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Monitoring a Sequencing Batch Reactor for the
Treatment of Wastewater by a Combination of
Multivariate Statistical Process Control and a
Classification Techniques
Magda Ruiz1, Joan Colomer1, and Joaquim Melendez1
University of Girona, Avenue Lluis Santallo Campus Montilivi Building PIV
CP 17071 Girona - Spain
mlruizo,colomer,quimmel@eia.udg.es
Abstract A combination of Multivariate Statistical Process Control (MSPC) and an
automatic classification algorithm is applied to monitor a Waste Water Treatment
Plant (WWTP). The goal of this work is to evaluate the capabilities of these tech-
niques for assessing the actual state of a WWTP. The research was performed in a
pilot WWTP operating with a Sequencing Batch Reactor (SBR). The results obtained
refer to the dependence of process behavior with environmental conditions and the
identification of specific abnormal operating conditions. It turned out that the com-
bination of tolls yields better classifications compared with those obtained by using
methods based on Partial Least Squares.
1 Introduction
This work makes a contribution to monitoring waste water plants (WWTP) operat-
ing with sequencing batch reactors (SBR). The work illustrates the use of statistical
techniques to describe and analyze the plant’s behavior aiming at identifying of sit-
uations which may lead to failures. The goal is to develop specifications for the
plant’s operation [18] including faulty or abnormal situations. Modern monitoring
techniques enable the collection of a huge number of data, which, however, neces-
sitates data reduction techniques, particularly in case of manufacturing processes
such as polymerization [12], industrial pharmaceutical process [29], fabrication of
flexible polyurethane foams [24], drying process [21], polyester film process [10],
WWTP [4]. The problems are generated by uncertainty which often is classified in
random noise (common cause) and randomly occurring special cause. Standard con-
trol strategies aim at detecting and removing special causes, but have no impact on
the common cause variation, which is inherent to the process. There is the same
pattern of variation for the same operating conditions implying that the mean and
variance remain unchanged unless the operating conditions have changed. Thus, it
2 Magda Ruiz, Joan Colomer, and Joaquim Melendez
becomes possible to distinguish different conditions and detect them automatically
by observing statistical characteristics and comparing them with certain thresholds
[11]. The corresponding methodology is known as Statistical Process Control (SPC)
and Multivariate SPC, where the latter makes extensively use of the Covariance Ma-
trix representing the relations among process variables.
This paper aims at illustrating a methodology for assessing the conditions of a
WWTP when eliminating organic matter, nitrogen and phosphorus to guarantee the
regulations for quality monitoring (directive 91/271/CEE [3]).
This project refers to a Sequencing Batch Reactor (SBR) pilot plant shown in
Figure 1 where sludge is used for removing nitrogen and eliminating organic mat-
ter. The processes are nonlinear, time-varying and subject to significant disturbances
such as equipment defects, atmospheric changes and variation in the composition
and dependence of the relevant variables. The dependence is modelled by a correla-
tion structure of the relevant variables.
Fig. 1. Real SBR pilot plant
Multivariate Statistic Process Control (MSPC) methods aim at detecting events
that cause a significant change in the structure of correlation of the process variables
[7]. An extension of the Multiway Principal Component Analysis (MPCA) has been
applied on SBR processes [16][25] for obtaining a classification scheme for batch
processes [20].
This paper is organized as follows: In section 2 the operation of a SBR process
is presented. The section 3 describes the PCA extensions for process monitoring and
section 4 presents the classification method. Section 5 contains a numerical example
using data recorded from a pilot SBR plant. Finally, future work and conclusions are
summarised in section 6.
MSPC and classification tool for situation assessment 3
2 The SBR Pilot Plant
This paper is an outcome of the research project Development of a system of control
and supervision applied to a Sequencing Batch Reactor (SBR) for the elimination
of organic matter, nitrogen and phosphorus DPI2002-04579-C02-01 funded by the
Spanish Government. The involved partners are the Control, Engineering and Intel-
ligent Systems (eXIT) group, the Laboratory of Chemical and Environmental Engi-
neering (LEQUIA), both from the University of Girona (Spain) and the firm Inima
Servicios del Medio Ambiente SA.
Fig. 2. Schematic overview of the SBR Pilot Plant.
