cooling load prediction for buildings using general regression neural networks

Energy Conversion and Management 45 (2004) 2127–2141www.elsevier.com/locate/enconman

Cooling load prediction for buildings using generalregression neural networks

Abdullatif E. Ben-Nakhi, Mohamed A. Mahmoud *

Department of Mechanical Engineering, College of Technology, Kuwait

Received 7 July 2003; accepted 14 October 2003

Abstract

General regression neural networks (GRNN) were designed and trained to investigate the feasibility of

using this technology to optimize HVAC thermal energy storage in public buildings as well as office

buildings. State of the art building simulation software, ESP-r, was used to generate a database covering the

years 1997–2001. The software was used to calculate hourly cooling loads for three office buildings using

climate records in Kuwait. The cooling load data for 1997–2000 was used for training and testing the neural

networks (NN), while robustness of the trained NN was tested by applying them to a ‘‘production’’ data set

(2001 data) that the networks have never ‘‘seen’’ before.

Three buildings of various densities of occupancy and orientational characteristics were investigated.Parametric studies were performed to determine optimum GRNN design parameters that best predict

cooling load profiles for each building. External hourly temperature readings for a 24 h period were used as

network inputs, and the hourly cooling load for the next day is the output. The performance of the NN

analysis was evaluated using a statistical indicator (the coefficient of multiple determination) and by sta-

tistical analysis of the error patterns, including confidence intervals of regression lines, as well as by

examination of the error patterns.

The results show that a properly designed NN is a powerful instrument for optimizing thermal energy

storage in buildings based only on external temperature records.� 2003 Elsevier Ltd. All rights reserved.

Keywords: Neural networks; Energy conservation; Air conditioning; Control; General regression; Building simulation;

Thermal energy storage; Cooling load

* Corresponding author. Address. P.O. Box 33145, Rumaithya 25562, Kuwait. Tel.: +965-535-1319; fax: +965-534-

9253/+965-481-1753.

E-mail address: [email protected] (M.A. Mahmoud).

0196-8904/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2003.10.009

mail to: [email protected]

2128 A.E. Ben-Nakhi, M.A. Mahmoud / Energy Conversion and Management 45 (2004) 2127–2141

1. Introduction

Thermal energy storage (TES) employment in heating, ventilating, and air conditioning(HVAC) systems have many significant advantages [1–5]. TES utilization usually reduces oper-ating costs, reduces initial costs, decreases the size of HVAC equipment (hence, lowers electricservice equipment), increases operating flexibility, facilitates backup cooling capacity, extends thecapacity of an existing system and reduces HVAC related pollutant emissions (e.g. CO2 andChlorofluorocarbon, CFC, refrigerants) [2]. Dincer [4,5] argued that TES can play a significantrole in meeting society�s needs for more efficient, environmentally benign energy use in varioussectors and appears to be one of the most promising solutions to correct the mismatch betweensupply and demand of energy.

Many storage HVAC systems perform below their expected performance [6,7]. To achieveoptimization of TES, two approaches can be implemented: optimizing TES system design, andoptimizing TES system control [8]. Several publications have covered the basics and approachesfor optimizing TES system design [9–11], while other studies were recently reported on theoptimization of TES systems via employing predictive control schemes that are capable of pre-dicting the next day thermal load with acceptable accuracy. Nakahara [12] investigated threekinds of load prediction methods, the Kalman filter (KF), group method of data handling(GMDH), and neural network (NN). Kawashima et al. [13] investigated four generally usedprediction methods to examine their accuracy for hourly thermal load prediction, concluding thatthe NN model produces the most accurate thermal load prediction. They also reported thatpredictive control could significantly reduce the operation cost without thermal energy shortage[14].

TES charging and discharging should be strongly linked with the actual weather for thenext day [15]. To the best of our knowledge, all reported predictive control schemes are basedon first predicting the weather data for the next day [12–17]. The proposed weather predic-tion schemes are based on weather forecasts issued by meteorological centers. The weathervariables considered include dry bulb temperature, relative humidity, solar radiation and cloud-iness condition. The inadequacy of these approaches lies mainly in the need for weather fore-cast reports, and usually, these reports are manually entered into the TES control. Systemsdirectly linked to the weather forecast reports, say via the internet, are, to some extent, compli-cated [15].

