A Water Demand Forecasting Model using BPNN. for Residential Building

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1 Contemporary Engineering Sciences, Vol. 9, 2016, no. 1, 1-10 HIKARI Ltd, A Water Demand Forecasting Model using BPNN for Residential Building Dongjun Suh Korea Institute of Science and Technology Information (KISTI), Daejeon, Korea Sungil Ham * School of Mechatronics, Gwangju Institute of Science and Technology (GIST) Gwangju, Korea * Corresponding author Copyright 2015 Dongjun Suh and Sungil Ham. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This paper presents a residential water demand forecasting model using a back propagation neural network (BPNN) in the context of residential buildings in Korea. The water demand of a building demonstrates a highly complex and non-linear phenomenon reflecting such features as geographic and climatic and special types of buildings. We describe the impact of several potential determinant factors affecting water use in residential buildings in four different provinces in Korea. Empirical data sets consisting of water consumption retrieved from multiple residential buildings in Korea were evaluated to verify the performance evaluation. Our results show that the proposed model can successfully predict estimated outputs through the BPNN. The model we propose can used in decision making for the residential water management policy in Korea through the optimal estimation of residential water consumption. Keywords: Water Demand Forecasting Model, Residential Water Use, BPNN, Machine Learning, Residential Building 1 Introduction Water demand forecasting influences various factors, including geographic,

2 2 Dongjun Suh and Sungil Ham climatic, population, socio economic and environmental factors. In particular, potential factors affecting water consumption related to size, shape and complexity of the buildings or the type of water supply infrastructures must not be underestimated. Water demand forecast modeling is crucial for designing water planning systems and managing water resources at the city or national level. It is also necessary for making reliable demand forecasting in management and creating the most benefit in terms of water conservation. Water conservation is efficient and economical as well as significant in protecting the environment. In Korea, reducing water use by 10% saved 2,883 thousand tons of water in the year (2011), and it saves 30 billion Won a year of total water production (report from the Ministry of the Environment). Approximately 25% of the total water use in Korea is from domestic and residential water consumption, which indicates that at least one fourth of the total water use comes from building sites. Residential water consumption occupies roughly 66.4% of the total water supply, which means that the building sector can have the most influence on improving water use efficiency [1]. Accurate forecasting of future demand for water by appropriate methodology is necessary for the operation and management of the municipal water supply to provide better planning of national or regional water policies. This study analyzes the unique features of the residential buildings regarding water consumption, and we propose a water demand forecasting model that estimates the amount of water use considering various residential building types in Korea. This paper is an extension of work published in [2]. 2 Research Background Water demand prediction modeling is a big issue in water management and policy in the residential sector in terms of environmental economics and preservation of our water resources. Research groups have studied residential water prediction modeling, which analyzes the main features affecting residential water consumption regarding the impact of price, income, population, inter-annual climate variability, housing types and household composition of residential consumption [2-4]. Most studies have used top-down or bottom-up approaches. Top-down approaches use macroscopic exploration at a regional or national level over a long-term scale such as annual estimations. Romano [5] analyzed relevant studies on water demand in European countries and derived the determinants which influence water consumption. He introduced a residential water demand model for Italian provinces in the period , which relied on econometric components, such as tariffs and income, as well as many other factors, including population characteristics and density, the presence of immigrants or tourists and household features.

