parameter estimation of internal thermal mass of building dynamic models using genetic algorithm

Energy Conversion and Management 47 (2006) 1927–1941

www.elsevier.com/locate/enconman

Parameter estimation of internal thermal mass of buildingdynamic models using genetic algorithm

Shengwei Wang *, Xinhua Xu

Department of Building Services Engineering, The Hong Kong Polytechnic University Kowloon, Hong Kong, PR China

Received 8 March 2005; accepted 11 September 2005Available online 27 October 2005

Abstract

Building thermal transfer models are essential to predict transient cooling or heating requirements for performancemonitoring, diagnosis and control strategy analysis. Detailed physical models are time consuming and often not cost effec-tive. Black box models require a significant amount of training data and may not always reflect the physical behaviors. Inthis study, a building is described using a simplified thermal network model. For the building envelope, the model param-eters can be determined using easily available physical details. For building internal mass having thermal capacitance,including components such as furniture, partitions etc., it is very difficult to obtain detailed physical properties. To over-come this problem, this paper proposes to present the building internal mass with a thermal network structure of lumpedthermal mass and estimate the lumped parameters using operation data. A genetic algorithm estimator is developed to esti-mate the lumped internal thermal parameters of the building thermal network model using the operation data collectedfrom site monitoring. The simplified dynamic model of building internal mass is validated in different weather conditions.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Lumped thermal parameter; Building internal mass; Thermal network model; Simplified model; Genetic algorithm; Dynamicthermal performance

1. Introduction

For diagnosis purposes of a whole building [6,16], or for thermal mass control strategies [1,12,18], or evenfor energy saving by system retrofitting [4,5,27], a reference model of the building is essential for load predic-tion or cost saving estimation. At the building level as a whole process, many researchers have developed dif-ferent reference models that can be categorized into physical models and data driven models.

Physical modeling, also called forward modeling, begins with a description of the building system or com-ponent of interest and defines the building being modeled according to its physical description. Most simula-tion models are based on first principles, such as EnergyPlus [7], DOE-2 [20]. However, a large number ofparameters are needed as inputs for the simulation model. The process of collecting a physical description

0196-8904/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2005.09.011

* Corresponding author. Tel.: +852 2766 5858; fax: +852 2774 6146.E-mail address: [email protected] (S. Wang).

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Nomenclature

A area (m2)C thermal capacitance (J/(m2K))df difference between two maximum fitness valuesf fitness functionJ objective functionQ cooling/heating load or heat (kW)R thermal resistance (m2K/W)T air temperature (�C or K)t time (s)

Greek symbol

ef threshold value

Subscripts

act actual cooling loadconv convective heatei associated with external wall at ith orientationest estimatedfr fresh airim associated with building internal massin inside, indoor airla latent heatr associated with radiationrf associated with roofrtn return airsol associated with solar air temperature

1928 S. Wang, X. Xu / Energy Conversion and Management 47 (2006) 1927–1941

is time consuming and often is not cost effective, or may even be impossible for some cases (the thermal prop-erties of furniture, partitions etc.). In the modeling process, such indefinite properties are usually assumed.Unsuitable assumptions can make the model deviate from reality, thus decreasing the confidence in models.

Data driven models, also called inverse models, include steady [26,28] and dynamic ones [10,17,24,30],which are capable of capturing dynamics such as mass dynamics to some extents and are better suited to han-dle inter-correlated forcing functions or independent parameters. Applying regression techniques to the abovecan lead to models. It is generally necessary to acquire data over a long period of time with widely varyingconditions in order to train the models for accurate predictions under all conditions. Furthermore, it is notknown how well the models would perform in predicting building energy use if there were a major changein the control strategies employed, such as would occur when going from a night set up control to a pre-cooling control strategy, because those parameters do not respect the proper physics or the parameters cannotrepresent the physical properties [2].

