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Development of water quality index for Godavari River (India) based on fuzzy inference system
Journal Pre-proof Development of water quality index for Godavari River (India) based on fuzzy inference system Jyotiprakash G. Nayak, L.G. Patil, Vinayak K. Patki PII:
S2352-801X(19)30425-4
DOI:
https://doi.org/10.1016/j.gsd.2020.100350
Reference:
GSD 100350
To appear in:
Groundwater for Sustainable Development
Received Date: 21 December 2019 Revised Date:
8 February 2020
Accepted Date: 11 February 2020
Please cite this article as: Nayak, J.G., Patil, L.G., Patki, V.K., Development of water quality index for Godavari River (India) based on fuzzy inference system, Groundwater for Sustainable Development (2020), doi: https://doi.org/10.1016/j.gsd.2020.100350. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Development of Water Quality Index for Godavari River (India) based on Fuzzy Inference System Jyotiprakash G. Nayaka, L. G. Patilb, Vinayak K. Patkic ______________________________________________________________________________________________________________ a-
b-
c-
Associate Professor, Department of Civil Engineering, Sandip Institute of Technology and Research Centre, Nashik, Maharashtra, India, [email protected]. Professor, Department of Civil Engineering, Shri Guru Gobind Singhji Institute of Engineering and Technology, Nanded, Maharashtra, India,[email protected]. Professor, Department of Civil Engineering, Nagesh Karajgi Orchid College of Engineering and Technology, Solapur, Maharashtra, India,[email protected].
Corresponding author: Email: [email protected], Tel.No: +91 8698299944
Development of Water Quality Index for Godavari River (India) based on Fuzzy Inference System Jyotiprakash G. Nayaka, L.G.Patilb, Vinayak K.Patkic
Abstract
In view of higher pollution strength of Indian rivers, prevalent water quality indices of the western countries like the National sanitation foundation water quality index (NSFWQI) and indigenous Vedprakash water quality index (VWQI) cannot truly represent the water quality status of Indian rivers. To overcome this limitation, fuzzy modeling has been used in this study for the prediction of water quality of Indian rivers. The fuzzy models have been developed using triangular and trapezoidal membership functions with centroid, bisector and mean of maxima (MOM) methods for defuzzification. It is observed that the fuzzy model with triangular membership function utilizing the bisector method of defuzzification performs better, compared to triangular and trapezoidal membership function utilizing the centroid and MOM method of defuzzification. The values of water quality index based on fuzzy logic have been compared with the NSFWQI and VWQI. It is observed that the values of fuzzy based water quality index are more representative to actual river water quality status of Indian rivers as compared to NSFWQI and VWQI.This is due to the fact that the adopted fuzzy logic approach is equally sensitive to all parameters and can truly represent the minor change in the value of any parameter, especially in case of river stretches having higher pollution.
Keywords:Fuzzy Inference System;Fuzzy Water Quality Index; Membership Function; National Sanitation Foundation Water Quality Index; Water Quality Index.
Nomenclature DO BOD WQI NSFWQI VWQI FWQI FIS MF MOM
Dissolved Oxygen Biological Oxygen Demand (over 5 days of incubation at 200 C ) Water Quality Index National Sanitation Foundation Water Quality Index Vedprakash Water Quality Index Fuzzy Water Quality Index Fuzzy Inference System Membership Function Mean of Maxima
1. Introduction To maintain
human health and to secure the environment, evaluation of water quality is
indispensable. Water quality index (i.e WQI) is a single dimensionless term, by which the water quality of a stream can be expressed as good, medium or bad. The water quality of different regions can easily be compared by comparing the values of WQI, instead of comparing the numerical values of several water quality parameters. To evolve a WQI, four steps have been utilised in the past (Abbasi and Abbasi, 2012); i) Choice of parameters ii) Determination of values of sub-index iii) Ascertaining appropriate weights iv) Establishing the final index after compounding the sub-indices. While establishing a WQI, the selection of water quality parameters is done based on, a) Referring the work of previous researchers (Said et al., 2004) b) Availability of the data sets (Cude, 2001) c) True representation of the quality scenario (Hanh et al., 2011) d) The proposed use of stream for a specific purpose (Hurley et al., 2012). The subsequent step is the development of sub-indices, which is done to convert the selected parameters onto a common platform, since the units of all the selected parameters cannot be same. The subsequent step is establishing weights to the parameters. Equal or unequal weights have been assigned to the parameters by the index developers, as per their judgment. Some researchers claimed that all parameters are equally important and assigned equal weights to all the parameters, during the development of WQIs (e.g. Cude, 2001; CCME, 2001). The index may suffer from ‘Sensitivity’ issue, if the different weights are assigned to the parameters. Equation
of the final index is decided on aggregation of sub-indices and considering the weights assigned to the different parameters. Additive and multiplicative methods have been used for aggregation of sub-indices. Most of the existing WQIs have used additive method (e.g. Brown et al., 1970; Sargaonkar and Deshpande, 2003) but the additive method suffers from ‘eclipsing’ issue (Swamee and Tyagi, 2000). While, some other researchers used multiplicative method for the development of the WQIs (e.g. Bhargava, 1985). It was reported that the multiplicative approach can not completely resolve the ‘eclipsing’ problem and also leads to ‘ambiguity’ issue sometimes (Swamee and Tyagi,2000). NSFWQI was developed by Brown (1970) and is used worldwide, including the Indian subcontinent to determine the water quality of the rivers (Sutadin et al., 2016). Considering the present scenario of Indian rivers, this index can no longer be used in the Indian subcontinent because most of the Indian rivers carry high pollution potential in the form of high BOD5 and total solids content. The use of NSFWQI becomes deficient in such cases, since its Q-value curves do not take into consideration high BOD5 and total solids content of natural streams (Nayak et al., 2017). Godavari River is one of the sacred river of India and Kumbhmela is celebrated on the banks of the Godavari in and around Nashik every twelve years. Thousands of people take a holy dip in Godavari during Kumbh and other festivals, hence it is the need of the hour to determine water quality of this river in and around Nashik. In view of the limitations of the prevalent WQIs viz. ‘eclipsing’, ‘ambiguity’ and inability to be representative on downstream side of a wastewater treatment plant, it is observed that these existing WQIs cannot represent the actual picture of water quality status of Indian rivers like Godavari. In the present study, an attempt has been made to utilise fuzzy logic approach to develop fuzzy inference system; to overcome the limitations of existing WQI approaches and for the identification of actual river water quality status (especially in such Indian scenario). Fuzzy logic approach has its inherent merits of ‘flexibility’ and capability to deal with ‘vagueness’ and ‘uncertainty’ more effectively. This approach also effectively addresses to ‘sensitivity’ and ‘ambiguity’ issues encountered in the determination of WQIs. In the present study suitability of Godavari river water have been investigated for drinking purpose and outdoor bathing purpose. 2. Materials and Methods 2.1 Study Area
The Godavari, one of the biggest river in India, emerges from Brahmagiri Mountain (at 0
19.56 N, 73.200E) is situated at Triambakeswar in Nashik District of Maharashtra state (Chavan et al., 2009). The present study was carried out to assess the water quality of the Godavari river in about 24 Km stretch in and around Nashik city. In the present study, fourteen river water quality sampling stations from the Gangapur dam to Dasak village were selected. The sampling stations are marked as S1 to S14 in fig.2. The water samples for analysis were collected once in a month for four years at a point 30 cm below the water surface. Analysis of all the parameters was performed using standard methods (APHA, 2012). Intense reconnaissance survey work was done to identify the point and nonpoint sources of wastewater addition in a selected stretch of the Godavari river and on that basis figure 2 has been developed. During the survey work, it was observed that partially treated or untreated sewage is getting added in the selected stretch of the Godavari river. These are the main point sources of pollution and are marked as P1 to P12 presented in figure 2. [Place Figure 1. Here] [Place Figure 2. Here]
2.2 National Sanitation Foundation Water Quality Index (NSFWQI) In the present study, one of the most extensively used index in the entire world, National sanitation foundation water quality index (NSFWQI) developed by Brown (1970) has been used to find WQI for surface water (Sutadin, 2016;Bhutani, 2014) NSFWQI = ∑ Wi Qi
(1)
Where Wi = Weightage of the concerned parameter & Qi = Q Value of the concerned parameter based on observed value, determined from concerned graph For calculation of NSFWQI five parameters (excluding Faecal Coliform, temperature change, phosphates and Nitrates) have been considered in the present study. The selection of parameters was done by using Delphi method. The weightages of the parameters and water quality class for NSFWQI are presented in Table 1 and 2 respectively and considered that the same are also applicable for the present study. [Place Table 1. Here]
[Place Table 2. Here]
2.3 Vedprakash Water Quality Index (VWQI) Vedprakash WQI (VWQI) is the other most commonly used WQI for determination of water quality of surface water bodies in Indian subcontinent (Bhutani, 2014; Water quality report,MPCB,2015). Vedprakash (1990) developed the index on observing the fact that in routine water quality analysis work, only a few numbers of important parameters viz. DO, BOD & pH should be considered, to ascertain the real water quality status of the streams in the Indian subcontinent. The list of parameters was selected using Delphi. This index was utilized to identify the stretches of river Ganga where the difference between the required and the actual water quality is considerably high, to indicate the need of pollution abatement initiatives. The index is expressed in equation 2 here: VWQI= ∑