In this paper, the feasibility of using neural networks to optimize HVAC thermal energystorage is demonstrated through prediction of the cooling load profile of the next day directly.Attention is focused on TES in public and office buildings in which the cooling load duringbusiness hours may be quite high due to high occupancy and high ambient temperature. Thetemperature in Kuwait in the summer months can exceed 50 �C in the shade during the daytimeand can exceed 37 �C even at dawn. With such an extreme condition, there is a great potential forenergy conservation in air conditioning in these public buildings if the cooling load is accuratelypredicted and the appropriate cooling charge is stored before business hours. The problem withaccurate prediction of the cooling load is that it depends on the weather conditions, which are notknown ahead of time. This requires an advanced tool to predict the cooling load profile based onpast weather history, and artificial neural networks offer an attractive and powerful option for thispurpose.

A.E. Ben-Nakhi, M.A. Mahmoud / Energy Conversion and Management 45 (2004) 2127–2141 2129

2. Building simulation software for calculation of cooling loads

One of the most powerful building simulation codes, the ESP-r [18], was used herein to cal-culate cooling loads for the buildings considered in this study. This state of the art, whole buildingsimulation software is being evolved and applied at several research centers throughout Europesince its selection by the European Commission as a reference program for building energysimulation. This software is based on using integrated dynamic simulation in which the thermalperformance of the building is systemic, i.e. different heat transfer mechanisms (such as the effectof wind velocity on external heat transfer coefficient) interact in a complex manner. Besidesconduction and convection, all significant heat flow paths are considered. These include internaland external long wave and short wave radiation and radiation absorption by transparentmaterials. The use of such an advanced simulation tool is necessary because thermal analysis ofbuildings and their environmental control systems is complex (i.e. transient, multi-dimensionaland highly interactive), making this task difficult and time consuming. The weather inputs toESP-r include diffuse solar radiation on the horizontal, external dry bulb temperature, directnormal solar intensity, prevailing wind speed, wind direction and relative humidity. Weather datain Kuwait, used herein, were obtained from the Kuwait Institute for Scientific Research for thefive years 1997–2001. The data for 1997–2000 were used to train and test the NNs, and therobustness of the trained networks was established by applying them to a ‘‘production’’ data set(data for the year 2001) that the networks have never ‘‘seen’’ before. The cooling load profilespredicted include hourly loads during business hours and the total load for the entire day.

Three public buildings of different characteristics are considered in this study. The first, denotedB1, is a two story structure 60 m long, 40 m wide and 9 m high. This building is a high occupancydensity structure and simulates the Immigration Office in Kuwait City. With an expatriate popu-lation estimated at 1.5 million in Kuwait, thousands visit this building every business day. Thetransparent area is about 17% of the total wall area. Table 1 presents other details pertinent to thisbuilding.

Table 1

Details for the three buildings considered in the study

Building B1 Building EW Building SN

Volume (m3) 21,600 10,800 10,800

Floor area (m2) 2400 1200 1200

Total wall area (m2) 1800 1440 1440

Glazing area (m2) 312 456 456

Working hours 08:00–15:00 08:00–17:00 08:00–17:00

Infiltration rate (ACH) 0.1 0.1 0.1

Occupancy (persons):

on working hours 1300 200 200

off working hours 5 2 2

Ventilation rate (ACH):

on working hours 1.7 1.0 1.0

off working hours 0.0 0.0 0.0

Lighting (W/m2 floor area):

on working hours 30.0 30.0 30.0

off working hours 1.0 1.0 1.0


The second building, denoted EW, is a light occupancy, two story 60 m long, 20 m wide and9 m high structure. The long side of the building faces east. Each of the eastern and western wallscontains a double glazing transparent area of 87 m2, while each of the northern and southern wallscontains a double glazing transparent area of 27 m2. This building simulates the MechanicalPower Department building on the College of Technology Campus in Kuwait. The large glasswindows allow sun radiation (both direct and indirect) and, thus, contribute to the cooling loadinside the building.

It will be noticed that the NN used in this study uses only external dry bulb temperature asinput to predict the cooling load. Therefore, it was decided to investigate the effect of buildingorientation on the NN performance by studying a third building, denoted SN, which is the secondbuilding but rotated 90�, i.e. the northern and southern fac�ades contain larger transparent areasthan the other two fac�ades. In this case, the effects on the cooling load of wind and sun radiationthrough the windows during business hours are expected to be different from those effects for thesecond building. Therefore, reasonably accurate predictions of cooling loads by the NN for bothbuildings are a further proof of the robustness of the NN approach.