The SBR Pilot plant (Figure 2. ) used in the research project has a reactor, which
is composed of a metal square tank of 1m3and the capacity of processing a volume
of 200 liters. The wastewater is obtained from a real plant sited in Cass`a(Girona)
(Spain) by means of a peristaltic pump and stored in a buffer tank which feeds the
reactor.
The treatment carried out by the SBR pilot plant is oriented to nitrogen removal.
Remember, that nitrogen and phosphorus are essential nutrients of life, but if they
are in overabundance in the water, algae develop quickly, die and decompose. Since
decomposition is done under aerobic conditions (with oxygen), oxygen level slumps
and does not permit life [26]. Nitrogen removal in this SBR pilot plant is performed
in two steps:
•Nitrification: Ammonia is converted to nitrate by aerobic microorganisms.
•Denitrification: Nitrate is converted to N2Oor nitrogen gas under anoxic (with-
out oxygen) conditions by anoxic microorganisms.
4 Magda Ruiz, Joan Colomer, and Joaquim Melendez
Figure 3 shows the alternation of the two phases in the operation cycle defined
by the reactor. Each cycle is based on alternating anoxic and aerobic reaction, where
filling only occurs during anoxic stages. The anoxic period is longer than the aerobic,
because of increasing denitrification. The total filling volume is 200 liters, divided
into six feeding parts during a 8-hours cycle. Settling and draw take 1hour and 0.46
hours, respectively [6].
Data gathered from the plant is organized in 8hours batches containing 5760
samples (obtained every 5seconds) per variable: pH, oxidation reduction potential
(ORP), dissolved oxygen (DO) and temperature. To monitor essential variables, the
SBR process is equipped with DO-Temperature (OXIMAX-W COS 41), pH (CPF
81) and ORP (CPF 82) Endress-Hauser probes. Signals, filtered in the transmitter,
are captured by a data acquisition card (PCI-6025E from National Instruments) [22].
Fig. 3. Fixed operational cycle apply in the pilot plant
The analysis of profiles of the relevant variables allows to interpret the process
behavior. Figure 4 displays ORP and pH profiles by means of which unusual in-
stances can be identified. One of them is the Nitrate Knee (in the ORP variable)
which appears in anoxic conditions and denotes the complete denitrification. Others
are Ammonia Valley (AV) and Nitrate Appex (NA), which appear in the pH variable.
AV indicates the end of nitrification (aerobic condition) while NA gives evidence of
the end of denitrification under anoxic conditions [5] [19].
3 MSPC for Batch Processes
Modern processes have in general large volumes of historical data stored in databases
and their exploitation is of crucial importance for an improvement of operation. Typ-
ically, these data are generated by highly depending variables. Therefore, it was de-
MSPC and classification tool for situation assessment 5
Fig. 4. ORP and pH profiles
cided to use for the reduction of dimensionality the Principal Component Analysis
(PCA) together with Partial Least Squares (PLS) [8]. PCA and PLS are techniques
that provide low dimensional models useful for a further analysis and efficient mon-
itoring [13] [11]. The application of statistical process control to monitor simulta-
neously multiple variables using these reduction techniques is known as Multivari-
ate Statistical Process Control (MSPC), [17] [10] [16] [9]. These techniques have
been widely used for monitoring continuous process. Only recently the application
of these methods has been extended to cover batch processes, too. Some approaches
proposed to deal with statistical batch process control are briefly introduced in the
next subsection.
3.1 Multiway Principal Component Analysis (MPCA)
Consider a typical batch run in which j=1,2,...,Jvariables are measured at k=1,2,...,K
time instants throughout the batch. Similar data will exist on a number of such batch
runs i=1,2,...,I. All the data are contained in the X(I×J×K) array illustrated
in figure 5, where different batches are organized along the vertical line, the mea-
surement variables along the horizontal line, and their time evolution takes the third
dimension. Each horizontal slice through this array is a (J×K) data matrix repre-
senting the time histories or trajectories for all variables of a single batch (i). Each
vertical slice is an (I×J) matrix representing the values of all the variables for all
batches at a common time interval (k) [16] [27].
