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  • 1. INTERNATIONAL JOURNAL and Technology (IJCIET), ISSN 0976 – 6308 International Journal of Civil Engineering OF CIVIL ENGINEERING AND (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 IJCIET© IAEME: www.iaeme.com/ijciet.aspJournal Impact Factor (2012): 3.1861 (Calculated by GISI) © IAEMEwww.jifactor.com EFFECTS OF STATISTICAL PROPERTIES OF DATASET IN PREDICTING PERFORMANCE OF VARIOUS ARTIFICIAL INTELLIGENCE TECHNIQUES FOR URBAN WATER CONSUMTION TIME SERIES H J Surendra1 and Paresh Chandra Deka2 1 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, ABSTRACT 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 426
  • 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME1. INTRODUCTION 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 onforecasting of water demand. Many important decision of various project are depends uponwater demand and its prediction. In recent years water demand have meaningfully increasedbecause 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 toforecast the future water consumption for proper planning and management of a watersystem. Water demand are highly variable and is affected by the factors such as size of thecity, characteristics of the population, nature and size of the commercial and industrialestablishment, climatic condition and cost of the supply [1]. There are different approaches towater demand forecasting including statistical or mathematical techniques. [2] used a roughset approach for water demand prediction to analyze a set of training data and generatedecision 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, projectionpursuit regression (PPR), multivariate adaptive regression splines (MARS), random forestand support vector regression (SVR) and they also used Monte Carlo simulation designed toestimate predictive performance of model obtained on data set and found that support vectorregression model is most accurate one followed by MARS, PPR. [5] Used system dynamicapproach for water demand forecasting based on sustainable utilization strategy of the waterresources. Although Conventional time series modeling methods have served the scientificcommunity for a long time and they provide reasonable accuracy, but suffer from theassumption of stationery and linearity [6]. Many new methodologies are developed formodeling 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) areprobably the most attractive techniques among the researchers, which is capable of handlingimprecise, fuzzy, noise and probabilistic information to solve complex problem in an efficientmanner. Artificial intelligence techniques, which emphasize gains in understanding systemsbehavior in exchange for unnecessary precision, have proved to be important practical toolfor many contemporary problems. Neural networks and fuzzy logic models are universallyapproximations of many multivariate functions because they can be used for modeling highlynonlinear, unknown or partially known complex system, plant or process. [7] Used fuzzylogic approach for monthly water consumption prediction of the Istanbul city, using TakagiSugeno 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 andalso further, auto regressive model is employed for the analysis and they found that ANFISmodel is better than autoregressive model. [8] Used ANFIS method to forecast monthly waterconsumption modeling and they have adopted cross correlation method for selection of theinput variables. [9] Used Mamdani inference system for modeling of drinking waterprediction 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 427
  • 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEinput variables. Even though many literatures are found using artificial intelligence techniques inurban water demand prediction, but anywhere information is not found regarding to develop a modelfor 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 encounteredin water demand modeling and forecasting. Long term prediction is concerned with large scaleplanning and management. Most of the long term development program in urban management isbased 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 greaterthan one month or less than the year. Short term prediction is concerned with low sale planning andmanagement 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, threeyears 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 forthe selection of best model and also further the analysis has been extended to develop multilinearregression model for comparison for daily, weekly and monthly data set. So the aim of this researchwork is to demonstrate the advantage of artificial intelligence technique such as fuzzy logic andANFIS method in modeling and prediction of daily, weekly and monthly time series data set of waterdemand.1.1 Study area New Mangalore Port (NMP) located at 12°52′N 74°53′E/ 12.87°N 74.88°E in the DakshinaKannada district of Karnataka, India. NMP has a total annual rainfall of approximately 3400 mm andreceives about 95% of its total annual rainfall within a period of about six months from May toOctober, 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 andaverage minimum humidity is 56% in January. Temperature during the day stays below 30 °C anddrop to about 19 °C at night. The current water supply system of the NMP includes several groundwater developments and also from the surface sources. City has most of the water from their groundsources in addition to municipal supply. Here apart from the residential, water is utilized for port operation and also for otheractivities. 