DESIGN OF MONITORING SYSTEM FOR OXIDATION DITCH
BASED ON FUZZY ASSISTED MULTIVARIATE STATISTICAL
PROCESS CONTROL
1
Katherin Indriawati 1, Metrik Kresna P 1
Engineering Physics Department, Faculty of Industrial Technology, Institut Teknologi Sepuluh Nopember
Kampus ITS, Keputih – Sukolilo, Surabaya 60111
email : katherin@ep.its.ac.id
ABSTRACT
Monitoring system in industrial process is
needed to diagnose any situation that happen the
process. For a complex system, there are many
variables affecting the process, therefore
Multivariate Statistical Process Control (MSPC) is
needed to replace Statistical Process Control (SPC)
to analyze situation of process.
In this paper, MSPC have been implemented to
monitor some situation modes in simulation
happened in oxidation ditch at the waste water
treatment system assisted by fuzzy system as
decision taker. Principal Component Analysis
(PCA) is a MSPC method that could reduce
multivariate data variable to become some new
variables, and then from the new variables is
applied T² to detect does the process stay in normal
condition. Each condition that described have
different T² value, then is applied fuzzy logic to
determine the condition from T² value. Result of
decision of simulation can identify the situation
with level of success of 100 %.
Keywords: MSPC, PCA, Oxidation Ditch, Fuzzy
Logic.
1
INTRODUCTION
Oxidation Ditch (OD) or also known as
oxidation pond is one of the methods used for waste
treatment system plant developed from direct liquid
waste disposal methods. It disposes liquid waste
directly to the tailing pond. In an oxidation pond
system, the concentration of microorganism is
relatively small and oxygen supply and agitation
takes place naturally. These cause degradation
process of organic materials occur naturally for
relatively long time over a wide area. The process
in the oxidation pond is very sensitive to direct
disturbances such as pressure variations from the
dividing valve, changes in weather (rain), and
variations of composition. Hence a monitoring
system is required to give information about the
state of the process and also about the process
behavior. Then, based on that information, further
handling or action can be taken to ensure optimal
running of the plant.
Modern system such as oxidation ditch is a
complex process therefore it involves multiple
process variables. Due to the number of variables, it
will be difficult to design a control or monitoring
system for the process. To solve this problem, it can
be used the Multivariate Statistical Process Control
(MSPC) method (Mac Gregor and Kourti, 1995).
MSPC changes multidimensional information into a
number of latent variables that explain the
variability of the measured variable, including the
relations between measured variables. MSPC makes
use of statistical methods to analyze, control and
influence improvement on process performance
based on the existing multivariable. Reducing
multivariable to a few main variables can be done
by using the Principle Component Analysis (PCA)
(Lowry and Montgomery, 1995).
However, the latent variable acquired from
PCA cannot explain the condition of the ongoing
process. This can cause difficulties for operators to
interpret them into physical forms. Therefore to
interpret these new variables and to classify the
current condition of the process, an algorithm for
decision-making is needed.
One of the current methods often used for
decision making is the Fuzzy System. The research
done by Indriawati and et. all (2006) incorporates
fuzzy system application on SPC which uses fuzzy
system for interpreting two control graphics
(Shewhart and CUSUM) to determine the
conditions of a non-correlated process whether it is
on Normal, Warning or Action.
In this paper, a fuzzy logic assisted MSPC
oxidation ditch monitoring system design is
explained. The system used fuzzy logic assistance
to make decision about the operating state of the
plant. The oxidation ditch modeled in this paper is
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based on the Waste Water Treatment Plant at IPAL
PT. SIER. Hypothetically the state mode for the
plant comprises of normal mode, varied
compositions, wastewater flow rate change,
temperature change and equipment malfunction.
For simulation purposes, the used model
complies with International Association on Water
Quality (IAWQ) Active Sludge model No.1. The
considered / monitored variables are biochemical
oxygen demand (BOD), ammonia concentration
and nitrate concentration.
2
The value of m is influenced by a number of
parameter changes, i.e. the maximum bacterial
growth rate are stated by:
DO
μ' = μ e0.098(T 15 ) 
 [1  0.833 (7.2  pH )] (3)
m
m
KO2 + DO
which ’m is the maximum bacteria growth rate
affected by temperature changes, oxygen and pH (h1
), T is temperature (ºC), DO is disolved oxygen
concentration (mg/l), KO2 is half saturation constant
of dissolved oxygen, and pH is pH level.