MPCA is equivalent to performing ordinary PCA on a large two-dimensional (2−
D) matrix constructed by unfolding the three-way. Six ways of unfolding the three-
way data matrix Xare possible, as indicated in table 1 [29]. In this work the ways A
and D are used. Undey and Cinar [25] used type A (figure 6), while Nomikos and
MacGregor used type D [16] (figure 7), which is particularly meaningful, because by
6 Magda Ruiz, Joan Colomer, and Joaquim Melendez
Fig. 5. Arrangement of a three-way array X
subtracting the mean of each column of the matrix Xthe main nonlinear and dynamic
components in the data are removed. A PCA performed on the mean-corrected data
is therefore a study of the variation of the variables in time with respect to their mean
trajectories [15].
Table 1. Types of unfolding a three-way data matrix, according to [28]
Type Structure Direction
AIK ×Jvariable
BJ I ×Ktime
CIJ ×Ktime
DI×KJ batch
EI×J K batch
FJ×IK variable
Structure1; Direction2
MPCA decomposes the three-way X, into a large two-dimensional matrix Xsep-
arating the data in an optimal way into two parts: The noise or residual part (E),
which is small in the sense of least squares, and the systematic part (PR
r=1 trN
Pr), which consists of a first factor (t)related to the batches and a second factor (P)
related to the variables and their time variation [16].
MPCA is performed by means of the NIPALS algorithm resulting in the matrix
X. It is the product of the score vector tr and the loading matrices Pr, plus a residual
matrix E, that is minimized in the sense of least-squares:
X=
R
X
r=1
trOPr(1)
1Structure of the unfolding matrix
2Direction that remains unaltered
MSPC and classification tool for situation assessment 7
Variables
Batches (I)
Variables (J)
Time (K)
T (K)
…
T (k)
…
T (2)
T (1)
X
1 J
1
K
2K
.
.
.
.
.
.
IK
I=1
I=2
.
.
.
.
.
.
I
Batches time x variable
X (IK x J)
Batches tiempo
Historical Batch Data
Fig. 6. Decomposition of X to 2-D (IK ×J)
Batches (I)
Variables (J)
Time (K)
T (K)
Variables x Times
1 J 2J
1 J 2J kJ
kJ KJ
KJ
Batches
…
T (k)
…
T (2)
T (1)
X
Time(1) Time(2) . . . Time(k) . . . Time(K)
Historical Batch Data
Batches x time variable
Fig. 7. Decomposition of X to 2-D (I×KJ )
X=
R
X
r=1
trPT
r+E=ˆ
X+E(2)
where Ndenotes the Kronecker product (X=tNPis X(i, j, k) = t(i)P(j, k))
and Rdenotes the number of principal components retained. Equation (1) is the 3-D
decomposition while Equation (2) displays the more common 2-D decomposition
[25].
Abnormal behavior of a batch is generally identified by means of the Q-statistic
or the D-statistic, which are compared with control limits determining whether the
process is in control or not. These methods are based on the assumption (generally
motivated with the central limit theorem) that the underlying process follows approx-
imately a multivariate normal distribution with zero first moment vector.
The Q-statistic is a measure of the lack of fit. For batch number i,Qiis defined
as:
8 Magda Ruiz, Joan Colomer, and Joaquim Melendez
Qi=
J
X
j=1
K
X
k=1
(ejk )2∼gx2
(h)(3)
where ejk are the elements of E.Qiindicates the distance between the actual values
of the batch and the projected values onto the reduced space.
The D-statistic or Hotelling T2statistic, measures the degree of fit:
Di=tT
iS−1ti∼I(I−R)
R(I2−1)FR,I−R(4)
where Sis the estimated covariance matrix of the scores.
4 Classification Method
For classification, the Learning Algorithm for Multivariate Data Analysis (LAMDA)
has been used [1]. This method takes advantage of hybrid logical connectives to per-
form a soft bounded classification.