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 datawere 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 monthlywater demand for a time series data is shown in the fig1(a),1(b),1(c) which reveals that variation isnon 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 428
  • 4. 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 consumption2. METHODOLOGY2.1 Fuzzy logic Fuzzy logic is capable of modeling vagueness, handling uncertainty, and supportinghuman type reasoning. They estimate a function without any mathematical model and learnfrom experience with sample data. Fuzzy logic starts with the concept of a fuzzy set. A fuzzyset is a set without a crisp; clearly defined boundary. Fuzzy set theory provides a systematiccalculus to deal with such information linguistically and it performs numerical computationsby using linguistic labels stipulated by membership functions. Moreover, a selection of fuzzyif then rules forms the key components of a fuzzy inference system that can be effectivelymodel human expertise in a specific application. Although the fuzzy inference system has astructured knowledge representation in the form of fuzzy if-then rules. A fuzzy inferencesystem (FIS) is an inference mechanism establishing a relationship between a series of inputand output sets. The inference system uses fuzzy sets theory, fuzzy logic principles whenestablishing such a relationship. Fuzzy inference system (FIS) is a rule based systemconsisting 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 usingdifferent fuzzy inference system such as Mamdan fuzzy inference system and Sugeno Fuzzyinference system in urban water demand prediction. The general structure of the Mamdanifuzzy inference system is shown in figure 2. Fig. 2 Structure of Mamdani fuzzy Inference System 429
  • 5. 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 membershipfunction and triangular membership function and also different rules criteria like three rulesand nine rules. From the results comparison it is found that three rules triangular membershipfunction is performed better, hence it is adopted for fuzzy modeling. It is also known that allwater resources data are ambiguity in nature, exact division of fuzzy set is not possible. Soassuming 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 tonew research into neuro-fuzzy system. In fuzzy logic there is no systematic procedure todefine the membership function parameters. The construction of fuzzy rule necessitates thedefinition of premises and consequences as fuzzy set. On the other hand ANN has the abilityto learn from input and output pairs and adapt to it in an interactive manner. ANFISeliminates the basic problem in fuzzy system design, defining the membership functionparameters and design of fuzzy if-then rules, by effectively using the learning capability ofANN 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 andfuzzy logic in a single frame work. For this reason in this study the ANFIS method is adoptedfor daily, weekly and monthly water consumption prediction. It has the advantage of allowingthe extraction of fuzzy rules from numerical data, for the first order Takagi-Sugeno fuzzyinference system. The general structure of ANFIS used in the analysis is shown in the figure3. For this analysis Sugeno fuzzy ANFIS model is employed along with centroiddefuzzification method. Here also numbers of ANFIS model are developed by changing inputscenarios for different time step and also different length of the data set. Fig. 3 Structure of Mamdani fuzzy Inference System3. MODEL DEVELOPMENT The whole data set has been divided for training and testing. For all the data set, it isobserved that the fluctuation of data is very high. One of the most important steps indeveloping a satisfactory prediction model is the selection of appropriate input variables, asthese 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 variablefor daily, weekly and monthly data set are presented in the table 1, table 2, table 3. From thetable 1, table 2 and table 3, we can say that, correlation is very high for current and tomorrowwater consumption, compare to one day, two days and three days water consumption. But for 430