The building materials used in the numerical models are similar to the common buildingmaterials in Kuwait and consist mainly of cement blocks, sand-lime bricks, cement mortar andinsulation. The thermophysical and optical properties of these materials, together with those ofthe double glazing glass, were used as part of the input data to ESP-r to predict cooling loads andare given in Tables 2 and 3. The site latitude and longitude for the three buildings were assumed tobe similar to Kuwait City (i.e., 29.3�N latitude and 47.9�E longitude) where the ground reflectanceis assumed as 0.2 (ground reflectance is used in external radiation simulation).

In the public buildings considered in this study, the temperature is to be maintained at 24 �Cwithin building B1 from 8 a.m. to 3 p.m. and within buildings EW and SN from 8 a.m. to 5 p.m.

Table 2

Thermophysical properties of the test cell construction materials

Description Conductivity

(W/m �C)Density

(kg/m3)

Heat capacity

(J/kg �C)Emissivity Absorptivity

Sand lime brick 1.310 1918.0 795.3 0.900 0.650

Insulation 0.032 30.0 1214.0 0.900 0.650

Cement mortar 1.000 2085.0 837.0 0.900 0.500

Cement block 1.640 2011.0 921.0 0.900 0.500

Glass (double) 0.760 2710.0 837.0 0.830 0.050

Table 3

Optical properties of glazing materials (double glazing)

Description Data at five angles

0� 40� 55� 70� 80�Transmission 0.676 0.651 0.604 0.441 0.201

Absorption for the 4 mm clear glass 0.113 0.124 0.134 0.148 0.154

Absorption for the 10 mm air gap 0.001 0.002 0.003 0.004 0.005

Absorption for the 4 mm clear glass 0.087 0.094 0.097 0.087 0.062


After business hours, the temperature is assumed to be maintained at 30 �C in each building.Building energy simulation programs may be used to predict cooling loads during these periodsonly when the weather conditions are known. This was done in the present study, using ESP-r,to prepare a database of past history to be used with the NN to predict cooling loads for newsituations before the weather conditions are known.

An artificial neural network is usually defined as a network composed of a large number ofprocessors (neurons) that are massively interconnected, operate in parallel and learn fromexperience (examples). The artificial neural network used in this study is of the general regressionneural network (GRNN) type. A brief description of the algorithm is given in the next section.

3. Neural network algorithm

The GRNN is a one pass learning algorithm that can be used for estimation of continuousvariables and converges to the underlying regression surface. The principal advantages of theGRNN are its quick learning and fast convergence to an optimal regression surface as the numberof samples becomes large. The overall block diagram of the GRNN in its adaptive form is shownin Fig. 1. The figure shows a feedforward network that can be used to estimate a vector Y from ameasured vector X . The input units are merely distribution units, which provide the (scaled)measured variables X to all of the neurons on the second layer, which contains the pattern units.Each pattern unit (neuron) is dedicated to one exemplar (pattern) or one cluster center. When anew vector X is entered into the network, it is subtracted from the stored vector representing eachcluster center. The squares of the differences are summed and fed into a nonlinear activationfunction. The activation function used herein is logistic, in the form f ðxÞ ¼ 1

1�e�x, where x is theinput. This function is the most popular one and has been found useful for most network

x1

x2

InputUnits

Pattern Units Summation

Units

OutputUnits

f(x)K

Kxfy )(ˆ

)(ˆ xy

)('ˆ xy

Kxfy )('ˆ

Fig. 1. Block diagram of a general regression neural network.


applications [20]. The pattern units� output is passed on to the summation units. Details of theGRNN paradigm were provided by Specht [19].

The network ‘‘learns’’ by adjusting the interconnection weights between layers. The answers thenetwork is producing are repeatedly compared with the correct answers, and each time, theconnecting weights are adjusted slightly in the direction of the correct answers. Eventually, ifthe problem is learned, a stable set of weights adaptively evolves that will provide good answersfor all of the sample predictions. The real test of neural networks occurs when the trained networkis able to produce good results for new data.

In this study, over training of the neural networks was prevented by using the so-called Net-Perfect algorithm [20]. This algorithm optimizes the network by applying the current network toan independent test set during training. The algorithm finds the optimum network for the data inthe test set (which means that the network is able to generalize well and give good results on newdata), and the algorithm optimizes the smoothing factor based upon the values in the test set. Itdoes this by trying different smoothing factors and choosing the one that minimizes the meansquared error between the actual and predicted answers.

