Comparison of four algorithms based on machine learning for cooling load forecasting of large-scale shopping mall

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Energy Procedia 142 Energy Procedia 00(2017) (2017)1799–1804 000–000 www.elsevier.com/locate/procedia

9th International Conference on Applied Energy, ICAE2017, 21-24 August 2017, Cardiff, UK

Comparison of four algorithms based on machine learning for The 15th International Symposium on District Heating and Cooling cooling load forecasting of large-scale shopping mall Assessing theZhubing feasibility of Liequan using the heat demand-outdoor aa b,* aa b,*, Yan Zhou Xuanaa, Fan , Liang Junwei , Pan Dongmeiaa temperature function for a long-term district heat demand forecast School School of of Mechanical Mechanical & & Automotive Automotive Engineering, Engineering, South South China China University University of of Technology, Technology, Guangzhou Guangzhou 510640, 510640, China China a a

b bInformation

Information Science Science School, School, Guangdong Guangdong University University of of Finance Finance & & Economics, Economics, Ghuangzhou Ghuangzhou 510320, 510320, China China

I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a

IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France

Abstract Abstract

Short-term Short-term forecasting forecasting of of air-conditioning air-conditioning cooling cooling load load of of shopping shopping mall mall is is hard hard with with much much accuracy accuracy due due to to its its chaotic chaotic and and nonnonlinear linear characteristic. characteristic. Four Four forecasting forecasting algorithms algorithms based based on on machine machine learning learning are are illustrated illustrated in in this this paper paper including including Chaos-SVR, Chaos-SVR, WD-SVR, WD-SVR, SVR SVR and and BP, BP, whose whose predicting predicting performances performances are are compared. compared. For For Chaos-SVR, Chaos-SVR, the the selection selection of of lag lag time time and and embedding embedding Abstract dimension dimension during during phase phase space space reconstruction reconstruction are are described, described, while while for for WD-SVR, WD-SVR, the the modeling modeling process process of of DB2 DB2 is is proposed. proposed. Furthermore, Furthermore, the the optimization optimization of of the the hyper-parameters hyper-parameters for for SVR SVR model model is is also also presented. presented. It’s It’s shown shown that that these these four four approaches approaches District heating networks are commonly addressed in the literature as one of time the most effective solutions for decreasing the have have different different characteristics characteristics which which are are suitable suitable for for different different types types of of cooling cooling load load time series. series. greenhouse gas emissions fromby theElsevier building sector. These systems require high investments which are returned through the heat © 2017 The Authors. Published Ltd. © 2017 The Authors. Published by Elsevier Ltd. ©sales. 2017 Due The Authors. Published by Elsevier Ltd. committee to the changed climate conditions and building renovation policies,Conference heat demandApplied in the future could decrease, Peer-review under of scientific of the 9th International Energy. Peer-review under responsibility responsibility of the the committee of of the the 9th 9th International International Conference Conference on on Applied Energy. Energy. Peer-review responsibility the scientific scientific committee on Applied prolonging under the investment returnofperiod. The mainMachine scope of this paper is toload assess the feasibility of using the heat Keywords: learning; cooling forecasting; Chaos-SVR, WD-SVR, SVR Keywords: Machine learning; cooling load forecasting; Chaos-SVR, WD-SVR, SVRdemand – outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were 1.renovation Introduction 1. Introduction compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications Energy consumption per unit floor area of commercial premises is higher other kind public Energy perwas unit floor premisesconsidered). is much much However, higher than than kind of of public (the error inconsumption annual demand lower thanarea 20%of forcommercial all weather scenarios afterother introducing renovation buildings due to its large lighting load, high population density, large window to wall ratio and aa big air buildings due to its large lighting load, high population density, large window to wall ratio and big air scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). [1] [1] conditioning demand, such as large scale shopping malls in particular . Energy consumption of air-conditioning conditioning demand, such as large scale shopping malls in particular . Energy consumption of air-conditioning The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the system up than of overall consumption especially system ininlarge-scale large-scale shopping mall takes up more more thanthe40% 40% of the the overall consumption especially in in subtropical decreasein the numbershopping of heatingmall hourstakes of 22-139h during heating season (depending on the combination of subtropical weather and areas. In of fact forecasting is key efficiency of air-conditioning areas. In view view of the the considered). fact that that cooling cooling load forecasting is the theintercept key to to upraise upraise energy efficiency ratio of (depending air-conditioning renovation scenarios On theload other hand, function increasedenergy for 7.8-12.7% per ratio decade on the system, summer peak electricity demand much effort has been the forecasting coupled reduce scenarios). The values could be usedand, to modify function for theon considered, and system, reduce summer peaksuggested electricity demand and, much the effort has parameters been focused focused onscenarios the load load forecasting technology air system. improve thefor accuracy of heat demand estimations. technology for air conditioning conditioning system. © 2017 The Authors. Published by Elsevier Ltd. ** Liang Tel.:+86-20-22236666; Liang Liequan Liequan Tel.:+86-20-22236666; Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and E-mail address: [email protected] E-mail address: [email protected] Cooling. Keywords: Heat demand; Forecast; Climate change 1876-6102 © 1876-6102 © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. Peer-review Peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the 9th 9th International International Conference Conference on on Applied Applied Energy. Energy. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy. 10.1016/j.egypro.2017.12.566