LAMDA is proposed as a classification technique to apply to principal compo-
nents selected for monitoring. The goal is to assess the actual situation according to
profiles previously learned [1][14].
xn
x2
x1
descriptorx1
of Cj
descriptorx2
of Cj
descriptorxn
of Cj
LmCj (x)
descriptorx1
of Cm
descriptorx2
of Cm
descriptorxn
of Cm
L
mCm (x)
descriptorx1
of C1
descriptorx2
of C1
descriptorxn
of C1
L
mC1(x)
Max
Object Descriptors m class MADs GADs Class
assignment
X
ˆ
Fig. 8. Basic LAMDA recognition methodology
Input data is presented to LAMDA as a set of observations or individuals char-
acterized by its descriptors or attributes and recorded as rows. Principal components
MSPC and classification tool for situation assessment 9
obtained in the MPCA step are used as input variables to be classified. Once, the
descriptors are loaded, every individual is processed individually according to the
desired goal [1]:
1. To classify the individuals according to a known and fixed set of classes.
2. To learn and adapt from a previous given set classes which can be modified
according to the new individuals.
3. To discover and learn representative partitions in the training set.
The basic assignment of an individual to a class follows the procedure repre-
sented by figure 8. In this, MAD and GAD stand for Marginal (it takes into account
only one attribute) and Global Adequacy Degree (obtained from the hybrid logical
combination of the previously obtained MADs) respectively, of an individual to a
given class. Equations (5) and (eq:GAD)are used to calculate them. This classifying
structure resembles that of a single neuron ANN [1].
MAD(dixj/ρi/k ) = ρdixj
i/k (1 −ρi/k)1−dixj(5)
where
dixj= Descriptor iof the object
j ρi/k =ρof descriptor iand class k
GAD =βT (M AD) + (1 −β)S(MAD)(6)
Formalizing the description of LAMDA, it is possible to define an individual as
a series of descriptors values d1, ...,dnsuch that each djtakes values from the either
finite or infinite set Dj. We will call universe or context to the Cartesian product U=
D1xD2... x Dj. Thus, any object or individual is represented as a vector x= (x1,...,
xn) from U, such that each component xjexpresses the value for the descriptor
djin the object x. The subset of Ugathering all these vectors will be called data
base or population. To assign individuals to classes MAD step will be calculated
for each individual, every class and each descriptor, and these partial results will
be aggregated in order to get the GAD of an individual to a class. The simplest
way to build this system would be by using probability distributions functions, and
aggregating them by the simple product, but that would force us to impose a series of
hypothesis on the data distribution and independence which are too arbitrary. Finally,
MAD and GAD have been used according to definitions of equation 5 and equation
6 respectively [1]. The hybrid connective used for GAD is a combination between a
t-norm and a t-conorm by means of the βparameter. β=0represents the intersection
and β=1means the union. This parameter will -inversely- determine the exigency
level of the classification, so it can be identified as a tolerance or exigency parameter.
10 Magda Ruiz, Joan Colomer, and Joaquim Melendez
5 Results and Discussion
5.1 Types of Batch Processes
The data obtained from the SBR process was analyzed by two different methods.
The first one is proposed proposes a profile study of the variables [20]. The second
analysis constitutes a preliminary MSPC. First and second component principal are
depicted in Figure 9. Abnormal behavior can be detected outside of the dotted line.
Besides, small groups are formed inside of the limit. One of them is conformed by
batches with a excellent denitrification and nitrification process (solid line).
Fig. 9. Score plot for batches. Dashed line is the model
The combination between both studies allow to identify five types of behavior in
SBR pilot plant which are summarized in Table 2.
MSPC and classification tool for situation assessment 11
Table 2. Type of Batch process
1. Electrical fault: Correspond to voltage sags, which are short lasting reductions
in rms voltage, caused by short circuits, overloads and starting of motors. Volt-
age sags cause problems on several types of equipment [2], e.g. a voltage sag
may lead to problems with the sensors. However, in the moment the voltage sag
disappears, the sensors retrieve their normal behavior.
2. Variation in the composition: Microorganisms or the influent composition can
change causing disturbances in the normal profiles of the variables [20].
3. Equipment defects: The SBR pilot plant is exposed at season changes with
rise and fall of temperature. These factors added with day-to-day cause wear-
ing down in sensors, acquisition card, computer, among others which induce to
missing data or not register of the process.
4. Atmospheric changes: During wet season, the relative amount of organic matter
and nitrogen are smaller.
5. Normal behavior: This is characterized by the removal of nitrogen and the elim-
ination of organic matter. According to the nitrogen removal, the quality was
classified in excellent, good and normal.
