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Estimating building energy consumption using extreme learning machine method
Energy 97 (2016) 506e516
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Energy journal homepage: www.elsevier.com/locate/energy
Estimating building energy consumption using extreme learning machine method Sareh Naji a, *, Afram Keivani b, Shahaboddin Shamshirband c, U. Johnson Alengaram a, Mohd Zamin Jumaat a, Zulkefli Mansor d, Malrey Lee e, ** a
Department of Civil Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia Department of Civil Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, Kuala Lumpur, Malaysia d Research Center for Software Technology and Management, Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, Malaysia e The Research Center for Advanced Image and Information Technology, School of Electronics & Information Engineering, ChonBuk National University, JeonJu, ChonBuk, 561e756, Republic of Korea b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 August 2015 Received in revised form 3 November 2015 Accepted 17 November 2015 Available online xxx
The current energy requirements of buildings comprise a large percentage of the total energy consumed around the world. The demand of energy, as well as the construction materials used in buildings, are becoming increasingly problematic for the earth's sustainable future, and thus have led to alarming concern. The energy efficiency of buildings can be improved, and in order to do so, their operational energy usage should be estimated early in the design phase, so that buildings are as sustainable as possible. An early energy estimate can greatly help architects and engineers create sustainable structures. This study proposes a novel method to estimate building energy consumption based on the ELM (Extreme Learning Machine) method. This method is applied to building material thicknesses and their thermal insulation capability (K-value). For this purpose up to 180 simulations are carried out for different material thicknesses and insulation properties, using the EnergyPlus software application. The estimation and prediction obtained by the ELM model are compared with GP (genetic programming) and ANNs (artificial neural network) models for accuracy. The simulation results indicate that an improvement in predictive accuracy is achievable with the ELM approach in comparison with GP and ANN. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Energy consumption Residential buildings Estimation Energy efficiency ELM (extreme learning machine)
1. Introduction Energy consumption has deep implications for the socioeconomic and political spheres of countries. The uncontrolled use of natural resources and energy reserves, has had a tendency to lead to environmental damage that endangers all life, hence the importance of saving energy. Energy waste presents an environmental hazard that warrants global attention to sustainability. In fact, a good percentage of energy waste is connected with buildings [1]. In 2012 alone, roughly 40% of the total U.S. energy consumption was used in buildings, both commercial and residential, thus, energy conscious construction is important to secure a sustainable future for humanity and the earth. Both, the commercial and
* Corresponding author. Tel.: þ61 451798393. ** Corresponding author. E-mail addresses: [email protected] (S. Naji), [email protected] (M. Lee). http://dx.doi.org/10.1016/j.energy.2015.11.037 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
residential sectors need to focus greater attention to energy use in the near future [2]. The operational energy of a building's useful life constitutes the greater part of its total energy usage (assuming the lifespan of a building is 75 years) [3]. Energy needs arise in various building and environment constituents, where climatic conditions, choice of building envelope and building insulation usually head the list. The thermal homeostatic regulation of interior spaces is greatly influenced by walls, roofs and glazing. Thus, the type of building envelope and its properties determine heat loss, heat gain, and air entering from outdoors [3,4]. Insulation is a major factor in helping steady interior temperature and reducing the energy needed for the acclimatization of heating and cooling. Insulating materials reduce thermal transmittance (U-value) in the building envelope components, which not only contributes in reducing the required HVAC system size but also reduces energy costs [5]. Hence, in both naturally ventilated and air-conditioned buildings, the heat storing capacity of wall and roof construction affect indoor thermal comfort and cooling loads.
S. Naji et al. / Energy 97 (2016) 506e516
It is essential today to understand thermal comfort under the light of energy efficiency [6e10]. The fulfillment of energy efficiency in buildings requires reduction of energy consumption during their operation years. This requirement highlights the importance of energy usage estimation prior to design and construction stages, which can lead to significant improvements in the new constructed buildings in terms of energy efficiency [11e13]. The reduction of energy usage by engineered materials and proper design of the physical structure is well documented in the literature. Other studies have centered on energy requirements during a building's operational life span [14e17]. The energy requirement and environmental impact of construction, has also been investigated [14e16,18,19]. Some studies have focused on the particular effects of a building material on energy consumption and have forecasted energy consumption by other software and neural network applications [11,12,20e22]. Then, several commercial products have been introduced to improve energy efficiency in residential buildings [6,7,10,58]. Some companies use lightweight frames with standardized sections and easily degradable and recyclable materials to reduce energy needs, construction waste and costs [23e26]. One of these systems is the common wooden ‘platform framing’. This lightweight framing can also be built in light steel, and is used widely around the globe [27]. The main objective of this study is to estimate a building's energy consumption using the extreme learning machine method, which will be referred to as ELM in the remainder following pages. The input data in the ELM method represent wall material parameters, such as type of material, thickness and thermal properties. The output data come from the EnergyPlus simulation results for sample buildings of different input parameters. The materials and systems focused in this study, are prevalent in Eastern Europe and Turkey [12]. Turkey is a country with rising significance in the world energy market, in which energy demands have increased sharply during past decades. It is expected that energy demands in this country will grow by 4.5% from 2015 to 2030 [28]. A significant percentage of total life expenses in Turkey are associated with energy costs since natural gas and crude oil are imported [29]. It is hence necessary to minimize the building energy consumption in this region. So far there has been several approaches of computational intelligence methods for application in prediction of energy consumption in buildings and other systems. For example there has been an investigation of prediction power consumption of graphic processing units with fuzzy wavelet neural networks in which the average error of the model was around 6% [30]. In another investigation a comparison of integrated clustering methods for prediction of building energy consumption was performed [31]. It was found in this paper that there was an inherent tradeoff between prediction accuracy and cluster stability. Furthermore, a prediction of building energy consumption using real coded genetic algorithm has been carried out based on support vector machine approach [32]. It was confirmed that genetic algorithm approach is superior to conventional approaches. Therefore to improve the prediction of building energy consumption and improve accuracy there is a need to analyze more sophisticated methods. The building energy-efficiency analysis needs accurate on-line identification to determine optimal energy consumption. In this study, we introduced an estimation model for energy consumption by using the soft computing approach of ELM. The application of this modern computational approach to determine optimal values and functions in real world problems, is receiving high attention from in various areas of science. Different engineering fields have been applied NN (neural network) as a chief computational platform. This method is able to solve complex nonlinear problems which are difficult to achieve using classic parametric methods.
507
Various algorithms such as SVM (support vector machine), BP (back propagation), and HMM (hidden Markov model) can be used for training in neural network. The downside of NN is the time required to learn it. ELM was introduced by Huang et al. as an algorithm for single layer feed forward NN. This algorithm is capable of solving problems caused by gradient descent based algorithms like back propagation which is applicable in ANNs. Training time required for using NNs can be reduced by ELM and by utilizing this method the learning process is much faster. A number of investigations have been carried out related to the application of the ELM algorithm to successfully solve problems in various scientific fields [36]. In this study, an attempt was made to retrieve the correlation between the main building envelope's parameters and the district heating and cooling loads. To achieve this purpose, up to 180 simulations were used to generate an ELM Predictive model. 2. Methodology 2.1. Sample building A residential building plan is used in EnergyPlus simulations (Fig. 1). This plan is an example of a typical single family house located in Istanbul, Turkey, built in a lightweight wood frame structure. Different building envelope scenarios were applied to this home plan. The architecture plans of ground floor and first floor are shown in Fig. 1. Also Table 1 provides some basic information about the same building. 2.2. Materials Fig. 2 shows the detailed section of wall construction used in the sample building. The wall, floor and roof materials were chosen in accord to prevalent light woodframe construction. The main structural members used in the walls of these systems include vertical and horizontal timber members. The vertical members (studs), are generally made of 50 100 mm lumbers placed in a standard spacing of 610 mm. The main horizontal members, called plates hold the studs. Engineered particleboard (Oriented strand board, OSB) acts as sheathing material. Glasswool is used as insulation, and two layers of gypsum board are the remaining wall components. Finally, cement-bonded particle board is applied as the exterior finishing of this building. 2.3. Modelling in EnergyPlus In order to analyze the energy performance of the sample building, it was modelled in EnergyPlus software, as explained. EnergyPlus is a robust building energy simulation software. Thanks to the user-friendly environment of this software, the user can easily impliment the geometry and material properties as well as thermal loads and HVAC system characteristics. In a comparison made by Neto and Fiorelli (2008) between EnergyPlus simulation methods and artificial neural network, using a reference building, both models were found to be suitable to estimate energy consumption. The results also show that the forecasts of EnergyPlus present an error range of 13% for 80% of the tested database [42]. As the building is located in Istanbul, Turkey, the regional weather data were imported to the software and used in the simulations [42] Since EnergyPlus analysis aims to find the role of wall material parameters on energy use, the variables of these simulations are restricted to wall materials and their details. Other factors such as building occupancy, equipment, HVAC devices, were left constant for all simulations. Wall components such as window
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S. Naji et al. / Energy 97 (2016) 506e516
Fig. 1. (a) Ground floor plan, (b) First floor plan.