Where is weightage of ith water quality parameter and
(2)
issubindex for ith water quality parameter and
p is the number of water quality parameters. The index is inspired from the NSFWQI, with little alteration in the weightages to affirm the water quality criteria for the uses of different categories. Subindex equations were used to determine the subindex values, as presented in table 3. In the present study Vedprakash water quality index (VWQI) has also been determined. [Place Table 3. Here]
Weightages ( ) of Parameters : DO- 0.43 , BOD - 0.26 , pH - 0.31 2. 4 Fuzzy Logic System 2.4.1Fuzzy Inference System Fuzzy inference system is resulted on combining the fuzzy logic with expert system (Zadeh, 1965). The real conditions are often uncertain and Zadeh (1965) defined this vagueness using the term “Fuzziness”. Chau (2006) had used concept of fuzzy sets to carry out water quality modeling, since it put forth a appropriate approach to deal with the issues, where the goals and boundaries are not properly defined or imprecise. Nasiri et al.(2007) developed a fuzzy riverpollution decision support system to make expert knowledge available for nonexpert users. Raman Bai el at.(2009) studied water quality in the Semenyih river (Malaysia) with physico chemical parameters and commented that fuzzy water quality index will assist the decision makers in reporting the condition of water quality.Semiromi (2011) et al. developed fuzzy water
quality index for Karoon river (Iran) and identified that fuzzy logic approach have superior capabilities to deal with non-linear, complex and uncertain systems.Gharibi et al. (2012) commented that fuzzy logic approach is a comprehensive tool for water quality assessment, especially for the analysis of human drinking water. Patki et al. (2013) used fuzzy inference system to assess the physicochemical parameters of municipal water, under the distribution system to determine its portability. Li et al. (2016) developed fuzzy water pollution index method for water quality determination of Qu river (China) and found that the method gives comprehensive water quality rank. There are some predominant reasons, which signify the merits of the models working on the concept of fuzzy logic. The reasons are: first, Issues involving nonlinear relationships among the variables can be addressed; second, local simple models have been utilised, rendering them simple to work with; third, they can be communicated and understood verbally; fourth, individual expertise and experience is used, which is not utilised by other methods (Lermontov et al.,2009; Gharibi,2009). 2.4.2 Fuzzy inference rules In fuzzy logic, if- then rules and fuzzy set operators are utilised to express the relationship between input and output variables of a system. Concepts of the formation of the fuzzy rules have been presented in table 6. 2.4.3 Basic structure of a Fuzzy inference system (FIS) A fuzzy inference system (FIS) works on fuzzy set theory, and incorporates the following four main steps (Ross 2004): a) Fuzzification: In this step, Crisp values of the input parameters are converted into corresponding linguistic terms by making use of membership functions. The adopted ranges of the different class for concerned parameters are used to find the value of membership function for different parameters. For determination of the value of triangular and trapezoidal membership functions, undermentioned equations are used 0 < <
(−) ≤ ≤
(−) Triangular : f (x; a,b,c ) = (−)
(−) ≤ ≤
0 < < (−) ≤ ≤
(−) 1 ≤ ≤ ( −)
≤ ≤ ( −)
Trapezoidal: f (x; a,b,c ) =
Where a, b, c and d are membership function parameters and x represents each single point on the x axis. b) Evaluation of the rules: Here compounding of the outcome of a fuzzy if- then rule is done. In this process, the lowermost class of any of the selected parameter becomes the class of fuzzy index for that particular rule. The lowermost class and corresponding value of membership function of any of the selected parameter becomes the class of the fuzzy index for the rule. In this step, applicable fuzzy rules for the given data are identified. c) Aggregation of rule outputs: In this step, applicable fuzzy if-then rules are considered. The maximum value of the fuzzy index having the same class, among the available applicable rules is considered. Outputs of all applicable rules are then clubbed into a single fuzzy distribution by carrying out the fuzzy union of applicable rules. d) Defuzzification: Defuzzification is the conversion of the fuzzified output to the crisp value by using the methods of defuzzification. 2.5 Modeling Performance Criterions To ascertain the prediction accuracy of the fuzzy models developed in the present study, two criterions have been utilized to assess the performance of the models. The criterions utilized are mean square error (MSE) and coefficient of correlation (CC ). 2.5.1 Mean Square Error(MSE) The mean squared error (MSE) of a particular case measures the average of the squared difference between the observed values and the predicted values. The MSE gives an indication of the error or residual variance.
MSE =" ∑+,![observed − predicted] 2 !
(3)
2.5.2 Coefficient of Correlation The Coefficient of correlation is an indication of the linear relationship between the two considered variables as presented here,
Where, n= number of data in the dependent data set, xi= the observed values, yi= the predicted values, x’=mean of the observed values and y’=mean of the predicted values Patki et al. (2013) and Tiri et. Al. (2018) used mean square error and coefficient of correlation as modeling performance criteria to assess the performance of the models. 2.6 Development of a Water Quality Index based on Fuzzy Logic Approach In the present study, to investigate the water quality of the Godavari river, fuzzy logic approach with five main parameters namely DO,BOD, Turbidity,Total solids and pH have been used. In the present study, comparison of river water quality using NSFWQI, VQWI and Fuzzy water quality index (i.e.FQWI) based on different membership functions; involving different methods of defuzzification have been done. To keep a common basis for ascertaining the value of the indices, five representative and important water quality parameters named DO, BOD, Turbidity, Total solids and pH have been considered. It was also considered that the number of fuzzy rules increases exponentially, with an increase in the number of parameters. So, considering only important parameters helps in reducing the number of fuzzy rules. Five types of class of water quality as Excellent, Good, Medium, Bad and Very Bad have been selected for both the indices viz. NSFWQI and FWQI. In this study, the ‘Mamdani’ approach has been utilised for development of the fuzzy inference system, to determine the FWQI. The process flow diagram for fuzzy inference system is as shown in figure 3. [Place Figure 3. Here]
The limits of the Classes for the considered water quality parameters, for the development of FWQI have been presented as per Table 4 and Table 5 respectively. [Place Table 4. Here] [Place Table 5. Here]
For development of FWQI five input parameters have been utilised. Each input parameter has been classified into five water quality classes as Very bad, Bad, Medium, Good and Excellent. As there are five water quality parameters with five classes, the number of fuzzy rules would be
3125 (i.e. 55). Total 3125 rules were used to develop fuzzy inference system. Some of the sample fuzzy rules are presented in table 6.
[Place Table 6. Here]
The ‘Mamdani’ approach has been used due to its simple structure and Max-Min inference. The implication method used was ‘Min’ and the aggregation method used was ‘Max’. The MATLAB ® 2014 toolbox was used for modeling the fuzzy inference system. Trapezoidal and triangular membership functions have been used for the development of fuzzy inference system. Water quality data of all fourteen stations for three years from 2013 to 2015 have been used for training, while data of one year viz. 2016 has been utilised for testing of the FIS. The study was carried out by considering triangular and trapezoidal Membership function (i.e.) for each of the input and output parameters. The defuzzification was carried out by using Centroid, Mean of Maxima (MOM) and bisector methods. The triangular MF for each input and output parameter is shown in figure 4. [Place Figure 4. Here]
3. Results and Discussions
[Place Figure 5. Here] [Place Figure 6. Here] [Place Figure 7. Here] [Place Table 7. Here]
[Place Table 8. Here] [Place Table 9. Here] [Place Table 10. Here]
In the present study, water quality analysis has been done for four years from 2013 to 2016 and for illustration purpose water quality data at station two, three, four, five, thirteen and fourteen have been presented in figures 5 to 7. In figures 5 to 7 four water quality indices have been presented viz. VWQI, NSFWQI & two no of FWQI based on triangular & trapezoidal membership functions respectively. Vedprakash WQI (i.e. VWQI) is developed in India and mainly inspired by NSFWQI. Therefore, there is a close correlation between the values of VWQI & NSFWQI. In India NSFWQI has been used both by central and various state pollution control