3 A water demand forecasting model using BPNN 3 Howe [6] econometrically explored the impact of the influence and effectiveness of water pricing in the United States and Canada according to the type of water service. Schleich [7] studied the influence of economic (prices and income), environmental and social determinants (household size, the effects of population age, the share of wells, housing patterns, meteorological information) for the per capita demand for water in about 600 water supply areas in Germany from the perspective of econometric analysis. On the other hand, bottom-up methods deal with a microscopic scale, inferring regional and national levels from the estimated water demand of a representative set of individual houses over a relatively short-term scale, such as daily or monthly estimations. This study mainly focused on a bottom-up approach on a residential building scale with monthly estimations, evaluating the impact of the water use of residential buildings in relation to national water use levels. Zhang [8] presented a residential water demand model for urban household units through both empirical investigations from surveys and analytical studies of Beijing and Tianjin in China. Höglund [9] examined household water use and the effects of a water tax in Sweden. Jorgensen [10] investigated individual level variables that affect household water use taking into account dwelling types, location, and income in addition to individual motivations and behaviors associated with household water consumption in South Australia. Blokker [11] developed a water demand end-use model in the Netherlands based on statistical information of users and water outlets with respect to behavior patterns with a small time scale and small spatial scale. Forecasting water demands in buildings mainly consider annual water usage characteristics from simple simulations using simple regression techniques [12-13] to very complicated models. Recently new predictive modeling using nonlinear estimation methods, including Artificial Neural Network (ANN) based models, have also been used in various forecasting areas, such as prediction outcomes for carbon emission [14, 15], stock market [16], and energy consumption [1, 17, 18]. We investigated the relationship of morphological and climatological variables with monthly water demand through a case study. We initially analyzed potential elements affecting water demand in apartment buildings and climate elements in relation to the empirical water consumption and then devised a Back Propagation Neural Network (BPNN) model, with any response of a nonlinear pattern through the training and learning system, and explored the features. 3 Back-Propagation Neural Network (BPNN) Artificial neural networks can be classified into several categories based on supervised and unsupervised learning methods and feed-forward and feedback recall architectures.

4 4 Dongjun Suh and Sungil Ham This study adopts the Back Propagation Neural Network (BPNN), one of the most novel supervised learning and multilayer perceptrons, where a hidden layer exists, feed-forward neural network architecture proposed by [19]. Back Propagation is the most employed in classification and regression to resolve complex non-linear issues [20-21] and has been utilized in training neural network models in conjunction with an optimization method such as gradient descent [22]. In the BPNN, the learning process was derived from the presentation of the entire training set during the network. The neural network produces results, and this output can be compared with the expected results. When an error is detected, the weighting values related to neurons of the entire network are regulated to reduce the errors. The error is then propagated back to the neural network, which causes the system to regulate the weight for the target system through minimizing criterion equivalents to the differences between the actual outputs and the desired outputs. Through the training of the entire neural network the same set of data is repeated until some criterion is met, with the connection weights being continually refined [23]. The architecture the BPNN is described in Figure 1. Figure 1. The architecture of a BPNN 4 Water Demand Prediction Method Through an extensive review of the models discussed so far, we examined the previous studies to determine the relevant factors affecting water consumption levels before we designed an appropriate neural network model.

5 A water demand forecasting model using BPNN 5 We analyzed the various factors related to residential buildings and their environment as input datasets for the BPNN. Then, we devised a BPNN model capable of modeling extremely complex nonlinear patterns through a training and learning system with the carefully investigated features. We verified the diverse elements constituting apartment buildings as input datasets for the BPNN, which is the most relevant supervised learning neural network based model according to the empirical water use data. Then, we used the BPNN model to analyze the complex nonlinear patterns accurately through a training and learning system encompassing carefully investigated factors. We analyzed the empirical data to show how those factors affect the water usage of apartment complexes and weather information that affected the changing water consumption patterns. Data obtained from other sources to estimate water demand included climate variables, geometric variables, and the types of residential buildings. Monthly averaged water consumption data for 2012 and 2014 were used in this case study. In addition, we selected residential complexes located in four different provinces, Choongnam, Gangwon, Gyeongnam, and Gyeonggi provinces in Korea. In accordance with water use, we explored the significant differences with 95% confidence interval for the calculated mean data. Table 1 describes the information on the selected residential buildings. Table 1 Information of Selected Residential Buildings (Residential Complex) Selected Province Subject No. of Complex es No. of Apartment Complexes Total num. of buildings Heating Type Selected Residential Buildings (residential complex) Choongnam, 3 Gangwon 2 Gyeongnam 5 Gyeonggi Individual Heating Study Period: yearly data, Jan Dec. 2012, Jan Dec. 2014