Using the above classification scheme, it is possible to quantify the number of
batches for each class. In Table 3 the classification of all batches of the SBR process
is given. There are 60 (equivalent to 33.5%) batches with abnormal behavior divided
into the four abnormal classes given in Table 2. Normal behavior was observed in
12 Magda Ruiz, Joan Colomer, and Joaquim Melendez
66.5% of all cases. The normal behavior exhibits a higher nitrogen removal than
legally required.
Table 3. Classification accord preliminary results.
5.2 Application of MSPC
MPCA
Each batch is treated 8hours and every 5seconds the relevant variables are mon-
itored yielding a total of 5760 samples. However, due to computational limitations
only a sample of 392 data sets from each batch can be used. For comparison, the
selected data (392) represents sufficiently well the totality of 5760 data samples. The
corresponding profiles are compared for both sampling in Figure 10 which shows a
satisfactory agreement. Finally, the MPCA algorithm was applied to the three-way
data array, X, with dimensions 179 ×4×392, where K= 392 is the number of
time instants throughout the batch (samples), J= 4 is the measured variables and
I= 179 is the historical data batches.
MPCA: Batch direction
The three-way array Xis unfolded in batch direction (I×KJ ) gets 8principal
components with a final data matrix dimension of (179 ×8). This model explains
92.79% of the total variability (see Table 4).
Table 4. Principal component extraction
MSPC and classification tool for situation assessment 13
Fig. 10. Comparison between 5760 and 392 samples for variables to determinate the validity
of the selection
Examining the process data in the reduced projection spaces, first and second
principal components are plotted (see Figure 9). One group of falls are outside of the
normal range. These batches correspond to Variations in the Composition. Abnormal
batch behavior can be identified by means of Qand T2control charts. Figure 11
shows Qand T2charts for all process batches. The Qchart identifies several batches
due several abnormal behaviors. In T2chart shows two batches falling excessively
outside the limits, both due to Electrical Fault (EF).
In Table 5 the batches outside the limits are summarized for both control charts.
The Qchart detects only one third of the total number of abnormal behavior and
produces, furthermore, 8false alarms. The T2chart identifies only 20 batches with
abnormal behavior and not produces false alarms. Only 39 cases of the 60 cases
14 Magda Ruiz, Joan Colomer, and Joaquim Melendez
Fig. 11. Graphics of Qand T2charts with 92.79% confidence limits
of the abnormal behavior are detected by the two charts and 9cases of abnormal
behavior is detected simultaneously by both charts.
Table 5. Results from Qand T2
MPCA: Variable direction
The three-way array Xis unfolded in variable direction (IK ×J) gets 3with a final
data matrix dimension of (70168 ×4). Three principal components explain 95.18%
of the total variability. In figure 12 a projection on the first and second component
MSPC and classification tool for situation assessment 15
plane is displayed.
Fig. 12. Weighs of the variables and the model graphic with two principal components in
variable direction
The batches can be separated in three different sections. Each section are dif-
ferent phase of process fitting. First section corresponds at month where the pilot
plant was tested. Second section corresponds at spring season. Finally, third section
corresponds at summer season. In this analysis, temperature contributes marginally
therefore, it is omitted and a new model is built using only 3variables. Figure 13
shows the model without temperature and Figure 12 shows the model with tempera-
ture .
Fig. 13. Weighs of the variables and the model graphic with two principal components in
variable direction without Temperature
16 Magda Ruiz, Joan Colomer, and Joaquim Melendez
Conclusions on MSPC
Combining MPCA with analytical methods it is possible to develop a classifica-
tion schemes for the batches. The model with MPCA in batch direction improve
the knowledge about the process while the model developed in variable direction al-
low to detect the relationship between process behavior and environment (test phase,
spring and summer seasons).
The investigation shows, MPCA is capable to detect abnormal behavior in SBR
process by projecting the data into a lower dimensional space. Applying the classi-
fication tool to principal components will allow identifying and grouping of similar
situations according to match criteria.
5.3 Classification for Situation Assessment
MPLS was used for reducing the dimensionality and maximizes the relation between
the matrix X(I×JK) and the predicted matrix Y[23] (179 ×5) where 179 is the
number of historical data batches and 5are the identified types of batch processes.
However, the model does not describe the process because matrix Ywas created
with the results obtained in the preliminary MSPC analysis (depicted in table 2).
Thus, MPCA and a classification tool is used for situation assessment.