boards, so the values of FWQI have been compared with NSFWQI, by identifying Cc at various sampling stations. In the subsequent deliberation, FQWI based on triangular & trapezoidal membership functions has been referred as FQWI-Triangular& FQWI-Trapezoidal respectively. In the present study, for the development of FIS, both triangular and trapezoidal membership functions have been adopted using centroid, Bisector and Mean of Maxima (i.e. MOM) as methods of defuzzification. The triangular membership functions used, have been presented in figure 4.The ranges for input and output parameters for triangular and trapezoidal MF are mentioned in table 4 and table 5. These ranges have been used to ascertain the water quality at different sampling stations in a selected stretch of Godavari river as Fuzzy water quality index (FWQI). FWQIs using Triangular and trapezoidal MF have been used as FWQITriangular and FWQI-Trapezoidal in the subsequent discussion. The NSFWQI and FWQI values have been taken as observed and predicted values respectively. Modeling performance criteria in the form of Mean square error (i.e. MSE) and coefficient of correlation (i.e. Cc) have been used for validation of predicted FWQIs. In table 9, error analysis during training and testing of fuzzy models for selected sampling stations has been mentioned. It is evident from table 10 that a change in the model’s performance occurs on changing the membership function and defuzzification method. The best fitting model for each sampling station has been selected, based on the value of Cc between the observed and predicted values. The performance of the model improves with the increase in the value of Cc. The model having the highest value of Cc during the testing shows a better correlation between the observed and predicted values of WQIs and therefore selected as best fitting model. But, if the value of Cc is same for two or more models , then the model having the lesser value of MSE is selected as best fitting model. The best fitting models for each sampling station has been presented in table 10. It can be readily perceived from tables 9 and 10 that the performance of models with triangular MF using the bisector method of defuzzification is better, as compared to the triangular and trapezoidal MF employing other methods of defuzzification. It can also be observed from table 10 that out of fourteen sampling stations in the study area, triangular MF performs better for thirteen stations as compared to trapezoidal MF, while trapezoidal MF performs better for one station only. It is evident from table 10 that the bisector method of defuzzification performs better for nine sampling stations, while centroid and mean of maxima method performs better for three and two stations respectively. The value of Cc at sampling stations 11 to 14 is relatively less, since the valve of
BOD5 and total solids at these stations is more than 30 mg/l and 500 mg/l respectively, due to which significant reduction in value of FWQI occurs, while NSFWQI and VWQI values are relatively more as compared to FWQI values. This significant difference in the values of FWQI as compared to values of NSFWQI and VWQI is due to the limitations of NSFWQI and VWQI. The limitations of NSFWQI and VWQI are that, they cannot truly represent water quality, when BOD5 and total solids are more than 30 mg/l and 500 mg/l respectively. Therefore the actual water quality cannot be truly reflected by NSFWQI & VWQI under these cases, due to their limitation of ‘Eclipsing’ caused on account of their aggregation function additive in nature. Whereas at these stations actual water quality status can be truly represented by FWQI, since the fuzzy approach is equally sensitive to a minor change in the value of each parameter. It is observed from figures 5 to 7 that FWQI-Triangular and FWQI-Trapezoidal values are on the relatively lower side as compared to NSFWQI and VWQI values. This is because FWQI approach gives equal weightage to each parameter. When the value of even a single parameter is in the ‘bad’ category (like BOD5 is more than 500 mg/l), then FWQI approach considers that the water quality is ‘bad’, even when the remaining parameters are in ‘good’ category. This change in water class is not truly reflected by NSFWQI and VWQI approach due to their limitation of ‘Eclipsing’. It is evident from figures 5 to 7 that during the summer season in all years except 2015, a significant reduction in WQI values occurs, which is effectively reflected by FWQITriangular approach and has not been depicted by NSFWQI and VWQI approaches due to their inherent limitation. KumbhMela was organized during 2015 on the banks of Godavari at Nashik, so waste water was not allowed to be entered into the Godavari before the prominent bathing ghats at Nashik. Therefore in summer 2015, a significant difference between FWQI and other WQI values is not visible. It can be readily observed from figures 5 to 7 that the performance of FWQI-Triangular is more representative to exhibit true water quality status as compared to FWQI-Trapezoidal. This is due to the observation that appropriate variation in the values of FWQI-Trapezoidal is not reflected like FWQI-Triangular. This is due to the flat shape of trapezoidal-MF in the central portion, which makes it relatively less representative as compared to triangular MF. As evident from table 10 that FWQI-Triangular model using the Bisector defuzzification method outperforms other considered FWQI models of the study. It has been observed from the study that from the Gangapur dam to the Someshwar temple only the Godavari river is CPCB ‘Class A’ river and fit to serve as drinking water after
disinfection only. Based on study, it is found that, Godavari is CPCB ‘Class C’ river from Anandwalli bridge to Ghatgebaba bridge. While from Tapovan STP to Dasak Bridge Godavari is CPCB ‘Class D’ river. It can be understood from the above deliberation that actual water quality status can not be truly represented by NSFWQI & VWQI approach at places, where pollution level increases beyond a certain limit. Therefore a more rational approach like fuzzy logic approach is required to represent the true picture of the actual water quality status of the Indian rivers, carrying high pollutional loads.
4. Conclusions The study for identification of water quality status of the Godavari river at Nashik was carried out by using the most prevalent NSFWQI and indigenous VWQI. It is evident that both NSFWQI and VWQI exhibits similar results and are in close correlation, but both indices suffer from ‘Eclipsing’ and can not truly represent the high concentration of parameters like BOD5 and total solids. Therefore these
indices become insensitive towards these parameters. To
overcome the limitations of these two indices, a more rational fuzzy logic approach has been adopted. The fuzzy models have been developed using triangular and trapezoidal membership functions with centroid, bisector and mean of maxima (MOM) methods for defuzzification. The study revealed that 1) Fuzzy logic approach is equally sensitive to all parameters and provides flexibility to choose the range of different parameters and corresponding quality class as per expert’s judgement. 2) Fuzzy logic approach is more sensitive for little change in the value of each parameter and takes cognizance of the water quality minutely. 3) Fuzzy logic approach can truly represent the water quality status in the cases of very high pollution of streams, observed in the Indian scenario, which cannot be depicted by NSFWQI and VWQI approach. 4) The performance of the fuzzy model changes considerably on changing the membership function and defuzzification method. 5) The
fuzzy models with triangular MF and bisector method of
defuzzification
outperforms other fuzzy models for indian streams. 6) The FWQI index developed by the present study produces reliable and accurate results, therefore its use should be preferred by the municipal corporations for assessment of surface
water quality, especially when assessing water for human consumption or use by mankind is under consideration.
Acknowledgements: The Authors are grateful to the Management and Principal of Sandip Foundation’s Sandip Institute of Technology and Research Centre, Nashik, India for providing all the facilities to carry out this study.
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https://doi.org/10.1016/j.gsd.2018.01.006. Zadeh, L.A.,1965. Fuzzy Sets, Information and Control.8, 338-353. http://mpcb.gov.in/ereports/pdf/waterqualityreport2014-15TERI.pdf
6,
235-244.
Table 1. NSFWQI Water Quality Parameters Sr. No. 1 2 3 4 5 6 7 8 9
Parameter Dissolved Oxygen Faecal Coliform pH Biochemical Oxygen Temperature change Total Phosphates Nitrates Turbidity Total Solids
Weightage 0.17 0.16 0.11 0.11 0.10 0.10 0.10 0.08 0.07
Table 2. NSF Water Quality Index Sr.
NSFWQI
Water
No.
Range
Quality
1 2 3 4 5
90-100 70-90 50-70 25-50 0-25
Excellent Good Medium Bad Very Bad
Table 3. Subindex Equations of Water Quality Index by Vedprakash _________________________________________________________________________________________
Parameter Range Applicable Equation ___________________________________________________________________________ DO (% saturation)
0-40 % saturation 40-100% saturation
IDO =0.18 + 0.66 x (% sat) IDO=-13.5+1.17 x (% sat)
BOD (mg/l)
0-10 10-30 >30
IBOD=96.67-7 x IBOD=38.9-1 x IBOD= 2
pH
2-5 5-7.3 7.3-10 10-12 <2, >12
IpH= 16.1+7.35 x IpH=-142.67+33.5 x IpH =316.96-29.85 x IpH= 96.17-8.0 x IpH=0
__________________________________________________________________________________________
Table 4.Values of Input and Output Parameters for Trapezoidal Membership Function Class
DO
Excellent Good Medium
a 6.5 4.5 2.75
b 8.0 5.5 3.75
c 9.0 6.5 4.5
d 9.0 8.0 5.5
a 0 2.0 5.0
b 0 3.0 6.0
c 2.0 5.0 8.0
d 3.0 6.0 10.0
a 0.0 7.25 22.5
Turbidity b c 0.0 7.5 15.0 22.5 30.0 45.0
Bad Very Bad
1.0 0.0
2.0 0.0
2.75 1.0
3.75 2.0
8.0 35.0
10.0 45.0
35.0 75.0
45.0 75.0
45.0 75.0
60.0 90.0
d 8.50 9.0 9.50 10.5 0 12.0 0
a 80.0 60.0 40.0 15.0 0.0
b 90.0 70.0 50.0 25.0 0.0
Class Excellent Good Medium Bad Very Bad
BOD
Total Solids a 0 150. 0 338. 0 464. 0 800.
b 0 244. 0 433. 0 537. 0 900.
0
0
c 150. 0 338. 0 464. 0 800. 0 1000
pH d 244. 0 433. 0 537. 0 900. 0 1000
a 6.5 8.25 8.75 9.25 10.0 0
b 6.5 8.50 9.0 9.50 10.5 0
c 8.25 8.75 9.25 10.0 0 12.0 0
75.0 125. FWQI0
d 15.0 30.0 60.0 90.0 125. 0
c 100. 0 80.0
d 100. 0 90.0
60.0 40.0 15.0
70.0 50.0 25.0
Table 5.: Values of Input and Output Parameters for Triangular Membership Function Class
DO
BOD
Turbidity
Excellent Good
a 6.5 4.5
b 8 6.5
c 9.0 8.0
a 0 2.0
b 2.0 4.0
c 4.0 8.0
a 0 7.5
b 7.5 19.0
c 19.0 40.0
Medium Bad Very Bad
2.5 1.0 0
4.5 2.5 1.0
6.5 4.5 2.5
4.0 8.0 28.0
8.0 28.0 45.0
28.0 45.0 75.0
19.0 40.0 65.0
40.0 65.0 90.0
65.0 90.0 125.0
Excellent Good
Total Solids a b c 0 150.0 290.0 150.0 290.0 433.0
a 6.50 8.25
pH b 8.25 8.50
c 8.50 9.00
a 80.0 60.0
FWQI b 90.0 80.0
c 100.0 90.0
Medium Bad Very Bad
290.0 433.0 668.0
8.50 9.00 9.50
9.00 9.50 10.50
9.50 10.50 12.00
38.0 15.0 0
60.0 38.0 15.0
80.0 60.0 38.0
Class
433.0 668.0 900.0
668.0 900.0 1000.0
Table 6. Development of Fuzzy Rules Sr. No. 1 2 3 4 5 6 7 ---------3125
DO
BOD
Turbidity
Excellent Excellent Excellent Medium Bad Very Bad Medium ----------------------------------Very Bad
Excellent Excellent Excellent Bad Very Bad Bad Bad ------------------------------Very Bad
Excellent Excellent Excellent Medium Medium Bad Very Bad ------------------------------Very Bad
Table 7. Water Quality as Per NSFWQI & FWQI Sr.