Table 1 Description of sample building. Building type Floor area (m2) Location Seismic zone according to “DBYBHY2007” [41]
Residential building First story: 81.7 Second Story: 48.38 Istanbul, Turkey Zone1
locations, their direction and orientations were adjusted on Sketchup 3D drawings using EnergyPlus Plugins. Two different “zones” were defined in the drawings for two separate stories to obtain more accurate results. This information was automatically transferred into EnergyPlus by opening the saved document in IDM format. The properties of windows (glazing and frame) and other wall components were carefully defined in EnergyPlus software as these properties affect the overall thermal behaviour of walls. Furthermore some properties of the roof and ground elements such as ground temperature and solar absorbance of the roof coverings were defined in EnergyPlus. Table 2 summarizes the most important design factors used in simulation. 2.4. Input and output variables In this article 5 different wall details with various layer thicknesses were considered in order to investigate the effects of wall material thicknesses and thermal properties on the whole building energy performance. Since the structure of the building contains standardized frames (certain standardized materials are used in all
Table 2 Design factors used in EnergyPlus simulation. Design category Building Location
Window glazing Window frame
Lighting Electric equipment HVAC template Fig. 2. Detailed section of walls for the sample buildings constructed with Wood light frame system.
Value Particulars Latitude (degree) Longitude (degree) Time zone (h) Elevation (m) Site ground temperature (ºC) U-factor (W/m2K) Solar heat gain Coefficient Frame conductance (W/m2K) Frame solar absorptance Frame thermal hemispherical emissivity Watts per zone area Fraction radiant Watts per zone floor area Fraction radiant Type Constant heating setpoint (ºC) Constant cooling setpoint (ºC)
Istanbul 40.97 28.82 2 37 18 1.6 0.44 4.5 0.7 0.7 12 0.32 10 0.3 Thermostat 21 26
S. Naji et al. / Energy 97 (2016) 506e516 Table 3 Properties of wall components. Wall component
Table 5 Input parameters for energy consumption of building. Density Thermal conductivity Specific heat r(kg/m3) K (W/m-K) Cp (J/kg-K)
Gypsum board OSB Acoustic gypsum board OSB Cement-bonded particle board
509
1300 640 1300 640 400
0.21 0.13 0.12 0.13 0.23
840 1880 840 1880 1470
buildings constructed with this method) simulations and the estimation process are much simpler to carry out and the results are more reliable compared to conventional construction systems. After defining 5 groups, insulation materials with different R-values and different thicknesses were assigned to wall details. Afterwards an EnergyPlus simulation was carried out for each material series and energy consumption value obtained from the simulation. As mentioned formerly, two layers of Gypsum board, two layers of OSB (oriented strand boards), a layer of cement bonded particle board and a layer of insulation material are the wall materials in all 5 groups. It is important to notice that the groups are introduced by the purpose of classification and organization of input data. However the thicknesses of each layer are different for the various groups, which helped us to investigate the relationships among layer thickness, insulation thickness and building energy performance in different scenarios. Table 3 shows the properties of wall layer materials while Table 4 shows the thicknesses of wall layers used in groups. In all groups there are two kinds of input variables, namely insulation thickness and insulation K-value. Insulation materials with thermal conductivity values of 0.03 W/m-K, 0.04 W/ m-K, 0.05 W/m-K, 0.08 W/m-K are considered in each group. Also insulation is used in different thicknesses as: 4 cm, 6 cm, 8 cm, 10 cm, 12 cm, 14 cm, 16 cm, 18 cm, and 20 cm. By using this method, a total of 180 data series were provided and the same number of simulations were carried out in EnergyPlus software. Tables 5 and 6 illustrate input and output variables in terms of both the defined and the obtained values. 2.5. Extreme learning machine ELM (extreme learning machine) is a tool of learning algorithm for SLFN (single layer feed-forward neural network) architecture [43,44]. Randomly choosing the input weights, ELM determines the output weights of SLFN analytically. ELM algorithm has more favourable general capability and faster learning speed. This algorithm requires less time for running compared to conventional algorithms since it minimises manual interventions by determining all the network parameters analytically. Ease of use, compatibility with many nonlinear activation and kernel functions, faster learning speed and superior performance are among advantages of this efficient algorithm. In general, ELM is a robust algorithm with faster learning speed and better performance compared to traditional algorithms like BP. ELM tends to get the least training errors and norm of weights.
Name
Parameters description
Parameters values
input 1 input 2
Insulation K value (W/m-K) Insulation Thickness (cm)
0.03, 0.04, 0.05, 0.08 4,6,8,10,12,14,16,18,20
2.5.1. Single hidden layer feed-forward neural network SLFN function, with L hidden nodes can be represented as mathematical description of SLFN, incorporating both additive and RBF hidden nodes in a unified way as follows [47]:
fL ðxÞ ¼
L X
bi Gðai ; bi ; xÞ;
x2Rn ;
ai 2Rn
(1)
i¼1
where ai and bi represent the learning parameters of hidden nodes. bi is the weight connecting the ith hidden node to the output node. Gðai ; bi ; xÞ is the output value of the ith hidden node with respect to the input x. The additive hidden node with the activation function of gðxÞ : R/R (e.g., sigmoid and threshold), Gðai ; bi ; xÞ is [44]:
Gðai ; bi ; xÞ ¼ gðai :x þ bi Þ;
bi 2R
(2)
where ai denotes the weight vector connecting the input layer to the ith hidden node. bi is the bias of the ith hidden node. Also ai. x is the inner product of vector ai and x in Rn. Gðai ; bi ; xÞ can be found for RBF hidden node with activation function gðxÞ : R/R (e.g., Gaussian), Gðai ; bi ; xÞ as [44]:
Gðai ; bi ; xÞ ¼ gðbi kx ai kÞ;
bi 2Rþ
(3)
where ai and bi represent the center and impact factor of ith RBF node. Rþ represents the set of all positive real values. The RBF network is a particular case of SLFN with RBF nodes in its hidden layer. For N arbitrary distinct samples ðxi ; ti Þ2Rn Rm , xi is n 1 input vector and ti is m 1 target vector. If an SLFN with L hidden nodes can approximate these N samples with zero error it implies the existence of bi, ai and bi so that [44]: L X fL xj ¼ bi G ai; ; bi ; xj ;
j ¼ 1; …; N
(4)
i¼1
Eq. (4) can be written compactly as:
Hb ¼ T
(5)
Table 6 Heating and cooling of building; as output parameter. Name
Parameters description
Parameters values
Output
Total heating and cooling energy (kWh)
Various depended on input data
Table 4 Thicknesses of wall layers in 5 defined groups (m). Group
Gypsum board
OSB
Acoustic gypsum board
OSB
Cement-bonded particle board
1 2 3 4 5
0.015 0.02 0.010 0.025 0.01
0.025 0.020 0.030 0.015 0.035
0.02 0.025 0.015 0.030 0.019
0.025 0.020 0.030 0.015 0.01
0.015 0.015 0.015 0.015 0.015
510
S. Naji et al. / Energy 97 (2016) 506e516
where
2
Gða1 ; b1 ; x1 Þ H e a; e b; e x ¼4 Gða1 ; b1 ; xN Þ
… … …
GðaL ; bL ; x1 Þ GðaL ; bL ; xN Þ
3 5
(6) NL
with e a ¼ a1 …; aL ; e b ¼ b1 …; bL ; e x ¼ x1 …; xL
2 T3 3 t1 bT1 b¼4 « 5 and T ¼ 4 « 5 tLT Nm bTL Lm
Zj ¼ f
2
n X
!