6 Normalized Water Use 6 Dongjun Suh and Sungil Ham 0,8 Comparison between actual values and forecasted result 0,7 0,6 0,5 0,4 0,3 0,2 0, No. of Cases Actual Value Forecasted Result Figure 2 Comparison between actual values and forecasted results in test cases in Korea (Jan Dec.2012 and Jan Dec.2014) The variables used in this study are classified into three broad categories: climate variables, geometric variables, and the factors of the buildings, details of which are discussed later. The geometric factors include the latitude and longitude of each region. The climate factors include months of the year, average monthly dry bulb temperature and the relative humidity. The morphological factors (for buildings) include volume size and number of buildings. These factors generated a total of 20 selected input parameters as described in (1). I BPNN = [C Month [1], + C Month [12], C Temp, C Humd, C Hdd, G Latitude, R N.building, R N.households, R G.area, R M.area ] (1) O BPNN = [Water Consumption] where I BPNN denotes the input vector and O BPNN represents output vector of the BPNN forecasting model. The range of the dataset used in this case study included 12 months for 18 apartment complexes which included 183 buildings. The raw data of the I BPNN consisted of 20 x 216 datasets that defined 20 attributes for 216 different cases that included 1-12 coded month of year, relative-temperature, relative humidity, latitude, heating degree days, number of buildings, number of households, gross area, and maintenance area, while the O BPNN of the raw data was 1 x 216 matrixes for the residential water use that was to be forecasted.

7 A water demand forecasting model using BPNN 7 The sample training data we used consisted of a matrix, and the sample test data had a 20 x 48 matrix. To perform the estimation process, all input and output data were linearly normalized to be within the range [0, 1] to avoid the masking effect because all the inputs and outputs had different ranges [1, 2]. In this study we used a BPNN model with only one hidden layer, but it is possible to have more complex neural network models that have two or more hidden layers to optimize the proposed model of the BPNN to derive the relationship among the various variables. In addition, the hyperbolic tangent described in (2) was applied as the activation function of the neurons in the hidden layer of the proposed model. tanh(x) = (ex e x ) (e x + e x ) (2) The network was operated with the training data set and the stopping criterion for the training process was when either the training goal was met or the number of the epoch encounters was 1,000. The training goal was met when the sum of squared error became less than 0.06, and the learning rate was To evaluate the performance for the prediction accuracy of the models, we used two distinct error related statistical indicators, the mean absolute percentage error (MAPE) and the root mean square error (RMSE) in this study [1, 38, 39]. Table 2 Estimation Result of BPNN based Water Demand Model Error Indicators Yearly water consumption MAPE (%) 19.6 RMSE 98,110(m 3 /yr) The statistical indicators representing the prediction performance shown in Table 4 show that the differences between the forecasted water use and the actual values are rather small. The RMSE of each case is also quite small regarding the scale of annual water use for each residential complex. The results confirm a significantly high accuracy of the prediction, which indicates the proposed model is reasonably reliable. This demonstrates that the proposed BPNN based water demand modeling is a reliable approach for Korea. 5 Conclusion This study introduced a BPNN based water demand forecasting model that considered the extraction of potential factors affecting water use of residential complexes in Korea.