NSFWQI FWQI-
Water
No.
Range
Quality
Triangular
Total Solids Excellent Good Good Bad Bad Bad Very Bad ------------------------------Very Bad
pH
FWQI
Excellent Excellent Medium Good Good Medium Bad ------------------------------Very Bad
Excellent Good Medium Bad Very Bad Very Bad Very Bad ------------------------------Very Bad
Table 8. Class of River as Per CPCB
Sr. No
Range
MF Range 1 2 3 4 5
90-100 70-90 50-70 25-50 0-25
85-100 70-85 48-70 27-48 0-27
Excellent Good Medium Bad Very Bad
Class of River as Triangular per MF Range CPCB
NSFWQI FWQI-
1
63-100
61-100
A
2
50- 63
48- 61
B
3
38- 50
36- 48
C
4
< 38
<
36
D&E
Table 9. Stationwise Error Analysis during Training and Testing of Fuzzy Inference System Station Membership Defuzzification Training Testing No. Function Method MSE CC MSE CC 1 Trapezoidal Centroid 162.53 0.60 80.82 0.80 Bisector 172.05 0.60 82.67 0.86 MOM 194.97 0.63 79.83 0.87 Triangular Centroid 85.27 0.69 47.73 0.75 Bisector 86.05 0.65 33.42 0.83 MOM 99.37 0.53 28.98 0.84 2 Trapezoidal Centroid 181.01 0.79 138.25 0.63 Bisector 175.92 0.79 114.75 0.58 MOM 201.60 0.75 117.66 0.80 Triangular Centroid 89.43 0.86 76.67 0.85 Bisector 86.83 0.84 61.17 0.86 MOM 95.61 0.74 57.62 0.80 3 Trapezoidal Centroid 174.06 0.85 154.62 0.46 Bisector 166.92 0.84 153.58 0.41 MOM 184.17 0.77 93.33 0.40 Triangular Centroid 90.61 0.86 82.06 0.93 Bisector 91.16 0.84 75.25 0.89 MOM 104.26 0.79 95.35 0.74 4 Trapezoidal Centroid 322.64 0.79 548.13 0.55 Bisector 332.72 0.79 568.83 0.38 MOM 586.92 0.36 562.58 0.35 Triangular Centroid 73.48 0.96 93.69 0.87 Bisector 77.58 0.96 91.25 0.85 MOM 121.92 0.84 150.03 0.66 5 Trapezoidal Centroid 348.27 0.75 556.8 0.50 Bisector 358.28 0.75 578.08 0.57 MOM 585.25 0.69 581.25 0.51 Triangular Centroid 76.61 0.91 94.49 0.97 Bisector 81.25 0.92 87.67 0.94 MOM 110.93 0.84 113.87 0.84 6 Trapezoidal Centroid 277.95 0.76 447.41 0.69 Bisector 290.11 0.76 458.25 0.63 MOM 450.08 0.60 447.41 0.61 Triangular Centroid 56.54 0.97 85.90 0.94 Bisector 63.92 0.96 71.92 0.94 MOM 90.49 0.83 63.22 0.85
Station Membership No. Function 7
Trapezoidal
Triangular
8
Trapezoidal
Triangular
9
Trapezoidal
Triangular
10
Trapezoidal
Triangular
11
Trapezoidal
Triangular
12
Trapezoidal
Triangular
Defuzzification Method Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM
Training MSE 230.57 206.16 321.14 77.51 72.69 180.35 215.98 205.64 365.36 56.21 62.75 87.62 256.23 262.72 384.75 85.30 88.27 115.64 301.36 329.55 433.36 99.15 149.89 136.52 49.10 57.72 148.15 49.29 70.66 209.36 96.22 124.44 288.17 91.27 120.17 287.27
CC 0.72 0.75 0.63 0.94 0.95 0.76 0.79 0.81 0.38 0.97 0.96 0.85 0.76 0.73 0.39 0.90 0.89 0.82 0.61 0.61 0.59 0.90 0.91 0.89 0.81 0.69 0.47 0.84 0.84 0.71 0.59 0.59 0.49 0.64 0.65 0.60
Testing MSE 338.34 326.75 321.42 109.76 102.58 192.27 342.03 345.08 341.25 97.87 68.83 111.12 395.21 403.83 394.58 94.27 77.33 52.85 389.60 372.58 364.75 91.75 84.83 75.18 116.94 115.33 142.71 107.40 135.75 241.08 218.36 218.42 292.08 158.47 167.42 406.811
CC 0.65 0.64 0.63 0.96 0.96 0.85 0.38 0.37 0.38 0.96 0.97 0.79 0.40 0.40 0.39 0.93 0.97 0.84 0.23 0.23 0.25 0.92 0.97 0.88 0.50 0.47 0.30 0.57 0.68 0.58 0.20 0.25 0.46 0.36 0.69 0.37
Station Membership No. Function 13
Trapezoidal
Triangular
14
Trapezoidal
Triangular
Defuzzification Method
Training MSE 251.88 262.78 366.72 136.63 152.64 138.22 242.55 260.69 360 148.60 170.94 354.79
Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM
CC 0.41 0.41 0.33 0.41 0.39 0.42 0.43 0.41 0.38 0.41 0.41 0.15
Testing MSE 271.99 264.17 335.83 132.55 138.08 245.58 280.91 276.83 31.68 139.55 149.50 20.02
CC 0.15 0.39 0.38 0.33 0.22 0.47 0.24 0.20 0.21 0.28 0.33 0.28
Table 10. Sampling Stationwise Best Fitting Model Station No.
Membership Function
Defuzzification Method
Cc
Station No.
Membership Function
Defuzzification Method
Cc
1
Trapezoidal
MOM
0.87
8
Triangular
Bisector
0.97
2
Triangular
Bisector
0.86
9
Triangular
Bisector
0.97
3
Triangular
Centroid
0.93
10
Triangular
Bisector
0.97
4
Triangular
Centroid
0.87
11
Triangular
Bisector
0.68
5
Triangular
Centroid
0.97
12
Triangular
Bisector
0.69
6
Triangular
Bisector
0.94
13
Triangular
MOM
0.47
7
Triangular
Bisector
0.96
14
Triangular
Bisector
0.33
Figure 1. Location Map of Study Area
Figure 2. Location Map of Water Quality Monitoring Stations and Wastewater Addition Points in Godavari River at Nashik
Figure 3.Process Flow Diagram for Fuzzy Inference System (F.I.S.)
(a) Triangular MF for DO
(b) Triangular MF for BOD
(c ) Triangular MF for Turbidity
(d) Triangular MF for Total Solids
(e) Triangular MF for pH
(f) Triangular MF for FWQI Figure 4. Triangular MF for DO, BOD, Turbidity, Total solids, pH and FWQI
(a) Variation of WQIs at Station 2-Balaji Temple (Avg. FQWI-Triangular-MF- 77.92 )
(b) Variation of WQIs at Station 3-Someshwar (Avg. FQWI-Triangular-MF- 76.85) Figure 5. Variation of WQIs for Sampling Stations with ‘Good’ Water Quality
(a) Variation of WQIs at Station 4- Anandwalli Bridge (Avg. FQWI-Triangular-MF- 45.52)
(b) Variation of WQIs at Station 5- Bapu Bridge (Avg. FQWI-Triangular-MF- 45.81) Figure 6. Variation of WQIs for Sampling Stations with ‘Bad’ Water Quality
(a) Variation of WQIs at Station 13- Agartakli STP (Avg. FQWI-Triangular-MF- 15.85)
(b) Variation of WQIs at Station 14 – Dasak Bridge (Avg. FQWI-Triangular-MF- 16.42) Figure 7. Variation of WQIs for Sampling Stations with ‘Very Bad’ Water Quality
1) In view of higher pollution strength of Indian rivers, prevalent water quality indices of the western countries like the National sanitation foundation water quality index (NSFWQI) and indigenous Vedprakash water quality index(VWQI) cannot truly represent the water quality status of Indian rivers. 2) Most of the Indian rivers carry high pollution potential in the form of high BOD5 and total solids content. The use of NSFWQI becomes deficient in such cases, since its Qvalue curves cannot take into consideration high BOD5 and total solids content of natural streams above 30mg/l and 500 mg/l respectively. 3) To overcome the limitation, fuzzy modelling has been used in this study for the prediction of water quality of Indian rivers. 4) The fuzzy models have been developed using triangular and trapezoidal membership functions with centroid, bisector and mean of maxima (MOM) methods for defuzzification. 5) It is observed that the values of fuzzy based water quality index are more representative to actual river water quality status of Indian rivers as compared to NSFWQI and VWQI, since the adopted fuzzy logic approach is equally sensitive to all parameters and can truly represent the minor change in the value of any parameter, especially in case of river stretches having higher pollution. 6) FWQI-Triangular model using the Bisector defuzzification method outperforms other considered FWQI models of the study.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S2352-801X(19)30425-4
DOI:
https://doi.org/10.1016/j.gsd.2020.100350
Reference:
GSD 100350
To appear in:
Groundwater for Sustainable Development
Received Date: 21 December 2019 Revised Date:
8 February 2020
Accepted Date: 11 February 2020
Please cite this article as: Nayak, J.G., Patil, L.G., Patki, V.K., Development of water quality index for Godavari River (India) based on fuzzy inference system, Groundwater for Sustainable Development (2020), doi: https://doi.org/10.1016/j.gsd.2020.100350. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Development of Water Quality Index for Godavari River (India) based on Fuzzy Inference System Jyotiprakash G. Nayaka, L. G. Patilb, Vinayak K. Patkic ______________________________________________________________________________________________________________ a-
b-
c-
Associate Professor, Department of Civil Engineering, Sandip Institute of Technology and Research Centre, Nashik, Maharashtra, India, [email protected]. Professor, Department of Civil Engineering, Shri Guru Gobind Singhji Institute of Engineering and Technology, Nanded, Maharashtra, India,[email protected]. Professor, Department of Civil Engineering, Nagesh Karajgi Orchid College of Engineering and Technology, Solapur, Maharashtra, India,[email protected].