Zhou Xuan/ Energy et al. / Energy Procedia 142000–000 (2017) 1799–1804 Author name Procedia 00 (2017)

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Nomenclature

Q

cooling load

c

heat capacity

t temperature difference between supply and return chilled water y ( k ) the actual cooling load for current time yˆ ( k ) the predicted cooling load value for current time

y n

m

mass flow

the actual average cooling load throughout the forecasting period the number of hours throughout the forecasting period.

It’s well known that the cooling load of shopping mall is affected by many factors, such as visitors’ flow, number and power in real time of terminal running units, outdoor weather conditions and so on. But most of the factors are not easy to be measured accurately due to the costly data acquisition devices and extensive field investigation. Therefore, univariate time series analysis was proposed for short-term of shopping mall cooling load prediction. That is to say, just the cooling load data of the current time and historic time are used as the input to predict the load of next time. Meanwhile, since cooling load time series of large scale shopping mall are in general characterized by nonstationary and nonlinear features, by which the difficulty of implementation in uni-variate time series forecasting is enhanced. Currently, the machine learning -based approach is an effective way to solve the problem. Machine Learning is the core of artificial intelligence which has been applied in the field of power load forecasting[2]. As typical machine learning methods, Artificial Neural Network and Support Vector Regression have drawn much attention recently because of their strong non-linear learning capability. So in this paper, four machine learning methods are discussed and compared for the cooling load forecasting of Commercial Building, such as ANN, SVR and hybrid methods, like Chaos-SVR and WD-SVR. Moreover, the accuracy and applicability of these methods are also compared and discussed in this article to provide useful information for engineering application. 2. Cooling load forecasting algorithm of air-conditioning system based on machine learning The cooling load forecasting process by machine learning is shown in Figure 1, the main steps of cooling load forecasting are as follows: (1) Original data acquisition: acquire historical hourly cooling capacity consumption from energy saving control system for air-conditioning system of large-scale shopping mall (2) Data cleaning: one of the most important and time consuming steps for identifying incomplete, incorrect, inaccurate, irrelevant data and then replacing, modifying, or deleting those dirty data or coarse data which influence forecast accuracy directly. (3) Data partition: dividing the total data set into training data set and test data set. (4) Data pre-processing: including data normalization which scales the data to fall within a small, specified range and feature construction which construct new features from the given ones. (5) Model training: the core part for machine learning process, in which the popular models include ANN, SVR and so on. (6) Parameter optimization: an important step of forecasting modeling. For example, the hyper parameter of SVR model need to be optimized by some optimization algorithms like particle swarm optimization algorithm, Generic Algorithm, ant colony optimization and so on. (7) Data Post-processing: including Data Reconstruction and Forecast accuracy evaluation. EEP(Expected Error Percentage), MBE(Mean Bias Error) and R2 are usually used to evaluate the prediction model. (8) Final Model Determination: in this step, the best training model of optimized parameters is selected by cross validation. (9) Data Forecasting: actual data of current time are input into the selected forecasting model and the forecasting result of next time is output.