8 8 Dongjun Suh and Sungil Ham Estimation of water use for residential buildings in Korea is a significant issue in supporting stable water supplies since approximately at least one fourth of the total water use comes from the building sector, and residential water use accounts for roughly seven tenths of the total water supply. Such a model can support reliable water supply management that considers the needs of customers and the local community can be used to design water infrastructure appropriately, such as reservoir supply and distribution facilities. Extensive reviews for residential water demand models confirm that the selection of potential factors affecting water consumption are crucial in water use estimation and determining the accuracy of prediction models. We hope that future research will concentrate on retrieving potential parameters that affect residential water use to overcome any limitations of the present research. References [1] D. Suh, S. Chang, An energy and water resource demand estimation model for multi-family housing complexes in Korea, Energies, 5 (2012), [2] D. Suh, H. Kim, J. Kim, Estimation of Water Demand in Residential Building using Machine Learning Approach, th International Conference on IT Convergence and Security (ICITCS), (2015), [3] A.C. Worthington, M. Hoffman, An empirical survey of residential water demand modelling, Journal of Economic Surveys, 22 (2008), [4] F. Arbues, M.A. Garcia-Valinas, and R. Martinez-Espineira, Estimation of residential water demand: a state-of-the-art review, The Journal of Socio-Economics, 32 (2003), no. 1, [5] G. Romano, N. Salvati, A. Guerrini, Estimating the determinants of residential water demand in Italy, Water, 6 (2014), no. 10, [6] C.W. Howe, The functions, impacts and effectiveness of water pricing: evidence from the United States and Canada, International Journal of Water Resources Development, 21 (2005), no. 1, [7] J. Schleich, T. Hillenbrand, Determinants of residential water demand in Germany, Ecological Economics, 68 (2009), no. 6,

9 A water demand forecasting model using BPNN 9 [8] H.H. Zhang, D.F. Brown, Understanding urban residential water use in Beijing and Tianjin, China, Habitat International, 29 (2005), no. 3, [9] L. Hoglund, Household demand for water in Sweden with implications of a potential tax on water use, Water Resources Research, 35 (1999), [10] B. Jorgensen, M. Graymore, K. O'Toole, Household water use behavior: An integrated model, Journal of Environmental Management, 91 (2009), no. 1, [11] E.J.M. Blokker, J.H.G. Vreeburg, J.C. Van Dijk, Simulating residential water demand with a stochastic end-use model, Journal of Water Resources Planning and Management, 136 (2010), [12] J.C. Lam, D.H. Li, Daylighting and energy analysis for air-conditioned office buildings, Energy, 23 (1998), [13] D. Li, S. Wong, K. Cheung, Energy performance regression models for office buildings with daylighting controls, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 222 (2008), [14] W. Wang, Y. Kuang, N. Huang, Study on the decomposition of factors affecting energy-related carbon emissions in Guangdong Province, China, Energies, 4 (2011), no. 12, [15] B. Zhu, A novel multiscale ensemble carbon price prediction model integrating empirical mode decomposition, genetic algorithm and artificial neural network, Energies, 5 (2012), no. 12, [16] T. Kimoto, K. Asakawa, M. Yoda, M. Takeoka, Stock market prediction system with modular neural networks, Proceeding of the International Joint Conference on Neural Networks, (1990), [17] N. Amjady, F. Keynia, A new neural network approach to short term load forecasting of electrical power systems, Energies, 4 (2011),

10 10 Dongjun Suh and Sungil Ham [18] A.E. Ben-Nakhi, M.A. Mahmoud, Cooling load prediction for buildings using general regression neural networks, Energy Conversion and Management, 45 (2004), no , [19] D.E. Rumelhart, G.E. Hinton and R.J. Williams, Learning representations by back-propagating errors, Cognitive Modeling, 5 (1988), no. 3. [20] D. Wu, Z. Yang, L. Liang, Using DEA-neural network approach to evaluate branch efficiency of a large Canadian bank, Expert Systems with Applications, 31 (2006), no. 1, [21] A. Jost, Neural networks: A logical progression in credit and marketing decision system, Credit World, 81 (1993), [22] Backpropagation from Wikipedia. [23] S. Osselaer, Iris data analysis using back propagation neural networks, Journal of Manufacturing System, 13 (2003), 262. [24] F. Wang, Z. Mi, S. Su, H. Zhao, Short-term solar irradiance forecasting model based on artificial neural network using statistical feature parameters, Energies, 5 (2012), [25] M. Yorukoglu, A. Celik, A critical review on the estimation of daily global solar radiation from sunshine duration, Energy Conversion and Management, 47 (2006), Received: December 15, 2015; Published: December 29, 2015

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