Corresponding author: Email: [email protected], Tel.No: +91 8698299944
Development of Water Quality Index for Godavari River (India) based on Fuzzy Inference System Jyotiprakash G. Nayaka, L.G.Patilb, Vinayak K.Patkic
Abstract
In view of higher pollution strength of Indian rivers, prevalent water quality indices of the western countries like the National sanitation foundation water quality index (NSFWQI) and indigenous Vedprakash water quality index (VWQI) cannot truly represent the water quality status of Indian rivers. To overcome this limitation, fuzzy modeling has been used in this study for the prediction of water quality of Indian rivers. The fuzzy models have been developed using triangular and trapezoidal membership functions with centroid, bisector and mean of maxima (MOM) methods for defuzzification. It is observed that the fuzzy model with triangular membership function utilizing the bisector method of defuzzification performs better, compared to triangular and trapezoidal membership function utilizing the centroid and MOM method of defuzzification. The values of water quality index based on fuzzy logic have been compared with the NSFWQI and VWQI. It is observed that the values of fuzzy based water quality index are more representative to actual river water quality status of Indian rivers as compared to NSFWQI and VWQI.This is due to the fact that the adopted fuzzy logic approach is equally sensitive to all parameters and can truly represent the minor change in the value of any parameter, especially in case of river stretches having higher pollution.
Keywords:Fuzzy Inference System;Fuzzy Water Quality Index; Membership Function; National Sanitation Foundation Water Quality Index; Water Quality Index.
Nomenclature DO BOD WQI NSFWQI VWQI FWQI FIS MF MOM
Dissolved Oxygen Biological Oxygen Demand (over 5 days of incubation at 200 C ) Water Quality Index National Sanitation Foundation Water Quality Index Vedprakash Water Quality Index Fuzzy Water Quality Index Fuzzy Inference System Membership Function Mean of Maxima
1. Introduction To maintain
human health and to secure the environment, evaluation of water quality is
indispensable. Water quality index (i.e WQI) is a single dimensionless term, by which the water quality of a stream can be expressed as good, medium or bad. The water quality of different regions can easily be compared by comparing the values of WQI, instead of comparing the numerical values of several water quality parameters. To evolve a WQI, four steps have been utilised in the past (Abbasi and Abbasi, 2012); i) Choice of parameters ii) Determination of values of sub-index iii) Ascertaining appropriate weights iv) Establishing the final index after compounding the sub-indices. While establishing a WQI, the selection of water quality parameters is done based on, a) Referring the work of previous researchers (Said et al., 2004) b) Availability of the data sets (Cude, 2001) c) True representation of the quality scenario (Hanh et al., 2011) d) The proposed use of stream for a specific purpose (Hurley et al., 2012). The subsequent step is the development of sub-indices, which is done to convert the selected parameters onto a common platform, since the units of all the selected parameters cannot be same. The subsequent step is establishing weights to the parameters. Equal or unequal weights have been assigned to the parameters by the index developers, as per their judgment. Some researchers claimed that all parameters are equally important and assigned equal weights to all the parameters, during the development of WQIs (e.g. Cude, 2001; CCME, 2001). The index may suffer from ‘Sensitivity’ issue, if the different weights are assigned to the parameters. Equation
of the final index is decided on aggregation of sub-indices and considering the weights assigned to the different parameters. Additive and multiplicative methods have been used for aggregation of sub-indices. Most of the existing WQIs have used additive method (e.g. Brown et al., 1970; Sargaonkar and Deshpande, 2003) but the additive method suffers from ‘eclipsing’ issue (Swamee and Tyagi, 2000). While, some other researchers used multiplicative method for the development of the WQIs (e.g. Bhargava, 1985). It was reported that the multiplicative approach can not completely resolve the ‘eclipsing’ problem and also leads to ‘ambiguity’ issue sometimes (Swamee and Tyagi,2000). NSFWQI was developed by Brown (1970) and is used worldwide, including the Indian subcontinent to determine the water quality of the rivers (Sutadin et al., 2016). Considering the present scenario of Indian rivers, this index can no longer be used in the Indian subcontinent because most of the Indian rivers carry high pollution potential in the form of high BOD5 and total solids content. The use of NSFWQI becomes deficient in such cases, since its Q-value curves do not take into consideration high BOD5 and total solids content of natural streams (Nayak et al., 2017). Godavari River is one of the sacred river of India and Kumbhmela is celebrated on the banks of the Godavari in and around Nashik every twelve years. Thousands of people take a holy dip in Godavari during Kumbh and other festivals, hence it is the need of the hour to determine water quality of this river in and around Nashik. In view of the limitations of the prevalent WQIs viz. ‘eclipsing’, ‘ambiguity’ and inability to be representative on downstream side of a wastewater treatment plant, it is observed that these existing WQIs cannot represent the actual picture of water quality status of Indian rivers like Godavari. In the present study, an attempt has been made to utilise fuzzy logic approach to develop fuzzy inference system; to overcome the limitations of existing WQI approaches and for the identification of actual river water quality status (especially in such Indian scenario). Fuzzy logic approach has its inherent merits of ‘flexibility’ and capability to deal with ‘vagueness’ and ‘uncertainty’ more effectively. This approach also effectively addresses to ‘sensitivity’ and ‘ambiguity’ issues encountered in the determination of WQIs. In the present study suitability of Godavari river water have been investigated for drinking purpose and outdoor bathing purpose. 2. Materials and Methods 2.1 Study Area
The Godavari, one of the biggest river in India, emerges from Brahmagiri Mountain (at 0
19.56 N, 73.200E) is situated at Triambakeswar in Nashik District of Maharashtra state (Chavan et al., 2009). The present study was carried out to assess the water quality of the Godavari river in about 24 Km stretch in and around Nashik city. In the present study, fourteen river water quality sampling stations from the Gangapur dam to Dasak village were selected. The sampling stations are marked as S1 to S14 in fig.2. The water samples for analysis were collected once in a month for four years at a point 30 cm below the water surface. Analysis of all the parameters was performed using standard methods (APHA, 2012). Intense reconnaissance survey work was done to identify the point and nonpoint sources of wastewater addition in a selected stretch of the Godavari river and on that basis figure 2 has been developed. During the survey work, it was observed that partially treated or untreated sewage is getting added in the selected stretch of the Godavari river. These are the main point sources of pollution and are marked as P1 to P12 presented in figure 2. [Place Figure 1. Here] [Place Figure 2. Here]
2.2 National Sanitation Foundation Water Quality Index (NSFWQI) In the present study, one of the most extensively used index in the entire world, National sanitation foundation water quality index (NSFWQI) developed by Brown (1970) has been used to find WQI for surface water (Sutadin, 2016;Bhutani, 2014) NSFWQI = ∑ Wi Qi
(1)
Where Wi = Weightage of the concerned parameter & Qi = Q Value of the concerned parameter based on observed value, determined from concerned graph For calculation of NSFWQI five parameters (excluding Faecal Coliform, temperature change, phosphates and Nitrates) have been considered in the present study. The selection of parameters was done by using Delphi method. The weightages of the parameters and water quality class for NSFWQI are presented in Table 1 and 2 respectively and considered that the same are also applicable for the present study. [Place Table 1. Here]
[Place Table 2. Here]
2.3 Vedprakash Water Quality Index (VWQI) Vedprakash WQI (VWQI) is the other most commonly used WQI for determination of water quality of surface water bodies in Indian subcontinent (Bhutani, 2014; Water quality report,MPCB,2015). Vedprakash (1990) developed the index on observing the fact that in routine water quality analysis work, only a few numbers of important parameters viz. DO, BOD & pH should be considered, to ascertain the real water quality status of the streams in the Indian subcontinent. The list of parameters was selected using Delphi. This index was utilized to identify the stretches of river Ganga where the difference between the required and the actual water quality is considerably high, to indicate the need of pollution abatement initiatives. The index is expressed in equation 2 here: VWQI= ∑
Where is weightage of ith water quality parameter and
(2)
issubindex for ith water quality parameter and
p is the number of water quality parameters. The index is inspired from the NSFWQI, with little alteration in the weightages to affirm the water quality criteria for the uses of different categories. Subindex equations were used to determine the subindex values, as presented in table 3. In the present study Vedprakash water quality index (VWQI) has also been determined. [Place Table 3. Here]