5.4 MPCA Classification
Principal components obtain by MPCA step is the input in the classification tool.
The dimension of this matrix is 8×179 (Table 6) which is called ˆ
X. LAMDA auto-
matically classifiy the data in eleven classes as shows Figure 14.
Batch X1 X2 X3 X4 X5 X6 X7 X8
1-1,1904 0,40769 -0,16347 0,68946 -0,37174 0,23784 -0,53304 -0,004255
2-0,60437 -0 ,46155 -0, 066138 0,76171 -0,24992 0,018755 -0,54621 -0,45446
3 2,3093 0,65529 -0,38676 -0,41 604 -0,27016 -1,0046 0,97096 -0,10937
4-0,97246 -0,74205 -0,034569 0,74955 -0,21184 -0,08357 5 -0,42195 -0,47152
5 -0,86 487 -0,82011 0,084196 0,53048 -0,05 9221 0,096665 -0,26612 -0,56957
.. . . . . . . .
.. . . . . . . .
.. . . . . . . .
177 1,2756 1 ,3431 0,2913 1 -0,34286 0,39309 0,26815 -0,52301 0,051984
178 1,1567 -0,19976 0,98883 -1,03 1,2953 1,1964 -0,098865 0,4853
1790,53993 0,87105 0,70009 -0,62414 0,93712 0,4453 -0,41136 -0,55916
X
ˆ
Table 6. Descriptors used for the batches
Figure 15 compares the classes and the types of the batch process. According to
these results, it is possible to identify classes with equipment defects, electrical faults,
atmospheric changes and variation in the composition. Classes 1,9and 10 correspond
to normal behavior. Class 6is associated to atmospheric changes. Classes 3and 11
MSPC and classification tool for situation assessment 17
Fig. 14. LAMDA Frame with two classes of batches identify
Fig. 15. Composition of the classes accord to type of batch
represent variations in the composition while classes 7and 8include electrical fault.
Finally, the classes 2,4and 5include different types of batches.
Table 7 shows amount and percentage of batches in each class. The predominant
is class 1which has 48.04% of the total historical data, this class represents normal
behavior.
Table 7. Numerical composition for each class accord to results of classification method
The similar form, Table 8 shows amount for every class, besides shows the com-
position of each one in which some batches are wrongly classified as. Nevertheless,
The classes can be identified (Table 9) with a name, e.g., class1is normal behavior.
18 Magda Ruiz, Joan Colomer, and Joaquim Melendez
In the case of class 5is called abnormal behavior due to atmospheric changes and
equipment defects.
Table 8. Composition by class
Table 9. Classification by type of batch process
The relationship between the class and the principal components is shown in
(Table 10). The relationship of the 8th component with every classes does not change
indicating that ˆ
Xcan be computed using only seven descriptors. Consequently, only
7principal components are used in Multiblock MPCA analysis. In this case, the total
explain is 90.54%.
Table 10. Composition of the classes accord to principal component
6 Conclusions and Future Work
Multivariate Statistical Process Control is an effective means for detecting abnormal
behavior in SBR processes by projecting the data into a lower dimensional space
that characterizes the state of the process. The type of the batch process and the
classes are identified by a classification tool (LAMDA). MSPC in conjunction with
the classification tool establish the relationships between batch behavior and type of
batch process. Splitting the data into meaningful groups enables to better identify the
batches with abnormal behavior and getting a characterization of the types of batch
process: normal behavior, atmospheric changes, etc.
In order to improve the results and to process the data faster, it would be desirable
to have a method which combines the dimensionality reduction and the nonlinear
MSPC and classification tool for situation assessment 19
classification. Furthermore, in future the SBR pilot plant will not begin to operate
with a fixed stage at each cycle. This become difficult the use of multiway strategies,
because it leads to registers of different length (duration), which has to be taken into
account.
7 Acknowledgement
This work is part of the research project Development of a system of control and su-
pervision applied to a Sequencing Batch Reactor by loads (SBR) for the elimination
of organic matter, nitrogen and phosphorus DPI2002-04579-C02-01 supported by
the Spanish Government and the FEDER Founds. The authors also appreciate the
valuable contributions made by the LEQUIA team: Jesus Colprim, Sebasti`
a Puig,
Lluis Corominas and Maria Dolors Balager.
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