GRNN work by measuring how far a given sample pattern is from patterns in the training setin N -dimensional space, where N is the number of inputs in the problem. In this study, the methodof measuring the distance between patterns was the so-called City-Block distance metric, which isthe sum of the absolute values of the differences in all dimensions between the pattern and theweight vector for that neuron [19].

The GRNN used in this study was genetic adaptive, i.e. it uses a genetic algorithm to find theinput smoothing factor adjustment. This is used to adapt the overall smoothing factor to providea new value for each input. Genetic algorithms use a ‘‘fitness’’ measure to determine which of theindividuals in the population survive and reproduce [21]. The measure of fitness for the GRNN isthe mean squared error of the outputs for the entire data set. The genetic adaptive algorithm seeksto minimize this mean squared error.

When variables are loaded into a neural network, they must be scaled from their numeric rangeinto the numeric range that the neural network deals with efficiently. There are two main numericranges the networks commonly operate in: zero to one, denoted ½0; 1�, and minus one to one,denoted ½�1; 1�. One choice is the use of linear scaling functions for this purpose. Two possiblealternatives to these linear scaling functions are two nonlinear scaling functions: logistic and tanh.The logistic function scales data to ð0; 1Þ according to the following formula: f ðxÞ ¼ 1=ð1þexpð�xm=sÞÞ where xm is the average of all of the values of that variable in the pattern file, and s isthe standard deviation of those values. The hyperbolic tangent function (tanh) scales data toð�1; 1Þ according to: f ðxÞ ¼ tanhðxm=sÞ. As detailed later, a parametric study was conducted toselect the best scaling function for the present application.

4. Neural network results and discussion

One of the objectives of this study was to investigate the feasibility of using neural networks toestimate the next day cooling load profile before the weather conditions are known. In order touse neural networks, the simulation algorithm ESP-r was used to generate a database for the years1997–2001. The data for 1997–2000 were used for training and testing the NN. The patterns in


this database were divided into two sets. The first set consisted of 80% of the data and was usedfor training the networks. The second set consisted of the remainder 20%, selected randomly, andwas used for testing the trained networks. To evaluate the usefulness of the networks, the trainednetworks are applied to a ‘‘production’’ data set (patterns for the year 2001) that the networkshave never ‘‘seen’’ before.

The input layer to the network consisted of 24 neurons to which temperature readings (re-corded every hour) between 1:00 and 24:00 (of the previous day) were fed. The hidden layer mustcontain a minimum of one neuron for each data pattern; the number was set to 1450. The numberof neurons in the output layer is 1, which corresponds to the output (either the cooling load at aparticular hour of the next day or the total cooling load for the entire day). The statisticalindicator used to evaluate the closeness of fit is the coefficient of multiple determination, R2, that

can be defined as [20] R2 ¼ 1�P

ðy�ypÞ2Pðy�ymÞ2

where y is the actual value, yp is the predicted value of y

and ym is the mean of the y values. The coefficient of multiple determination, R2, compares theaccuracy of the model to the accuracy of a trivial benchmark model wherein the prediction issimply the mean of all of the samples. A perfect fit would result in an R2 value of 1 and a verygood fit, near 1. The quality of fit decreases as R2 decreases.

A comparison of the NN predictions and the actual values of the hourly cooling load (calcu-lated using the simulation software ESP-r) at 12:00 is shown in Fig. 2 for building B1 and the year1999. The figure shows that the NN very closely predicts the cooling load (R2 for this network is0.9858, which is proof of a very good fit). This shows that the NN is able to learn the trainingpatterns.

The real test of NN analysis is when it is applied to �production� data, i.e. data the networkshave never �seen�. The trained networks were applied to the temperature records of the year 2001for building B1. Fig. 3 shows a sample comparison of the NN predictions of the cooling load at14:00 and the actual values, and Table 4 shows R2 for each business hour. The figure shows closeagreement between the NN predictions and the actual values. Further analysis of the correlationbetween actual values (from ESP-r) and NN predictions were performed Fig. 4 shows another

0 40 80 120 160 200 240 280 320 3600

100

200

300

400

500

ESP-r

NN

Coo

ling

load

, kW

-hr

Julian Day

Fig. 2. Comparison of actual (from ESP-r) and neural hourly cooling load at 12:00, 1999, building B1.