Weightages ( ) of Parameters : DO- 0.43 , BOD - 0.26 , pH - 0.31 2. 4 Fuzzy Logic System 2.4.1Fuzzy Inference System Fuzzy inference system is resulted on combining the fuzzy logic with expert system (Zadeh, 1965). The real conditions are often uncertain and Zadeh (1965) defined this vagueness using the term “Fuzziness”. Chau (2006) had used concept of fuzzy sets to carry out water quality modeling, since it put forth a appropriate approach to deal with the issues, where the goals and boundaries are not properly defined or imprecise. Nasiri et al.(2007) developed a fuzzy riverpollution decision support system to make expert knowledge available for nonexpert users. Raman Bai el at.(2009) studied water quality in the Semenyih river (Malaysia) with physico chemical parameters and commented that fuzzy water quality index will assist the decision makers in reporting the condition of water quality.Semiromi (2011) et al. developed fuzzy water
quality index for Karoon river (Iran) and identified that fuzzy logic approach have superior capabilities to deal with non-linear, complex and uncertain systems.Gharibi et al. (2012) commented that fuzzy logic approach is a comprehensive tool for water quality assessment, especially for the analysis of human drinking water. Patki et al. (2013) used fuzzy inference system to assess the physicochemical parameters of municipal water, under the distribution system to determine its portability. Li et al. (2016) developed fuzzy water pollution index method for water quality determination of Qu river (China) and found that the method gives comprehensive water quality rank. There are some predominant reasons, which signify the merits of the models working on the concept of fuzzy logic. The reasons are: first, Issues involving nonlinear relationships among the variables can be addressed; second, local simple models have been utilised, rendering them simple to work with; third, they can be communicated and understood verbally; fourth, individual expertise and experience is used, which is not utilised by other methods (Lermontov et al.,2009; Gharibi,2009). 2.4.2 Fuzzy inference rules In fuzzy logic, if- then rules and fuzzy set operators are utilised to express the relationship between input and output variables of a system. Concepts of the formation of the fuzzy rules have been presented in table 6. 2.4.3 Basic structure of a Fuzzy inference system (FIS) A fuzzy inference system (FIS) works on fuzzy set theory, and incorporates the following four main steps (Ross 2004): a) Fuzzification: In this step, Crisp values of the input parameters are converted into corresponding linguistic terms by making use of membership functions. The adopted ranges of the different class for concerned parameters are used to find the value of membership function for different parameters. For determination of the value of triangular and trapezoidal membership functions, undermentioned equations are used 0 < <
(−) ≤ ≤
(−) Triangular : f (x; a,b,c ) = (−)
(−) ≤ ≤
0 < < (−) ≤ ≤
(−) 1 ≤ ≤ ( −)
≤ ≤ ( −)
Trapezoidal: f (x; a,b,c ) =
Where a, b, c and d are membership function parameters and x represents each single point on the x axis. b) Evaluation of the rules: Here compounding of the outcome of a fuzzy if- then rule is done. In this process, the lowermost class of any of the selected parameter becomes the class of fuzzy index for that particular rule. The lowermost class and corresponding value of membership function of any of the selected parameter becomes the class of the fuzzy index for the rule. In this step, applicable fuzzy rules for the given data are identified. c) Aggregation of rule outputs: In this step, applicable fuzzy if-then rules are considered. The maximum value of the fuzzy index having the same class, among the available applicable rules is considered. Outputs of all applicable rules are then clubbed into a single fuzzy distribution by carrying out the fuzzy union of applicable rules. d) Defuzzification: Defuzzification is the conversion of the fuzzified output to the crisp value by using the methods of defuzzification. 2.5 Modeling Performance Criterions To ascertain the prediction accuracy of the fuzzy models developed in the present study, two criterions have been utilized to assess the performance of the models. The criterions utilized are mean square error (MSE) and coefficient of correlation (CC ). 2.5.1 Mean Square Error(MSE) The mean squared error (MSE) of a particular case measures the average of the squared difference between the observed values and the predicted values. The MSE gives an indication of the error or residual variance.
MSE =" ∑+,![observed − predicted] 2 !
(3)
2.5.2 Coefficient of Correlation The Coefficient of correlation is an indication of the linear relationship between the two considered variables as presented here,
Where, n= number of data in the dependent data set, xi= the observed values, yi= the predicted values, x’=mean of the observed values and y’=mean of the predicted values Patki et al. (2013) and Tiri et. Al. (2018) used mean square error and coefficient of correlation as modeling performance criteria to assess the performance of the models. 2.6 Development of a Water Quality Index based on Fuzzy Logic Approach In the present study, to investigate the water quality of the Godavari river, fuzzy logic approach with five main parameters namely DO,BOD, Turbidity,Total solids and pH have been used. In the present study, comparison of river water quality using NSFWQI, VQWI and Fuzzy water quality index (i.e.FQWI) based on different membership functions; involving different methods of defuzzification have been done. To keep a common basis for ascertaining the value of the indices, five representative and important water quality parameters named DO, BOD, Turbidity, Total solids and pH have been considered. It was also considered that the number of fuzzy rules increases exponentially, with an increase in the number of parameters. So, considering only important parameters helps in reducing the number of fuzzy rules. Five types of class of water quality as Excellent, Good, Medium, Bad and Very Bad have been selected for both the indices viz. NSFWQI and FWQI. In this study, the ‘Mamdani’ approach has been utilised for development of the fuzzy inference system, to determine the FWQI. The process flow diagram for fuzzy inference system is as shown in figure 3. [Place Figure 3. Here]
The limits of the Classes for the considered water quality parameters, for the development of FWQI have been presented as per Table 4 and Table 5 respectively. [Place Table 4. Here] [Place Table 5. Here]
For development of FWQI five input parameters have been utilised. Each input parameter has been classified into five water quality classes as Very bad, Bad, Medium, Good and Excellent. As there are five water quality parameters with five classes, the number of fuzzy rules would be
3125 (i.e. 55). Total 3125 rules were used to develop fuzzy inference system. Some of the sample fuzzy rules are presented in table 6.
[Place Table 6. Here]
The ‘Mamdani’ approach has been used due to its simple structure and Max-Min inference. The implication method used was ‘Min’ and the aggregation method used was ‘Max’. The MATLAB ® 2014 toolbox was used for modeling the fuzzy inference system. Trapezoidal and triangular membership functions have been used for the development of fuzzy inference system. Water quality data of all fourteen stations for three years from 2013 to 2015 have been used for training, while data of one year viz. 2016 has been utilised for testing of the FIS. The study was carried out by considering triangular and trapezoidal Membership function (i.e.) for each of the input and output parameters. The defuzzification was carried out by using Centroid, Mean of Maxima (MOM) and bisector methods. The triangular MF for each input and output parameter is shown in figure 4. [Place Figure 4. Here]
3. Results and Discussions
[Place Figure 5. Here] [Place Figure 6. Here] [Place Figure 7. Here] [Place Table 7. Here]
[Place Table 8. Here] [Place Table 9. Here] [Place Table 10. Here]
In the present study, water quality analysis has been done for four years from 2013 to 2016 and for illustration purpose water quality data at station two, three, four, five, thirteen and fourteen have been presented in figures 5 to 7. In figures 5 to 7 four water quality indices have been presented viz. VWQI, NSFWQI & two no of FWQI based on triangular & trapezoidal membership functions respectively. Vedprakash WQI (i.e. VWQI) is developed in India and mainly inspired by NSFWQI. Therefore, there is a close correlation between the values of VWQI & NSFWQI. In India NSFWQI has been used both by central and various state pollution control
