International Journal of Civil Engineering OF CIVIL ENGINEERING AND
  INTERNATIONAL JOURNAL and Technology (IJCIET), ISSN 0976 – 6308
  (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME
                            TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 3, Issue 2, July- December (2012), pp. 426-436
© IAEME: www.iaeme.com/ijciet.asp
Journal Impact Factor (2012): 3.1861 (Calculated by GISI)                 © IAEME

                         TIME SERIES

                            H J Surendra1 and Paresh Chandra Deka2
       Research Scholar, 2Associate Professor, Department of Applied Mechanics and Hydraulics,
           National Institute of Technology Karnataka, Surathkal, Mangalore- 575025, India
                      E-mail: paresh_deka@sify.com, careof.indra@gmail.com,


           Water Consumption forecasting is very essential for any development program in an
   urban area and also for proper planning and management of water resources. Both variability
   and uncertainty in determining water consumption includes several concepts which depends
   on issues related to vague and incomplete information. In this context, Artificial intelligence
   (AI) techniques such as fuzzy logic and Adaptive Neuro Fuzzy Inference system (ANFIS)
   method which integrates ANN and Fuzzy logic methods shown the potential benefits in a
   single framework. In this study,ANFIS methodology is proposed to self organize model
   structure and to adapt parameters of fuzzy system for short term, medium and long term
   water consumption prediction. In addition to this, the model results of various AI methods
   were also compared with the single Fuzzy Logic model and statistical method of multiple
   linear regression (MLR) .The time series water consumption data from a mixed medium
   growth urban area under Mangalore city corporation, Karnataka, India were used in the
   analysis. The performances of the model is evaluated using criteria such as Mean square error
   (MSE) and Mean relative error (MRE).From the results,it was found that ANFIS model
   which used Takaki-Sugeno inference system performed better than Fuzzy logic model based
   on Mamdani inference system. In majority of cases,MLR model performed better than fuzzy
   logic model but distinct down compared to ANFIS model. The results shown that ANFIS
   method can be successfully employed to estimate the daily, weekly and monthly water
   consumption with better accuracy.

   Keywords: Data Length, Time series, ANFIS, MLR, Fuzzy logic

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME


         Water is known as the most important resource in any urban development program.
Most of the decision in urban planning and sustainable development are highly dependent on
forecasting of water demand. Many important decision of various project are depends upon
water demand and its prediction. In recent years water demand have meaningfully increased
because of various factors such as local population growth, migration from the localities,
industrial growth and expansion, general rise in the living standard. So it is necessary to
forecast the future water consumption for proper planning and management of a water
         Water demand are highly variable and is affected by the factors such as size of the
city, characteristics of the population, nature and size of the commercial and industrial
establishment, climatic condition and cost of the supply [1]. There are different approaches to
water demand forecasting including statistical or mathematical techniques. [2] used a rough
set approach for water demand prediction to analyze a set of training data and generate
decision rules and it was found to be useful for incomplete and deterministic information. [3]
Used Multicriteria spatial decision explanatory variables for water demand forecasting. [4]
developed predictive models for forecasting hourly water demand using ANN, projection
pursuit regression (PPR), multivariate adaptive regression splines (MARS), random forest
and support vector regression (SVR) and they also used Monte Carlo simulation designed to
estimate predictive performance of model obtained on data set and found that support vector
regression model is most accurate one followed by MARS, PPR. [5] Used system dynamic
approach for water demand forecasting based on sustainable utilization strategy of the water
         Although Conventional time series modeling methods have served the scientific
community for a long time and they provide reasonable accuracy, but suffer from the
assumption of stationery and linearity [6]. Many new methodologies are developed for
modeling the data but current trend seems to be model the data rather than physical process.
For modeling the data, artificial intelligence techniques (AI) such as fuzzy logic (FL),
artificial neural network (ANN) and adaptive neuro fuzzy inference system(ANFIS) are
probably the most attractive techniques among the researchers, which is capable of handling
imprecise, fuzzy, noise and probabilistic information to solve complex problem in an efficient
manner. Artificial intelligence techniques, which emphasize gains in understanding systems
behavior in exchange for unnecessary precision, have proved to be important practical tool
for many contemporary problems. Neural networks and fuzzy logic models are universally
approximations of many multivariate functions because they can be used for modeling highly
nonlinear, unknown or partially known complex system, plant or process. [7] Used fuzzy
logic approach for monthly water consumption prediction of the Istanbul city, using Takagi
Sugeno method for time series data by considering only one lag as input for the analysis. [6]
used normalized data for monthly water consumption prediction using ANFIS method and
also further, auto regressive model is employed for the analysis and they found that ANFIS
model is better than autoregressive model. [8] Used ANFIS method to forecast monthly water
consumption modeling and they have adopted cross correlation method for selection of the
input variables. [9] Used Mamdani inference system for modeling of drinking water
prediction using different fuzzy sets and rules in the analysis.
         Also, there were many reports of using ANN in forecasting water demand
([10],[11],[12],[13]). Most of the literatures were related to ANN and ANFIS using various