MODEL, ANALYSIS, DESIGN,
AND IMPLEMENTATION
2.1 Oxidation Ditch Modeling
Oxidation ditch is a stabilization basin that
resembles an open oval-shaped waterway equipped
with four aerators called mammoth rotor. The usage
of oxidation ditch is determined by pollution of an
incoming wastewater flow rate. The aerator serves
as oxygen circulator from the air to the water. In
this pond, the biological processes that take place
are nitrification and de-nitrification which need
oxygen for the microorganism (aerobic bacteria)
during the wastewater degradation process. The
oxidation ditch process is a completely mixed
activated sludge process with aeration typically
accomplished by mechanical aerators.
At oxidation ditch there are multiple input and
output variables that influence the process.
Therefore, the model structure of oxidation ditch is
multi input multi output (MIMO). Both nitrification
and de-nitrification process is occurred in the same
reactor and works continuously for every process.
Each process (nitrification / de-nitrification) can be
modeled as one continuous stirred tank reactor
(CSTR). As a whole, oxidation ditch is a series of
CSTR as shown in figure 1 (Metcalf & Eddy,
1991).
In each CSTR, mass balance for every
component can be written as:
dx
Vr = Q x0  Q x +Vr rg
dt
rg = - k x
(1)
which Vr is the reactor volume (l), Q is flow rate
(l/h), x0 is influent concentration (mg/l), x is effluent
concentrration (mg/l), and k is reaction rate (h-1).
In the nitrification process, maximum reaction
rate as follows :
k=
μm
Y
(2)
Figure 1. Oxidation Ditch (Metcalf & Eddy, 1991)
The concentration change rate of DO in aerator
area is:
dC
(4)
= K L a(C s  C)
dt
which Cs is concentration of saturated oxygen
(mg/l), C is concentration of oxygen (mg/l), and
KLa is mass transfer coefficient for oxygen (s-1)
where generally affected by temperature based on
van't Hollf – Arrhenius equation:
(5)
K L a(T) = K L a( 20°C)θ T  20
BOD decline rate under aerobic condition:
(6)
kT = k20θ T  20
Under anerobic condition, nitrate from the
nitrification reaction will be disintegrated into
nitogen. The nitrification reaction rate is stated by :
(7)
U'DN = U DN 1.09(T  20 ) ( 1  DO)
which U’DN is total de-nitrification reaction rate (h1
) and UDN is de-nitrification reaction rate (h-1).
BOD decline rate is stated using the same equation
in (6).
Hypothetically, the state mode for the plant
comprises of normal mode, varied compositions,
wastewater flow rate change, temperature change
and equipment malfunction. To acquire simulation
data, it was assumed that for every state, changes in
input variables occured and interconnecte, as
described in table 1.
2.2 Monitoring System Design
The design of monitoring system based MSPC
are mentioned in the following section:
which m is the maximum specific bacterial growth
rate and Y is the true yield coefficient.
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Multiway PCA Implementation
Principal Component Analysis (PCA) is one of
MSPC methods which is usually applied to analyze
a set of variables. The purpose of PCA is to reduce
data dimension by finding a new variables (called
as principal components) which is a linear
combination of the original set of variables so that
the variation of the new components became
maximum and the new components became
independent to each other. There are some PCA
methods that has been developed, and for the
monitoring system design in this paper, the applied
method is multiway principal component analysis
(MPCA).
Table 1. State Mode in Oxidation Ditch
Condition
State in Oxidation Ditch
Normal
behavior
Composition
Variations
Weather
Change
No changes that affects the process
state
Influent concentration of BOD and
NH4 changes
Temperature change detected.
Wastewater flow rate change due to
rain fall.
Aerator malfunction caused O2
transfer disturbance that lead to
declining of Dissolved Oxygen.
The pump in sedimentation basin is
malfunctioning, this caused changes in
flow rate inside oxidation ditch.
Equipment
Malfunction
Figure 2. Data Grouping in MPCA
In simple terms, the data grouping in MPCA is
described in figure 2. Measurement data acquired
from aeration basin is grouped based on the matrix
x  RIJK, for i oxidation ditch with j = 1,2...J
measurment variable based on time k = 1,2...K. The
matrix data (I x J) represents the numbers of
reaction basin variables j = 1,2....J, and the matrix (J
x K) at horizontal side represent changes in every
variable for reaction basin at time of k.
The principle components are not correlated to
each other and group from the smallest to biggest
variant. The first principle component is the linear
combination of the maximum variant value.
Generally the MPCA method is described in figure
3.