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Therefore, hybrid machine learning algorithms have usually better performance than single use of machine learning algorithms. Meanwhile, most of the hybrid algorithms focus on the combination of ANN or SVR with other analysis algorithms. Furthermore, hybrid forecasting models were widely attracted more focus than single model. In the light of the above reason, there are four algorithms compared in this paper to forecast the actual cooling load of large-scale shopping mall, including Chaos-SVR and wavelet-SVR hybrid forecasting algorithms, BP neural network and SVR forecasting algorithms. Furthermore, the forecasting performance and applicability of the four models are also compared and analyzed. 3. Case Study 3.1. Data source This case study is based on hourly cooling load data from a large-scale shopping mall, which locates at Guangzhou city, in the south of China. This shopping mall whose building area is 100,000m2 and air-conditioning area is 52,000m2, is a six-story building built in 2006. The cold source data acquisition and control system has been added to the air-conditioning system by which the operation parameters, including chilled water, cooling water supply and return temperature difference, volume, pressure differential, are under dynamic collected. The hourly cooling load data used in this paper were recorded by the data acquisition system automatically as formula (1): (1) Q  cmt The cooling load data in summer from May 1st in 2014 to October 31st in 2015 were selected for forecasting models which were divided into training data set and test data set. The whole data size in 2014 is 3246 used for training without 1113 missing values while the data size in 2015 is 4359 for test without 57 missing values. As figure 1 shown, the hourly cooling load of this mall in the first three weeks of May in 2014 has certain regularity, strong volatility and randomness. 6000

Cooling Load（ KW)

5000

4000

3000

2000

1000

0

0

50

100

150

200

250 Hours

300

350

400

450

500

Fig.1. The hourly cooling load of this mall in the first three weeks of May in 2014

3.2. Evaluation Metrics EEP(Expected Error Percentage), MBE(Mean Bias Error) and R2(correlation coefficient) are used to evaluate the prediction accuracy of the forecasting model whose definition are described as following formula (2)-(4) [4]. n

  yˆ(k )  y(k )  k=1

EEP 

n

n

max[ y (k )]

2

 100

(2)

k 1

n

  yˆ(k )  y(k )  k 1

MBE 

n y

 100

(3)

Zhou Xuan et al. / Energy Procedia 142 (2017) 1799–1804 Author name / Energy Procedia 00 (2017) 000–000

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2

n n  n   n  yˆ  k  y k    yˆ k  y k  k 1 k 1  k 1  R2  2 2  n  n   n  n   2 2  n  yˆ  k     yˆ k    n  y k     y k     k 1  k 1    k 1    k 1

(4)

3.3. Four cooling load forecasting modeling methods (1) BP neural network method BP neural network forecasting method was discussed due to its outstanding nonlinear mapping capability[3]. In this paper, a three-layer BP neural network is used. There is one hidden layer. For a good effect on convergence, the number of neurons on hidden layer is set as 5 after experiment and the precision pre-set is 0.0000004 while the learning rate is set as 0.1. After training for 100 times, the error finally converged to the precision pre-set. The forecasting result is shown in 2.4. (2) Support Vector Regression method Support vector Regression forecasting method was proposed due to its good forecasting performance. RBF kernel function was selected as kernel function of SVR[4], and the hyper-parameters were optimized by Particle Swarm optimization algorithm[5], whose range are as following:  0.001,0.1 ， C  [1,1000] ，    0.1,100  (3) Hybrid Chaos-SVR method Chaos-SVR is a hybrid algorithm combining chaotic time series algorithm with SVR both of which show effective forecasting ability for nonlinear system. The key steps of Chaos-SVR forecasting method comprise of the determination of time lag and embedding dimension. According to Takens embedding theory, after the time lag   7 and embedding dimension m  14 are determined by mutual information method and CAO method [6-8] as Fig.2. and Fig.3. shown, the maximum Lyapunov exponents is calculated   0.0661 . It can be concluded that the cooling load time series of the large shopping mall behaves chaotically. Finally, the input and output of cooling load prediction Chaos-SVR model for training and testing datasets are used for Phase Space Reconstructed shown as Table 1 and Table 2 respectively. Mutual information method