Therefore, a kind of simplified models, which can represent the physical properties of the building systemare preferred for diagnosis, optimal control etc. Braun and Chaturvedi [2] developed an inverse gray box ther-mal network model for transient building load prediction. In the approach, a second order transfer functionwas established from an assumed 3R2C (three resistances, two capacitances) thermal network model to predictbuilding load. All the parameters of the 3R2C models for the external walls, roof, internal walls etc., whosevalues are assumed in certain ranges, need to be identified by a non-linear regression algorithm to minimizeerrors between the predictions of the transfer functions and the measured operation data. Liao and Dexter [22]developed a method to establish a simplified second order physical model to simulate the dynamic behavior ofexisting multi-zone heating systems of a residential building. In their method, the total resistance and capac-

S. Wang, X. Xu / Energy Conversion and Management 47 (2006) 1927–1941 1929

itance of the envelopes and internal mass contribute to the parameters of a simplified second order model, andthe parameters are commissioned with the monitoring operation data. With the simplified model developed, asoft sensor was built to estimate the average room air temperature for an inferential control scheme for opti-mizing the boiler controls in multi-zone heating systems [21].

However, some information of building systems, such as building envelopes, is easily available. We canestablish detailed physical models or identify the parameters of them using available property data. Otherinformation of building systems, such as internal structures, partitions, carpet, furniture etc., is difficult toobtain. Nevertheless, we can view all the heat storage materials inside the building as a lumped thermal mass,namely building internal mass, which are physically meaningful. Consequently, half of the building model isrepresented by detailed physical parameters and another half is described by identified parameters using oper-ation data. 3R2C models are usually utilized to simulate building envelopes. The nodal placement of 3R2Cmodels can be determined with simple configurations [29] or an optimized configuration [2] with the detailedphysical description. Building internal mass is represented by a 2R2C (two resistances, two capacitances)model whose resistances and capacitances are assumed to be constant. The node placement of the buildinginternal mass is identified with the 3R2C models of the building envelope and the operation data. Searchingfor the best values of the model parameters is a non-linear optimization process. A genetic algorithm [23] canquickly find a sufficiently good solution (i.e. near optimal solution) and can also be utilized to search for opti-mal parameters of the internal mass model to minimize the errors between measured values and prediction.The parameters of the building internal mass model (2R2C) are identified for a real commercial office buildingwith the operation data in a short period time. The model was also validated with different operation condi-tions. The results show that the simplified model with lumped building internal mass has good stability to pre-dict the thermal performance for different conditions because it not only describes the behavior orperformance of the building internal mass but also represents the building internal mass with physically mean-ingful lumped parameters.

2. Thermal network model of buildings

For retrofitting analysis, performance monitoring and diagnosis, control strategy development and controlapplications of HVAC systems at the building level, a virtual concept is proposed to describe the building sys-tem as a whole. A schematic virtual system for a typical building is shown in Fig. 1. The major components ofthe system are the building envelopes, internal mass, cooling/heating sources and a virtual air handling unit(AHU). The virtual AHU can accomplish the functions of maintaining air temperature and humidity withinthe building and satisfying the indoor air quality with optimized energy consumption during working hours,

ExhaustAir Damper

Flow Station

Mix Air Plenum

Outdoor Air Damper

Re-circulationAir Damper

Filter

Supply Fan

HeatingCoil

Return Fan

Temp. & Humidity Sensor

HH

CC

CoolingCoil

Fresh Air Fan

From

Chi

ller

From

Boi

ler

Building envelopes

Internal mass

Exfiltration

Infiltration

-

Internal mass

Fig. 1. Schematics of a building system.


representing all the installed AHUs in the building. In order to predict overall energy requirements conve-niently, a simplified physical model is needed to represent the whole building, including occupant activities,lighting etc., relative to cooling/heating loads. To arrive at a clear, physically interpretable model, the funda-mental assumption is necessary that the whole indoor circulated air volume is at a uniform temperature. Thisassumption is fairly common, being employed by most simulation models. It also corresponds with the usualair temperature measurement in building zones where it is customary to place a few temperature sensors atrepresentative positions in rooms and determine the average value.

The cooling requirement for a building can be separated into latent and sensible contributions. Latent heatgains, which become cooling load directly, are associated with the addition of water vapor to the air, whichmust ultimately be removed by the air handling system. In a building, latent heat gains primarily consist ofoccupant respiration, infiltration (exfiltration) of moisture, induced fresh air and aesthetic sources such asplants and fountains. Among these, the latent gains from occupants and induced fresh air are easy to estimateand measure.

The sensible heat gain of buildings is due to the heat transfer from ‘‘warm’’ surfaces within the buildings.The sources of sensible heat gains can be categorized as internal and external to the building. Typical internalsources are occupants, lights, equipments (computers, copy machines etc.), internal structures and furnitureetc., which are warned by all sorts of radiation. External sources of heat gains consist of solar radiation, whichis transmitted through windows and absorbed on external walls and energy conduction through external wallsand windows due to the difference between the ambient and indoor space temperatures.

The simplified second order physical models of the building system are the compounding of both physicalmodeling and data driven modeling. They begin with physical descriptions of certain components if theirdetailed physical characteristics are available and assumptions of the physical structures of other componentsif their detailed physical characteristics cannot be available. The parameters of the assumed physical modelsare identified with known physical descriptions and monitored operation data to provide the most accuraterepresentation of the building thermal dynamic characteristic on the basis of the assumed models and theavailable data. The models not only describe the behavior or performance of the system but also explainthe system physically. Therefore, the models can predict reliably the performance of the global buildingsystem.

laQ

2,imC 1,imC

)(2, tTim

)(1, tTim

2,imR 1,imR

1,rQ

4,rfC

2,rfC

)(4, tTrf

)(2, tTrf

5,rfR

3,rfR

1,rfR

)(, tT esol

2,rQ

frQ

convQ

inC

)(tTin4,eiC2,eiC

5,eiR)(4, tTei3,eiR)(2, tTei

1,eiR)(, tT eisol

i: the number of walls atdifferent orientations

rf: roof t: timee: external wallin: indoor airim: internal massr: radiationconv: convectivefr: fresh airla: latent heat gainact: actual cooling load

actQactQ

2R2C modelof internal mass

Fig. 2. Schematics of the thermal network model of building.


Fig. 2 depicts a schematic representation of an electrical analog for the thermal network building model.Three main categories are considered: (1) external walls, (2) roof(s) and (3) building internal mass (groundfloor is incorporated into building internal mass). External walls should be considered, respectively, accordingto their orientations because the dynamic models of the external walls at different orientations have differentforcing functions due to the changing position of the sun. External walls and the ceiling/roof are considered inthe 3R2C models. The building internal mass includes floors, partitions, crawl space in ceiling, internal walls,furniture etc. It absorbs radiant heat through the windows and that from occupants, lighting, machines etc.and then releases the heat gradually to the air space. Building internal mass is viewed as a 2R2C model, whichconsists of two resistances and two capacitances, as shown in Fig. 2. All resistances and capacitances areassumed to be time invariant. The windows have negligible energy storage and are represented as pure resis-tances. The effect of varying wind velocity on external wall convection coefficients is not considered.

The whole building energy balance can be represented with the following differential equations:

