm holes and covered by a wire mesh to prevent
sand passing through the orifices. A scale was made in
front of tube column to estimate bed height. The labo-
ratory filter was used to measure the experimental re-
moval efficiency of suspension clay in multimedia fil-
ter and concentration profiles through the filter bed.
The Deep Bed Filter Column is a clear acrylic unit
mounted in a floor standing framework approximately
2 m high with flanged end pieces to allow easy access.
The medium is supported on a corrosion resistant gauze
mesh below is packed 1 kg of 0.01 m Ballotini to en-
sure good wash water distribution . Slotted sampling
tubes inserted through the wall penetrate into the media,
and are fitted with control valves so that suspension
samples can be taken are kinetically. Plain tubes also
penetrate the medium through the wall to transmit
pressure to a manometer system. These sampling and
manometer probes are located at 0.02 m depth intervals,
but staggered in position, over 0.8 m depth which is 0.2
m GAC media over 0.6 m sand media and. Conse-
quently as shown in Figure 1 where Deep bed filter
consist of pump, sump tank, flow controller, rotameter,
control valves, tubing, sampling tubes and bank of wa-
ter differential manometers as shown in figure below.
2.2. Model Architecture and Model Components
The schematic architecture of the neural fuzzy model is
depicted in Figure 2. It consists of the five key com-
ponents: inputs and outputs database and preprocessor,
a fuzzy system generator, a fuzzy inference system, and,
an adaptive neural network representing the fuzzy sys-
tem. The input and output parameters are selected or
generated from the major parameters that is influence
on removal efficiency which are flow rate, influent
concentration of suspended solid, filter depth, types of
media, grain size, diameter of suspension particle and
operating time. One output parameter is the removal
efficiency of filter. Table 1 showed the range of each
input that is used in this work.
3. Adaptive Network-Based Fuzzy Inference
System (ANFIS)
In this work, both the (FLC) and ANNS have been em-
ployed together to design a neuron -Fuzzy logic con-
troller. A fuzzy system with learning ability has been
constructed and is trained directly from the in-
put-output data of the plant. Since the ANFIS has the
property of learning; membership functions and fuzzy
Figure 1. Laboratory pilot filtration unit schematic.

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 440
Inference
Engine
Fuzzifier
Defuzzifier
Rule Base II
FIS. eff.
eff (n + 1)
Depth (n)
Flow rate (n)
Grain size (sand) (n)
Grain size (GAC) (n)
Feed concentration (n)
Diameter of particle (n)
O
p
erati on Time
(
n
)
Figure 2. Corresponding ANF I S schematic architec t ur e.
Table 1. Ranges of input variables.
Input variable The range
Flow rate (cm3/min) 500-1300
Feed concentration (mg/l) 2750-34000
Sand grain size (mm) 0.5-1.18
GAC grain size (mm) 1.5- 2 .36
Sand depth (m) 0.1-0.7
GAC depth (m) 0.2
Diameter of particle (µm) 0.01-100
Operation time (sec) 0-8400
rules of the controller can be tuned automatically by
the learning algorithm. Learning is based on the per-
formance error, which is evaluated by comparing the
process output with the desired or required output.
ANFIS provides two main perspectives: one is to tran-
sform human knowledge or experience into the rule
base and database of a fuzzy inference system and
second is to tune the membership functions resulting to
minimize the output error measure or maximize per-
formance index. ANFIS can also act as for building a
set of fuzzy if-then rules with appropriate membership
functions to generate the stipulated input–output pairs
[13].
3.1. Fuzzy Rule-Based Modeling
Fuzzy sets are the sets with boundaries that are not
precise. A fuzzy set is an extension of the traditional
set theory (in which x is either a member of set A or
not) in that an x can be a member of set A with a cer-
tain degree of membership µ among the various types
of fuzzy sets. A fuzzy number describes the relation-
ship between an uncertain quantity x and a membership
function µ which ranges between 0 and 1 it is assumed
that the fuzzy inference system under consideration has
two inputs and one output. The rule basis contains two
fuzzy if- then rules of Takagi and Surgeon’s type as
follows [14]:
If x is A and y is B then Z is f(x.y)
Where, A and B are the fuzzy sets in the antecedents
and z = f(x.y) is a crisp function in the consequent. f(x.y)
is usually a polynomial for the input variables x and y.
But it can also be any other function for approximate
description of the output of the system within the fuzzy
region as specified by the antecedent. When f(x.y) is a
constant, a zero order, Sugeno fuzzy model is formed,
which may be considered to be a special case of Mam-
dani fuzzy inference system where each rule conse-
quence is specified by a fuzzy single ton, Therefore first
order Sugeno fuzzy model is derived in this study to
modeling the ANFIS algorithm for a first order rules
Sugeno fuzzy inference system, the rules may be stated
as:
R1: If x is A1 and y is Bi then f1i = r1i (1a)
R2: If x is A2 and y is Bi then f2i = r2i (1b)
where x is the input (antecedent) variable and Ai is the
antecedent linguistic constants (the qualitatively defined
functions).
Similarly, y is the inpu t (anteceden t) linguistic v ariable
and Bi is the consequent linguistic constants. The values
of x and y, and Ai and Bi are fuzzy sets defined in the
domains of their respective base variables. The lingu istic
terms Ai and Bi are usually selected from sets of prede-
fined terms, such as high depth, medium and low.
The rule base R = {Ri/i = 1, 2…, K} and the sets A and
B constitute the knowledge base of the linguistic model.
Each rule is regarded as a fuzzy relation (fuzzy restric-
tion on the simultaneous occurrences of values x and y)
Ri(x,y) Fuzzy number describes the relationship between
an uncertain quantity x and a membership function



which ranges between 0 and 1. All the input membership

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 441
functions



Ai
x
 are Gaussian Membership Func-
tions give n by:

 


2
2
1
1
or
exp
Ai bi
Ai
xxciai
xci
xai






 



(2)
where, ai and bi are the lower and upper limits of the
integral which determines the validity domain of the
membership function. This relation can be computed in
two basic ways by using fuzzy implications or fuzzy
conjunctions. In this study, the Sugeno method was used,
in which conjun ction
A
B is computed by a minimum
operator.
i.e. Ri = (Ai . Bi),



,
RiAi Bi
x
yxy  

(3)
The minimum operator is computed on the Cartesian
product space of x and y, i.e., for all possible pairs of x
and y. The fuzzy relation R represents the entire model
(Equation (3)) and is given by the disjunction (union or
maximum, i.e., s-norms) of the (n) individual rule rela-
tions Ri:



1
1
,max
n
i
i
RinAiBi
nR
x
yxy 



 

 (4)
Now the entire base is enco ded in the fuzzy relation R
and the output of the linguistic model can be computed
by the max–min composition (°):
o
y
xR (5)
Suppose an input fuzzy value x = A which has the
output value ' B given by the re l a t i onal composition:



,max ,
BxAR
x
yxxy  

(6)
By substituting Equation (3) into Equation (6), get:

 

1
,max max
BxAinAiBi
x
yx xy  



 


(7)
Assuming


max ,
xA Ai
Bixx y  

is the de-
gree of fulfillment of the (ith) rule’s antecedent. The
output fuzzy set of the linguistic. The output fuzzy set of
the linguistic model is thus
  max
BxBi
yBiy 




 (8)
Equation (8) represents the output fuzzy Set of the lin-
guistic model.
The most common methods used for defuzzification is
Yager’s censorial method, is always used for defuzzifica-
tion due to its simplicity that can be determined as:



'
'
.
b
B
ab
B
a
yy
Defuzzified valueu
y




(9)
where: y is the censorial distance from the origin.
This algorithm is for single input and single output
(SISO). It can be extended to multiple inputs and single
output (MISO) and multiple outputs (MIMO). The MI-
MO model is a set of MISO models.
In this study, the predicting of removal efficiency
should have been multi input and one output, therefore
(MISO) model was used as follow:
Ri: If x1 is A1i and x2 is A2i and xp is Api then f is ri (10)
The above model is the special case of (Equation (1)),
as the set Ai is obtained by the Cartesian product of fuzzy
sets:
123
...........
iiii ip
A
AAA A

  (11)
j = 1, 2….p
Hence the degree of fulfillment (Bi) becomes:






1122
.......
AiAiAip p
Bi xxx    (12)
4. Removal Efficiency Modeling
4.1. Data Set for Training and Validating
The data collected for 575 operating conditions were
used for developing a fuzzy rule-based model to predict
the optimum removal efficiency of multimedia filter .The
control parameters of (FLC) with Sugeno model, are
seven parameters which are media depths, media grain
size, filtration rate, particle diameter, feed concentration,
and operation time. The output parameter is removal ef-
ficiency of media filter whereas these data are collocated
from my experimental work of deep bed filter and for
multimedia filter the overall removal efficiency was de-
termined.
From the derivation as follow:
0
10
GAC
i
CC
EC


 (13)
1GAC i
iGAC
CC
EC


 (14)
From Equation (13)

01
1
GAC i
CCE

 (15)
Substituted Equation (15) into Equation (14) yields:



011
01
1
1
ii
ii
CEC
ECE



 (16)

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 442
The overall efficiency (Efilter) of filter is equal to sum
of efficiency for all layer in depth filter, thus can be ex-
press as:


11
1
i
filteri i
EEEE

 (17)
where, Ci+1,i+2,…..N indicate to sand bed, i = The number
of output layer.
The mean and standard deviation of the inputs and
output were used to define the granularities (the levels of
scale). The variability in the input control parameter un-
der any given condition was us ed for fuzzificaion. A two
granule scale, low and high, was used for operation time.
Similarly, feed concentration of dispersed particles and
filtration rate were expressed by three (low, medium,
high) and four granule scale for media depths (very low,
low, medium, high), finally five scale was taken for di-
ameter of particle (very low, Medium, high, vary high) as
shown in Figures 3(a)-(g).
The fuzzy rule based model was developed in the fol-
lowing for mat:
R1: If x is high and y is Low and ……the n E is ……
R2: If x is Low and y is high and …th en E is ……
4.2. Modeling Results
In this study, the input parameters are subdivided into
several types of reference fuzzy sets with the 575 training
dataset, we choose some of these rules and inputs pa-
rameter to build the last structure of ANFIS model as
shown Figure 4 after the model was trained, the infer-
ence was performed in accordance with 575 rule of FLC.
(a)
(b)
(c)

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 443
(d)
(e)
(f)
(g)
Figure 3. (a)-(g) The qualitative scales for inputs and output of (MISO) model.

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 444
Figure 4. ANFIS structure for removal efficiency.
These rules are applied with deferent boundary conditio n
to predict th e removal efficiency ( Figure 5). Those rules
were obtained after the network was trained. Some other
rules were also included theoretically in terms of com-
paring output values in accordance with input values.
Figures 6(a)-(b) shows the results of applied ru les and
their corresponding outputs according to the input date
that should been determined. Using the interface, de-
fuzzified values for output variables can be derived by
changing input values manually. We selected the input
data flow rate, 500-1300 cm3/min, bed height 0.5-0.8 m,
feed concentration of dispersed particles is 14000-34000
mg/l, grain size is 0.5-0.7 mm of sand and 1.5-1.9 mm of
GAC with 600-8400 second of operation time, finally
diameter of particle is 0.01-10 µm. the removal effi-
ciency of multimedia filter is pred icted by FLC that equal
to 96.9% and 80% as shown in Figures 6(a)-(b) respec-
tively. It is not flexible to get defuzzified output values
for all the real input values using the interface. For that
reason, a program is written using Matlab codes to drive
defuzzified output results in accordance with real input
values.
Figures 7(a)-(g) shows the result of prediction the
removal efficiency of multimedia filter and the inputs
variable by Surgeon system. These results are plotted by
three dimensional graphic which illustrates several sur-
face viewer that obtained from the fuzzy logic toolbox.
4.3. Simulation Result by (ANFIS) Model
In this study, the final adaptive of neuron inference sys-
tem (ANFIS) was proposed by of training data set that
show perversely. (ANFIS) model was employed to pre-
dict the removal efficiency of suspended solids with re-
spect to sample number. The performance of this predic-
tion was evaluated based on mean absolute percentage
error (MAPE) as follow:
exp
1
1100
Np
tp
yy
MAPE Ny



 (18)
Another evaluation is used in (ANFIS) model is the
correlation coefficient (R) which can be defined as fol-
low:
Figure 5. Rule editor of fuzzy logic control tool.

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 445
(a)
(b)
Figure 6. (a)-(b) Rule viewer screen to obtain of defuzzified results.


exp
1
22
exp
11
N
pp
t
NN
pp
tt
yyyy
Ryy yy






 (19)
Figure 8 shows the simulation result, between the ex-
perimental data and the prediction of (ANFIS) model.
The best performance is achieved by MAPE that equal
7.0458.
5. Conclusions
Modeling of filter performance is very difficult because
of complexity of the defining physical and chemical
events in the filtration system whereas the knowledge of
functionality of filter coefficient. So, in this study, AN

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 446
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Figure 7. (a)-(g) 3-D Response surface graph for removal
efficiency with different input parameter.
FIS models were used to predict the performance of mul-
timedia filter. The results of this study can be depicted as
follows:
1) The fuzzy logic control model (FLC) was estab-
lished in multimedia deep bed filter to predict the per-
formance of multimedia filter (sand + GAC) and to eva-
luate both initial and transient stage of suspension parti-
cle removal. Whereas the result showed that it is a flexi-
ble tool to study the performance of multimedia filter for
dispersed particles removal in terms of different operating

A Fast Predicting Neural Fuzzy Model for Suspended Solid Removal Efficiency in Multimedia Filter 447
Figure 8. Simulation result of removal efficiency by (ANFS) model.
parameter whereas the optimal removal efficiency 95-
100 achieved by 0.5-0.7 mm grain size of sand, 1.5-1.9
mm grain size of GAC, with media depths should range
from 0.3 to 0.6 m.
2) The overall removal efficiency depends on filtration
velocity, physical properties of media, media type and
the quality of row water, the result illu strates that there is
a relationship between flow rate, effective size and opti-
mum bed depth. For all filter media, the increment of
effective size generates a higher value of optimum filter
bed depth for a lower value of filtration rate; in addition
to that the high removal efficiency can be achieved by
using smaller grain size.
3) Adaptive Nauruan fuzzy inference system (ANFIS)
was used to simulate the experimental result. The Simu-
lation result showed a good agreement between observed
and predicted values for both training and testing data
whereas the MABE is equal to 7.0458.
REFERENCES
[1] C. T. Alan, D. R. Don and J. B. Malcolm, “Water Sup-
ply,” 5th Edition, 2000, pp. 335-347.
[2] K. Yao, M. T. Habiban and C. R. O’Melia, “Water and
Wastewater Concept and Applications,” Environmental
Science Technology, Vol. 5, No. 11, 1971, pp. 1105-1112.
[3] C. Tien and B. V. Remoarao, “Granuler Filtration of Aer-
sols and Hydrosols,” 2007, pp. 29-31.
[4] A. Salim, S. Sizert and A. Bruand. “Development of
Adarcy Brinkman Model to Simulate under Flow and
Tracer Transport in a Heterogeneous Karstic Aquifer,”
Hydrogeology Journal, Vol. 15, 2008.
[5] Y. Sung and Andrew “Simulation of Pore-Scale Particle
Deposition and Clogging,” Journal of Transpiration in
Porous Media, Vol. 65, No. 11, 2005, pp. 53-87.
[6] L. A. Zadeh, “Fuzzy Logic Computing with Words,”
IEEE Transactions—Fuzzy Systems, Vol. 4, No. 2, 1996,
pp. 103-111.
[7] S. R. Al-Zahrani, M. A. Sheikh, A. K. T. Husain and S.
Farooq, “Performance Evaluation of Slow Sand Filters
Using Fuzzy Rule-Based Modeling,” Environmental
Modeling & Software, Vol. 19, No. 5, 2003, pp. 507-515.
[8] A. Altunkaynak, M. Ozger and M. Cakmakci, “Fuzzy
Logic Modeling of the Dissolved Oxygen Fluctuations in
Golden Horn,” Ecological Modelling, Vol. 189, No. 34,
2005, pp. 436-446.
[9] O. Terzi, M. E. Keskin and E. D. Taylan, “Estimating
Evaporation Using ANFIS,” Journal of Irrigation and
Drainage Engineering – ASCE, Vol. 32, No. 5, 2006, pp.
503-507.
[10] A. Altunkaynak, M. Özger and M. Cakmakci, “Consümp-
tion Prediction of Istanbul City by Using Fuzzy Logic
Approach,” Water Resources Management, Vol. 19, No.
5, 2005b, pp. 641-654.
[11] F. J. Chang and Y. T. Chang, “Adaptive Neuro-Fuzzy
Inference System for Prediction of Water Level in Res-
ervoir,” Advances in Water Resources, Vol. 29, No. 1,
2005(b), pp. 1-10.
[12] M. Cakmakci, “Adaptive Neuro-Fuzzy Modeling of An-
aerobic Digestion of Primary Sedimentation Sludge,”
Bioprocess and Biosystems Engineering, Vol. 30, No. 5,
2005(b), pp. 349-357.
[13] S. R. Jang, “ANFIS: Adaptive-Network-based Fuzzy
Inference Systems,” IEEE Transaction on Systems, Man
and Cybernetics, Vol. 23, No. 3, 1993, pp. 665-685.
[14] M. Z. Huang, J. Q. Wan, Y. W. Ma, and W. J. Li, “A Fast
Predicting Neural Fuzzy Model for On-Line Estimation
of Nutrient Dynamics in an Anoxic Process,” Journal of
Science Direct Bioresource Technology, Vol. 101, No. 6,
2010, pp. 1642-1651.