0 40 80 120 160 200 240 280 320 3600

100

200

300

400

500

ESP-r

NN

Coo

ling

load

, kW

-hr

Julian Day

Fig. 3. Comparison of actual (from ESP-r) and neural hourly cooling load at 14:00, 2001, building B1.

Table 4

R2 for hourly cooling load predictions, building B1, 2001 data

Hour 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00

R2 0.923 0.951 0.944 0.939 0.939 0.937 0.935 0.935

The NN uses City-Block distance metric and a linear scaling function ½�1; 1�.

0 200 400 6000

200

400

600

ESP-r

GR

NN

Fig. 4. Comparison of ESP-r and NN predictions of the hourly cooling load (in kWh) in building B1 at 14:00 h in 2001.


plot of the data of Fig. 3. Ideally, the data should fall on a line of slope 1.0. A linear least squarefit through the data showed that the slope of the line of best fit has a slope �b� of 0.986. The 95%


confidence interval on �b� lies between 1.013 and 0.960. This means that one cannot reject the nullhypothesis that b ¼ 1, i.e. a 1:1 correlation between ESP-r and NN. This statistical analysis wasperformed for each business hour and the results are listed in Table 5. The table shows that for allcases, one may accept the hypothesis of a 1:1 correlation between the ESP-r values and the NNpredictions. Histogram plots of the errors (difference between NN and best line of fit), show aclose to normal distribution with mean close to 0; these histogram plots are not included hereinfor the sake of brevity.

The results presented above were obtained with GRNN using a genetic adaptive algorithm, aso-called City-Block distance metric and a linear scaling factor for the input data ½�1; 1�. Thisnetwork design was selected as a result of a parametric study of the network design as shown inTable 6. The study was intended to determine quantitatively the GRNN design that best predictsthe �production data� (i.e. for year 2001). The variables investigated included (a) different scalingfunctions (linear between ½�1; 1�, linear between ½0; 1�, logistic, and hyperbolic tangent ‘‘tanh’’)and (b) two possible ways of measuring the distance between patterns, namely the City-Blockdistance metric [19] and the Euclidean distance metric [22]. Based on the R2 results presented in thetable (top five rows), the optimum design of the GRNN for the present application and buildingB1 is one that uses the City-Block distance metric and a linear scaling function between ½�1; 1� forthe input data.

Table 5

Point estimates of slope �b� and the 95% confidence intervals for building B1 at each business hour

Hour b Confidence intervals

08:00 0.985 1:015P bP 0:95609:00 0.987 1:011P bP 0:96410:00 0.988 1:013P bP 0:96411:00 0.987 1:012P bP 0:96112:00 0.986 1:012P bP 0:96113:00 0.985 1:011P bP 0:96014:00 0.986 1:013P bP 0:96015:00 0.986 1:012P bP 0:959

b is the slope of the ESP-r vs. NN plot for 2001.

Table 6

R2 for hourly cooling load predictions and different network parameters, building B1, 2001

Distance metric and scaling

function

Hour

08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00

City-Block, linear ½�1; 1� 0.923 0.951 0.944 0.939 0.939 0.937 0.935 0.935

Euclidean, linear ½�1; 1� 0.920 0.948 0.940 0.937 0.934 0.932 0.93 0.931

City-Block, linear ½0; 1� 0.922 0.951 0.943 0.940 0.937 0.934 0.934 0.935

City-Block, logistic 0.921 0.949 0.942 0.939 0.936 0.934 0.934 0.935

City-Block, tanh 0.917 0.947 0.939 0.935 0.932 0.93 0.929 0.931

City-Block, linear ½�1; 1�;30 h training

0.927 0.957 0.948 0.944 0.940 0.938 0.938 0.940


The neural network predictions reported in the foregoing were obtained at 00:00 hour of agiven day (using temperature readings for the previous 24 h as inputs) with the intention of using

0 40 80 120 160 200 240 280 320 3600

1000

2000

3000

4000

5000

ESP-r

NN

Tot

al c

oolin

g lo

ad, k

W-h

r

Julian Day

Fig. 5. Comparison of actual (from ESP-r) and neural total daily cooling load, 2001, building B1.