  • 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEa monthly data set correlation for two days and three days water consumption with tomorrowwater consumption is poor. The statistical parameters of all data set for daily, weekly andmonthly is shown in the table 4 and also for different length of data set for daily series areshown in the table 5. From the statistical parameter we can identify the lowest, average andhighest value of water consumption in a day, week and month and also skewness, which isvery useful in modeling process. From the table 5 we can observe that, as the length of dataset changes the statistical parameters also changes, so the effect of data length is very muchinfluencing in the modeling process. Similarly the input and output combination used in themodel are shown in the table 6. From the table 6 it can be observed that three days previousand present day water consumption is used as input to forecast the future water consumptionfor one day lead period.The performances of all models are evaluated according to criteria such as, Mean Relativeerror (MRE) and Mean Square Error (MSE) .The structure of the models with different inputscenarios used in the analysis is shown below. Table 1 Correlation coefficient Ratios of Daily data set CC 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 CC 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 CC 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 1.00 431
  • 7. 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 X 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 differencebetween values implied by an estimator and the true values of the quantity being estimated. Itis the residual or error sum of squares divided by the number of degree of freedom of thesum. This gives an estimate of the error or residual variance. The mean square error is givenby, ∑ሺଡ଼ିଢ଼ሻమ MSE ൌ ୬ 432
  • 8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEMean Relative Error (MRE):The relative error is the absolute error divided by the magnitude of the exact value. Thepercent error is the relative error expressed in terms of per 100. 1 N X −YMRE = ∑ × 100 N i =1 XX= Observed values, Y=Predicted values, X’=Mean of X, Y’=Mean of Y4. RESULTS AND DISCUSSIONS Based on the given methodology, various models were developed for forecastingwater consumption on daily, weekly and monthly time step unit of datasets. Within aparticular AI models, input combinations were kept changing to optimize the best model. Theresults 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 offorecasting performance. In general, ANFIS model performed better than FL and MLRconsidering the various performance indices used in the study. Although sometimescontradictory results yield confusion over the ranking of a particular model, selection of bestmodel 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 ofdataset to obtain the influence of more number of data points .As observed from the table7,for all data points (more than four years),The testing performances of ANFIS and MLR arealmost similar considering CC and MSE indices. However, ANFIS was better than MLR interms of MRE.FL models performed poorly in all the input combinations as well as in all themodel performance indices. The ANFIS model performances are further improved as numberof inputs increases.Similar performance trend were observed for shortened data length of three years aspresented in table 7.Here, MLR and ANFIS offers similar performance in terms of MSEwhich were better than FL. The predicting performance was also improved for more numberof inputs such as model M3 and M4.The mean relative error (MRE) was lowest for ANFISmodel.A little contradictory revelation were obtained for various models using one year dataset aspresented 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 asaverage, minimum, maximum, skewness, standard deviation and distribution behavior wereclearly depicted on the forecasting performance of various AI models. FL models suffers dueto improper system modeling as only two fuzzy sets and triangular MF were used appliedwith Mamdani fuzzy inference system. Further, widening the options with more fuzzy setsalong with appropriate membership functions might improve the performance. ANFIS wasbetter in all the length of dataset due to the combined strength of both ANN and FL as ANNcan better handle non-linearity along with Takaki-Sugeno Fuzzy inference method .In all thecases, MLR performance was satisfactory because of degree of non-linearity in the datasetswere low. 433
  • 9. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME4.2 Weekly and Monthly dataset For medium and long term planning, one week ahead and one month aheadforecasting were also modeled by using weekly and monthly data set. Here surprisingly,MLR performed almost similarly and even slightly better than ANFIS for different inputcombinations as referred to MSE. FL performed poorly compared to other two models.Consistent forecasting performances were observed for all the MLR models which wasbased on different input combinations. On the other hand, ANFIS was better for one monthahead 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 theFL,ANFIS and MLR models as obtained from the table 4.Errors were not too muchsignificant 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 FLwhich uses Mamdani method performed better for two and three weeks lead time whereasANFIS which uses Sugeno method was found