boards, so the values of FWQI have been compared with NSFWQI, by identifying Cc at various sampling stations. In the subsequent deliberation, FQWI based on triangular & trapezoidal membership functions has been referred as FQWI-Triangular& FQWI-Trapezoidal respectively. In the present study, for the development of FIS, both triangular and trapezoidal membership functions have been adopted using centroid, Bisector and Mean of Maxima (i.e. MOM) as methods of defuzzification. The triangular membership functions used, have been presented in figure 4.The ranges for input and output parameters for triangular and trapezoidal MF are mentioned in table 4 and table 5. These ranges have been used to ascertain the water quality at different sampling stations in a selected stretch of Godavari river as Fuzzy water quality index (FWQI). FWQIs using Triangular and trapezoidal MF have been used as FWQITriangular and FWQI-Trapezoidal in the subsequent discussion. The NSFWQI and FWQI values have been taken as observed and predicted values respectively. Modeling performance criteria in the form of Mean square error (i.e. MSE) and coefficient of correlation (i.e. Cc) have been used for validation of predicted FWQIs. In table 9, error analysis during training and testing of fuzzy models for selected sampling stations has been mentioned. It is evident from table 10 that a change in the model’s performance occurs on changing the membership function and defuzzification method. The best fitting model for each sampling station has been selected, based on the value of Cc between the observed and predicted values. The performance of the model improves with the increase in the value of Cc. The model having the highest value of Cc during the testing shows a better correlation between the observed and predicted values of WQIs and therefore selected as best fitting model. But, if the value of Cc is same for two or more models , then the model having the lesser value of MSE is selected as best fitting model. The best fitting models for each sampling station has been presented in table 10. It can be readily perceived from tables 9 and 10 that the performance of models with triangular MF using the bisector method of defuzzification is better, as compared to the triangular and trapezoidal MF employing other methods of defuzzification. It can also be observed from table 10 that out of fourteen sampling stations in the study area, triangular MF performs better for thirteen stations as compared to trapezoidal MF, while trapezoidal MF performs better for one station only. It is evident from table 10 that the bisector method of defuzzification performs better for nine sampling stations, while centroid and mean of maxima method performs better for three and two stations respectively. The value of Cc at sampling stations 11 to 14 is relatively less, since the valve of
BOD5 and total solids at these stations is more than 30 mg/l and 500 mg/l respectively, due to which significant reduction in value of FWQI occurs, while NSFWQI and VWQI values are relatively more as compared to FWQI values. This significant difference in the values of FWQI as compared to values of NSFWQI and VWQI is due to the limitations of NSFWQI and VWQI. The limitations of NSFWQI and VWQI are that, they cannot truly represent water quality, when BOD5 and total solids are more than 30 mg/l and 500 mg/l respectively. Therefore the actual water quality cannot be truly reflected by NSFWQI & VWQI under these cases, due to their limitation of ‘Eclipsing’ caused on account of their aggregation function additive in nature. Whereas at these stations actual water quality status can be truly represented by FWQI, since the fuzzy approach is equally sensitive to a minor change in the value of each parameter. It is observed from figures 5 to 7 that FWQI-Triangular and FWQI-Trapezoidal values are on the relatively lower side as compared to NSFWQI and VWQI values. This is because FWQI approach gives equal weightage to each parameter. When the value of even a single parameter is in the ‘bad’ category (like BOD5 is more than 500 mg/l), then FWQI approach considers that the water quality is ‘bad’, even when the remaining parameters are in ‘good’ category. This change in water class is not truly reflected by NSFWQI and VWQI approach due to their limitation of ‘Eclipsing’. It is evident from figures 5 to 7 that during the summer season in all years except 2015, a significant reduction in WQI values occurs, which is effectively reflected by FWQITriangular approach and has not been depicted by NSFWQI and VWQI approaches due to their inherent limitation. KumbhMela was organized during 2015 on the banks of Godavari at Nashik, so waste water was not allowed to be entered into the Godavari before the prominent bathing ghats at Nashik. Therefore in summer 2015, a significant difference between FWQI and other WQI values is not visible. It can be readily observed from figures 5 to 7 that the performance of FWQI-Triangular is more representative to exhibit true water quality status as compared to FWQI-Trapezoidal. This is due to the observation that appropriate variation in the values of FWQI-Trapezoidal is not reflected like FWQI-Triangular. This is due to the flat shape of trapezoidal-MF in the central portion, which makes it relatively less representative as compared to triangular MF. As evident from table 10 that FWQI-Triangular model using the Bisector defuzzification method outperforms other considered FWQI models of the study. It has been observed from the study that from the Gangapur dam to the Someshwar temple only the Godavari river is CPCB ‘Class A’ river and fit to serve as drinking water after
disinfection only. Based on study, it is found that, Godavari is CPCB ‘Class C’ river from Anandwalli bridge to Ghatgebaba bridge. While from Tapovan STP to Dasak Bridge Godavari is CPCB ‘Class D’ river. It can be understood from the above deliberation that actual water quality status can not be truly represented by NSFWQI & VWQI approach at places, where pollution level increases beyond a certain limit. Therefore a more rational approach like fuzzy logic approach is required to represent the true picture of the actual water quality status of the Indian rivers, carrying high pollutional loads.
4. Conclusions The study for identification of water quality status of the Godavari river at Nashik was carried out by using the most prevalent NSFWQI and indigenous VWQI. It is evident that both NSFWQI and VWQI exhibits similar results and are in close correlation, but both indices suffer from ‘Eclipsing’ and can not truly represent the high concentration of parameters like BOD5 and total solids. Therefore these
indices become insensitive towards these parameters. To
overcome the limitations of these two indices, a more rational fuzzy logic approach has been adopted. The fuzzy models have been developed using triangular and trapezoidal membership functions with centroid, bisector and mean of maxima (MOM) methods for defuzzification. The study revealed that 1) Fuzzy logic approach is equally sensitive to all parameters and provides flexibility to choose the range of different parameters and corresponding quality class as per expert’s judgement. 2) Fuzzy logic approach is more sensitive for little change in the value of each parameter and takes cognizance of the water quality minutely. 3) Fuzzy logic approach can truly represent the water quality status in the cases of very high pollution of streams, observed in the Indian scenario, which cannot be depicted by NSFWQI and VWQI approach. 4) The performance of the fuzzy model changes considerably on changing the membership function and defuzzification method. 5) The
fuzzy models with triangular MF and bisector method of
defuzzification
outperforms other fuzzy models for indian streams. 6) The FWQI index developed by the present study produces reliable and accurate results, therefore its use should be preferred by the municipal corporations for assessment of surface
water quality, especially when assessing water for human consumption or use by mankind is under consideration.
Acknowledgements: The Authors are grateful to the Management and Principal of Sandip Foundation’s Sandip Institute of Technology and Research Centre, Nashik, India for providing all the facilities to carry out this study.
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Table 1. NSFWQI Water Quality Parameters Sr. No. 1 2 3 4 5 6 7 8 9
Parameter Dissolved Oxygen Faecal Coliform pH Biochemical Oxygen Temperature change Total Phosphates Nitrates Turbidity Total Solids
Weightage 0.17 0.16 0.11 0.11 0.10 0.10 0.10 0.08 0.07
Table 2. NSF Water Quality Index Sr.
NSFWQI
Water
No.
Range
Quality
1 2 3 4 5
90-100 70-90 50-70 25-50 0-25
Excellent Good Medium Bad Very Bad
Table 3. Subindex Equations of Water Quality Index by Vedprakash _________________________________________________________________________________________
Parameter Range Applicable Equation ___________________________________________________________________________ DO (% saturation)
0-40 % saturation 40-100% saturation
IDO =0.18 + 0.66 x (% sat) IDO=-13.5+1.17 x (% sat)
BOD (mg/l)
0-10 10-30 >30
IBOD=96.67-7 x IBOD=38.9-1 x IBOD= 2
pH
2-5 5-7.3 7.3-10 10-12 <2, >12
IpH= 16.1+7.35 x IpH=-142.67+33.5 x IpH =316.96-29.85 x IpH= 96.17-8.0 x IpH=0
__________________________________________________________________________________________
Table 4.Values of Input and Output Parameters for Trapezoidal Membership Function Class
DO
Excellent Good Medium
a 6.5 4.5 2.75
b 8.0 5.5 3.75
c 9.0 6.5 4.5
d 9.0 8.0 5.5
a 0 2.0 5.0
b 0 3.0 6.0
c 2.0 5.0 8.0
d 3.0 6.0 10.0
a 0.0 7.25 22.5
Turbidity b c 0.0 7.5 15.0 22.5 30.0 45.0
Bad Very Bad
1.0 0.0
2.0 0.0
2.75 1.0
3.75 2.0
8.0 35.0
10.0 45.0
35.0 75.0
45.0 75.0
45.0 75.0
60.0 90.0
d 8.50 9.0 9.50 10.5 0 12.0 0
a 80.0 60.0 40.0 15.0 0.0
b 90.0 70.0 50.0 25.0 0.0
Class Excellent Good Medium Bad Very Bad
BOD
Total Solids a 0 150. 0 338. 0 464. 0 800.
b 0 244. 0 433. 0 537. 0 900.
0
0
c 150. 0 338. 0 464. 0 800. 0 1000
pH d 244. 0 433. 0 537. 0 900. 0 1000
a 6.5 8.25 8.75 9.25 10.0 0
b 6.5 8.50 9.0 9.50 10.5 0
c 8.25 8.75 9.25 10.0 0 12.0 0
75.0 125. FWQI0
d 15.0 30.0 60.0 90.0 125. 0
c 100. 0 80.0
d 100. 0 90.0
60.0 40.0 15.0
70.0 50.0 25.0
Table 5.: Values of Input and Output Parameters for Triangular Membership Function Class
DO
BOD
Turbidity
Excellent Good
a 6.5 4.5
b 8 6.5
c 9.0 8.0
a 0 2.0
b 2.0 4.0
c 4.0 8.0
a 0 7.5
b 7.5 19.0
c 19.0 40.0
Medium Bad Very Bad
2.5 1.0 0
4.5 2.5 1.0
6.5 4.5 2.5
4.0 8.0 28.0
8.0 28.0 45.0
28.0 45.0 75.0
19.0 40.0 65.0
40.0 65.0 90.0
65.0 90.0 125.0
Excellent Good
Total Solids a b c 0 150.0 290.0 150.0 290.0 433.0
a 6.50 8.25
pH b 8.25 8.50
c 8.50 9.00
a 80.0 60.0
FWQI b 90.0 80.0
c 100.0 90.0
Medium Bad Very Bad
290.0 433.0 668.0
8.50 9.00 9.50
9.00 9.50 10.50
9.50 10.50 12.00
38.0 15.0 0
60.0 38.0 15.0
80.0 60.0 38.0
Class
433.0 668.0 900.0
668.0 900.0 1000.0
Table 6. Development of Fuzzy Rules Sr. No. 1 2 3 4 5 6 7 ---------3125
DO
BOD
Turbidity
Excellent Excellent Excellent Medium Bad Very Bad Medium ----------------------------------Very Bad
Excellent Excellent Excellent Bad Very Bad Bad Bad ------------------------------Very Bad
Excellent Excellent Excellent Medium Medium Bad Very Bad ------------------------------Very Bad
Table 7. Water Quality as Per NSFWQI & FWQI Sr.