wij $Xi
(9)
i¼1
(7)
H is the hidden layer output matrix of SLFN with ith column of H being the ith hidden node's output with respect to inputs x1 ; …xN . 2.5.2. The principle behind ELM ELM is designed as a SLFN with L hidden neurons, capable of learning L distinct samples with zero error. Even if the number of hidden neurons (L)< the number of distinct samples (N), ELM can allocate random parameters to the hidden nodes and calculate the output weights by pseudo inverse of H giving only a small error ε > 0. Therefore, it is not necessary to tune the hidden node parameters of ELM ai and bi, since they can easily be allocated with random values. The following theorems state the same. Theorem 1: (Liang et al. [47]) Let an SLFN with L additive or RBF hidden nodes and an activation function g(x) which is infinitely differentiable in any interval of R be given. Then for arbitrary L distinct input vectors; fxi jxi 2Rn ; i ¼ 1; …Lg and fðai ; bi ÞgLi¼1 , randomly produced by any continuous probability distribution, respectively, the hidden layer output matrix is invertible with probability one, the hidden layer output matrix H of the SLFN is invertible and kHb Tk ¼ 0. Theorem 2: (Liang et al. [47]) Given any small positive value ε > 0 and activation function gðxÞ : R/R which is infinitely differentiable in any interval, there exists L N such that for N arbitrary distinct input vectors fxi jxi 2Rn ; i ¼ 1; …Lg for any fðai ; bi ÞgLi¼1 for any randomly produced based upon any continuous probability distribution kHNL bLm TNm k < ε with probability one. Since the hidden node parameters of ELM should not be tuned throughout training and they are easily assigned with random values, Eq. (5) becomes a linear system and the output weights can be estimated as [44]:
b ¼ Hþ T
Here it is assumed that the weight and the threshold between the input layer and the hidden layer are wij and yj respectively, and the weight and the threshold between the hidden layer and output layer are wjk and yk respectively. The outputs of each neuron in a hidden layer and output layer are as follows:
(8)
where H þ is the MooreePenrose generalized inverse of the hidden layer output matrix H which can be computed via several approaches consisting orthogonal projection, orthogonalization, iterative, singular value decomposition (SVD), etc. The orthogonal projection method can be utilized only when HT T is non-singular and H þ ¼ ðH T TÞ1 H T . Owing to the use of searching and iterations, orthogonalization method and iterative method have limitations. Implementations of ELM uses SVD to compute the MooreePenrose generalized inverse of H, because it can be utilized in all situations. ELM is thus a batch learning method. 2.6. Artificial neural networks The multilayer feed forward network with a back propagation learning algorithm is among the most common neural network architectures, which have been widely studied and used in many disciplines. Three main layers included in a neural network are: (1) an input layer; (2) an output layer; and (3) an intermediate or hidden layer. The input vectors are, D2Rn and D ¼ ðX1 ; X2 ; …; Xn ÞT ; the outputs of q neurons in the hidden layer are Z ¼ ðZ1 ; Z2 ; …; Zn ÞT ; and the outputs of the output layer are Y2Rm , Y ¼ ðY1 ; Y2 ; …; Yn ÞT .
0 Yk ¼ f @
q X
1 wkj $Zj A
(10)
j¼1
where f is a transfer function, which is the rule for mapping the neuron's summed input to its output, and using a suitable choice as the instrument for introducing a non-linearity into the network design. One of the most commonly used functions is the sigmoid function, which is monotonically increasing and ranges from zero to one. Details on ANNs can be found in Refs. [49,50]. 2.7. Genetic programming GP is known as an evolutionary algorithm based on Darwinian theories of natural selection and survival used to approximate the equation, in symbolic form. GP has the best ability of describing the connection between input and output variables. This algorithm presumes an initial population of accidently generated programs (equations), derived from the random combination of input variables, numbers and functions, including arithmetic operators ðþ; ; ; ÷Þ mathematical functions (sin, cos, exp, log), logical/comparison functions, etc. These functions have to be selected properly according to perceptions of the process. Subsequently, this population of potential solution go through an evolutionary process after which the ‘fitness’ (a measure of how well they solve the problem) of the evolved programs is evaluated. The individual programs that best conform to the data are then chosen from the initial population. Afterwards, selected programs interchange parts of the information among each other to produce better programs through ‘crossover’ and ‘mutation’, which mimics the natural world's reproduction process. The process of exchanging the parts of the selected programs among each other is called crossover, and the act of randomly changing programs to create new programs is called mutation. The programs which conform to the data less than others are discarded. This evolution process is repeated over successive generations and driven towards achieving symbolic expressions describing the data, which can be scientifically interpreted to derive knowledge about the process. Details on GP can be obtained from Refs. [52e54]. 3. Results and discussion 3.1. Energy consumption Table 7 shows the results of EnergyPlus software for all 180 simulations. The results obtained from EnergyPlus software are annual energy use for total district heating and cooling for all five groups. Annual energy use for interior lighting and equipment are the same for all buildings as the default inputs for lighting and equipment are constant in all models. These values are eliminated in this evaluation. In Table 7 it can be seen that the total energy needed for heating and cooling of the buildings decreases by the reduction of the K-value. In addition, the output data from the simulations indicate that the variations in building energy consumption are significantly affected by the properties of the insulation materials rather than the changes in different groups, i.e., different thickness configurations of wall materials. By increasing the thickness of the
S. Naji et al. / Energy 97 (2016) 506e516
511
Table 7 Output data values in five groups with insulation thermal conductivity classified as 5 (a) k ¼ 0.03 W/m-K, (b) k ¼ 0.04 W/m-K, (c) k ¼ 0.05 W/m-K, (d) k ¼ 0.08 W/m-K (kWh). Thickness of insulation (m) 0.04 (a) K ¼ 0.03 W/m-K Group1 8312.79 Group2 8362.87 Group3 8270.78 Group4 8350.18 Group5 8420.6 (b) K ¼ 0.04 W/m-K Group1 9017.31 Group2 9087.24 Group3 8957.07 Group4 9062.41 Group5 9167.76 (c) K ¼ 0.05 w/m-K Group1 9593.51 Group2 9681.74 Group3 9517.86 Group4 9650.4 Group5 9782.94 (d) K ¼ 0.08 W/m-K Group1 10,804.35 Group2 10,939.86 Group3 10,688.79 Group4 10,891.93 Group5 11,095.06
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
7457.24 7486.46 7432.76 7481.50 7520.24
6960.86 6982.04 6942.21 6976.93 7005.65
6651.46 6667.53 6637.87 6661.93 6686
6447.59 6459.35 6437.56 6456.33 6473.31
6310.84 6319.85 6303.26 6316.52 6330.56
6217.75 6224.91 6211.12 6222.72 6233.72
6149.9 6156.38 6144.23 6154.89 6164.23
6100.22 6107.24 6094.24 6105.64 6114.98
8044.68 8087.26 8008.81 8072.8 8136.92
7456.3 7485.37 7431.9 7475.4 7519
7062.05 7084.98 7042.35 7076.62 7110.9
6788.14 6806.15 6772.22 6799.71 6827.2
6591.7 6606.14 6579.11 6601.12 6623.13
6446.3 6457.71 6436.25 6453.87 6471.5
6338.78 6348.08 6330.66 6344.97 6359.28
6259.02 6266.96 6251.54 6263.77 6276.01
8561.7 8618.04 8513.33 8598.28 8683.23
7903.69 7942.39 7871.24 7929.71 7988.19
7455.3 7484.26 7431.09 7474.42 7517.76
7129.11 7153.83 7107.46 7144.27 7181.08
6885.05 6904.85 6868.03 6897.77 6927.52
6700.06 6716.65 6686.25 6711.43 6736.61
6557.38 6571.33 6545.87 6567.00 6588.14
6444.86 6456.11 6434.99 6452.35 6469.72
9760.5 9853.89 9679.53 9820.46 9961.4
9014.42 9083.94 8954.71 9059.32 9163.94
8461.15 8514.71 8415.81 8496.07 8576.33
8041.33 8083.15 8006.07 8069.28 8132.5
7713.43 7748.21 7684.85 7736.4 7787.95
7452.51 7481.04 7428.28 7471.21 7514.15
7237.74 7263.13 7216.27 7254.15 7292.04
7057.49 7079.74 7038.3 7071.85 7105.41
insulating material the effects of other materials’ properties on building energy performance decreases, i.e., the changes in thickness of other materials happen to become less effective.
3) Coefficient of determination (R2)
"
Pn i¼1
R2 ¼ P n
3.2. Evaluating accuracy of proposed models
i¼1
Predictive performances of proposed models were presented as RMSE (root mean square error), Coefficient of determination (R2) and Pearson coefficient (r). These statistics are defined as follows:
Oi Oi , Pi Pi
#
2
P Oi Oi , ni¼1 Pi Pi
(13)
where Pi and Oi are known as the simulation and forecast values of building's energy consumption, respectively, and n is the total number of test data.
1) RMSE (root-mean-square error)
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðPi Oi Þ ; RMSE ¼ n
3.3. Architecture of soft computing models
(11)
2) Pearson correlation coefficient (r)
n
Pn
!
i¼1 Oi ,Pi
Pn
!
i¼1 Oi ,
Pn
i¼1 Pi
ffi r ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u0 !2 1 0 !2 1 u P Pn Pn u@ Pn t n O2 Oi A,@n n P2 Pi A i¼1
i
i¼1
i¼1
i¼1
i
(12)
The parameters of the ELM, ANN and GP modelling frameworks employed in this study are presented in Table 8. 70% data of each group (22 out of 32) was used for training and 30% (10 out of 32) for testing of the models. In this case all groups are included in the training of the models and in later in testing as well. The average computation time for the ELM modelling was around 330 s using a PC with Intel Core Duo CPU E7600 @3.06 GHz and 2-GB RAM. The average computation time for the ANN with back propagation training algorithm and GP modelling using the same PC with the same performances was 424 and 436 s, respectively. For the ELM modelling, MATLAB software was used.
Table 8 User-defined parameters for the ELM, ANN and GP models. ELM Number of layers Neurons
e e Learning rule e
ANN [55,56] 3 Input: 6 Hidden: 3, 6, 10 Output: 1 e
Number of layers Neurons
e ELM for SLFNs e
GP [57]
Number of iteration
3 Input: 6 Hidden: 3, 6, 10 Output: 1 1000
Population size
Activation function
Sigmoid Function
Head size
5e9
Learning rule e
Back propagation e
Chromosomes Number of genes
20e30 2e3
e Neurons
e e e Output: 1 512
e
e
e
e
Mutation rate
91.46
e
e
e
e
Crossover rate
30.56
e
e
e
e
Inversion rate
108.53
512
S. Naji et al. / Energy 97 (2016) 506e516
3.4. Performance evaluation of the proposed ELM model In this section performance results of the ELM building energy consumption predictive model are reported. Fig. 3(a) presents the accuracy of developed ELM building energy consumption predictive model. Moreover, Fig. 3(b) and (c) present the accuracy of developed GP and ANN building energy consumption predictive models, respectively. It can be seen that most of the points fall along the diagonal line for the ELM prediction model. Consequently, it shows that prediction results are in very good agreement with the simulated values for the ELM method. This observation can be confirmed with very high value for the coefficient of determination.
The number of either overestimated or underestimated values produced is limited, which indicates that the predicted values enjoy high levels of precision. Fig. 4 shows scatter plots separately for ELM prediction of energy consumption in buildings for different wall groups. One can note the similar R2 coefficient for all groups. As mentioned previously, different thickness configurations of wall layers in defined groups has insignificant effect on energy consumption of buildings. Fig. 5 shows scatter plots for ELM prediction of energy consumption in buildings for different thermal conductivity coefficients. According to R2 coefficient, the more and less accurate predictions were observed for K ¼ 0.03 W/m-K and K ¼ 0.08 W/m-K
Fig. 3. Scatter plots of actual and predicted values of energy consumption in buildings, using (a) ELM, (b) GP and (c) ANN method.
S. Naji et al. / Energy 97 (2016) 506e516
respectively. It is concluded that the ELM model has better prediction for lower thermal conductivity. 3.5. Performance comparison of ELM, ANN and GP In order to demonstrate the merits of the proposed ELM approach on a more definite and tangible basis, the prediction accuracy of ELM models was compared to the prediction accuracy of GP and ANN methods, which were used as benchmarks. Conventional error statistical indicators, RMSE, r and R2, were used for comparison. Table 9 summarizes the prediction accuracy results for test data sets since a training error is not a credible indicator for prediction potential of a particular model. The smaller RMSE value represents more accurate predictive model. Furthermore the r and
513
R2 show better correlation with measured and predicted values, as their values reach closer to 1. ELM model outperforms GP and ANN models according to the results of Table 9. The ELM model provides significantly better results than the benchmark models. On the basis of RMSE analysis with comparison with ANN and GP, it is concluded that the proposed ELM outperformed the results obtained with benchmark models. The ELM RMSE in training phase was 40.85604 while ELM RMSE in testing phase was 74.02189. On the other hand ANN RMSEs were 301.347 and 331.5657 in training and testing phase respectively. GP RMSEs were 287.4788 and 314.3471 in training and testing phase respectively. Very high difference can be noticed between RMSEs of the ELM and the benchmark models. In order to prove the predictive accuracy of the ELM approach on a more
Fig. 4. Scatter plots of actual and predicted values of energy consumption in buildings for (a) group 1, (b) group 2, (c) group 3, (d) group 4 and (e) group 5.
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Fig. 5. Scatter plots of actual and predicted values of energy consumption in buildings for (a) K ¼ 0.03 W/m-K, (b) K ¼ 0.04 W/m-K, (c) K ¼ 0.05 W/m-K and (d) K ¼ 0.08 W/m-K.
definitive basis other parameters like r and R2 are investigated as well. These two parameters have similar characteristics. Table 9 verifies very high correlation of the measured and predicted data by the ELM approach, in which r and R2 coefficients are very close to 1, which means that the number of overestimated points are very limited. Finally, the proposed ELM model was analyzed for all groups as well as thermal conductivities separately. Tables 10 and 11 show the statistical indicators for the ELM models. Also the best prediction was observed for K ¼ 0.03 W/m-K according to RMSE. The worst prediction accuracy was observed for K ¼ 0.08 W/m-K.
Table 10 Comparative performance statistics of the ELM energy consumption predictive model of building for 5 groups.
Group Group Group Group Group
1 2 3 4 5
RMSE
R2
r
26.46982 28.16473 60.10535 58.18796 74.62387
0.9998 0.9998 0.9998 0.9979 0.9998
0.999905 0.999905 0.999888 0.998972 0.999887
simulation procedure. It seeks a solution to achieve a method that can forecast the energy consumption of buildings by entering input data as material properties and thicknesses. The outcome of this research indicate that the proposed model can efficiently predict the energy consumption of buildings regarding the main building envelope parameters.
4. Conclusion This study carried out a systematic methodology to create an ELM building energy consumption predictive model. This method is applicable in residential projects to save time in an energy
Table 9 Comparative performance statistics of the ELM, ANN and GP energy consumption predictive model of building for (a) training and (b) testing data. (a) Training ANN
ELM RMSE 40.85604 (b)
R2 0.999
r 0.999503
GP R2 0.9433
r 0.971219
Testing ANN
ELM RMSE 74.02189
RMSE 301.247
2
R 0.997
r 0.998518
RMSE 331.5657
RMSE 287.4788
R2 0.95
r 0.974703
R2 0.9541
r 0.976781
GP 2
R 0.9432
r 0.971177
RMSE 314.3471
S. Naji et al. / Energy 97 (2016) 506e516 Table 11 Comparative performance statistics of the ELM energy consumption predictive model of building for different thermal conductivity.
K K K K
¼ ¼ ¼ ¼
0.03 0.04 0.05 0.08
W/m-K W/m-K W/m-K W/m-K
RMSE
R2
r
31.07514 40.26692 50.42344 78.22584
0.9982 0.998 0.9976 0.9958
0.999102 0.999 0.998777 0.997898
It can be concluded from the simulation outputs that the variations in building energy consumption are affected mostly by the insulation materials, more so than by changes in configurations of wall components. The parameters associated with insulation materials play a significant role in determining the energy consumption of a building. By increasing the thickness of the insulating material, the variations in the configurations of other wall materials are less effective by comparison. A comparison of ELM method with GP and ANN was performed in order to assess the prediction accuracy. The accuracy, measured in terms of RMSE, r and R2, indicated that ELM predictions are superior to GP and ANN. As previously stated, results revealed the robustness of the ELM method. The developed ELM model has many appealing and remarkable features which make it distinguishable from traditional popular gradient-based learning algorithms for feedforward neural networks. ELMs are much faster in learning speed compared to the traditional feedforward network-learning algorithms such as BP algorithm. Furthermore, unlike the traditional learning algorithms, ELM algorithm is able to achieve the smallest training error and also norm the weights. This study highlights the importance of computer science applications for the building industry. The estimation of the total building energy usage can help the architects and engineers to conceive more clearly the building energy efficiency level. This can be carried out early in the design, and during the construction of a building resulting in more realistic and accurate energy efficient building design. Acknowledgment This research work is funded by High Impact Research Grant (HIRG) no. UM.C/625/HIR/VC/206 (Synthesis of Energy Redeemable Material from Local Wastes for Building). References [1] Energy Consumption by Sector, U.S. Energy Information Administration (EIA), Independent Statistics & Analysis, retrieved: 27.01.2014, Address: http:// www.eia.gov/totalenergy/data/monthly/pdf/sec2_3.pdf. [2] Bokalders V, Block M. The whole building handbook-how to design healthy, efficient and sustainable buildings. London: Earthscan; 2010. [3] Guertin M. Green applications for residential construction. Residential Construction Academy; 2011. [4] Center for Sustainable Systems. Residential buildings factsheet. University of Michigan; 2009. Pub. No. CSS01e08. [5] Kumar Ashok, Suman BM. Experimental evaluation of insulation materials for walls and roofs and their impact on indoor thermal comfort under composite climate. Build Environ 2013;59:635e43. [6] Spence WP. Residential framing: a homebuilder's construction guide. 1st ed. Canada: Sterling Publishing; 1993. [7] RSMEANS. Residential & light commercial construction standards. 3rd ed. 2008. The All-In One Reference Compiled From Major Building Codes, Recognized Trade Customs, Industry Standards, Updated Reed Construction Data, USA. [8] Smith P. Architecture in a climate of change. 2nd ed. Amsterdam: Elsevier; 2005. [9] Makelainen P, Hassinen P. Light-weight steel and aluminum structures, fourth international conference on steel and aluminium structures. 1st ed. Finland: Elsevier; 1999.
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Estimating building energy consumption using extreme learning machine method Sareh Naji a, *, Afram Keivani b, Shahaboddin Shamshirband c, U. Johnson Alengaram a, Mohd Zamin Jumaat a, Zulkefli Mansor d, Malrey Lee e, ** a
Department of Civil Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia Department of Civil Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, Kuala Lumpur, Malaysia d Research Center for Software Technology and Management, Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, Malaysia e The Research Center for Advanced Image and Information Technology, School of Electronics & Information Engineering, ChonBuk National University, JeonJu, ChonBuk, 561e756, Republic of Korea b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 August 2015 Received in revised form 3 November 2015 Accepted 17 November 2015 Available online xxx
The current energy requirements of buildings comprise a large percentage of the total energy consumed around the world. The demand of energy, as well as the construction materials used in buildings, are becoming increasingly problematic for the earth's sustainable future, and thus have led to alarming concern. The energy efficiency of buildings can be improved, and in order to do so, their operational energy usage should be estimated early in the design phase, so that buildings are as sustainable as possible. An early energy estimate can greatly help architects and engineers create sustainable structures. This study proposes a novel method to estimate building energy consumption based on the ELM (Extreme Learning Machine) method. This method is applied to building material thicknesses and their thermal insulation capability (K-value). For this purpose up to 180 simulations are carried out for different material thicknesses and insulation properties, using the EnergyPlus software application. The estimation and prediction obtained by the ELM model are compared with GP (genetic programming) and ANNs (artificial neural network) models for accuracy. The simulation results indicate that an improvement in predictive accuracy is achievable with the ELM approach in comparison with GP and ANN. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Energy consumption Residential buildings Estimation Energy efficiency ELM (extreme learning machine)
1. Introduction Energy consumption has deep implications for the socioeconomic and political spheres of countries. The uncontrolled use of natural resources and energy reserves, has had a tendency to lead to environmental damage that endangers all life, hence the importance of saving energy. Energy waste presents an environmental hazard that warrants global attention to sustainability. In fact, a good percentage of energy waste is connected with buildings [1]. In 2012 alone, roughly 40% of the total U.S. energy consumption was used in buildings, both commercial and residential, thus, energy conscious construction is important to secure a sustainable future for humanity and the earth. Both, the commercial and
* Corresponding author. Tel.: þ61 451798393. ** Corresponding author. E-mail addresses: [email protected] (S. Naji), [email protected] (M. Lee). http://dx.doi.org/10.1016/j.energy.2015.11.037 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
residential sectors need to focus greater attention to energy use in the near future [2]. The operational energy of a building's useful life constitutes the greater part of its total energy usage (assuming the lifespan of a building is 75 years) [3]. Energy needs arise in various building and environment constituents, where climatic conditions, choice of building envelope and building insulation usually head the list. The thermal homeostatic regulation of interior spaces is greatly influenced by walls, roofs and glazing. Thus, the type of building envelope and its properties determine heat loss, heat gain, and air entering from outdoors [3,4]. Insulation is a major factor in helping steady interior temperature and reducing the energy needed for the acclimatization of heating and cooling. Insulating materials reduce thermal transmittance (U-value) in the building envelope components, which not only contributes in reducing the required HVAC system size but also reduces energy costs [5]. Hence, in both naturally ventilated and air-conditioned buildings, the heat storing capacity of wall and roof construction affect indoor thermal comfort and cooling loads.
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It is essential today to understand thermal comfort under the light of energy efficiency [6e10]. The fulfillment of energy efficiency in buildings requires reduction of energy consumption during their operation years. This requirement highlights the importance of energy usage estimation prior to design and construction stages, which can lead to significant improvements in the new constructed buildings in terms of energy efficiency [11e13]. The reduction of energy usage by engineered materials and proper design of the physical structure is well documented in the literature. Other studies have centered on energy requirements during a building's operational life span [14e17]. The energy requirement and environmental impact of construction, has also been investigated [14e16,18,19]. Some studies have focused on the particular effects of a building material on energy consumption and have forecasted energy consumption by other software and neural network applications [11,12,20e22]. Then, several commercial products have been introduced to improve energy efficiency in residential buildings [6,7,10,58]. Some companies use lightweight frames with standardized sections and easily degradable and recyclable materials to reduce energy needs, construction waste and costs [23e26]. One of these systems is the common wooden ‘platform framing’. This lightweight framing can also be built in light steel, and is used widely around the globe [27]. The main objective of this study is to estimate a building's energy consumption using the extreme learning machine method, which will be referred to as ELM in the remainder following pages. The input data in the ELM method represent wall material parameters, such as type of material, thickness and thermal properties. The output data come from the EnergyPlus simulation results for sample buildings of different input parameters. The materials and systems focused in this study, are prevalent in Eastern Europe and Turkey [12]. Turkey is a country with rising significance in the world energy market, in which energy demands have increased sharply during past decades. It is expected that energy demands in this country will grow by 4.5% from 2015 to 2030 [28]. A significant percentage of total life expenses in Turkey are associated with energy costs since natural gas and crude oil are imported [29]. It is hence necessary to minimize the building energy consumption in this region. So far there has been several approaches of computational intelligence methods for application in prediction of energy consumption in buildings and other systems. For example there has been an investigation of prediction power consumption of graphic processing units with fuzzy wavelet neural networks in which the average error of the model was around 6% [30]. In another investigation a comparison of integrated clustering methods for prediction of building energy consumption was performed [31]. It was found in this paper that there was an inherent tradeoff between prediction accuracy and cluster stability. Furthermore, a prediction of building energy consumption using real coded genetic algorithm has been carried out based on support vector machine approach [32]. It was confirmed that genetic algorithm approach is superior to conventional approaches. Therefore to improve the prediction of building energy consumption and improve accuracy there is a need to analyze more sophisticated methods. The building energy-efficiency analysis needs accurate on-line identification to determine optimal energy consumption. In this study, we introduced an estimation model for energy consumption by using the soft computing approach of ELM. The application of this modern computational approach to determine optimal values and functions in real world problems, is receiving high attention from in various areas of science. Different engineering fields have been applied NN (neural network) as a chief computational platform. This method is able to solve complex nonlinear problems which are difficult to achieve using classic parametric methods.
507
Various algorithms such as SVM (support vector machine), BP (back propagation), and HMM (hidden Markov model) can be used for training in neural network. The downside of NN is the time required to learn it. ELM was introduced by Huang et al. as an algorithm for single layer feed forward NN. This algorithm is capable of solving problems caused by gradient descent based algorithms like back propagation which is applicable in ANNs. Training time required for using NNs can be reduced by ELM and by utilizing this method the learning process is much faster. A number of investigations have been carried out related to the application of the ELM algorithm to successfully solve problems in various scientific fields [36]. In this study, an attempt was made to retrieve the correlation between the main building envelope's parameters and the district heating and cooling loads. To achieve this purpose, up to 180 simulations were used to generate an ELM Predictive model. 2. Methodology 2.1. Sample building A residential building plan is used in EnergyPlus simulations (Fig. 1). This plan is an example of a typical single family house located in Istanbul, Turkey, built in a lightweight wood frame structure. Different building envelope scenarios were applied to this home plan. The architecture plans of ground floor and first floor are shown in Fig. 1. Also Table 1 provides some basic information about the same building. 2.2. Materials Fig. 2 shows the detailed section of wall construction used in the sample building. The wall, floor and roof materials were chosen in accord to prevalent light woodframe construction. The main structural members used in the walls of these systems include vertical and horizontal timber members. The vertical members (studs), are generally made of 50 100 mm lumbers placed in a standard spacing of 610 mm. The main horizontal members, called plates hold the studs. Engineered particleboard (Oriented strand board, OSB) acts as sheathing material. Glasswool is used as insulation, and two layers of gypsum board are the remaining wall components. Finally, cement-bonded particle board is applied as the exterior finishing of this building. 2.3. Modelling in EnergyPlus In order to analyze the energy performance of the sample building, it was modelled in EnergyPlus software, as explained. EnergyPlus is a robust building energy simulation software. Thanks to the user-friendly environment of this software, the user can easily impliment the geometry and material properties as well as thermal loads and HVAC system characteristics. In a comparison made by Neto and Fiorelli (2008) between EnergyPlus simulation methods and artificial neural network, using a reference building, both models were found to be suitable to estimate energy consumption. The results also show that the forecasts of EnergyPlus present an error range of 13% for 80% of the tested database [42]. As the building is located in Istanbul, Turkey, the regional weather data were imported to the software and used in the simulations [42] Since EnergyPlus analysis aims to find the role of wall material parameters on energy use, the variables of these simulations are restricted to wall materials and their details. Other factors such as building occupancy, equipment, HVAC devices, were left constant for all simulations. Wall components such as window
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Fig. 1. (a) Ground floor plan, (b) First floor plan.
Table 1 Description of sample building. Building type Floor area (m2) Location Seismic zone according to “DBYBHY2007” [41]
Residential building First story: 81.7 Second Story: 48.38 Istanbul, Turkey Zone1
locations, their direction and orientations were adjusted on Sketchup 3D drawings using EnergyPlus Plugins. Two different “zones” were defined in the drawings for two separate stories to obtain more accurate results. This information was automatically transferred into EnergyPlus by opening the saved document in IDM format. The properties of windows (glazing and frame) and other wall components were carefully defined in EnergyPlus software as these properties affect the overall thermal behaviour of walls. Furthermore some properties of the roof and ground elements such as ground temperature and solar absorbance of the roof coverings were defined in EnergyPlus. Table 2 summarizes the most important design factors used in simulation. 2.4. Input and output variables In this article 5 different wall details with various layer thicknesses were considered in order to investigate the effects of wall material thicknesses and thermal properties on the whole building energy performance. Since the structure of the building contains standardized frames (certain standardized materials are used in all
Table 2 Design factors used in EnergyPlus simulation. Design category Building Location
Window glazing Window frame
Lighting Electric equipment HVAC template Fig. 2. Detailed section of walls for the sample buildings constructed with Wood light frame system.
Value Particulars Latitude (degree) Longitude (degree) Time zone (h) Elevation (m) Site ground temperature (ºC) U-factor (W/m2K) Solar heat gain Coefficient Frame conductance (W/m2K) Frame solar absorptance Frame thermal hemispherical emissivity Watts per zone area Fraction radiant Watts per zone floor area Fraction radiant Type Constant heating setpoint (ºC) Constant cooling setpoint (ºC)
Istanbul 40.97 28.82 2 37 18 1.6 0.44 4.5 0.7 0.7 12 0.32 10 0.3 Thermostat 21 26
S. Naji et al. / Energy 97 (2016) 506e516 Table 3 Properties of wall components. Wall component
Table 5 Input parameters for energy consumption of building. Density Thermal conductivity Specific heat r(kg/m3) K (W/m-K) Cp (J/kg-K)
Gypsum board OSB Acoustic gypsum board OSB Cement-bonded particle board
509
1300 640 1300 640 400
0.21 0.13 0.12 0.13 0.23
840 1880 840 1880 1470
buildings constructed with this method) simulations and the estimation process are much simpler to carry out and the results are more reliable compared to conventional construction systems. After defining 5 groups, insulation materials with different R-values and different thicknesses were assigned to wall details. Afterwards an EnergyPlus simulation was carried out for each material series and energy consumption value obtained from the simulation. As mentioned formerly, two layers of Gypsum board, two layers of OSB (oriented strand boards), a layer of cement bonded particle board and a layer of insulation material are the wall materials in all 5 groups. It is important to notice that the groups are introduced by the purpose of classification and organization of input data. However the thicknesses of each layer are different for the various groups, which helped us to investigate the relationships among layer thickness, insulation thickness and building energy performance in different scenarios. Table 3 shows the properties of wall layer materials while Table 4 shows the thicknesses of wall layers used in groups. In all groups there are two kinds of input variables, namely insulation thickness and insulation K-value. Insulation materials with thermal conductivity values of 0.03 W/m-K, 0.04 W/ m-K, 0.05 W/m-K, 0.08 W/m-K are considered in each group. Also insulation is used in different thicknesses as: 4 cm, 6 cm, 8 cm, 10 cm, 12 cm, 14 cm, 16 cm, 18 cm, and 20 cm. By using this method, a total of 180 data series were provided and the same number of simulations were carried out in EnergyPlus software. Tables 5 and 6 illustrate input and output variables in terms of both the defined and the obtained values. 2.5. Extreme learning machine ELM (extreme learning machine) is a tool of learning algorithm for SLFN (single layer feed-forward neural network) architecture [43,44]. Randomly choosing the input weights, ELM determines the output weights of SLFN analytically. ELM algorithm has more favourable general capability and faster learning speed. This algorithm requires less time for running compared to conventional algorithms since it minimises manual interventions by determining all the network parameters analytically. Ease of use, compatibility with many nonlinear activation and kernel functions, faster learning speed and superior performance are among advantages of this efficient algorithm. In general, ELM is a robust algorithm with faster learning speed and better performance compared to traditional algorithms like BP. ELM tends to get the least training errors and norm of weights.
Name
Parameters description
Parameters values
input 1 input 2
Insulation K value (W/m-K) Insulation Thickness (cm)
0.03, 0.04, 0.05, 0.08 4,6,8,10,12,14,16,18,20
2.5.1. Single hidden layer feed-forward neural network SLFN function, with L hidden nodes can be represented as mathematical description of SLFN, incorporating both additive and RBF hidden nodes in a unified way as follows [47]:
fL ðxÞ ¼
L X
bi Gðai ; bi ; xÞ;
x2Rn ;
ai 2Rn
(1)
i¼1
where ai and bi represent the learning parameters of hidden nodes. bi is the weight connecting the ith hidden node to the output node. Gðai ; bi ; xÞ is the output value of the ith hidden node with respect to the input x. The additive hidden node with the activation function of gðxÞ : R/R (e.g., sigmoid and threshold), Gðai ; bi ; xÞ is [44]:
Gðai ; bi ; xÞ ¼ gðai :x þ bi Þ;
bi 2R
(2)
where ai denotes the weight vector connecting the input layer to the ith hidden node. bi is the bias of the ith hidden node. Also ai. x is the inner product of vector ai and x in Rn. Gðai ; bi ; xÞ can be found for RBF hidden node with activation function gðxÞ : R/R (e.g., Gaussian), Gðai ; bi ; xÞ as [44]:
Gðai ; bi ; xÞ ¼ gðbi kx ai kÞ;
bi 2Rþ
(3)
where ai and bi represent the center and impact factor of ith RBF node. Rþ represents the set of all positive real values. The RBF network is a particular case of SLFN with RBF nodes in its hidden layer. For N arbitrary distinct samples ðxi ; ti Þ2Rn Rm , xi is n 1 input vector and ti is m 1 target vector. If an SLFN with L hidden nodes can approximate these N samples with zero error it implies the existence of bi, ai and bi so that [44]: L X fL xj ¼ bi G ai; ; bi ; xj ;
j ¼ 1; …; N
(4)
i¼1
Eq. (4) can be written compactly as:
Hb ¼ T
(5)
Table 6 Heating and cooling of building; as output parameter. Name
Parameters description
Parameters values
Output
Total heating and cooling energy (kWh)
Various depended on input data
Table 4 Thicknesses of wall layers in 5 defined groups (m). Group
Gypsum board
OSB
Acoustic gypsum board
OSB
Cement-bonded particle board
1 2 3 4 5
0.015 0.02 0.010 0.025 0.01
0.025 0.020 0.030 0.015 0.035
0.02 0.025 0.015 0.030 0.019
0.025 0.020 0.030 0.015 0.01
0.015 0.015 0.015 0.015 0.015
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S. Naji et al. / Energy 97 (2016) 506e516
where
2
Gða1 ; b1 ; x1 Þ H e a; e b; e x ¼4 Gða1 ; b1 ; xN Þ
… … …
GðaL ; bL ; x1 Þ GðaL ; bL ; xN Þ
3 5
(6) NL
with e a ¼ a1 …; aL ; e b ¼ b1 …; bL ; e x ¼ x1 …; xL
2 T3 3 t1 bT1 b¼4 « 5 and T ¼ 4 « 5 tLT Nm bTL Lm
Zj ¼ f
2
n X
!
wij $Xi
(9)
i¼1
(7)
H is the hidden layer output matrix of SLFN with ith column of H being the ith hidden node's output with respect to inputs x1 ; …xN . 2.5.2. The principle behind ELM ELM is designed as a SLFN with L hidden neurons, capable of learning L distinct samples with zero error. Even if the number of hidden neurons (L)< the number of distinct samples (N), ELM can allocate random parameters to the hidden nodes and calculate the output weights by pseudo inverse of H giving only a small error ε > 0. Therefore, it is not necessary to tune the hidden node parameters of ELM ai and bi, since they can easily be allocated with random values. The following theorems state the same. Theorem 1: (Liang et al. [47]) Let an SLFN with L additive or RBF hidden nodes and an activation function g(x) which is infinitely differentiable in any interval of R be given. Then for arbitrary L distinct input vectors; fxi jxi 2Rn ; i ¼ 1; …Lg and fðai ; bi ÞgLi¼1 , randomly produced by any continuous probability distribution, respectively, the hidden layer output matrix is invertible with probability one, the hidden layer output matrix H of the SLFN is invertible and kHb Tk ¼ 0. Theorem 2: (Liang et al. [47]) Given any small positive value ε > 0 and activation function gðxÞ : R/R which is infinitely differentiable in any interval, there exists L N such that for N arbitrary distinct input vectors fxi jxi 2Rn ; i ¼ 1; …Lg for any fðai ; bi ÞgLi¼1 for any randomly produced based upon any continuous probability distribution kHNL bLm TNm k < ε with probability one. Since the hidden node parameters of ELM should not be tuned throughout training and they are easily assigned with random values, Eq. (5) becomes a linear system and the output weights can be estimated as [44]:
b ¼ Hþ T
Here it is assumed that the weight and the threshold between the input layer and the hidden layer are wij and yj respectively, and the weight and the threshold between the hidden layer and output layer are wjk and yk respectively. The outputs of each neuron in a hidden layer and output layer are as follows:
(8)
where H þ is the MooreePenrose generalized inverse of the hidden layer output matrix H which can be computed via several approaches consisting orthogonal projection, orthogonalization, iterative, singular value decomposition (SVD), etc. The orthogonal projection method can be utilized only when HT T is non-singular and H þ ¼ ðH T TÞ1 H T . Owing to the use of searching and iterations, orthogonalization method and iterative method have limitations. Implementations of ELM uses SVD to compute the MooreePenrose generalized inverse of H, because it can be utilized in all situations. ELM is thus a batch learning method. 2.6. Artificial neural networks The multilayer feed forward network with a back propagation learning algorithm is among the most common neural network architectures, which have been widely studied and used in many disciplines. Three main layers included in a neural network are: (1) an input layer; (2) an output layer; and (3) an intermediate or hidden layer. The input vectors are, D2Rn and D ¼ ðX1 ; X2 ; …; Xn ÞT ; the outputs of q neurons in the hidden layer are Z ¼ ðZ1 ; Z2 ; …; Zn ÞT ; and the outputs of the output layer are Y2Rm , Y ¼ ðY1 ; Y2 ; …; Yn ÞT .
0 Yk ¼ f @
q X
1 wkj $Zj A
(10)
j¼1
where f is a transfer function, which is the rule for mapping the neuron's summed input to its output, and using a suitable choice as the instrument for introducing a non-linearity into the network design. One of the most commonly used functions is the sigmoid function, which is monotonically increasing and ranges from zero to one. Details on ANNs can be found in Refs. [49,50]. 2.7. Genetic programming GP is known as an evolutionary algorithm based on Darwinian theories of natural selection and survival used to approximate the equation, in symbolic form. GP has the best ability of describing the connection between input and output variables. This algorithm presumes an initial population of accidently generated programs (equations), derived from the random combination of input variables, numbers and functions, including arithmetic operators ðþ; ; ; ÷Þ mathematical functions (sin, cos, exp, log), logical/comparison functions, etc. These functions have to be selected properly according to perceptions of the process. Subsequently, this population of potential solution go through an evolutionary process after which the ‘fitness’ (a measure of how well they solve the problem) of the evolved programs is evaluated. The individual programs that best conform to the data are then chosen from the initial population. Afterwards, selected programs interchange parts of the information among each other to produce better programs through ‘crossover’ and ‘mutation’, which mimics the natural world's reproduction process. The process of exchanging the parts of the selected programs among each other is called crossover, and the act of randomly changing programs to create new programs is called mutation. The programs which conform to the data less than others are discarded. This evolution process is repeated over successive generations and driven towards achieving symbolic expressions describing the data, which can be scientifically interpreted to derive knowledge about the process. Details on GP can be obtained from Refs. [52e54]. 3. Results and discussion 3.1. Energy consumption Table 7 shows the results of EnergyPlus software for all 180 simulations. The results obtained from EnergyPlus software are annual energy use for total district heating and cooling for all five groups. Annual energy use for interior lighting and equipment are the same for all buildings as the default inputs for lighting and equipment are constant in all models. These values are eliminated in this evaluation. In Table 7 it can be seen that the total energy needed for heating and cooling of the buildings decreases by the reduction of the K-value. In addition, the output data from the simulations indicate that the variations in building energy consumption are significantly affected by the properties of the insulation materials rather than the changes in different groups, i.e., different thickness configurations of wall materials. By increasing the thickness of the
S. Naji et al. / Energy 97 (2016) 506e516
511
Table 7 Output data values in five groups with insulation thermal conductivity classified as 5 (a) k ¼ 0.03 W/m-K, (b) k ¼ 0.04 W/m-K, (c) k ¼ 0.05 W/m-K, (d) k ¼ 0.08 W/m-K (kWh). Thickness of insulation (m) 0.04 (a) K ¼ 0.03 W/m-K Group1 8312.79 Group2 8362.87 Group3 8270.78 Group4 8350.18 Group5 8420.6 (b) K ¼ 0.04 W/m-K Group1 9017.31 Group2 9087.24 Group3 8957.07 Group4 9062.41 Group5 9167.76 (c) K ¼ 0.05 w/m-K Group1 9593.51 Group2 9681.74 Group3 9517.86 Group4 9650.4 Group5 9782.94 (d) K ¼ 0.08 W/m-K Group1 10,804.35 Group2 10,939.86 Group3 10,688.79 Group4 10,891.93 Group5 11,095.06
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
7457.24 7486.46 7432.76 7481.50 7520.24
6960.86 6982.04 6942.21 6976.93 7005.65
6651.46 6667.53 6637.87 6661.93 6686
6447.59 6459.35 6437.56 6456.33 6473.31
6310.84 6319.85 6303.26 6316.52 6330.56
6217.75 6224.91 6211.12 6222.72 6233.72
6149.9 6156.38 6144.23 6154.89 6164.23
6100.22 6107.24 6094.24 6105.64 6114.98
8044.68 8087.26 8008.81 8072.8 8136.92
7456.3 7485.37 7431.9 7475.4 7519
7062.05 7084.98 7042.35 7076.62 7110.9
6788.14 6806.15 6772.22 6799.71 6827.2
6591.7 6606.14 6579.11 6601.12 6623.13
6446.3 6457.71 6436.25 6453.87 6471.5
6338.78 6348.08 6330.66 6344.97 6359.28
6259.02 6266.96 6251.54 6263.77 6276.01
8561.7 8618.04 8513.33 8598.28 8683.23
7903.69 7942.39 7871.24 7929.71 7988.19
7455.3 7484.26 7431.09 7474.42 7517.76
7129.11 7153.83 7107.46 7144.27 7181.08
6885.05 6904.85 6868.03 6897.77 6927.52
6700.06 6716.65 6686.25 6711.43 6736.61
6557.38 6571.33 6545.87 6567.00 6588.14
6444.86 6456.11 6434.99 6452.35 6469.72
9760.5 9853.89 9679.53 9820.46 9961.4
9014.42 9083.94 8954.71 9059.32 9163.94
8461.15 8514.71 8415.81 8496.07 8576.33
8041.33 8083.15 8006.07 8069.28 8132.5
7713.43 7748.21 7684.85 7736.4 7787.95
7452.51 7481.04 7428.28 7471.21 7514.15
7237.74 7263.13 7216.27 7254.15 7292.04
7057.49 7079.74 7038.3 7071.85 7105.41
insulating material the effects of other materials’ properties on building energy performance decreases, i.e., the changes in thickness of other materials happen to become less effective.
3) Coefficient of determination (R2)
"
Pn i¼1
R2 ¼ P n
3.2. Evaluating accuracy of proposed models
i¼1
Predictive performances of proposed models were presented as RMSE (root mean square error), Coefficient of determination (R2) and Pearson coefficient (r). These statistics are defined as follows:
Oi Oi , Pi Pi
#
2
P Oi Oi , ni¼1 Pi Pi
(13)
where Pi and Oi are known as the simulation and forecast values of building's energy consumption, respectively, and n is the total number of test data.
1) RMSE (root-mean-square error)
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðPi Oi Þ ; RMSE ¼ n
3.3. Architecture of soft computing models
(11)
2) Pearson correlation coefficient (r)
n
Pn
!
i¼1 Oi ,Pi
Pn
!
i¼1 Oi ,
Pn
i¼1 Pi
ffi r ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u0 !2 1 0 !2 1 u P Pn Pn u@ Pn t n O2 Oi A,@n n P2 Pi A i¼1
i
i¼1
i¼1
i¼1
i
(12)
The parameters of the ELM, ANN and GP modelling frameworks employed in this study are presented in Table 8. 70% data of each group (22 out of 32) was used for training and 30% (10 out of 32) for testing of the models. In this case all groups are included in the training of the models and in later in testing as well. The average computation time for the ELM modelling was around 330 s using a PC with Intel Core Duo CPU E7600 @3.06 GHz and 2-GB RAM. The average computation time for the ANN with back propagation training algorithm and GP modelling using the same PC with the same performances was 424 and 436 s, respectively. For the ELM modelling, MATLAB software was used.
Table 8 User-defined parameters for the ELM, ANN and GP models. ELM Number of layers Neurons
e e Learning rule e
ANN [55,56] 3 Input: 6 Hidden: 3, 6, 10 Output: 1 e
Number of layers Neurons
e ELM for SLFNs e
GP [57]
Number of iteration
3 Input: 6 Hidden: 3, 6, 10 Output: 1 1000
Population size
Activation function
Sigmoid Function
Head size
5e9
Learning rule e
Back propagation e
Chromosomes Number of genes
20e30 2e3
e Neurons
e e e Output: 1 512
e
e
e
e
Mutation rate
91.46
e
e
e
e
Crossover rate
30.56
e
e
e
e
Inversion rate
108.53
512
S. Naji et al. / Energy 97 (2016) 506e516
3.4. Performance evaluation of the proposed ELM model In this section performance results of the ELM building energy consumption predictive model are reported. Fig. 3(a) presents the accuracy of developed ELM building energy consumption predictive model. Moreover, Fig. 3(b) and (c) present the accuracy of developed GP and ANN building energy consumption predictive models, respectively. It can be seen that most of the points fall along the diagonal line for the ELM prediction model. Consequently, it shows that prediction results are in very good agreement with the simulated values for the ELM method. This observation can be confirmed with very high value for the coefficient of determination.
The number of either overestimated or underestimated values produced is limited, which indicates that the predicted values enjoy high levels of precision. Fig. 4 shows scatter plots separately for ELM prediction of energy consumption in buildings for different wall groups. One can note the similar R2 coefficient for all groups. As mentioned previously, different thickness configurations of wall layers in defined groups has insignificant effect on energy consumption of buildings. Fig. 5 shows scatter plots for ELM prediction of energy consumption in buildings for different thermal conductivity coefficients. According to R2 coefficient, the more and less accurate predictions were observed for K ¼ 0.03 W/m-K and K ¼ 0.08 W/m-K
Fig. 3. Scatter plots of actual and predicted values of energy consumption in buildings, using (a) ELM, (b) GP and (c) ANN method.
S. Naji et al. / Energy 97 (2016) 506e516
respectively. It is concluded that the ELM model has better prediction for lower thermal conductivity. 3.5. Performance comparison of ELM, ANN and GP In order to demonstrate the merits of the proposed ELM approach on a more definite and tangible basis, the prediction accuracy of ELM models was compared to the prediction accuracy of GP and ANN methods, which were used as benchmarks. Conventional error statistical indicators, RMSE, r and R2, were used for comparison. Table 9 summarizes the prediction accuracy results for test data sets since a training error is not a credible indicator for prediction potential of a particular model. The smaller RMSE value represents more accurate predictive model. Furthermore the r and
513
R2 show better correlation with measured and predicted values, as their values reach closer to 1. ELM model outperforms GP and ANN models according to the results of Table 9. The ELM model provides significantly better results than the benchmark models. On the basis of RMSE analysis with comparison with ANN and GP, it is concluded that the proposed ELM outperformed the results obtained with benchmark models. The ELM RMSE in training phase was 40.85604 while ELM RMSE in testing phase was 74.02189. On the other hand ANN RMSEs were 301.347 and 331.5657 in training and testing phase respectively. GP RMSEs were 287.4788 and 314.3471 in training and testing phase respectively. Very high difference can be noticed between RMSEs of the ELM and the benchmark models. In order to prove the predictive accuracy of the ELM approach on a more
Fig. 4. Scatter plots of actual and predicted values of energy consumption in buildings for (a) group 1, (b) group 2, (c) group 3, (d) group 4 and (e) group 5.
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S. Naji et al. / Energy 97 (2016) 506e516
Fig. 5. Scatter plots of actual and predicted values of energy consumption in buildings for (a) K ¼ 0.03 W/m-K, (b) K ¼ 0.04 W/m-K, (c) K ¼ 0.05 W/m-K and (d) K ¼ 0.08 W/m-K.
definitive basis other parameters like r and R2 are investigated as well. These two parameters have similar characteristics. Table 9 verifies very high correlation of the measured and predicted data by the ELM approach, in which r and R2 coefficients are very close to 1, which means that the number of overestimated points are very limited. Finally, the proposed ELM model was analyzed for all groups as well as thermal conductivities separately. Tables 10 and 11 show the statistical indicators for the ELM models. Also the best prediction was observed for K ¼ 0.03 W/m-K according to RMSE. The worst prediction accuracy was observed for K ¼ 0.08 W/m-K.
Table 10 Comparative performance statistics of the ELM energy consumption predictive model of building for 5 groups.
Group Group Group Group Group
1 2 3 4 5
RMSE
R2
r
26.46982 28.16473 60.10535 58.18796 74.62387
0.9998 0.9998 0.9998 0.9979 0.9998
0.999905 0.999905 0.999888 0.998972 0.999887
simulation procedure. It seeks a solution to achieve a method that can forecast the energy consumption of buildings by entering input data as material properties and thicknesses. The outcome of this research indicate that the proposed model can efficiently predict the energy consumption of buildings regarding the main building envelope parameters.
4. Conclusion This study carried out a systematic methodology to create an ELM building energy consumption predictive model. This method is applicable in residential projects to save time in an energy
Table 9 Comparative performance statistics of the ELM, ANN and GP energy consumption predictive model of building for (a) training and (b) testing data. (a) Training ANN
ELM RMSE 40.85604 (b)
R2 0.999
r 0.999503
GP R2 0.9433
r 0.971219
Testing ANN
ELM RMSE 74.02189
RMSE 301.247
2
R 0.997
r 0.998518
RMSE 331.5657
RMSE 287.4788
R2 0.95
r 0.974703
R2 0.9541
r 0.976781
GP 2
R 0.9432
r 0.971177
RMSE 314.3471
S. Naji et al. / Energy 97 (2016) 506e516 Table 11 Comparative performance statistics of the ELM energy consumption predictive model of building for different thermal conductivity.
K K K K
¼ ¼ ¼ ¼
0.03 0.04 0.05 0.08
W/m-K W/m-K W/m-K W/m-K
RMSE
R2
r
31.07514 40.26692 50.42344 78.22584
0.9982 0.998 0.9976 0.9958
0.999102 0.999 0.998777 0.997898
It can be concluded from the simulation outputs that the variations in building energy consumption are affected mostly by the insulation materials, more so than by changes in configurations of wall components. The parameters associated with insulation materials play a significant role in determining the energy consumption of a building. By increasing the thickness of the insulating material, the variations in the configurations of other wall materials are less effective by comparison. A comparison of ELM method with GP and ANN was performed in order to assess the prediction accuracy. The accuracy, measured in terms of RMSE, r and R2, indicated that ELM predictions are superior to GP and ANN. As previously stated, results revealed the robustness of the ELM method. The developed ELM model has many appealing and remarkable features which make it distinguishable from traditional popular gradient-based learning algorithms for feedforward neural networks. ELMs are much faster in learning speed compared to the traditional feedforward network-learning algorithms such as BP algorithm. Furthermore, unlike the traditional learning algorithms, ELM algorithm is able to achieve the smallest training error and also norm the weights. This study highlights the importance of computer science applications for the building industry. The estimation of the total building energy usage can help the architects and engineers to conceive more clearly the building energy efficiency level. This can be carried out early in the design, and during the construction of a building resulting in more realistic and accurate energy efficient building design. Acknowledgment This research work is funded by High Impact Research Grant (HIRG) no. UM.C/625/HIR/VC/206 (Synthesis of Energy Redeemable Material from Local Wastes for Building). References [1] Energy Consumption by Sector, U.S. Energy Information Administration (EIA), Independent Statistics & Analysis, retrieved: 27.01.2014, Address: http:// www.eia.gov/totalenergy/data/monthly/pdf/sec2_3.pdf. [2] Bokalders V, Block M. The whole building handbook-how to design healthy, efficient and sustainable buildings. London: Earthscan; 2010. [3] Guertin M. Green applications for residential construction. Residential Construction Academy; 2011. [4] Center for Sustainable Systems. Residential buildings factsheet. University of Michigan; 2009. Pub. No. CSS01e08. [5] Kumar Ashok, Suman BM. Experimental evaluation of insulation materials for walls and roofs and their impact on indoor thermal comfort under composite climate. Build Environ 2013;59:635e43. [6] Spence WP. Residential framing: a homebuilder's construction guide. 1st ed. Canada: Sterling Publishing; 1993. [7] RSMEANS. Residential & light commercial construction standards. 3rd ed. 2008. The All-In One Reference Compiled From Major Building Codes, Recognized Trade Customs, Industry Standards, Updated Reed Construction Data, USA. [8] Smith P. Architecture in a climate of change. 2nd ed. Amsterdam: Elsevier; 2005. [9] Makelainen P, Hassinen P. Light-weight steel and aluminum structures, fourth international conference on steel and aluminium structures. 1st ed. Finland: Elsevier; 1999.
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