Table 7

R2 for hourly cooling load predictions and different network parameters, building EW, 2001

Distance metric and

scaling function

Hour

08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

City-Block, logistic 0.92 0.937 0.929 0.928 0.926 0.922 0.92 0.922 0.933 0.939

Euclidean, linear ½�1; 1� 0.918 0.933 0.925 0.924 0.922 0.917 0.915 0.918 0.929 0.937

City-Block, linear ½0; 1� 0.92 0.936 0.927 0.926 0.924 0.92 0.918 0.921 0.933 0.940

City-Block, linear ½�1; 1� 0.919 0.935 0.927 0.925 0.923 0.918 0.916 0.92 0.932 0.939

City-Block, tanh 0.917 0.936 0.928 0.926 0.925 0.92 0.918 0.92 0.931 0.939


0.922 0.940 0.933 0.932 0.931 0.927 0.925 0.927 0.937 0.943

Table 8

R2 for hourly cooling load predictions and different network parameters, building SN, 2001

Distance metric and scaling

function

Hour

08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

City-Block, linear ½�1; 1� 0.917 0.937 0.926 0.915 0.909 0.904 0.902 0.908 0.926 0.94

Euclidean, linear ½�1; 1� 0.915 0.934 0.923 0.911 0.905 0.899 0.896 0.901 0.92 0.935

City-Block, linear ½0; 1� 0.916 0.935 0.925 0.913 0.907 0.902 0.900 0.906 0.924 0.938

City-Block, logistic 0.914 0.934 0.923 0.911 0.904 0.899 0.897 0.904 0.922 0.937

City-Block, tanh 0.911 0.93 0.918 0.905 0.898 0.892 0.891 0.899 0.919 0.935


0.92 0.939 0.928 0.917 0.912 0.908 0.907 0.914 0.932 0.945


them to optimize thermal storage for that particular day. Some authors [13–15] reported thatupdating the NN predictions at a later time, say 06:00 hour, would help further in the storageoptimization since the predictions at that time are more realistic. Nevertheless, it should be bornein mind that by that time most of the storage decisions would have been already made. Toinvestigate whether prediction updates at 06:00 a.m. are in better agreement with actual values, itwas decided to design and train a new network for each business hour to predict hourly coolingloads using, as input, temperature readings for the previous 30 h (from 01:00 the day before to06:00 of the given day). The R2 results presented in the last row of Table 6 show a slight butconsistent improvement in the NN predictions.

One other important aspect for optimizing thermal energy storage in buildings is the total dailycooling load (TDCL) for the building. To investigate the ability of the NN to predict the TDCL,

0 40 80 120 160 200 240 280 320 3600

100

200

300

ESP-r

NN

Coo

ling

load

, kW

-hr

Julian Day

Fig. 6. Comparison of actual (from ESP-r) and neural hourly cooling load at 17:00, 2001, building EW.

0 40 80 120 160 200 240 280 320 3600

1000

2000

3000

ESP-r NNT

otal

coo

ling

load

, kW

-hr

Julian Day

Fig. 7. Comparison of actual (from ESP-r) and neural daily total cooling load, 2001, building EW.


a new network was designed and trained; the input layer to the network consisted of 24 neurons towhich temperature readings (recorded every hour) between 1:00 and 24:00 (of the previous day)were fed, and the number of neurons in the output layer is 1, which corresponds to the output(TDCL for the day being investigated). Fig. 5 shows a comparison of the NN predictions of theTDCL and the actual values for the production data (year 2001). The figure shows close agree-ment between the NN predictions and the actual values; R2 in this case is 0.9552.

The same procedure used to generate Figs. 2–5 and Tables 4–6 for building B1 was used forbuildings EW and SN. This involved (a) using ESP-r to predict hourly and daily total coolingloads for the years 1997–2001, (b) training six new networks for each business hour using tem-perature data for 1997–2000 (to determine best NN design as in Table 6) and (c) applying thesetrained networks to the temperature records of the ‘‘production’’ year 2001. Tables 7 and 8

0 40 80 120 160 200 240 280 320 3600

100

200

300

ESP-r

NN

Coo

ling

load

, kW

-hr

Julian Day

Fig. 8. Comparison of actual (from ESP-r) and neural hourly cooling load at 16:00, 2001, building SN.