In MPCA, the data must be changed into 2
dimensional form. From the simulation result of the
oxidation ditch model, a three dimensional data is
acquired (i,j,k) for i oxidation ditch, j measurement
variable, and k time. Then they are grouped into a
(ij x k) matrix form. For the case in this paper, i = 1
and k = 21 with sampling time of 168 hours. j is the
number of variables (BOD, NH4, and NO3
concentration). Mean of each variable can be
determine as:
1 n
(8)
xj =
x
n

k
k =1
and the standard deviation is:
1 n
(9)
 (xkj  x j )2
n  1 k =1
The principal components can be calculated
directly or, more commonly, after different
centering and scaling operations on the data matrix
x according to:
 Mean centering: x j  x j
sj =
 Scalling:
xj  xj
s
One of the techniques to find principle
components are Singular Value Decomposition
(SVD) algorithm, where the matrix for principle
components and it's variations could be find
directly. In singular value decomposition, SVD, the
matrix x is decomposed according to:
x = U  VT
(10)
which U is a matrix (k x j), V is a matrix ( j x j), and
Σ is a diagonal matrix (k x j) containing the
eigenvalue of covariance matrix x, σ on the
diagonal. The largest singular value (σ) in column
of matrix V, (p1) determines the direction of the
first principal component, and the second largest
singular value (σ) in column of matrix V, (p2)
determines the direction of the second principal
component, and so on. Each observation in time
xk  R J of the variables is projected on to the
score space tR(k), by multiplying x(k) with matric of
T
principal components P R , with R is the number
of principal components in the model, and it is
defined as:
(11)
t R k  = PRT xk 
A new matrix projection is acquired
(12)
xk  = PRtR k 
giving the residual
~
(13)
x k  = xk   xk  .
To determine if the value of principle
component stays within the limit, a statistical test
Hotelling T² control map is used to check whether
the process is in controlled state. The statistical test
used is:
(14)
T 2 k  = t R S R1t Rk 
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which S R  R R R is the matrix with R as the first
eigenvector.
Determining State Mode Using Fuzzy
From the hotelling T² control chart, it can be
acquired the data of the deviation value in every
state, by finding the mean and deviation from the T 2
value. Then, those values are used to build a
membership function for the input of fuzzy (takagi
sugeno). The number of fuzzy input for every
considered state depends on the number of choosed
principle components. If the membership
components of the fuzzy input for every considered
state is joined each other, then it should use two
principal components as fuzzy inputs to prevent
classification mistakes.
Fuzzy rule for 1 principle components is:
If (input 1 is state 1) then (output is state 1)
Fuzzy rule for 2 principle components is:
If (input 1 is state 1) and (input 2 is state 1) then
(output is state 1)
3
RESULT
3.1 Model Response for Some State
Mode
From the SVD result, the variation of the
principle components matrix (3x3) are:
 First principal component = 89.75 % of variation
 Second principal component = 10.11 % of
variation
 Third principal component = 0.14 % of variation
Principle Components analysis shows the first
principle components has the biggest variation so it
can be picked to be used in finding the original data
projection.
For the normal condition of the oxidation
ditch, the variable input is listed in table 2. Figure 4
shows the output model respond and hotelling T²
chart for normal state. Under normal state, all T2
values are below the upper limit control.
Table .2. Input variable for normal state plant
Variable input
Wastewater flow rate
Temperature
BOD concentration
NH4 concentration
Start
Acquiring data from output
variable process
Value
17.5 L/sec ± 1.5 L/sec
25° C
240 mg/L ± 5 mg/L
30 mg/L ± 2 mg/L
Data grouping into matrix form
_
Data column Mean centering_ with Xj – Xj,
and Scalling (Xj – Xj) / s
Count the principle component matrix using
SVD algorithm
(a)
Determining the number of principle
components based on the variant size
New data projection using equation 11
Statistical test using Hotelling Control
Map with equation 14
STOP
(b)
Figure 4 (a) Model respond in normal condition (b) Hotelling T²
control chart
Figure 3. The Flowcart of MPCA method
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(a)
Figure 9. Hotelling T² control chart for DO concentration
change.
(b)
Figure 5. (a) Model respond with increase of waste water flow
rate to ± 5.25 L/s . (b). Hotelling T² control chart
The model respond of the case increasing
wastewater flowrate to ± 5.25 l/sec and its hotelling
T² control chart is shown in figure 5. It is shown
that the increase in wastewater flow cause the T2
values are above the upper control limit of the
hotelling T² control chart. The same resut is
obtained for the concentration change case in
influent, BOD, NH4, and DO as well as for the
temperature change case, as shown in figure 6 – 10.