Crf ;2dT rf;2ðtÞ

dt¼ T sol;rfðtÞ � T rf ;2ðtÞ

Rrf ;1

� T rf ;2ðtÞ � T rf;4ðtÞRrf ;3

ð1Þ

Crf ;4

dT rf;4ðtÞdt

¼ T rf;2ðtÞ � T rf ;4ðtÞRrf ;3

� T rf ;4ðtÞ � T inðtÞRrf ;5

ð2Þ

Cei;2dT ei;2ðtÞ

dt¼ T sol;eiðtÞ � T ei;2ðtÞ

Rei;1� T ei;2ðtÞ � T ei;4ðtÞ

Rei; 3ð3Þ

Cei; 4dT ei;4ðtÞ

dt¼ T ei;2ðtÞ � T ei;4ðtÞ

Rei;3� T ei;4ðtÞ � T inðtÞ

Rei;5ð4Þ

Cim;1

dT im;1ðtÞdt

¼ Qr;1 �T im;1ðtÞ � T im;2ðtÞ

Rim;1

ð5Þ

Cim;2

dT im;2ðtÞdt

¼ Qr;2 þT im;1ðtÞ � T im;2ðtÞ

Rim;1

� T im;2ðtÞ � T inðtÞRim;2

ð6Þ

Qest ¼Xn

i¼1

ðT ei;4ðtÞ � T inðtÞRei;5

Þ þ T rf ;4ðtÞ � T inðtÞRrf;5

þ T im;2ðtÞ � T inðtÞRim;2

� Cin

dT inðtÞdt

þ ðQconv þ Qfr þ QlaÞ ð7Þ

Qest ffi Qact ð8Þ

where C and R are resistance and capacitance, T is temperature, subscripts rf, im, ei and in, indicate roof,internal mass, the ith external wall and inside, respectively. Qr,1 and Qr,2 absorbed by nodes Cim,1 andCim,2, respectively, are the radiation, which includes the radiation from solar radiation through the windowsand from occupants, lights etc. Qconv is the convective heat from windows surfaces, occupants, lights etc. Qfr isthe heat transfer because of fresh air induction, infiltration (exfiltration). Qla is the latent heat gain from occu-pants etc. Qest andQact are the estimated cooling load with the model and the actual cooling load, which can bemeasured from the central plant.

The model parameters of the building envelope (i.e. external walls and roofs) can be determined with simpleconfigurations or optimized configurations using the property data of the envelope. The model parametersCim,1, Rim,1, Cim,2 and Rim,2 of the building internal mass are identified using the operation data, while themodel parameters of the building envelope are obtained in advance. A genetic algorithm (GA) based methodis used for parameter identification as illustrated in the next section.

3. Parameter identification of building internal mass with GA

Finding the best values of the parameters of the 2R2C model of the building internal thermal mass is a non-linear optimization process. House and Smith [15] employed sequential quadratic programming to computethe optimal values. Nizet et al. [25] used a conjugate gradient method to develop an optimal control method.Both optimization methods, as well as other conventional optimization methods have to start from initial


guesses of the optimal variables and their convergence speed is affected by their initial guesses in most cases. Agenetic algorithm (GA) is a better optimization method, especially when an optimal problem is not perfectlysmooth and uni-modal [23]. It can quickly find a sufficiently good solution (i.e. near optimal solution) and canbe applied when a task does not require an ‘‘absolute’’ optimum. The algorithm has been used to search forglobal optimal solutions in air conditioning fields [31,32]. In this study, a GA is utilized to search for optimalparameters of the 2R2C model of the building internal mass to minimize the errors between measured valuesand prediction of the building model. The GA based method is described as follows.

3.1. Objective function of optimization

The simulated prediction of the building model with the differential equations (1)–(7) is used to comparewith the measured cooling load. The optimized parameters are the resistances and capacitances of the2R2C model of the building internal mass that give the best fit with the operation data. The objective function(J) of such optimization employs the integrated root mean square error defined in Eq. (9).

JðCim;1;Rim;1;Cim;2;Rim;2Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNk¼1

ðQact;k � Qest;kÞ2

N � 1

vuuutð9Þ

where Qact is the actual measured cooling/heating load, Qest is the model predicted cooling/heating load andCim,1, Rim,1, Cim,2, Rim,2 are the parameters of the 2R2C model. This is a typical non-linear optimization prob-lem. A GA (genetic algorithm) is employed to search for the optimal values as illustrated in Section 3.2.

The measured cooling/heating load is calculated using the return and supply water temperature difference and

the water flow rate retrieved from the BMS (building management system). To predict the building cooling/heating load using the building thermal network model, the indoor air temperature and humidity, outdoor

air temperature and humidity, fresh air flow rate, solar radiation, occupancy and internal gains are needed.The means to collect these data for parameter identification of the internal mass are described in detail in Sec-tion 4.

3.2. GA estimator

A GA is an advanced search and optimization technique. It has been developed to imitate the evolutionaryprinciple of natural genetics. The GA was invented by Holland [14] and further developed in the 1960s and1970s. Goldberg [11], Davis [8] and Mitchell [23] provided comprehensive overviews and introductions toGAs. Deb [9] compared the GA search method with traditional methods (the direct exhaustive search methodand the gradient directed search method) for function optimization. One of the main advantages of a GA isthat it is generally robust in finding global optimal solutions, particularly in multi-modal and multi-objectiveoptimization problems [9]. Extensive research on the theoretical fundamentals and applications of GAs is stillgoing on, aimed at better computation efficiency, improved robustness and so on.

Fig. 3 shows schematically the flow chart of the GA estimator developed for parameter identification of the2R2C model of building internal mass. It starts with the initial estimates of the individual capacitances andresistances within assumed ranges. The component with grey background represents the procedures of aGA run. Multiple runs are allowed. Eq. (10) represents the fitness function (f), which is the reciprocal ofthe objective function (Eq. (9)).

f ¼ f ðCim;1;Rim;1;Cim;2;Rim;2Þ ¼1

JðCim;1;Rim;1;Cim;2;Rim;2Þð10Þ

In the genetic algorithm, the four parameters (Cim,1, Rim,1, Cim,2, Rim,2) constitute the chromosome of an indi-vidual, the assumed ranges of these parameters are the search space for these parameters. Initializing the fourparameters produces the initial population to start a GA run.

Termination of a GA run is decided if the number of the current generation is equal to a predefined max-imum number. At least two runs of the GA process are necessary when running the GA estimator. The

Fig. 3. Flow chart of the GA estimator for parameter estimation of building internal mass model (2R2C).


criterion to stop the GA estimator is based on the comparison of the best fitness values of two consecutiveruns. If the relative difference between the two maximum fitness values (df) is less than a threshold value(ef, e.g. equals 0.0001), the GA estimator is stopped. A GA driver developed by Carroll [3] is revised and usedin this study.

4. Building system description and data collection

The simplified building dynamic model and the identification method of the lumped thermal parameters ofthe building internal mass are validated in a real building. The building system description and simplificationmeasures, as well as data collection, are briefed below.

4.1. Building system description and simplification

The building in consideration, China Resources Buildings, located at 26th Harbor Road, Hong Kong, wascompleted in 1983. The buildings consist of a main building of 50 floors with 180 m height, an attachedbuilding of seven floors with about 28 m height and a basement of three floors. For the main building, the


first and second floors serve as a shopping center with open corridors at the perimeter zone connecting thedifferent buildings. The third, fourth and fifth floors are restaurants. The sixth floor is used for the chillerplant. The commercial offices are located from the 7th to the 49th floors with 2262 m2 (58 by 39 m) per floorexcept that the 15th, 31st and 48th floors are for refuge use. The 50th floor is used for a banquet hall with 6 mheight. For the attached building, the first and second floors also serve as a shopping center with open corri-dors at the perimeter zone connecting different buildings. The third and fourth floors are used as an exhibitionhall with atrium in the center. The 5th, 6th and 7th floors are used for offices with 1738 m2 (22 by 79 m) perfloor, and the roof is covered with a swimming pool. The basements are used as a garage.

All the buildings are constructed primarily of heavy weight steel concrete with transportation systems andAHU plants in the cores. The external walls above the 2nd floor are a multi-layer construction consisting offive layers of homogeneous materials including 300 mm high density concrete between 13 mm face brick andabout 13 mm plaster with outside and inside air films. The floors are 150 mm high density concrete with abouta 50 mm refurbishment layer. For the office floors, the ratio of window to wall is about 25%. For restaurantfloors and exhibition hall, there are almost no external windows. The exterior of the 1st and 2nd floors of themain building and the attached building are glass curtains and mostly shaded outside.

All the buildings are air conditioned with the chiller water plant on the 6th floor except that the banquethall on the 50th floor is supplied with a separate air cooled package unit, and the basements are almost not airconditioned. The condensing heat is taken away by a sea water cooling system. The plant is equipped withthree centrifugal chillers with each having 3866 kW cooling capacity, two chillers with each having1055 kW cooling capacity and one chiller with 3164 kW cooling capacity. Therefore, the cooling capacityis approximately 137 W/m2 (gross area 123,000 m2 not including the 50th floor and basements). The watersystem configuration is constant primary and variable secondary water. Most of the air conditioningterminals are AHUs, which are located in the core areas. Basically, in the office floors, two CAVs (constantair volume) service the perimeter zone and two or three VAVs (variable air volume) service the innerzone.