0 40 80 120 160 200 240 280 320 3600

1000

2000

3000

ESP-r

NN

Tot

al c

oolin

g lo

ad, k

W-h

r

Julian Day

Fig. 9. Comparison of actual (from ESP-r) and neural daily total cooling load, 2001, building SN.


present R2 for the predicted hourly cooling load for buildings EW and SN, respectively. Fromthese tables, it was determined that the best network design for both buildings is one based onusing the City-Block distance metric, rather than a Euclidean one, and that the best scalingfunction for building EW is a logistic function, while the best one for building SN is a linear½�1; 1� function. The last row of each table presents R2 for the hourly load predictions at 06:00a.m., i.e. when the input temperature readings for the previous 30 h (from 01:00 the day before to06:00 of the given day) were used. As with building B1, these results show a slight but consistentimprovement in the NN predictions for both buildings.

Figs. 6–9 show sample comparisons of the NN predictions and the actual values for the hourlyand the daily total cooling loads for buildings EW and SN. The figures show close agreementbetween the NN predictions and the actual values. The values of R2 for the total daily cooling loadpredictions shown in Figs. 7 and 9 are 0.964 and 0.949, respectively.

Further analysis of the correlation between the actual values (from ESP-r) and the NN pre-dictions for buildings EW and SN were performed as for building B1. Least square regression wasused to determine the slope of the line of best fit between the actual and predicted values (similar

Table 9

Point estimates of slope �b� and the 95% confidence intervals for building EW


08:00 0.992 1:011P bP 0:97209:00 0.986 1:016P bP 0:95610:00 0.989 1:015P bP 0:96211:00 0.988 1:016P bP 0:96012:00 0.987 1:015P bP 0:95913:00 0.987 1:015P bP 0:95914:00 0.987 1:017P bP 0:95815:00 0.988 1:018P bP 0:95816:00 0.99 1:019P bP 0:96117:00 0.992 1:020P bP 0:965

b is slope of NN vs. ESP-r plot for 2001.

Table 10

Point estimates of slope �b� and the 95% confidence intervals for building SN


08:00 0.981 1:011P bP 0:95009:00 0.984 1:010P bP 0:95810:00 0.983 1:011P bP 0:95511:00 0.982 1:011P bP 0:95212:00 0.982 1:012P bP 0:95113:00 0.983 1:014P bP 0:95114:00 0.984 1:016P bP 0:95215:00 0.986 1:018P bP 0:95516:00 0.988 1:017P bP 0:96017:00 0.991 1:017P bP 0:966

b is slope of NN vs. ESP-r plot for 2001.


to Fig. 4). Tables 9 and 10 list the slope �b� of the lines of best fit and the 95% confidence intervalson �b� for buildings EW and SN, respectively. The tables show that for all hourly predictions inboth buildings, one may accept the hypothesis of a 1:1 correlation between the ESP-r values andthe NN predictions. Histogram plots of the errors (difference between NN and best line of fit foreach case) showed close to normal distributions with means close to 0 for all cases.

5. Conclusions

GRNN were designed and trained to investigate the feasibility of using this technology tooptimize HVAC thermal energy storage in public and office buildings. A state of the art wholebuilding simulation software, the ESP-r system, was used to prepare a database of past history tobe used with the NN to predict cooling load profiles for new situations before the weather con-ditions are known. Parametric studies of the NN architecture showed that the optimum GRNNdesign might differ slightly from one building to another. Six NNs for each business hour weredesigned and trained for this purpose. The performance of the NN analysis was evaluated using astatistical indicator (the coefficient of multiple determination R2), establishing confidence intervalsof the slope of regression lines and by examination of the error patterns.

To evaluate the usefulness of the neural networks, the trained networks were applied to a‘‘production’’ data set (weather patterns for the year 2001) that the networks have never ‘‘seen’’before. The results of applying the technique on data for three buildings of different occupancyand orientation characteristics show good prediction (R2 values are high as shown in Tables 6–8).

The success of the NN in accurately predicting cooling load profiles is significant for tworeasons. The first is that the NN can predict these loads before the weather conditions are known.The second is that building simulation softwares require many more weather inputs than the NNsdo. ESP-r, for instance, requires as inputs diffuse solar radiation on the horizontal, external drybulb temperature, direct normal solar intensity, prevailing wind speed, wind direction and relativehumidity. The NN predictions, on the other hand, are based on using the external temperatureonly as input. Temperature is perhaps the easiest and most reliable weather data to measure.Based on this fact, one expects that controllers based on the NN approach will be simple to makeand reliable to use.

Acknowledgements

This work was supported by the Public Authority for Applied Education and Training,Kuwait, Grant No. TS-98-014.

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