Figure 6. Hotelling T² control chart for influent concentration
change (± 30 %)
Figure 7. Hotelling T² control chart for BOD concentration
change.
.
Figure 10. Hotelling T² control chart for surrounding
temperature change (±3° C)
3.2 Determining the membership
function for Fuzzy Input
Based on the T² value of the first principal
component for every state mode, then the mean
value and its deviation was got as follows:
State
Mean
Deviation
Normal
15.03
29.16
DO decrease
72.34
8.37
Temperatur change
98.74
39.25
Concentration change
228
57.16
Flow rate change
476.5
68.27
A fuzzy membership function was made due to
each state by using gaussian function. The result is
shown in figure 11. It is shown that under
temperature change and DO concentration change,
the membership function curve is joined. Therefore
to prevent misclassification, an input membership
function for the second principle component is
introduced for both states. Meanwhile for other
states, it is concluded that one principle component
is sufficient.
Based on the T² value of the second principal
component for temperature change and DO
decrease state mode, then the mean value and its
deviation was got as follows:
State
Mean
Deviation
DO decrease
9.571
3.474
Temperatur change
3.136
1.199
The input membership function for this problem is
shown in figure 12.
Figure 8. Hotelling T² control chart for NH4 concentration
change.
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Table 3. Simulation results for DO concentration change
Figure 11. Input membership function for the first principal
components
Trial
DO
Concentration
State Classification
Results
1
1 mg/L
2
0.7 mg/L
3
0.5 mg/L
4
0.2 mg/L
DO concentration
changes
DO concentration
changes
DO concentration
changes
DO concentration
changes
Table 4. Simulation results for temperature change
Trial
1
2
3
4
Figure 12. Input membership function for the second principal
components
The fuzzy rule for the proposed monitoring
system are as follows:
If (T² value from the first principle components is
normal) then (output is normal)
If (T² value from the first principle components is
DO) and (T² value from the second principle
components is DO) then (output is DO
concentration change)
If (T² value from the first principle components is
temp) and (T² value from the second principle
components is temp) then (output is
temperature change)
If (T² value from the first principle components is
konsent) then (output is concentration change)
If (T² value from the first principle components is
debit) then (output is wastewater flow rate
change)
3.3 Mode State Classification
The proposed monitoring system had been
applied to the oxidation ditch model. To investigate
the performance of the monitoring system, it was
conducted four experiments due to four mode state.
The simulation result is shown in tables 3 to 6.
Based on the results, it is shown that the proposed
monitoring system yields decision of the state
condition correctly.
Temperature
Change
± 2° C
± 3° C
± 4° C
± 5° C
State Classification
Results
Temperature changes
Temperature changes
Temperature changes
Temperature changes
Table 5 Simulation results for concentration change
Trial
Concentration
Change
1
± 20 % BOD & NH4
2
± 25 % BOD & NH4
3
± 30 % BOD & NH4
4
± 30 % BOD
5
± 30 % NH4
State
Classification
Results
Concentration
changes
Concentration
changes
Concentration
changes
Concentration
changes
Concentration
changes
Table 6 Simulation results for waste water flow rate change
Trial
1
Waste Water
Flow Rate
Change
± 10000 L/hour
2
± 15000 L/hour
3
± 20000 L/hour
4
± 25000 L/hour
5
± 30000 L/hour
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State
Classification
Results
Wastewater flow
rate change
Wastewater flow
rate change
Wastewater flow
rate change
Wastewater flow
rate change
Wastewater flow
rate change
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CONCLUSION
There are a number of conclusions drawn
during this research, i.e.:
 Membership function using single principle
component may result in two joined
membership function curve, such as the case in
DO concentration change and temperature
change condition. Therefore two fuzzy inputs
are needed to reduce misclassification.
 The simulation results is able to identify the
state comprehensively with 100% success rate.
Interpretasi Data SPC Untuk Pemantauan Kinerja
Plant”, Industri - Jurnal Ilmiah Sains dan
Teknologi: Volume 5 No. 2.
Metcalf dan Eddy. 1991. Wastewater
Engineering, Treatment Disposal, and Reuse.
McGraw Hill, New York.
Mac Gregor , J. F., Kourti , T., 1995, Statistical
process control of multivariate processes. Contr.
Engng Pr., 3, 403±414.
Lowry CA, Montgomery DC (1995) A review of
Multivariate control of training NDCs by
comparing those restricted to particular recharts. IIE
Trans 27:800–810
REFERENCES
Indriawati, K., Kurniadi, D., Yuliar, S., (2006)
”Penerapan Fuzzy Inferential System Pada
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