Non-linear modeling using fuzzy principal component
regression for Vidyaranyapuram sewage treatment plant,
Mysore – India
Ayesha Sulthana, K. C. Latha, Mohammad Imran, Ramya Rathan,
R. Sridhar and S. Balasubramanian
ABSTRACT
Fuzzy principal component regression (FPCR) is proposed to model the non-linear process of
sewage treatment plant (STP) data matrix. The dimension reduction of voluminous data was done
by principal component analysis (PCA). The PCA score values were partitioned by fuzzy-c-means
(FCM) clustering, and a Takagi–Sugeno–Kang (TSK) fuzzy model was built based on the FCM
functions. The FPCR approach was used to predict the reduction in chemical oxygen demand (COD)
and biological oxygen demand (BOD) of treated wastewater of Vidyaranyapuram STP with respect to
the relations modeled between fuzzy partitioned PCA scores and target output. The designed FPCR
model showed the ability to capture the behavior of non-linear processes of STP. The predicted
values of reduction in COD and BOD were analyzed by performing the linear regression analysis. The
predicted values for COD and BOD reduction showed positive correlation with the observed data.
Ayesha Sulthana (corresponding author)
K. C. Latha
Ramya Rathan
S. Balasubramanian
Department of Water and Health – JSS University,
S.S. Nagar,
Mysore-570 015,
Karnataka,
India
E-mail: ayeshasulthanaa@gmail.com
R. Sridhar
Department of Computer Science,
Sri Ramakrishna Mission Vidyalaya,
Coimbatore-641020,
Tamil Nadu,
India
Mohammad Imran
Department of Information Technology,
College of Applied Sciences,
Sohar-311,
Oman
Key words | FPCR, fuzzy-c-means, principal component analysis, TSK fuzzy model
INTRODUCTION
To overcome the upsurge of water pollution there is a need
for effective wastewater treatment; therefore competent
modeling and efficient monitoring of wastewater treatment
systems are very much essential. The wastewater treatment
plant (WWTP) process is a combination of physical, chemi-
cal and biological non-linear processes; therefore the
WWTP process cannot be modeled by linear statistical
approaches (Oliveira-Esquerre et al. ). Understanding
the behavior of complex non-linear relations between the
process variables, the system parameters, the control
inputs and the external perturbations of the WWTP is a dif-
ficult task. The non-linear behavioral processes are a
requirement to develop a model which describes this real-
life phenomenon; however, wastewater treatment par-
ameters can be employed to construct the model for
predicting its performance (Ruicheng & Xulei ). An
explicit valid modeling and monitoring technique is an
imperative requirement to retain the optimal functioning
of wastewater treatment systems. An efficient model
intensifies the interpretation of biological non-linear pro-
cesses and it also constitutes a footing for improved
process, operation and control.
Statistical data-based modeling approaches like ‘black-
box’ do not require a specific mathematical structure of
the process to be modeled; the black-box approach has
been used to describe the input–output non-linear relation-
ships of WWTPs (Lee et al. ; Motta et al. ).
Artificial neural networks (ANNs) are non-linear black-
box type models, which have been used to model the exist-
ing non-linear relationships between the influents and to
predict the operational parameters of the WWTP (Mjalli
et al. ; Mohammed et al. ). ANN models were
developed to predict the conduct of a WWTP based on
the past information (Hamed et al. ; Farouq et al.
). Optimal coagulant dosage in a drinking water
plant was predicted, even in the unexpected conditions
such as heavy rain and high turbidity, by ANN models
(Sengul & Gormez ). Residual aluminum level in
1040 © IWA Publishing 2014 Water Science & Technology | 70.6 | 2014
doi: 10.2166/wst.2014.333
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