better in one week lead time forecastconsidering both MSE and MRE error criteria. Also, it was observed from the table 7 thatincrease 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 withthe fuzzy logic and multiple linear regressions. The comparisons of different models arerepresented in the table 7. From the results table, it is found that ANFIS method shows betterperformance compare to fuzzy logic and multiple linear regressions considering variousperformance indices such as MRE and MSE. Comparison among all models shows that waterdemand of three days lag and current day produces better performance than other inputsparameters 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(%) Data 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 0.58 434
  • 10. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEInitially in order to check how the length of the data set affecting the performance of themodel, 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 thefuzzy logic technique is used to forecast the future water consumption for daily data set. Heretriangular membership function and three rules criteria are used for different data length.5. CONCLUSIONS In this study, applicability of the artificial intelligence techniques such as fuzzy logicand ANFIS method are adopted for water consumption modeling and prediction. Further, themodel results were also compared with MLR method for various input scenarios. Comparingthe performances of all models in fuzzy logic, M4 model which used three lagged dataperformed reasonably well. In multiple linear regression based on performance criteria ofMRE M4 model is selected as the best one. In ANFIS method based on MRE performancecriteria, M4 model is selected as best one. Totally among artificial intelligence techniquesANFIS method with three days previous water consumption and current day waterconsumption (M4) model performing better. The results of M4 ANFIS model shows that itcan be successfully applied to establish a daily water consumption prediction. Since lessnumber of data point on weekly and monthly data, model performed was poor compare todaily data set, and also we can observed that model performance was better for all year’s dataset. Finally we can conclude that hybrid model performed better than single model andcompare to multiple linear regression in reliable forecast.6. ACKMOWLEDGEMENT The authors are grateful to Director, Executive Engineer (civil) and AssistantEngineers (civil) of New Mangalore Port Trust, for their valuable support and access to datafor the research work.7. REFERENCES[1] Zhou, S.L., McMahon, T.A., Walton, A., Lewis, J., 2002. Forecasting operationaldemand for an urban water supply zone. Journal of hydrology 259(2002):189-202.[2] Aijun, AN., Shan, N., Chan, C., Cercone, N., Ziarko, W. Discovering rules for waterdemand prediction: AN enhanced Rough-set approach.PII:SO952-1976(96):00059-0.[3] Durga Rao, K.H.V., 2005.Multicriteria spatial decision analysis for forecasting urbanwater requirement: A case study of Dehradun city, India. Landscape and Urban planning(2005) 71:163-174.[4] Herrera, M., Torgo, L., Izquierdo, J., Garcia, R., 2010. Predictive models for forecastinghourly urban water demand. Journal of hydrology 387 (2010): 141-150.[5] Hongwei, Z ., Xuehua , Z., Bao, Z., 2009. System Dynamic Approach to Urban WaterDemand Forecasting. : A Case Study of Tianjin. Tianjin University and Springer-Verlag 15(2009):070-074.[6] Kermani, Z., Teshnehlab, M., 2008. Using adaptive Neuro fuzzy inference system forhydrological time series prediction. Applied soft computing 8 (2008):928-936. 435
  • 11. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME[7] Altunkaynak, A., Ozger, M., Cakmakci, M., 2005. Water consumption prediction ofIstanbul city by using Fuzzy logic approach. Water resources management (2005) 19:641-654.[8] Yurdusev, A., Firat, M., 2009. Adaptive neuro fuzzy inference system approach formunicipal water consumption modeling. Journal of hydrology 265(2009): 225-234.[9] Sen, Z., Altunkaynak, A., 2009. Fuzzy system modeling of drinking water consumptionprediction. Expert systems with applications 36 (2009); 11745-11752.[10] Babel, M., Shinde, R., 2011.Identifying prominent explanatory variables for waterdemand prediction using artificial neural network: A case of Bangkok. Water resourcemanagement (2011) 25:1653-1676.[11] Jain, A., Varshney, K., Joshi, U., 2001. Short Term Water Demand ForecastingModeling at IIT Kanpur Using Artificial Neural Networks. Water Resources Management 15(2001): 299-321.[12] Firat, M., Yurdusev, M., Turan, M., 2009. Evaluation of Artificial Neural NetworkTechniques for Municipal Water Consumption Modeling. Water Resour Manage (2009)23:617-632.[13] Firat, M., Tarun, M., Yurdusev, M., 2010. Comparative analysis of Neural networktechnique for predicting water consumption time series. Journal of hydrology 384(2010): 46-51.[14] Nasseri, M., Moeini, A., Tabesh, M., 2011. Forecasting monthly urban water demandusing extended Kalman filter and Genetic programming. Expert system withapplications38(2011):738 436