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

input variables. Even though many literatures are found using artificial intelligence techniques in
urban water demand prediction, but anywhere information is not found regarding to develop a model
for limited data set and for different time steps such as daily, weekly and monthly in a single work.
Three types of temporal resolution such as short term, middle term and long term may be encountered
in water demand modeling and forecasting. Long term prediction is concerned with large scale
planning and management. Most of the long term development program in urban management is
based on their type of prediction and this prediction resolution is equal or greater than one year.
Middle term prediction is applied in middle time management and its resolution is equal or greater
than one month or less than the year. Short term prediction is concerned with low sale planning and
management and the resolution of this type of approach varies from one hour to some days [14].
         So in this study using AI techniques, effect of length of data set such as four years, three
years and one year on the performance of models has been investigated. Also using time series data,
various fuzzy logic and ANFIS models has been developed and their performances were evaluated for
the selection of best model and also further the analysis has been extended to develop multilinear
regression model for comparison for daily, weekly and monthly data set. So the aim of this research
work is to demonstrate the advantage of artificial intelligence technique such as fuzzy logic and
ANFIS method in modeling and prediction of daily, weekly and monthly time series data set of water

1.1 Study area
         New Mangalore Port (NMP) located at 12°52′N 74°53′E/ 12.87°N 74.88°E in the Dakshina
Kannada district of Karnataka, India. NMP has a total annual rainfall of approximately 3400 mm and
receives about 95% of its total annual rainfall within a period of about six months from May to
October, while remaining extremely dry from December to March. Humidity is approximately 75%
on average and peaks during May, June and July. The maximum average humidity is 93% in July and
average minimum humidity is 56% in January. Temperature during the day stays below 30 °C and
drop to about 19 °C at night. The current water supply system of the NMP includes several ground
water developments and also from the surface sources. City has most of the water from their ground
sources in addition to municipal supply.
         Here apart from the residential, water is utilized for port operation and also for other
activities. Offen there is irregularity in supply from the municipal; the other works may get affected,
so it is necessary for managing the ground water resources. The time series water consumption data
were collected on daily basis from the year 2006 December to 2011 august. Out of 1723 data point,
1123 is used for training and 600 are used for testing. The variation of daily, weekly and monthly
water demand for a time series data is shown in the fig1(a),1(b),1(c) which reveals that variation is
non linear, non-stationary, time varying, where statistical method is assumed to be not suitable.

   Fig 1(a) - Daily water consumption                         Fig 1(b)- weekly water consumption

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

                           Fig 1(c) - Monthly water consumption

2.1 Fuzzy logic
         Fuzzy logic is capable of modeling vagueness, handling uncertainty, and supporting
human type reasoning. They estimate a function without any mathematical model and learn
from experience with sample data. Fuzzy logic starts with the concept of a fuzzy set. A fuzzy
set is a set without a crisp; clearly defined boundary. Fuzzy set theory provides a systematic
calculus to deal with such information linguistically and it performs numerical computations
by using linguistic labels stipulated by membership functions. Moreover, a selection of fuzzy
if then rules forms the key components of a fuzzy inference system that can be effectively
model human expertise in a specific application. Although the fuzzy inference system has a
structured knowledge representation in the form of fuzzy if-then rules. A fuzzy inference
system (FIS) is an inference mechanism establishing a relationship between a series of input
and output sets. The inference system uses fuzzy sets theory, fuzzy logic principles when
establishing such a relationship. Fuzzy inference system (FIS) is a rule based system
consisting of three conceptual components. These are: (1) a rule base containing fuzzy if–
then rules, (2) defining the membership functions (MF) and (3) an inference system,
combining the fuzzy rules and producing the system results. Reports were found using
different fuzzy inference system such as Mamdan fuzzy inference system and Sugeno Fuzzy
inference system in urban water demand prediction. The general structure of the Mamdani
fuzzy inference system is shown in figure 2.

                   Fig. 2 Structure of Mamdani fuzzy Inference System

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

 In fuzzy logic method, different models are developed using trapezoidal membership
function and triangular membership function and also different rules criteria like three rules
and nine rules. From the results comparison it is found that three rules triangular membership
function is performed better, hence it is adopted for fuzzy modeling. It is also known that all
water resources data are ambiguity in nature, exact division of fuzzy set is not possible. So
assuming fifty percent as overlapping different fuzzy set are employed in the analysis.

2.2 Adaptive Neuro Fuzzy Inference System (ANFIS).
        In recent years, the integration of neural network and fuzzy logic has given birth to
new research into neuro-fuzzy system. In fuzzy logic there is no systematic procedure to
define the membership function parameters. The construction of fuzzy rule necessitates the
definition of premises and consequences as fuzzy set. On the other hand ANN has the ability
to learn from input and output pairs and adapt to it in an interactive manner. ANFIS
eliminates the basic problem in fuzzy system design, defining the membership function
parameters and design of fuzzy if-then rules, by effectively using the learning capability of
ANN for automatic fuzzy rule generation and parameter optimization (yurdusev & Firat,
2009). Neuro fuzzy system has a potential to capture the benefits of both neural network and
fuzzy logic in a single frame work. For this reason in this study the ANFIS method is adopted
for daily, weekly and monthly water consumption prediction. It has the advantage of allowing
the extraction of fuzzy rules from numerical data, for the first order Takagi-Sugeno fuzzy
inference system. The general structure of ANFIS used in the analysis is shown in the figure
3. For this analysis Sugeno fuzzy ANFIS model is employed along with centroid
defuzzification method. Here also numbers of ANFIS model are developed by changing input
scenarios for different time step and also different length of the data set.

                     Fig. 3 Structure of Mamdani fuzzy Inference System


        The whole data set has been divided for training and testing. For all the data set, it is
observed that the fluctuation of data is very high. One of the most important steps in
developing a satisfactory prediction model is the selection of appropriate input variables, as
these variables determine the structure of the model and affect the results of the model.
Conventionally, the choice of appropriate input variables can be made using the cross-
correlations between the variables. The correlation coefficient of all input and output variable
for daily, weekly and monthly data set are presented in the table 1, table 2, table 3. From the
table 1, table 2 and table 3, we can say that, correlation is very high for current and tomorrow
water consumption, compare to one day, two days and three days water consumption. But for

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

a monthly data set correlation for two days and three days water consumption with tomorrow
water consumption is poor. The statistical parameters of all data set for daily, weekly and
monthly is shown in the table 4 and also for different length of data set for daily series are
shown in the table 5. From the statistical parameter we can identify the lowest, average and
highest value of water consumption in a day, week and month and also skewness, which is
very useful in modeling process. From the table 5 we can observe that, as the length of data
set changes the statistical parameters also changes, so the effect of data length is very much
influencing in the modeling process. Similarly the input and output combination used in the
model are shown in the table 6. From the table 6 it can be observed that three days previous
and present day water consumption is used as input to forecast the future water consumption
for one day lead period.
The performances of all models are evaluated according to criteria such as, Mean Relative
error (MRE) and Mean Square Error (MSE) .The structure of the models with different input
scenarios used in the analysis is shown below.

                    Table 1 Correlation coefficient Ratios of Daily data set
      Ratio            Wt-3          Wt-2           Wt-1            Wt           Wt+1
      Wt-3             1.00          0.85           0.80            0.74         0.70
      Wt-2             0.85          1.00           0.85            0.80         0.74
      Wt-1             0.80          0.85           1.00            0.85         0.80
       Wt              0.74          0.80           0.85            1.00         0.85
      Wt+1             0.70          0.74           0.80            0.85         1.00

                  Table 2 Correlation coefficient Ratios of Weekly data set
      Ratio            Wt-3          Wt-2           Wt-1            Wt           Wt+1
      Wt-3             1.00          0.85           0.80            0.74         0.70
      Wt-2             0.85          1.00           0.85            0.80         0.74
      Wt-1             0.80          0.85           1.00            0.85         0.80
       Wt              0.74          0.80           0.85            1.00         0.85
      Wt+1             0.70          0.74           0.80            0.85         1.00

                  Table 3 Correlation coefficient Ratios of Monthly data set
   Ratio      Wt-3            Wt-2          Wt-1             Wt                Wt+1
   Wt-3       1.00            0.70           0.37           0.13               0.09
   Wt-2       0.70            1.00           0.70           0.39               0.15
   Wt-1       0.37            0.70           1.00           0.75               0.43
    Wt        0.13            0.39           0.75           1.00               0.75
   Wt+1        09             0.15           0.43           0.75               1.00

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

                              Table 4 Statistical parameters of data set
      Models  Type           X max     X min      mean       Std.Dev    C.V      Skewness
             Training         4.79      1.29       3.29        0.54     0.17       -0.15
      Daily  Testing          5.53       2.7       3.66        0.46     0.13       0.81
             Overall          5.53      1.29        3.5        0.55     0.16       -0.03
             Training         30.99    13.66       23.15        3.4     0.15        -0.2
     Weekly Testing           32.45    14.28       25.29        2.8     0.11       -0.35
             Overall          32.45    13.66       24.21       3.42     0.14       -0.33
             Training        126.16    72.53       98.71      14.17     0.14       -0.04
     Monthly Testing         132.12    95.51      111.77       8.26     0.07       0.47
             Overall         132.12    72.53      105.57      13.55     0.13       -0.38

                Table 5 Statistical parameters of different length of daily data set
        Data                                           X
       length    Type    X max           X min       mean    Std.Dev     C.V      Skewness
                Training 5.21             1.29        3.53    0.508     0.144      -0.585
                Testing   5.53            2.72        3.71    0.536     0.144       0.517
    Three years Overall   5.53            1.29        3.58    0.529     0.148      -0.211
                Training 5.21             2.79       3.725     0.46     0.123       0.651
                Testing   5.53            2.72        3.59    0.617     0.172       1.106
     One year   Overall   5.53            2.72        3.7     0.508     0.137       0.773

                             Table 6 Model Development
   Model        Inputs                        Output
   M1           WD(t)                         WD(t+1)
   M2           WD(t)WD(t-1)                  WD(t+1)
   M3           WD(t)WD(t-1)WD(t-2)           WD(t+1)
   M4           WD(t)WD(t-1)WD(t-2)WD(t-3)    WD(t+1)

Where WD (t): current day water consumption, WD (t-1): one day lag water consumption,
     WD (t-2): two day lag water consumption, WD (t-3): three day water consumption,
      WD (t+1): tomorrow water consumption.

Mean Square Error (MSE):
The mean squared error of an estimator is one of many ways to quantify the difference
between values implied by an estimator and the true values of the quantity being estimated. It
is the residual or error sum of squares divided by the number of degree of freedom of the
sum. This gives an estimate of the error or residual variance. The mean square error is given

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

Mean Relative Error (MRE):

The relative error is the absolute error divided by the magnitude of the exact value. The
percent error is the relative error expressed in terms of per 100.
          1 N X −Y
MRE = ∑                  × 100
         N i =1 X
X= Observed values, Y=Predicted values, X’=Mean of X, Y’=Mean of Y


        Based on the given methodology, various models were developed for forecasting
water consumption on daily, weekly and monthly time step unit of datasets. Within a
particular AI models, input combinations were kept changing to optimize the best model. The
results of all the analysis has been presented in the following sections.

4.1 Daily data set
        All the model results were presented in the table 7 to make logical comparison of
forecasting performance. In general, ANFIS model performed better than FL and MLR
considering the various performance indices used in the study. Although sometimes
contradictory results yield confusion over the ranking of a particular model, selection of best
model was finally linked up to MSE which is reflecting predictive power of model.
The predicting performances of various models are also examined for different length of
dataset to obtain the influence of more number of data points .As observed from the table
7,for all data points (more than four years),The testing performances of ANFIS and MLR are
almost similar considering CC and MSE indices. However, ANFIS was better than MLR in
terms of MRE.FL models performed poorly in all the input combinations as well as in all the
model performance indices. The ANFIS model performances are further improved as number
of inputs increases.
Similar performance trend were observed for shortened data length of three years as
presented in table 7.Here, MLR and ANFIS offers similar performance in terms of MSE
which were better than FL. The predicting performance was also improved for more number
of inputs such as model M3 and M4.The mean relative error (MRE) was lowest for ANFIS
A little contradictory revelation were obtained for various models using one year dataset as
presented in table 7.ANFIS was better than other models with lowest number of inputs
(model M1).Predicting capability further deteriorates as number of inputs increases.
The influence of length of dataset which carries different statistical properties such as
average, minimum, maximum, skewness, standard deviation and distribution behavior were
clearly depicted on the forecasting performance of various AI models. FL models suffers due
to improper system modeling as only two fuzzy sets and triangular MF were used applied
with Mamdani fuzzy inference system. Further, widening the options with more fuzzy sets
along with appropriate membership functions might improve the performance. ANFIS was
better in all the length of dataset due to the combined strength of both ANN and FL as ANN
can better handle non-linearity along with Takaki-Sugeno Fuzzy inference method .In all the
cases, MLR performance was satisfactory because of degree of non-linearity in the datasets
were low.

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

4.2 Weekly and Monthly dataset
        For medium and long term planning, one week ahead and one month ahead
forecasting were also modeled by using weekly and monthly data set. Here surprisingly,
MLR performed almost similarly and even slightly better than ANFIS for different input
combinations as referred to MSE. FL performed poorly compared to other two models
.Consistent forecasting performances were observed for all the MLR models which was
based on different input combinations. On the other hand, ANFIS was better for one month
ahead forecast than others. Also, on the contrary, FL ahead above others is considering MRE.
The statistical behavior of Weekly and monthly dataset were seems to be suitable for all the
FL,ANFIS and MLR models as obtained from the table 4.Errors were not too much
significant for various models.

4.3 Different lead-time
       Further, to investigate the predicting capability of FL as well as ANFIS model,
analyses were performed for multiple lead times forecasting using weekly dataset. The FL
which uses Mamdani method performed better for two and three weeks lead time whereas
ANFIS which uses Sugeno method was found better in one week lead time forecast
considering both MSE and MRE error criteria. Also, it was observed from the table 7 that
increase in inputs provide inferior performance as appeared from various models (M1, M2,
M3 and M4).
The results of testing part for the four different models of ANFIS methods are compared with
the fuzzy logic and multiple linear regressions. The comparisons of different models are
represented in the table 7. From the results table, it is found that ANFIS method shows better
performance compare to fuzzy logic and multiple linear regressions considering various
performance indices such as MRE and MSE. Comparison among all models shows that water
demand of three days lag and current day produces better performance than other inputs
parameters in forecasting future demand for time series data.

         Table 7 Testing results of FL, MLR and ANFIS for different data length
                                      MSE (MLD)2                        MRE(%)
     Models       length      FL        MLR         ANFIS       FL     MLR       ANFIS
                 all years    0.16      0.06         0.06       6.78   0.43       0.38
       M1       three years   0.18      0.09         0.09       5.82   0.28       0.74
                 one years    0.29      0.15         0.09       5.32    0.9       0.14
                 all years    0.19      0.06         0.06       7.09   0.42       0.19
       M2       three years   0.22      0.09         0.09       5.99   0.31       0.35
                 one years     0.4      0.15         0.17       5.17    0.9       0.17
                 all years    0.22      0.06         0.06       7.16   0.42       0.16
       M3       three years   0.26      0.08         0.09       6.07    0.3       0.26
                 one years    0.46      0.15         0.16       5.03    0.9       0.27
                 all years    0.23      0.06         0.06       7.13   0.42        0.1
       M4       three years   0.27      0.08         0.08       5.97   0.28       0.18
                 one years     0.5      0.15         0.15       4.6    0.88       0.58

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

Initially in order to check how the length of the data set affecting the performance of the
model, three different length of the data set are used. First length containing all years data,
second length containing three years and third one containing one year data set. First the
fuzzy logic technique is used to forecast the future water consumption for daily data set. Here
triangular membership function and three rules criteria are used for different data length.


         In this study, applicability of the artificial intelligence techniques such as fuzzy logic
and ANFIS method are adopted for water consumption modeling and prediction. Further, the
model results were also compared with MLR method for various input scenarios. Comparing
the performances of all models in fuzzy logic, M4 model which used three lagged data
performed reasonably well. In multiple linear regression based on performance criteria of
MRE M4 model is selected as the best one. In ANFIS method based on MRE performance
criteria, M4 model is selected as best one. Totally among artificial intelligence techniques
ANFIS method with three days previous water consumption and current day water
consumption (M4) model performing better. The results of M4 ANFIS model shows that it
can be successfully applied to establish a daily water consumption prediction. Since less
number of data point on weekly and monthly data, model performed was poor compare to
daily data set, and also we can observed that model performance was better for all year’s data
set. Finally we can conclude that hybrid model performed better than single model and
compare to multiple linear regression in reliable forecast.


        The authors are grateful to Director, Executive Engineer (civil) and Assistant
Engineers (civil) of New Mangalore Port Trust, for their valuable support and access to data
for the research work.


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