3.5

CAO method

1.1

E1 E2

1

3

0.9 0.8

2.5

E1&E2

0.7 2

0.6 0.5

1.5

0.4 1

0.5

0.3 0.2 0

20

Fig.2 Time lag

40



60

tau

80

100

120

140

0.1

by mutual information method

Table1 Phase Space Reconstruction result of training dataset Input

 x(1)  x(2)    x(3154)

x (8) x (9)  x (3161)

x (92)  x (93)    x(3245) 

 x(93)   x(94)      x(3246) 

5

10

15 维数

20

25

30

Table2 Phase Space Reconstruction result of testing dataset Input

Output

   

0

Fig.3 Embedding dimension by CAO method

 x(3247)  x(3248)    x(7513)

x(3254) x(3255)  x (7514)

Output

   

x(3338)  x(3339)    x (7604) 

 xˆ (3339)   xˆ (3340)      xˆ (7605) 

(4) Hybrid Wavelet-SVR The popularity of Wavelet analysis is increasing in the economics and finance fields due to its capability of decomposing time series into high- and low-frequency components, which are localized in time. The capability of



Zhou Xuan et al. / Energy Procedia 142 (2017) 1799–1804 Author name / Energy Procedia 00 (2017) 000–000

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wavelets to model the cyclical or frequency properties of cooling load by the use of multi-resolution decomposition (MRD) decompose the time series into orthogonal components at different frequencies[9]. In this paper, the DB2 wavelet was chosen by compared with other DB’s wavelet family and other wavelet basis functions whose modeling process is shown as Fig.4.

Fig.4. Hybrid Modeling Process of WD-SVR on DB2

3.4. Hyper-parameters of SVR Forecasting methods During the process of support vector machine prediction modeling, hyper-parameters optimization of SVR model is one of the most important factors that affect the prediction performance. The particle swarm optimization algorithm was used to optimize the hyper-parameters of Chao-SVR, WD-SVR and SVR models[5]. Furthermore, RBF is one of the most popular SVR kernels. And it is necessary to optimize values for the hyper-parameters which were optimized by Particle Swarm optimization algorithm, whose range are same as the range of hyper-parameters of SVR and the optimization results are as Table 3 shown: Table 3. Hyper-Parameters optimization results by particle swarm optimization



Hybrid-parameter SVR Chaos-SVR Low frequency part A1 High frequency part D1

WD-SVR

C 1000 1 1 1

0.067334 0.048046 0.001 0.094

γ 0.1 0.1 47.22 0.1

3.5. Comparative study of four forecasting methods By the above four modeling methods, the forecasting result are compared. As shown in Fig.5(a), predicted results and actual results of one week by the four methods are compared, and the blue dot line graph represents the actual value of cooling load, while the red, green, blue and purple ones represent the forecasting results of chaos-SVR, wavelet-SVR, SVR and BP network respectively. Then in Fig. 5(b), the prediction error between predicted results and actual values are identified from which it can be seen that among the four forecasting methods, Chaos-SVR is the most accurate at the cooling load prediction with Chaotic characteristic, followed by WD-SVR, BP neural network and SVR method in descending order. 7000

Cooling Load (KW)

5000

Abs ( predicted data - original data ) Value/KW

6000

4000 3000 2000 1000 0 -1000

0

20

40

60

80

Hours

100

120

140

160

Abs(predicted data - original data)

5000

Actual Chaos-SVR WD-SVR SVR BP

4000 3500 3000 2500 2000 1500 1000 500 0

180

(a) Comparison of the actual cooling load and the forecasting results

Chaos-SVR WD-SVR SVR BP

4500

0

20

40

60

80

Hours

100

120

Fig.5. Comparison of four forecasting models EEP（%） 6.04 6.48 8.32 8.00

MBE(%) -0.85 -0.27 4.93 0.54

160

(b)Prediction error comparison

Table 4. Predicting performance comparison of four forecasting methods Prediction models Chaos-SVR WD-SVR SVR BP

140

R2 0.85 0.83 0.72 0.74

Prediction time（s） 2.07 0.88 2.88 7.28

180

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Author name / Energy Procedia 00 (2017) 000–000 Zhou Xuan et al. / Energy Procedia 142 (2017) 1799–1804

The predicting performance of these four algorithm are shown as Table 4, and it can be seen that the Chaos-SVR time series hybrid forecasting model is the most accurate, whose EEP index is lower than WD-SVR and SVR by 7.28% and 37.75%, and MBE index is higher by 68.24% and 680.00%, and R2 is higher by 2.35% and 15.29%. The WD-SVR algorithm ranks second while superior to the SVR and BP, whose EEP index is lower than SVR by 28.40%, and MBE index is much lower, and R2 is higher by 13.25%. From the perspective of prediction time, Chaos-SVR takes longest time because it includes feature extraction, separation and phase space reconstruction which costs much more time than other algorithm while SVR takes shortest. However, the predicting time by Chaos-SVR is still less than 1 min and it can also meet the requirement of air conditioning energy saving control. In general, it could be concluded that the WD-SVR and C-SVR time series hybrid forecasting methods have a strong applicability in the field of air conditioning load short time forecasting. It was illustrated that the air conditioning load time series of the shopping mall exhibit chaotic behavior and strongly non-linear characteristic due to its complicated time-varying visitor flow rate. By reconstructing the phase space and searching for the time series with the highest degree of correlation with the prediction results, the ChaosSVR makes the prediction precision further improved. 4. Conclusions. Air-conditioning cooling load for shopping malls shows strongly non-linear characteristic due to its instability and randomness affected by outside factors, like visitor flow rate, outdoor weather conditions, and it is hard to ensure its predicting accuracy. In this paper, four different proposed approach based on machine learning are illustrated through applications to predict air-conditioning load for a large-scale shopping mall and their predicting performance are compared. It can be concluded that from the perspective of comprehensive predicting performance, for this kind of building, the hybrid algorithms including Chaos-SVR and WD-SVR are better than other two single ones but the algorithmic complexity increases. Furthermore, Chaos-SVR is most suitable prediction algorithm for shopping mall cooling load because of its chaos characteristic, and WD-SVR is also a good choice in forecasting this kind of cooling load while DB2 wavelet is chosen to decompose the time series. Acknowledgements This work was supported by Science and Technology Planning Project of Guangdong Province (No. 2016B090918105) , and Natural Science Foundation of Guangdong Province (No. 2016A030313708). We thank Mr. Liu Qingdian for assistance with data. References [1] Van der Geer J, Hanraads JAJ, Lupton RA. The art of writing a scientific article. J Sci Commun 2000, 163:51-9. [2] Rahman, S M Mahbobur, Dong, Bing, Vega, Rolando. Machine Learning Approach Applied in Electricity Load Forecasting: Within Residential Houses Context[J]. ASHRAE Transactions, 2015, 121: 1-8. [3] Li Q. Prediction Model of Hourly Air Conditioning Load of Building Based on RBF Neural Network[J]. Journal of South China University of Technology, 2008, 36(10):25-30. [4] Zhou Xuan, Yang Jiancheng. An algorithm for hourly load rolling forecasting of air conditioning system based on SVR[J]. Journal of Central South University (Science and Technology), 2014, 45(3): 952-957. [5] Zhou Xuan, Yang Jiancheng. Parameters optimization of air conditioning load prediction model based on PSO-SVR[C].Proceedings of the 32nd Chinese Controi Conference, Juily 26-28, 2013, Xi'an, China. [6] Stark J, Broomhead D S, Davies M E, et al. Takens embedding theorems for forced and stochastic systems[J]. Nonlinear Analysis, 1997, 30(8):5303-5314. [7] Niu D, Wang Y, Duan C, et al. A New Short-term Power Load Forecasting Model Based on Chaotic Time Series and SVM[J]. Journal of Universal Computer Science, 2009, 15(13):2726-2745. [8] Cao L. Practical method for determining the minimum embedding dimension of a scalar time series[J]. Physica D Nonlinear Phenomena, 1997, 110(1-2):43-50. [9] Fernandez V. Wavelet- and SVM-based forecasts: An analysis of the U.S. metal and materials manufacturing industry[J]. Resources Policy, 2007, 32(1):80-89.