NSFWQI FWQI-
Water
No.
Range
Quality
Triangular
Total Solids Excellent Good Good Bad Bad Bad Very Bad ------------------------------Very Bad
pH
FWQI
Excellent Excellent Medium Good Good Medium Bad ------------------------------Very Bad
Excellent Good Medium Bad Very Bad Very Bad Very Bad ------------------------------Very Bad
Table 8. Class of River as Per CPCB
Sr. No
Range
MF Range 1 2 3 4 5
90-100 70-90 50-70 25-50 0-25
85-100 70-85 48-70 27-48 0-27
Excellent Good Medium Bad Very Bad
Class of River as Triangular per MF Range CPCB
NSFWQI FWQI-
1
63-100
61-100
A
2
50- 63
48- 61
B
3
38- 50
36- 48
C
4
< 38
<
36
D&E
Table 9. Stationwise Error Analysis during Training and Testing of Fuzzy Inference System Station Membership Defuzzification Training Testing No. Function Method MSE CC MSE CC 1 Trapezoidal Centroid 162.53 0.60 80.82 0.80 Bisector 172.05 0.60 82.67 0.86 MOM 194.97 0.63 79.83 0.87 Triangular Centroid 85.27 0.69 47.73 0.75 Bisector 86.05 0.65 33.42 0.83 MOM 99.37 0.53 28.98 0.84 2 Trapezoidal Centroid 181.01 0.79 138.25 0.63 Bisector 175.92 0.79 114.75 0.58 MOM 201.60 0.75 117.66 0.80 Triangular Centroid 89.43 0.86 76.67 0.85 Bisector 86.83 0.84 61.17 0.86 MOM 95.61 0.74 57.62 0.80 3 Trapezoidal Centroid 174.06 0.85 154.62 0.46 Bisector 166.92 0.84 153.58 0.41 MOM 184.17 0.77 93.33 0.40 Triangular Centroid 90.61 0.86 82.06 0.93 Bisector 91.16 0.84 75.25 0.89 MOM 104.26 0.79 95.35 0.74 4 Trapezoidal Centroid 322.64 0.79 548.13 0.55 Bisector 332.72 0.79 568.83 0.38 MOM 586.92 0.36 562.58 0.35 Triangular Centroid 73.48 0.96 93.69 0.87 Bisector 77.58 0.96 91.25 0.85 MOM 121.92 0.84 150.03 0.66 5 Trapezoidal Centroid 348.27 0.75 556.8 0.50 Bisector 358.28 0.75 578.08 0.57 MOM 585.25 0.69 581.25 0.51 Triangular Centroid 76.61 0.91 94.49 0.97 Bisector 81.25 0.92 87.67 0.94 MOM 110.93 0.84 113.87 0.84 6 Trapezoidal Centroid 277.95 0.76 447.41 0.69 Bisector 290.11 0.76 458.25 0.63 MOM 450.08 0.60 447.41 0.61 Triangular Centroid 56.54 0.97 85.90 0.94 Bisector 63.92 0.96 71.92 0.94 MOM 90.49 0.83 63.22 0.85
Station Membership No. Function 7
Trapezoidal
Triangular
8
Trapezoidal
Triangular
9
Trapezoidal
Triangular
10
Trapezoidal
Triangular
11
Trapezoidal
Triangular
12
Trapezoidal
Triangular
Defuzzification Method Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM
Training MSE 230.57 206.16 321.14 77.51 72.69 180.35 215.98 205.64 365.36 56.21 62.75 87.62 256.23 262.72 384.75 85.30 88.27 115.64 301.36 329.55 433.36 99.15 149.89 136.52 49.10 57.72 148.15 49.29 70.66 209.36 96.22 124.44 288.17 91.27 120.17 287.27
CC 0.72 0.75 0.63 0.94 0.95 0.76 0.79 0.81 0.38 0.97 0.96 0.85 0.76 0.73 0.39 0.90 0.89 0.82 0.61 0.61 0.59 0.90 0.91 0.89 0.81 0.69 0.47 0.84 0.84 0.71 0.59 0.59 0.49 0.64 0.65 0.60
Testing MSE 338.34 326.75 321.42 109.76 102.58 192.27 342.03 345.08 341.25 97.87 68.83 111.12 395.21 403.83 394.58 94.27 77.33 52.85 389.60 372.58 364.75 91.75 84.83 75.18 116.94 115.33 142.71 107.40 135.75 241.08 218.36 218.42 292.08 158.47 167.42 406.811
CC 0.65 0.64 0.63 0.96 0.96 0.85 0.38 0.37 0.38 0.96 0.97 0.79 0.40 0.40 0.39 0.93 0.97 0.84 0.23 0.23 0.25 0.92 0.97 0.88 0.50 0.47 0.30 0.57 0.68 0.58 0.20 0.25 0.46 0.36 0.69 0.37
Station Membership No. Function 13
Trapezoidal
Triangular
14
Trapezoidal
Triangular
Defuzzification Method
Training MSE 251.88 262.78 366.72 136.63 152.64 138.22 242.55 260.69 360 148.60 170.94 354.79
Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM Centroid Bisector MOM
CC 0.41 0.41 0.33 0.41 0.39 0.42 0.43 0.41 0.38 0.41 0.41 0.15
Testing MSE 271.99 264.17 335.83 132.55 138.08 245.58 280.91 276.83 31.68 139.55 149.50 20.02
CC 0.15 0.39 0.38 0.33 0.22 0.47 0.24 0.20 0.21 0.28 0.33 0.28
Table 10. Sampling Stationwise Best Fitting Model Station No.
Membership Function
Defuzzification Method
Cc
Station No.
Membership Function
Defuzzification Method
Cc
1
Trapezoidal
MOM
0.87
8
Triangular
Bisector
0.97
2
Triangular
Bisector
0.86
9
Triangular
Bisector
0.97
3
Triangular
Centroid
0.93
10
Triangular
Bisector
0.97
4
Triangular
Centroid
0.87
11
Triangular
Bisector
0.68
5
Triangular
Centroid
0.97
12
Triangular
Bisector
0.69
6
Triangular
Bisector
0.94
13
Triangular
MOM
0.47
7
Triangular
Bisector
0.96
14
Triangular
Bisector
0.33
Figure 1. Location Map of Study Area
Figure 2. Location Map of Water Quality Monitoring Stations and Wastewater Addition Points in Godavari River at Nashik
Figure 3.Process Flow Diagram for Fuzzy Inference System (F.I.S.)
(a) Triangular MF for DO
(b) Triangular MF for BOD
(c ) Triangular MF for Turbidity
(d) Triangular MF for Total Solids
(e) Triangular MF for pH
(f) Triangular MF for FWQI Figure 4. Triangular MF for DO, BOD, Turbidity, Total solids, pH and FWQI
(a) Variation of WQIs at Station 2-Balaji Temple (Avg. FQWI-Triangular-MF- 77.92 )
(b) Variation of WQIs at Station 3-Someshwar (Avg. FQWI-Triangular-MF- 76.85) Figure 5. Variation of WQIs for Sampling Stations with ‘Good’ Water Quality
(a) Variation of WQIs at Station 4- Anandwalli Bridge (Avg. FQWI-Triangular-MF- 45.52)
(b) Variation of WQIs at Station 5- Bapu Bridge (Avg. FQWI-Triangular-MF- 45.81) Figure 6. Variation of WQIs for Sampling Stations with ‘Bad’ Water Quality
(a) Variation of WQIs at Station 13- Agartakli STP (Avg. FQWI-Triangular-MF- 15.85)
(b) Variation of WQIs at Station 14 – Dasak Bridge (Avg. FQWI-Triangular-MF- 16.42) Figure 7. Variation of WQIs for Sampling Stations with ‘Very Bad’ Water Quality
1) In view of higher pollution strength of Indian rivers, prevalent water quality indices of the western countries like the National sanitation foundation water quality index (NSFWQI) and indigenous Vedprakash water quality index(VWQI) cannot truly represent the water quality status of Indian rivers. 2) Most of the Indian rivers carry high pollution potential in the form of high BOD5 and total solids content. The use of NSFWQI becomes deficient in such cases, since its Qvalue curves cannot take into consideration high BOD5 and total solids content of natural streams above 30mg/l and 500 mg/l respectively. 3) To overcome the limitation, fuzzy modelling has been used in this study for the prediction of water quality of Indian rivers. 4) The fuzzy models have been developed using triangular and trapezoidal membership functions with centroid, bisector and mean of maxima (MOM) methods for defuzzification. 5) It is observed that the values of fuzzy based water quality index are more representative to actual river water quality status of Indian rivers as compared to NSFWQI and VWQI, since the adopted fuzzy logic approach is equally sensitive to all parameters and can truly represent the minor change in the value of any parameter, especially in case of river stretches having higher pollution. 6) FWQI-Triangular model using the Bisector defuzzification method outperforms other considered FWQI models of the study.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: