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Building's electricity consumption prediction using optimized artificial neural networks and principal component analysis
Accepted Manuscript Title: Building’s electricity consumption prediction using optimized artificial neural networks and principal component analysis Author: Kangji Li Chenglei Hu Guohai Liu Wenping Xue PII: DOI: Reference:
S0378-7788(15)30243-7 http://dx.doi.org/doi:10.1016/j.enbuild.2015.09.002 ENB 6122
To appear in:
ENB
Received date: Revised date: Accepted date:
8-5-2015 1-9-2015 1-9-2015
Please cite this article as: Kangji Li, Chenglei Hu, Guohai Liu, Wenping Xue, Building’s electricity consumption prediction using optimized artificial neural networks and principal component analysis, Energy & Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.09.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Building’s electricity consumption prediction using optimized artificial neural networks and principal component analysis
School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, PR China
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Kangji Lia,∗, Chenglei Hua , Guohai Liua , Wenping Xuea
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Abstract
As a popular data driven method, Artificial Neural Networks (ANNs) have
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been widely applied in building energy prediction field for decades. To improve the short term prediction accuracy, this paper presents a kind of opti-
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mized ANN model for hourly prediction of building electricity consumption.
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An improved Particle Swarm Optimization algorithm (iPSO) is applied to adjust ANN structure’s weights and threshold values. The principal compo-
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nent analysis (PCA) is used to select the significant modeling inputs and simplify the model structure. The investigation utilizes two different historical data sets in hourly interval, which are collected from the Energy Prediction Shootout contest I and a campus building located in East China. For performance comparison, another two prediction models, ANN model and hybrid Genetic Algorithm - ANN (GA-ANN) model are also constructed in this study. The comparison results reveal that both iPSO-ANN and GA-ANN ∗
Corresponding author. Email addresses: [email protected] (Kangji Li), [email protected] (Chenglei
Hu)
Preprint submitted to Energy and buildings
September 1, 2015
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models have better accuracy than that of ANN ones. From the perspective
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of time consuming, the iPSO-ANN model has shorter modeling time than GA-ANN method. The proposed prediction model can be thought as an
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alternative technique for online prediction tasks of building electricity consumption.
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Keywords: Building Energy Prediction, Particle Swarm Optimization, Genetic Algorithm, Artificial Neural Networks, Principal Component
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Analysis 1. Introduction
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Nowadays, with the increasing population and gross domestic product (GDP), energy consumption is much higher, leading to a large amount of en-
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vironmental problems [1]. As respect of the energy consumption and carbon
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emissions, buildings energy consumption accounts for an important proportion worldwide [2, 3]. In European Union countries, building energy con-
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sumption is close to 40% of the total energy consumption [4]. In China, it accounts for 28% in 2011, and the statistical data is expected to reach 35% by 2020 [5]. To realize a suitable energy demand management in an efficient way, the establishment of a reliable and accurate prediction for energy consumption is of crucial importance, which makes the construction of prediction models for building energy consumption become an essential issue [6, 7].
It is difficult to predict the building energy consumption precisely, since there are many factors influencing the energy usage, such as weather conditions, building structure and characters, geographic location, occupancy,
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operation of appliances, etc. [8, 9, 10]. During the past two decades, there
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were various forecasting techniques that had been applied to the building energy consumption, such as engineering methods [11], statistical methods
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[12, 13], Artificial Neural Networks (ANNs) [14, 15], Support Vector Ma-
chines (SVMs) [16, 17], fuzzy logic [18, 19], grey models techniques [20, 21],
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etc.. Among the existing energy prediction methods, the most widely applied approaches are ANNs and their developments. A variety of studies
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discussed the developments of ANN based energy prediction methods ,where input variables selection, network structure construction and training algorithm improvement are three vital issues [22, 23, 24, 25, 26]. For selecting
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input variables, Karatasou [24] utilized a systematic approach based on least squares estimation (LSE) and statistical tests. Principal component analy-
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sis (PCA) was also used to analyze the pre-input variables [25]. Mena [26]
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developed a short-term predictive ANN model for the electricity demand of a bio-climatic building. The study also revealed that the outdoor tempera-
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ture and the solar radiation exert a significant influence on building energy consumption. More reviews and analysis on ANN based energy consumption prediction may be referenced at [9, 27, 28]. In the last ten years, with the development of intelligent optimization
technologies, various kinds of intelligent optimization algorithms have been applied to the field of building energy prediction. Fan [29] utilized an adaptive two-stage hybrid network with self-organized map (SOM) and SVM for load forecasting, which was robust with different data types and could deal well with the non-stationary of load series. Khashei [30] proposed a ANN and ARIMA based hybrid model, which showed good accuracy for energy
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consumption prediction. He and Lu [31] developed a chaotic particle swarm
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optimization algorithm (CPSO) modified ANN prediction model to forecast time series, and the results proved that the method had better nonlinear
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fitting ability and higher prediction accuracy than ANN itself. A hybrid Genetic Algorithm - Adaptive Network-based Fuzzy Inference System (GA-
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ANFIS) method was studied by Li in 2011 [32]. The best prediction accuracy was improved by 19.5% compared with a regular ANN method.
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The contributions of this study are (a) development of an optimized ANN model for building energy forecasting based on an improved particle swarm optimization (iPSO) algorithm, (b) investigating the forecasting performance
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of the proposed model with two sets of historical data, and (c) comparison with other two prediction models on forecasting accuracy and modeling time.
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For the model construction, the iPSO algorithm is used to optimize ANN’s
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weights and threshold values, which helps to improve the ANN model’s fitting ability. The principal component analysis (PCA) is applied to reduce
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the input dimension and simplify the model structure in this study. The proposed prediction model can be used with energy management system to help indicate above-normal energy use and diagnose the possible cause of the malfunction if sufficient historical data has been previously gathered. The rest of the paper is organized as follows. Next, the description of
the proposed forecasting model is given. Section 3 describes two data sets collected from energy prediction contest I and a campus building. The data pre-processing is also described in this section. In section 4, prediction tests and comparisons are provided, and the performance of the proposed model is fully discussed. Section 5 gives the conclusion of the paper.
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2. Model Description
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2.1. Artificial Neural Network
ANNs, inspired by the thinking mechanism of human brain, are parallel
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nonlinear adaptive systems composed of a large number of simple processing
layer to output layer takes the following form: Y = f (b0 +
k X
h(ψj +
i=1
pi wij )bj )
(1)
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j=1
m X
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units [33]. For a three-layer network, the basic mapping function from input
where the network outputs are the predicted values Y , denoted by nonlinear
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transfer function f (·) of the inputs pi , b0 are the output bias, bj are the weight values from hidden layer to output layer, ψj are the hidden layer biases, wij are the weights from input layer to hidden layer and h(·) is hidden layer
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activation function. For the initialized network, there are several different
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training algorithms for model approximation. All of them use the gradient
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performance function to determine how to adjust the weights to minimize error. In this study, a three-layer feed forward network with back-propagation training algorithm is constructed and the topology structure is illustrated in Fig. 1.
Figure 1 is about here
2.2. Improved Particle Swarm Optimization Algorithm Particle swarm optimization is a bio-inspired global optimization technique that was proposed by James Kennedy and Russell Eberhart in 1995 [34]. PSO performs a population-based search, using particles to represent potential solutions within the search space. Each particle is characterized by 5
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its position, velocity, and a record of its previous performance [35]. At each
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flight cycle (iteration), each particle’s velocity and position is formulated as: vj (n + 1) = ωvj (n) + c1r1(pj (n) − xj (n)) + c2r2(pg (n) − xj (n))
(2)
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x (n + 1) = v (n + 1) + x (n) j j j
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where vj (n) is the speed of the jth particle in the nth generation, r1 and r2 are random numbers obeying uniform distribution in the range of [0,1], c1 and c2 are constants named acceleration coefficients, xj (n) is the position
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of the jth particle in the nth generation, pj (n) is the best previous position yielding the best fitness value for the jth particle, pg (n) is the best position
global and local search abilities.
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discovered by the whole particles, ω is the inertia weight used to balance the
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PSO method has several advantages for exploring the hyperspace global optimum, especially the fast convergence. In order to improve its capability
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of global search and avoid local minima, the genetic operations including
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crossover and mutation are further introduced to the update method of PSO algorithm in this study [36, 37]. The improved PSO algorithm is specified as follows:
Firstly, all initialized particles are evolved by PSO, and the individual
best and group best are recorded. According to the crossover rate and fitness value, T -optimized particles are selected as parental particles for the implementation of crossover operations. Then the fitness values of all new particles are calculate. When parental particle’s fitness value is worse than that of corresponding offspring, these particles’ location and velocity values are updated with the better ones. Thirdly, in order to avoid local minima, mutation operation is executed according to the mutation rate. Finally, the 6
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velocity and position values of all particles are updated after genetic op-
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erations accomplished and the group best is also updated. The iterations continue until the stopping criteria is satisfied. The crossover and muta-
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tion equations are the essential part of the algorithm, which are described as follows:
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crossover equations:
child1 (Xi ) = pi ∗ parent1 (Xi ) + (1 − pi ) ∗ parent2 (Xi )
(3)
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child (X ) = p ∗ parent (X ) + (1 − p ) ∗ parent (X ) 2 i i 2 i i 1 i parent1 (Vi )+parent2 (Vi ) |parent1 (Vi )+parent2 (Vi )|
∗ |parent1 (Vi )|
child (V ) = 2 i
parent1 (Vi )+parent2 (Vi ) |parent1 (Vi )+parent2 (Vi )|
∗ |parent2 (Vi )|
and mutation equation:
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child1 (Vi ) =
(5)
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Xi 0 = Xi + rand ∗ N (0, 1)
(4)
where Pi is a uniformly distributed random value between 0 and 1, parentj (Xi )
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and parentj (Vi ) represent the position and velocity of parental particle, childj (Xi ) and childj (Vi ) stand for the position and velocity of offspring, respectively (j = 1, 2).
Figure 2 is about here
2.3. Hybrid iPSO-ANN model As we mentioned above, gradient based training algorithms for neural networks have a strong ability in the aspect of local optima search, but their capability of finding the global optimal solution is quite weak. In contrast, the iPSO algorithm is convinced of having the ability for global optima searching 7
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with fast convergence. In order to combine the advantages of this two meth-
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ods, a hybrid iPSO-ANN model is proposed for building energy prediction in this study. In the proposed model, a three-layer feed forward network with
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back-propagation training algorithm is constructed for model initialization.
Then all of the weight and threshold values of the network are regarded as
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particles’ position, and the iPSO algorithm is applied to optimize the network’s parameters. The flow diagram of the hybrid iPSO-ANN method is
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illustrated in Fig. 3 and the detailed procedure can be conducted as follows: Step 1: load input data set and select the training and testing samples; Step 2: initialize the parameters of ANN including weight and threshold
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values corresponding to the initialized particle of iPSO; Step 3: calculate the fitness function and find the optimal solution;
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iPSO;
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Step 4: execute crossover and mutation operation, update group best of
Step 5: assign the weight and threshold values of ANN with the group
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best of iPSO, if maximum iteration of iPSO is reached, go to step 6, else generate new particles and return to step 3; Step 6: test the optimized ANN prediction model until the stopping
criteria are satisfied.
Figure 3 is about here
2.4. Principal Component Analysis PCA, a statistical correlation analysis technique, is commonly used to reveal the linear relationship between the input variables and reduce dimension of input data [38]. Supposed that the data set to be analyzed is expressed 8
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as a matrix X = [x1 , x2 , ..., xn ], xm = [x1 , x2 , ..., xf ]Tm , λ1 ≥ λ2 ≥ ... ≥ λf ≥ 0
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are the eigenvalues of the covariance matrix of X, and Li = [γ1i , γ2i , ..., γf i ]T are the unit orthogonal eigenvectors of the covariance matrix correspond-
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ing to the eigenvalues. Then the ith principal component Yi of data set X can be donated as Yi = XLi according to the cumulative contribution t P
λi /
i=1
n P
λi . The results of PCA consist of implicit variables
k=1
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rate G(t) =
that can’t be directly observed from observable explicit variable. PCA can
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be employed to eliminate redundant information and identify the significant modeling inputs.
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3. Data Description
Two different data sets are used to evaluate the performances of prediction
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models , which are called data set A and data set B respectively. Both data
described as follows.
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sets represent real energy data of buildings and their general characters are
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The data set A derives from the Great Building Energy Predictor Shootout
I, organized by ASHRAE in 1990s. The data set includes the following variables, namely, outdoor dry bulb temperature, solar radiation, humidity ratio and wind speed [39, 40]. For the input variables, data were available at hourly intervals for the period from September 1989 to February 1990, whereas energy consumption data were available only for September to December 1989 [24].
The data set B comes from a library building located in Hangzhou, East China. The library has ten floors on the ground with gross floor area of 25,542 m2 (in Fig. 4). There are about 1100 seats in the library and most of 9
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the building occupancy occurs at 8:30 to 22:00. The data set merely consists
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of daily temperature and occupancy. The daily temperature is acquired from the local meteorological station. The opening schedule of each reading room
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Figure 4 is about here
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is roughly considered as the library’s hourly occupancy variable.
The energy consumption data of set A and set B are both hourly elec-
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tricity consumption value of the whole building including energy items of heating, cooling, ventilation, lighting, plug load, etc..
[-1,1] by the following formula:
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All inputs and outputs in the two data sets are normalized to the interval
x − xmin −1 xmax − xmin
(6)
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y =2×
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where x is input data, xmin and xmax are the minimum and maximum value
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within the entire data of x.
4. Modeling and Results 4.1. Data Set A
4.1.1. Data Pre-processing
In order to reduce the dimension of the data set A, all original envi-
ronmental variables are analyzed by PCA in advance. These environmental variables include outdoor dry bulb temperature, solar radiation, humidity ratio and wind speed. The analysis result is shown in Table 1. The contribution rate and cumulative contribution rate of four principal components are given in Fig. 5. It is indicated that the first two principal components 10
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explained 82.389% of the total variance. By refining the principal compo-
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nents, we use the first two variables, named P C1 and P C2, to represent the
Table 1 is about here
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Figure 5 is about here
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original environmental variables mentioned above.
Further, considering that the occupancy has a strong effect on the energy
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use, days are classified as weekday (1) and weekend/holiday (0). The hour of the day is coded by its sine and cosine value as below. 2πh(t) 2πh(t) , ch = cos 24 24
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sh = sin 4.1.2. iPSO-ANN Results
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The hybrid iPSO-ANN model is applied to predict the whole building
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electricity power consumption (WBE) with the data set A. The network consists of a single hidden layer of tansig neurons. The input set include
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principal components of environmental variables P C1 and P C2, occupancy flag oc, sine of the hour of the day sh, cosine of the hour of the day ch, and
short past values of energy consumption y(t − 1) and y(t − 2). The output is hourly WBE y(t). The neuron number of hidden layer is selected in the light of Eq. 7 [33].
k=
√
m+n+l
(7)
where m is output number, n is input number, k is concealed number, and l is an integer between 1 and 10. The data set A contains 4208 group of energy consumption data, where data [1,2926] are available for training, and [2927,4208] for testing which are 11
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not used during the training phase. Two different indicators, the coefficient
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of variation of the root mean square deviation (CV) and mean absolute percentage error (MAPE), are utilized to assess the prediction accuracy in this
s
(ypred,i − ydata,i )2 /N
i=1
y data
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CV =
N P
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study. They are described as follows:
(9)
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N X 1 |ypred,i − ydata,i | M AP E = × ( ) N i=1 ydata,i
(8)
where ypred,i is predicted WBE value, ydata,i is real WBE value, y data is the
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average value of real WBE, N is the number of testing data set. In the hybrid model, the fitness function for iPSO based parameter opti-
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mization is defined as follows:
K X
(|ypred,i − ydata,i |)
(10)
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f itness =
i=1
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where K is the number of training data set. The main parameters used in the prediction model are given in Table 2. Table 2 is about here
The hybrid iPSO-ANN prediction is tested for a dozen times. The best
five results are recorded in Table 3. The average and best results are also recorded.
Table 3 is about here
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4.1.3. Results of Other Two Models
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In order to investigate the prediction performances of the hybrid iPSOANN model, other two different models are also constructed for performance
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comparisons.
ANN models have been widely used in building energy prediction field
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for decades. In this section, a regular three-layer BP neural network is constructed. The same data sets are used to train the ANN model. The best
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five results of total twelve predictions are recorded in Table 4. The average and best results are also given.
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Table 4 is about here
Because of the global search ability and good scalability, GA has a broad
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application in various optimization issues. For performance comparison pur-
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pose, GA is combined with ANN model for the same prediction task. Like iPSO algorithm, GA is also used to train the weight and threshold values
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of the network. The main parameters used in GA-ANN model are given in Table 5. The performance of the hybrid GA-ANN model is investigated using the same data set and the same precision evaluation indicators. The GA-ANN results are shown in Table 6. Table 5 is about here Table 6 is about here
4.2. Performance Comparison It is seen from the above investigations that the two hybrid ANN models generally achieve better accuracies compared with regular ANN method. 13
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Concretely, iPSO-ANN model decrease CV by 21.8% (23.2% for MAPE) in
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the case of data set A. GA-ANN model decrease CV by 13.2% (12.3% for MAPE). Graphical comparisons between the predictions and the real loads
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are given in Fig. 6. When intelligent optimization algorithms, such as iPSO and GA join to adjust ANN’s internal parameters, the weights and thresh-
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olds of the network are globally optimized, which are probably unavailable by gradient based algorithms, namely, BP training method. An accuracy
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comparison of different prediction models is summarized in Table 7 and Fig. 7.
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Figure 6 is about here
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Table 7 is about here
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Figure 7 is about here Moreover, the obtained three models are compared in terms of time con-
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suming by measuring the total modeling time. It can be seen from Table 7, ANN model has the shortest modeling time because of its simplest structure of three models. iPSO-ANN has shorter modeling time than GA-ANN. We believe the fast convergence speed of iPSO algorithm is the main reason. 4.3. Data Set B
The data set B is obtained from a real library building in East China,
which has fewer environment variables and rough information about the building energy consumption. The iPSO-ANN model is applied to investigate its performance using such rough data. Considering the influence of
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time-lagged loads on the prediction, the input set contains two short past
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~x(t) = (y(t − 1), y(t − 2), T (t), oc, ch)
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values of the hourly load. The input set is described as follows:
where T (t) is daily dry-bulb temperature, oc is the hourly occupancy of the
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library, ch represents cosine of the hour of the day.
The data set is collected from October 9, 2009 to January 15, 2010, which
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includes 2472 hourly energy consumption data of the whole library building. Like data set A, data set B is divided into training set and testing set. The early 2304 groups data are set as the training data, and the last one week
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data are used for test. A dozen times of prediction are executed using iPSOANN method, and the other two models, GA-ANN and ANN models, are
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also applied for the prediction. A graphical comparison between the real
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and prediction loads using the three models is given in Fig. 8. Performance
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comparison is summarized in Table 8 and Fig. 9. Figure 8 is about here Table 8 is about here
Figure 9 is about here
From Table 8, we can find that with rough environment variable which is
of common situation in building energy prediction field, the proposed model achieves best accuracy compared with other two methods. Considering the fast convergence speed of iPSO algorithm, the iPSO-ANN model is very suitable for online building energy prediction tasks. 15
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It is noted that as a kind of data-driven method, the proposed model also
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can be adopted for energy prediction at the building design stage. In such applications, input/output data is extracted from simulation softwares, such
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as Energy-Plus, DOE2, DeST, etc.. The obtained data-driven model has much simpler structure than full simulation programs, and can be embedded
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into various optimization schemes for building parameters design.
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5. Conclusion
This study has demonstrated the application of an improved PSO (iPSO)
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algorithm to optimize the internal parameters of ANN model instead of the default gradient based methods to forecast building energy consumption. In the application of Great Building Energy Predictor Shootout I, the
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PCA is utilized to reduce the dimension of input variables. The iPSO-ANN
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model is constructed to predict the short term electricity loads of the whole building. The prediction results are compared with GA-ANN and ANN mod-
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els. Moreover, a library’s electricity loads are also predicted by the proposed model. The data has fewer environment variables and rough information, which is more common in the field of building energy prediction. The prediction results illustrate that the optimized ANN model is more
effective than traditional ANN method. Furthermore, with the rapid convergence and capability of searching the optimal solution, iPSO-ANN model is more suitable for online prediction tasks compared with GA-ANN method. It is noted that the proposed model is just for a single building that needs the knowledge of related weather and historical energy consumption data. How to construct typical energy prediction models at different scales 16
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(single building, building group, and area/city scale) is the main interest of
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our future work.
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Acknowledgements
This work is supported by the National Natural Science Foundation of
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China (Grant No. 61304075), the Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20130538), and the Senior Professionals in
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Jiangsu University Scientific Research Funds (Grant No. 13JDG112).
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11 (2011) 2664–2675.
Prediction of particulate matter at
an
[31] H. di He, W.-Z. Lu, Y. Xue,
street level using artificial neural networks coupling with chaotic particle swarm optimization algorithm, Building and Environment 78 (2014)
M
111 – 117.
[32] K. Li, H. Su, J. Chu, Forecasting building energy consumption using
d
neural networks and hybrid neuro-fuzzy system: A comparative study,
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Energy and Buildings 43 (2011) 2893–2899.
Ac ce p
[33] R. J. Schalkoff, Artificial neural networks, McGraw-Hill New York, 1997. [34] R. C. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, Proceedings of the sixth international symposium on micro machine and human science 1 (1995) 39–43.
[35] J. Kennedy, Particle swarm optimization, in: C. Sammut, G. Webb (Eds.), Encyclopedia of Machine Learning, 2010, pp. 760–766.
[36] M. Lovbjerg, T. K. Rasmussen, T. Krink, Hybrid particle swarm optimiser with breeding and subpopulations, Proceedings of the Genetic and Evolutionary Computation Conference 2001 (2001) 469–476. 21
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[37] R. Kuo, Y. Han, A hybrid of genetic algorithm and particle swarm opti-
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mization for solving bi-level linear programming problem - A case study on supply chain model, Applied Mathematical Modelling 35 (2011)
cr
3905–3917.
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[38] I. Jolliffe, Principal component analysis, Wiley Online Library, 2002. [39] J. F. Kreider, J. S. Haberl, Predicting hourly building energy use: The
an
great energy predictor shootout - Overview and discussion of results, ASHRAE Transactions 100 (1994) 1104–1118.
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[40] M. B. Ohlsson, T. Roegnvaldsson, C. Peterson, H. Pi, B. Soederberg, Predicting system loads with artificial neural networks: Methods and results from“The great energy predictor shootout”, ASHRAE Transac-
Ac ce p
te
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tions 100 (1994) 1063–1074.
22
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Table 1: Principal component analysis result Eigen Values
Contribution Rate (%)
Cumulative contribution Rate (%)
PC1
2.620
43.436
43.436
PC2
2.349
38.953
82.389
PC3
0.685
11.357
93.746
PC4
0.377
6.254
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Component
Main parameters
us
100.00
Maximum number of generations
10
Population size
20
Table 2: Main parameters used in iPSO-ANN
M
an
iPSO-ANN
0.5
Mutation rate
0.5
The initial weight value
0.9
The final weight value
0.4
Acceleration coefficient c1
2
Acceleration coefficient c2
1.8
Number of hidden layer in ANN
11
Number of epochs in ANN
100
Ac ce p
te
d
Crossover rate
23
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Table 3: Predicted building electricity loads using iPSO-ANN, data set A
1
2
3
4
5
Average
Best
CV
0.0259
0.0254
0.0266
0.0267
0.0262
0.0262
0.0254
MAPE
0.0163
0.0162
0.0169
0.0166
0.0171
0.0166
0.0162
Time(s)
20.7
23.2
25.3
23.7
25.3
23.4
20.7
us
cr
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Index
Table 4: Predicted building electricity loads using ANN model, data set A
2
3
CV
0.0352
0.0325
0.0340
MAPE
0.0222
0.0211
0.0238
Time(s)
11.6
12.2
10.4
4
5
Average
Best
0.0333
0.0339
0.0339
0.0325
0.0213
0.0224
0.0222
0.0211
7.3
10.7
7.3
an
1
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Index
d
11.9
te
Table 5: Main parameters used in GA-ANN model
GA-ANN
Maximum number of generations
10
Ac ce p
Main parameters
Population size
20
Crossover probability in GA
0.9
Mutation probability in GA
0.8
Table 6: Predicted building electricity loads using GA-ANN model, data set A
Index
1
2
3
4
5
Average
Best
CV
0.0292
0.0287
0.0296
0.0282
0.0293
0.0290
0.0282
MAPE
0.0185
0.0190
0.0201
0.0187
0.0189
0.0190
0.0185
Time(s)
74.2
78.4
73.9
76.2
77.7
76.1
73.9
24
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Table 7: Performance comparison of different prediction models using data set A
iPSO-ANN
GA-ANN
ANN
GA-ANFIS[32]
CV
0.0254
0.0282
0.0325
0.0260
MAPE
0.0162
0.0185
0.0211
-
Time(s)
20.7
73.9
7.3
cr
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Index
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-
Table 8: Performance of different prediction models using data set B
Prediction Model
iPSO-ANN
GA-ANN
Evaluation Indices
CV
MAPE
1
0.0800
0.0603
2
0.0803
0.0574
3
0.0758
0.0588
4
0.0819
5 Average
CV
MAPE
0.0975
0.0706
0.1196
0.0792
0.0940
0.0732
0.1158
0.0845
0.0957
0.0762
0.1078
0.0837
0.0614
0.0934
0.0701
0.1063
0.0760
0.0776
0.0601
0.0936
0.0672
0.1055
0.0798
0.0791
0.0596
0.0948
0.0715
0.1110
0.0806
0.0758
0.0574
0.0934
0.0672
0.1055
0.0760
te
d
M
an
MAPE
Ac ce p
Best
CV
ANN
Input layer w1,1
Hidden layer
Output layer
h(×)
b1
P1
y1
P2
b2
h(×)
y2
Pj
f (×)
Y
b0 bj
wi,j h(×)
yj
Figure 1: A three layer feed-forward ANN structure
25
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Initialize population and parameters
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PSO evolution
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Ranked by fitness value
Genetic operation
crossover
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selection
mutation
d
Update individual best and global best
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Update individual best and global best
No
Stopping criteria are satified? Yes Output the optimal solution
Figure 2: The flow chart of iPSO optimization model
26
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Select the training samples and test samples
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Initialize the weight and threshold values of ANN corresponding to the particle of iPSO
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Calculate the fitness function (ANN training error)
d
Generate new particles
Execute crossover and mutation operations, and update Pbest and Gbest of iPSO
Ac ce p
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Assign the weight and threshold values of ANN with the best particle of iPSO
Initialize parameters of ANN
Initialize parameters of iPSO
Assign the weight and threshold values of ANN with the Gbest particle of iPSO
Data training and test using BP algorithm
Yes
iter<=maxiter? Exit No
Figure 3: The flow chart of hybrid iPSO-ANN prediction model
27
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ip t cr us an M
90
100% 90% 80%
Variance Explained
Ac ce p
80
contribution rate cumulative contribution rate
te
100
d
Figure 4: Outside of the library building
70
70%
60
60%
50
50%
40
40%
30
30%
20
20%
10
10%
0
PC1
PC2 PC3 Principal Component
PC4
0%
Figure 5: The contribution rate and cumulative contribution rate of principal components
28
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1000
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Prediction(iPSO−ANN,S1) Real
900
700
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WBE(kW)
800
500
200
400
600 800 Hours
900
1400
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WBE(kW)
800 700
te
d
600
400 0
1200
Prediction(GA−ANN,S1) Real
1000
500
1000
an
400 0
us
600
200
400
600 800 Hours
1000
1200
1400
Prediction(ANN,S1) Real
Ac ce p
1000 900
WBE(KW)
800 700 600 500
400 0
200
400
600 800 Hours
1000
1200
1400
Figure 6: Predicted building electricity loads using iPSO-ANN, GA-ANN and ANN, data set A
29
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Figure 7: Graphical comparison of prediction performance with different models, data set A
30
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700
ip t
Prediction(iPSO−ANN,S2) Real
600
400
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WBE(kW)
500
200 100 0
100 Hours
700
200
Prediction(GA−ANN,S2) Real
600
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500 WBE(KW)
150
an
50
us
300
400
te
200
d
300
100 0
50
Ac ce p
700
100 Hours
150
200
150
200
Prediction(ANN,S2) Real
600
WBE(KW)
500 400 300 200
100 0
50
100 Hours
Figure 8: Predicted building electricity loads using iPSO-ANN, GA-ANN and ANN, data set B
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Figure 9: Graphical comparison of prediction performance with different models, data set B
32
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Research Highlights:
1. Present a hybrid iPSO-ANN prediction model for short term
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building electricity consumption forecasting; 2. An improved PSO algorithm is applied to adjust ANN
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structure's weights and threshold values;
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3. PCA method is used for the selection of the input variables, which helps to reduce the input dimension;
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4. Better performances are obtained compared with regular
Ac ce pt e
d
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ANN and GA-ANN models using two different data sets;
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S0378-7788(15)30243-7 http://dx.doi.org/doi:10.1016/j.enbuild.2015.09.002 ENB 6122
To appear in:
ENB
Received date: Revised date: Accepted date:
8-5-2015 1-9-2015 1-9-2015
Please cite this article as: Kangji Li, Chenglei Hu, Guohai Liu, Wenping Xue, Building’s electricity consumption prediction using optimized artificial neural networks and principal component analysis, Energy & Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.09.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Building’s electricity consumption prediction using optimized artificial neural networks and principal component analysis
School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, PR China
us
a
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Kangji Lia,∗, Chenglei Hua , Guohai Liua , Wenping Xuea
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Abstract
As a popular data driven method, Artificial Neural Networks (ANNs) have
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been widely applied in building energy prediction field for decades. To improve the short term prediction accuracy, this paper presents a kind of opti-
d
mized ANN model for hourly prediction of building electricity consumption.
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An improved Particle Swarm Optimization algorithm (iPSO) is applied to adjust ANN structure’s weights and threshold values. The principal compo-
Ac ce p
nent analysis (PCA) is used to select the significant modeling inputs and simplify the model structure. The investigation utilizes two different historical data sets in hourly interval, which are collected from the Energy Prediction Shootout contest I and a campus building located in East China. For performance comparison, another two prediction models, ANN model and hybrid Genetic Algorithm - ANN (GA-ANN) model are also constructed in this study. The comparison results reveal that both iPSO-ANN and GA-ANN ∗
Corresponding author. Email addresses: [email protected] (Kangji Li), [email protected] (Chenglei
Hu)
Preprint submitted to Energy and buildings
September 1, 2015
Page 1 of 33
models have better accuracy than that of ANN ones. From the perspective
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of time consuming, the iPSO-ANN model has shorter modeling time than GA-ANN method. The proposed prediction model can be thought as an
cr
alternative technique for online prediction tasks of building electricity consumption.
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Keywords: Building Energy Prediction, Particle Swarm Optimization, Genetic Algorithm, Artificial Neural Networks, Principal Component
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Analysis 1. Introduction
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Nowadays, with the increasing population and gross domestic product (GDP), energy consumption is much higher, leading to a large amount of en-
d
vironmental problems [1]. As respect of the energy consumption and carbon
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emissions, buildings energy consumption accounts for an important proportion worldwide [2, 3]. In European Union countries, building energy con-
Ac ce p
sumption is close to 40% of the total energy consumption [4]. In China, it accounts for 28% in 2011, and the statistical data is expected to reach 35% by 2020 [5]. To realize a suitable energy demand management in an efficient way, the establishment of a reliable and accurate prediction for energy consumption is of crucial importance, which makes the construction of prediction models for building energy consumption become an essential issue [6, 7].
It is difficult to predict the building energy consumption precisely, since there are many factors influencing the energy usage, such as weather conditions, building structure and characters, geographic location, occupancy,
2
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operation of appliances, etc. [8, 9, 10]. During the past two decades, there
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were various forecasting techniques that had been applied to the building energy consumption, such as engineering methods [11], statistical methods
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[12, 13], Artificial Neural Networks (ANNs) [14, 15], Support Vector Ma-
chines (SVMs) [16, 17], fuzzy logic [18, 19], grey models techniques [20, 21],
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etc.. Among the existing energy prediction methods, the most widely applied approaches are ANNs and their developments. A variety of studies
an
discussed the developments of ANN based energy prediction methods ,where input variables selection, network structure construction and training algorithm improvement are three vital issues [22, 23, 24, 25, 26]. For selecting
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input variables, Karatasou [24] utilized a systematic approach based on least squares estimation (LSE) and statistical tests. Principal component analy-
d
sis (PCA) was also used to analyze the pre-input variables [25]. Mena [26]
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developed a short-term predictive ANN model for the electricity demand of a bio-climatic building. The study also revealed that the outdoor tempera-
Ac ce p
ture and the solar radiation exert a significant influence on building energy consumption. More reviews and analysis on ANN based energy consumption prediction may be referenced at [9, 27, 28]. In the last ten years, with the development of intelligent optimization
technologies, various kinds of intelligent optimization algorithms have been applied to the field of building energy prediction. Fan [29] utilized an adaptive two-stage hybrid network with self-organized map (SOM) and SVM for load forecasting, which was robust with different data types and could deal well with the non-stationary of load series. Khashei [30] proposed a ANN and ARIMA based hybrid model, which showed good accuracy for energy
3
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consumption prediction. He and Lu [31] developed a chaotic particle swarm
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optimization algorithm (CPSO) modified ANN prediction model to forecast time series, and the results proved that the method had better nonlinear
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fitting ability and higher prediction accuracy than ANN itself. A hybrid Genetic Algorithm - Adaptive Network-based Fuzzy Inference System (GA-
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ANFIS) method was studied by Li in 2011 [32]. The best prediction accuracy was improved by 19.5% compared with a regular ANN method.
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The contributions of this study are (a) development of an optimized ANN model for building energy forecasting based on an improved particle swarm optimization (iPSO) algorithm, (b) investigating the forecasting performance
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of the proposed model with two sets of historical data, and (c) comparison with other two prediction models on forecasting accuracy and modeling time.
d
For the model construction, the iPSO algorithm is used to optimize ANN’s
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weights and threshold values, which helps to improve the ANN model’s fitting ability. The principal component analysis (PCA) is applied to reduce
Ac ce p
the input dimension and simplify the model structure in this study. The proposed prediction model can be used with energy management system to help indicate above-normal energy use and diagnose the possible cause of the malfunction if sufficient historical data has been previously gathered. The rest of the paper is organized as follows. Next, the description of
the proposed forecasting model is given. Section 3 describes two data sets collected from energy prediction contest I and a campus building. The data pre-processing is also described in this section. In section 4, prediction tests and comparisons are provided, and the performance of the proposed model is fully discussed. Section 5 gives the conclusion of the paper.
4
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2. Model Description
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2.1. Artificial Neural Network
ANNs, inspired by the thinking mechanism of human brain, are parallel
cr
nonlinear adaptive systems composed of a large number of simple processing
layer to output layer takes the following form: Y = f (b0 +
k X
h(ψj +
i=1
pi wij )bj )
(1)
an
j=1
m X
us
units [33]. For a three-layer network, the basic mapping function from input
where the network outputs are the predicted values Y , denoted by nonlinear
M
transfer function f (·) of the inputs pi , b0 are the output bias, bj are the weight values from hidden layer to output layer, ψj are the hidden layer biases, wij are the weights from input layer to hidden layer and h(·) is hidden layer
d
activation function. For the initialized network, there are several different
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training algorithms for model approximation. All of them use the gradient
Ac ce p
performance function to determine how to adjust the weights to minimize error. In this study, a three-layer feed forward network with back-propagation training algorithm is constructed and the topology structure is illustrated in Fig. 1.
Figure 1 is about here
2.2. Improved Particle Swarm Optimization Algorithm Particle swarm optimization is a bio-inspired global optimization technique that was proposed by James Kennedy and Russell Eberhart in 1995 [34]. PSO performs a population-based search, using particles to represent potential solutions within the search space. Each particle is characterized by 5
Page 5 of 33
its position, velocity, and a record of its previous performance [35]. At each
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flight cycle (iteration), each particle’s velocity and position is formulated as: vj (n + 1) = ωvj (n) + c1r1(pj (n) − xj (n)) + c2r2(pg (n) − xj (n))
(2)
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x (n + 1) = v (n + 1) + x (n) j j j
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where vj (n) is the speed of the jth particle in the nth generation, r1 and r2 are random numbers obeying uniform distribution in the range of [0,1], c1 and c2 are constants named acceleration coefficients, xj (n) is the position
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of the jth particle in the nth generation, pj (n) is the best previous position yielding the best fitness value for the jth particle, pg (n) is the best position
global and local search abilities.
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discovered by the whole particles, ω is the inertia weight used to balance the
d
PSO method has several advantages for exploring the hyperspace global optimum, especially the fast convergence. In order to improve its capability
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of global search and avoid local minima, the genetic operations including
Ac ce p
crossover and mutation are further introduced to the update method of PSO algorithm in this study [36, 37]. The improved PSO algorithm is specified as follows:
Firstly, all initialized particles are evolved by PSO, and the individual
best and group best are recorded. According to the crossover rate and fitness value, T -optimized particles are selected as parental particles for the implementation of crossover operations. Then the fitness values of all new particles are calculate. When parental particle’s fitness value is worse than that of corresponding offspring, these particles’ location and velocity values are updated with the better ones. Thirdly, in order to avoid local minima, mutation operation is executed according to the mutation rate. Finally, the 6
Page 6 of 33
velocity and position values of all particles are updated after genetic op-
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erations accomplished and the group best is also updated. The iterations continue until the stopping criteria is satisfied. The crossover and muta-
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tion equations are the essential part of the algorithm, which are described as follows:
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crossover equations:
child1 (Xi ) = pi ∗ parent1 (Xi ) + (1 − pi ) ∗ parent2 (Xi )
(3)
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child (X ) = p ∗ parent (X ) + (1 − p ) ∗ parent (X ) 2 i i 2 i i 1 i parent1 (Vi )+parent2 (Vi ) |parent1 (Vi )+parent2 (Vi )|
∗ |parent1 (Vi )|
child (V ) = 2 i
parent1 (Vi )+parent2 (Vi ) |parent1 (Vi )+parent2 (Vi )|
∗ |parent2 (Vi )|
and mutation equation:
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child1 (Vi ) =
(5)
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d
Xi 0 = Xi + rand ∗ N (0, 1)
(4)
where Pi is a uniformly distributed random value between 0 and 1, parentj (Xi )
Ac ce p
and parentj (Vi ) represent the position and velocity of parental particle, childj (Xi ) and childj (Vi ) stand for the position and velocity of offspring, respectively (j = 1, 2).
Figure 2 is about here
2.3. Hybrid iPSO-ANN model As we mentioned above, gradient based training algorithms for neural networks have a strong ability in the aspect of local optima search, but their capability of finding the global optimal solution is quite weak. In contrast, the iPSO algorithm is convinced of having the ability for global optima searching 7
Page 7 of 33
with fast convergence. In order to combine the advantages of this two meth-
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ods, a hybrid iPSO-ANN model is proposed for building energy prediction in this study. In the proposed model, a three-layer feed forward network with
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back-propagation training algorithm is constructed for model initialization.
Then all of the weight and threshold values of the network are regarded as
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particles’ position, and the iPSO algorithm is applied to optimize the network’s parameters. The flow diagram of the hybrid iPSO-ANN method is
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illustrated in Fig. 3 and the detailed procedure can be conducted as follows: Step 1: load input data set and select the training and testing samples; Step 2: initialize the parameters of ANN including weight and threshold
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values corresponding to the initialized particle of iPSO; Step 3: calculate the fitness function and find the optimal solution;
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iPSO;
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Step 4: execute crossover and mutation operation, update group best of
Step 5: assign the weight and threshold values of ANN with the group
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best of iPSO, if maximum iteration of iPSO is reached, go to step 6, else generate new particles and return to step 3; Step 6: test the optimized ANN prediction model until the stopping
criteria are satisfied.
Figure 3 is about here
2.4. Principal Component Analysis PCA, a statistical correlation analysis technique, is commonly used to reveal the linear relationship between the input variables and reduce dimension of input data [38]. Supposed that the data set to be analyzed is expressed 8
Page 8 of 33
as a matrix X = [x1 , x2 , ..., xn ], xm = [x1 , x2 , ..., xf ]Tm , λ1 ≥ λ2 ≥ ... ≥ λf ≥ 0
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are the eigenvalues of the covariance matrix of X, and Li = [γ1i , γ2i , ..., γf i ]T are the unit orthogonal eigenvectors of the covariance matrix correspond-
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ing to the eigenvalues. Then the ith principal component Yi of data set X can be donated as Yi = XLi according to the cumulative contribution t P
λi /
i=1
n P
λi . The results of PCA consist of implicit variables
k=1
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rate G(t) =
that can’t be directly observed from observable explicit variable. PCA can
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be employed to eliminate redundant information and identify the significant modeling inputs.
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3. Data Description
Two different data sets are used to evaluate the performances of prediction
d
models , which are called data set A and data set B respectively. Both data
described as follows.
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sets represent real energy data of buildings and their general characters are
Ac ce p
The data set A derives from the Great Building Energy Predictor Shootout
I, organized by ASHRAE in 1990s. The data set includes the following variables, namely, outdoor dry bulb temperature, solar radiation, humidity ratio and wind speed [39, 40]. For the input variables, data were available at hourly intervals for the period from September 1989 to February 1990, whereas energy consumption data were available only for September to December 1989 [24].
The data set B comes from a library building located in Hangzhou, East China. The library has ten floors on the ground with gross floor area of 25,542 m2 (in Fig. 4). There are about 1100 seats in the library and most of 9
Page 9 of 33
the building occupancy occurs at 8:30 to 22:00. The data set merely consists
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of daily temperature and occupancy. The daily temperature is acquired from the local meteorological station. The opening schedule of each reading room
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Figure 4 is about here
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is roughly considered as the library’s hourly occupancy variable.
The energy consumption data of set A and set B are both hourly elec-
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tricity consumption value of the whole building including energy items of heating, cooling, ventilation, lighting, plug load, etc..
[-1,1] by the following formula:
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All inputs and outputs in the two data sets are normalized to the interval
x − xmin −1 xmax − xmin
(6)
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y =2×
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where x is input data, xmin and xmax are the minimum and maximum value
Ac ce p
within the entire data of x.
4. Modeling and Results 4.1. Data Set A
4.1.1. Data Pre-processing
In order to reduce the dimension of the data set A, all original envi-
ronmental variables are analyzed by PCA in advance. These environmental variables include outdoor dry bulb temperature, solar radiation, humidity ratio and wind speed. The analysis result is shown in Table 1. The contribution rate and cumulative contribution rate of four principal components are given in Fig. 5. It is indicated that the first two principal components 10
Page 10 of 33
explained 82.389% of the total variance. By refining the principal compo-
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nents, we use the first two variables, named P C1 and P C2, to represent the
Table 1 is about here
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Figure 5 is about here
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original environmental variables mentioned above.
Further, considering that the occupancy has a strong effect on the energy
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use, days are classified as weekday (1) and weekend/holiday (0). The hour of the day is coded by its sine and cosine value as below. 2πh(t) 2πh(t) , ch = cos 24 24
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sh = sin 4.1.2. iPSO-ANN Results
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The hybrid iPSO-ANN model is applied to predict the whole building
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electricity power consumption (WBE) with the data set A. The network consists of a single hidden layer of tansig neurons. The input set include
Ac ce p
principal components of environmental variables P C1 and P C2, occupancy flag oc, sine of the hour of the day sh, cosine of the hour of the day ch, and
short past values of energy consumption y(t − 1) and y(t − 2). The output is hourly WBE y(t). The neuron number of hidden layer is selected in the light of Eq. 7 [33].
k=
√
m+n+l
(7)
where m is output number, n is input number, k is concealed number, and l is an integer between 1 and 10. The data set A contains 4208 group of energy consumption data, where data [1,2926] are available for training, and [2927,4208] for testing which are 11
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not used during the training phase. Two different indicators, the coefficient
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of variation of the root mean square deviation (CV) and mean absolute percentage error (MAPE), are utilized to assess the prediction accuracy in this
s
(ypred,i − ydata,i )2 /N
i=1
y data
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CV =
N P
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study. They are described as follows:
(9)
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N X 1 |ypred,i − ydata,i | M AP E = × ( ) N i=1 ydata,i
(8)
where ypred,i is predicted WBE value, ydata,i is real WBE value, y data is the
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average value of real WBE, N is the number of testing data set. In the hybrid model, the fitness function for iPSO based parameter opti-
d
mization is defined as follows:
K X
(|ypred,i − ydata,i |)
(10)
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f itness =
i=1
Ac ce p
where K is the number of training data set. The main parameters used in the prediction model are given in Table 2. Table 2 is about here
The hybrid iPSO-ANN prediction is tested for a dozen times. The best
five results are recorded in Table 3. The average and best results are also recorded.
Table 3 is about here
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4.1.3. Results of Other Two Models
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In order to investigate the prediction performances of the hybrid iPSOANN model, other two different models are also constructed for performance
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comparisons.
ANN models have been widely used in building energy prediction field
us
for decades. In this section, a regular three-layer BP neural network is constructed. The same data sets are used to train the ANN model. The best
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five results of total twelve predictions are recorded in Table 4. The average and best results are also given.
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Table 4 is about here
Because of the global search ability and good scalability, GA has a broad
d
application in various optimization issues. For performance comparison pur-
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pose, GA is combined with ANN model for the same prediction task. Like iPSO algorithm, GA is also used to train the weight and threshold values
Ac ce p
of the network. The main parameters used in GA-ANN model are given in Table 5. The performance of the hybrid GA-ANN model is investigated using the same data set and the same precision evaluation indicators. The GA-ANN results are shown in Table 6. Table 5 is about here Table 6 is about here
4.2. Performance Comparison It is seen from the above investigations that the two hybrid ANN models generally achieve better accuracies compared with regular ANN method. 13
Page 13 of 33
Concretely, iPSO-ANN model decrease CV by 21.8% (23.2% for MAPE) in
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the case of data set A. GA-ANN model decrease CV by 13.2% (12.3% for MAPE). Graphical comparisons between the predictions and the real loads
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are given in Fig. 6. When intelligent optimization algorithms, such as iPSO and GA join to adjust ANN’s internal parameters, the weights and thresh-
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olds of the network are globally optimized, which are probably unavailable by gradient based algorithms, namely, BP training method. An accuracy
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comparison of different prediction models is summarized in Table 7 and Fig. 7.
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Figure 6 is about here
d
Table 7 is about here
te
Figure 7 is about here Moreover, the obtained three models are compared in terms of time con-
Ac ce p
suming by measuring the total modeling time. It can be seen from Table 7, ANN model has the shortest modeling time because of its simplest structure of three models. iPSO-ANN has shorter modeling time than GA-ANN. We believe the fast convergence speed of iPSO algorithm is the main reason. 4.3. Data Set B
The data set B is obtained from a real library building in East China,
which has fewer environment variables and rough information about the building energy consumption. The iPSO-ANN model is applied to investigate its performance using such rough data. Considering the influence of
14
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time-lagged loads on the prediction, the input set contains two short past
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~x(t) = (y(t − 1), y(t − 2), T (t), oc, ch)
ip t
values of the hourly load. The input set is described as follows:
where T (t) is daily dry-bulb temperature, oc is the hourly occupancy of the
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library, ch represents cosine of the hour of the day.
The data set is collected from October 9, 2009 to January 15, 2010, which
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includes 2472 hourly energy consumption data of the whole library building. Like data set A, data set B is divided into training set and testing set. The early 2304 groups data are set as the training data, and the last one week
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data are used for test. A dozen times of prediction are executed using iPSOANN method, and the other two models, GA-ANN and ANN models, are
d
also applied for the prediction. A graphical comparison between the real
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and prediction loads using the three models is given in Fig. 8. Performance
Ac ce p
comparison is summarized in Table 8 and Fig. 9. Figure 8 is about here Table 8 is about here
Figure 9 is about here
From Table 8, we can find that with rough environment variable which is
of common situation in building energy prediction field, the proposed model achieves best accuracy compared with other two methods. Considering the fast convergence speed of iPSO algorithm, the iPSO-ANN model is very suitable for online building energy prediction tasks. 15
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It is noted that as a kind of data-driven method, the proposed model also
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can be adopted for energy prediction at the building design stage. In such applications, input/output data is extracted from simulation softwares, such
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as Energy-Plus, DOE2, DeST, etc.. The obtained data-driven model has much simpler structure than full simulation programs, and can be embedded
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into various optimization schemes for building parameters design.
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5. Conclusion
This study has demonstrated the application of an improved PSO (iPSO)
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algorithm to optimize the internal parameters of ANN model instead of the default gradient based methods to forecast building energy consumption. In the application of Great Building Energy Predictor Shootout I, the
d
PCA is utilized to reduce the dimension of input variables. The iPSO-ANN
te
model is constructed to predict the short term electricity loads of the whole building. The prediction results are compared with GA-ANN and ANN mod-
Ac ce p
els. Moreover, a library’s electricity loads are also predicted by the proposed model. The data has fewer environment variables and rough information, which is more common in the field of building energy prediction. The prediction results illustrate that the optimized ANN model is more
effective than traditional ANN method. Furthermore, with the rapid convergence and capability of searching the optimal solution, iPSO-ANN model is more suitable for online prediction tasks compared with GA-ANN method. It is noted that the proposed model is just for a single building that needs the knowledge of related weather and historical energy consumption data. How to construct typical energy prediction models at different scales 16
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(single building, building group, and area/city scale) is the main interest of
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our future work.
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Acknowledgements
This work is supported by the National Natural Science Foundation of
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China (Grant No. 61304075), the Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20130538), and the Senior Professionals in
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Jiangsu University Scientific Research Funds (Grant No. 13JDG112).
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Table 1: Principal component analysis result Eigen Values
Contribution Rate (%)
Cumulative contribution Rate (%)
PC1
2.620
43.436
43.436
PC2
2.349
38.953
82.389
PC3
0.685
11.357
93.746
PC4
0.377
6.254
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ip t
Component
Main parameters
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100.00
Maximum number of generations
10
Population size
20
Table 2: Main parameters used in iPSO-ANN
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an
iPSO-ANN
0.5
Mutation rate
0.5
The initial weight value
0.9
The final weight value
0.4
Acceleration coefficient c1
2
Acceleration coefficient c2
1.8
Number of hidden layer in ANN
11
Number of epochs in ANN
100
Ac ce p
te
d
Crossover rate
23
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Table 3: Predicted building electricity loads using iPSO-ANN, data set A
1
2
3
4
5
Average
Best
CV
0.0259
0.0254
0.0266
0.0267
0.0262
0.0262
0.0254
MAPE
0.0163
0.0162
0.0169
0.0166
0.0171
0.0166
0.0162
Time(s)
20.7
23.2
25.3
23.7
25.3
23.4
20.7
us
cr
ip t
Index
Table 4: Predicted building electricity loads using ANN model, data set A
2
3
CV
0.0352
0.0325
0.0340
MAPE
0.0222
0.0211
0.0238
Time(s)
11.6
12.2
10.4
4
5
Average
Best
0.0333
0.0339
0.0339
0.0325
0.0213
0.0224
0.0222
0.0211
7.3
10.7
7.3
an
1
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Index
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11.9
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Table 5: Main parameters used in GA-ANN model
GA-ANN
Maximum number of generations
10
Ac ce p
Main parameters
Population size
20
Crossover probability in GA
0.9
Mutation probability in GA
0.8
Table 6: Predicted building electricity loads using GA-ANN model, data set A
Index
1
2
3
4
5
Average
Best
CV
0.0292
0.0287
0.0296
0.0282
0.0293
0.0290
0.0282
MAPE
0.0185
0.0190
0.0201
0.0187
0.0189
0.0190
0.0185
Time(s)
74.2
78.4
73.9
76.2
77.7
76.1
73.9
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Table 7: Performance comparison of different prediction models using data set A
iPSO-ANN
GA-ANN
ANN
GA-ANFIS[32]
CV
0.0254
0.0282
0.0325
0.0260
MAPE
0.0162
0.0185
0.0211
-
Time(s)
20.7
73.9
7.3
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ip t
Index
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-
Table 8: Performance of different prediction models using data set B
Prediction Model
iPSO-ANN
GA-ANN
Evaluation Indices
CV
MAPE
1
0.0800
0.0603
2
0.0803
0.0574
3
0.0758
0.0588
4
0.0819
5 Average
CV
MAPE
0.0975
0.0706
0.1196
0.0792
0.0940
0.0732
0.1158
0.0845
0.0957
0.0762
0.1078
0.0837
0.0614
0.0934
0.0701
0.1063
0.0760
0.0776
0.0601
0.0936
0.0672
0.1055
0.0798
0.0791
0.0596
0.0948
0.0715
0.1110
0.0806
0.0758
0.0574
0.0934
0.0672
0.1055
0.0760
te
d
M
an
MAPE
Ac ce p
Best
CV
ANN
Input layer w1,1
Hidden layer
Output layer
h(×)
b1
P1
y1
P2
b2
h(×)
y2
Pj
f (×)
Y
b0 bj
wi,j h(×)
yj
Figure 1: A three layer feed-forward ANN structure
25
Page 25 of 33
ip t cr
Initialize population and parameters
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PSO evolution
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Ranked by fitness value
Genetic operation
crossover
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selection
mutation
d
Update individual best and global best
Ac ce p
te
Update individual best and global best
No
Stopping criteria are satified? Yes Output the optimal solution
Figure 2: The flow chart of iPSO optimization model
26
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ip t cr
us
Select the training samples and test samples
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Initialize the weight and threshold values of ANN corresponding to the particle of iPSO
M
Calculate the fitness function (ANN training error)
d
Generate new particles
Execute crossover and mutation operations, and update Pbest and Gbest of iPSO
Ac ce p
te
Assign the weight and threshold values of ANN with the best particle of iPSO
Initialize parameters of ANN
Initialize parameters of iPSO
Assign the weight and threshold values of ANN with the Gbest particle of iPSO
Data training and test using BP algorithm
Yes
iter<=maxiter? Exit No
Figure 3: The flow chart of hybrid iPSO-ANN prediction model
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ip t cr us an M
90
100% 90% 80%
Variance Explained
Ac ce p
80
contribution rate cumulative contribution rate
te
100
d
Figure 4: Outside of the library building
70
70%
60
60%
50
50%
40
40%
30
30%
20
20%
10
10%
0
PC1
PC2 PC3 Principal Component
PC4
0%
Figure 5: The contribution rate and cumulative contribution rate of principal components
28
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1000
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Prediction(iPSO−ANN,S1) Real
900
700
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WBE(kW)
800
500
200
400
600 800 Hours
900
1400
M
WBE(kW)
800 700
te
d
600
400 0
1200
Prediction(GA−ANN,S1) Real
1000
500
1000
an
400 0
us
600
200
400
600 800 Hours
1000
1200
1400
Prediction(ANN,S1) Real
Ac ce p
1000 900
WBE(KW)
800 700 600 500
400 0
200
400
600 800 Hours
1000
1200
1400
Figure 6: Predicted building electricity loads using iPSO-ANN, GA-ANN and ANN, data set A
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Figure 7: Graphical comparison of prediction performance with different models, data set A
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700
ip t
Prediction(iPSO−ANN,S2) Real
600
400
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WBE(kW)
500
200 100 0
100 Hours
700
200
Prediction(GA−ANN,S2) Real
600
M
500 WBE(KW)
150
an
50
us
300
400
te
200
d
300
100 0
50
Ac ce p
700
100 Hours
150
200
150
200
Prediction(ANN,S2) Real
600
WBE(KW)
500 400 300 200
100 0
50
100 Hours
Figure 8: Predicted building electricity loads using iPSO-ANN, GA-ANN and ANN, data set B
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Figure 9: Graphical comparison of prediction performance with different models, data set B
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Research Highlights:
1. Present a hybrid iPSO-ANN prediction model for short term
ip t
building electricity consumption forecasting; 2. An improved PSO algorithm is applied to adjust ANN
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structure's weights and threshold values;
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3. PCA method is used for the selection of the input variables, which helps to reduce the input dimension;
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4. Better performances are obtained compared with regular
Ac ce pt e
d
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ANN and GA-ANN models using two different data sets;
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