For convenient modeling, the following simplification measures are assumed: (1). The refuge floors areopen air with window orifices. The heat transfer from the refuge floors to the adjacent floors are calculatedthrough the structure of 150 mm high density concrete with a simplified 3R2 C model; (2). The ceiling ofthe 49th floor is considered as adiabatic because the 50th floor is air conditioned with a separate unit; (3).The ceiling of the 7th floor of the attached building is also considered as adiabatic because the roof is coveredwith a swimming pool; (4). The ground floor is merged into the building internal mass without specialconsiderations.

4.2. Data collection and processing

A site survey was conducted and original design information was collected to build the complete profiles ofoccupancy and the use of lighting and equipment. The occupancy load and the internal load from lighting andequipment were estimated according to the rules established in a previous research on Hong Kong buildings[13] as briefed in the following. The normal occupancy period of the offices, shopping center and restaurant isfrom 8:00 am to 6:00 pm, from 10:30 am to 10:00 pm and from 6:30 am to 10:00 pm or later, respectively. Thedesign densities of occupancy for the three places are 9, 4.5 and 2 m2 per person, respectively. The designequipment powers for the three places are 25, 30 and 55 W/m2, respectively. The design lighting powers forthe three places are 25, 70 and 35 W/m2, respectively. The normal patterns of occupancy, equipment powerand lighting power are shown in Fig. 4 (occupancy load, light power and equipment power pattern are in frac-tions of their respective peak values). The internal gain from occupancy, lighting and equipments can be splitinto convective and radiative components (occupancy heat gains: latent heat 40%, convective 20% and radi-ative 40%; lighting heat gains: convective 50% and radiative 50% (mostly fluorescent lights); equipment heatgains: convective 80–20% and radiative 20–80%).

The offices, shopping centers and restaurants are supplied with fixed amounts of fresh air with the ventila-tion rates of 10, 7 and 7 L/s per person in the occupancy periods. Although the building is tight, mostly withfixed windows, the infiltration rate is considered as 0.1 ach (air changes per hour) in the occupied periods and0.5 ach in the unoccupied periods.

Time (h)

Dai

lypa

ttern

ofeq

ipm

entl

oad

(-)

0 4 8 12 16 20 240.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0OfficeShopping centerRestaurant

Time (h)

Dai

lypa

tter

nof

Ligh

ting

load

(-)

0 4 8 12 16 20 240.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Office perimeter zoneOffice interior zoneShopping centerRestaurant

Time (h)

Dai

lypa

tter

nof

occu

pant

load

(-)

0 4 8 12 16 20 240.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0OfficeShopping centerRestaurant

(a)

(b)

(c)

Fig. 4. Normal patterns of occupancy load, equipment power load and lighting power load.


The return air temperature of the AHUs and the actual cooling load of the chiller plant were measured andrecorded by the BMS. The outdoor air temperature and humidity were measured by the BMS as well. An aver-age return air temperature was taken as the uniform indoor air temperature, as shown in Eq. (11).

T in ¼XN

i¼1

Ai

A0

T rtnðiÞ ð11Þ


where Tin and Trtn is the uniform indoor air temperature and the return air temperature of the ith AHU. Ai

and A0 are the served area of the ith AHU and the total served area.Solar radiation cannot be measured directly at the site. Instead, the horizontal global solar radiation was

obtained from the Hong Kong Royal Observatory. It was decomposed into direct normal solar radiation anddiffuse solar radiation with the relationship established by Lam and Li [19] or by Yik and Chung et al. [33] forHong Kong. The direct normal solar radiation and diffuse solar radiation were used to calculate the ‘‘solar airtemperature’’ on the different external wall surfaces and the solar radiation transmitted through the windows.

5. Validation results and analysis

The parameters of the 2R2C model of the building internal mass were identified using the monitored dataof fourteen consecutive days (two weeks) in the summer season. The indoor air temperature can also be esti-mated with the identified parameters and the recorded cooling load. The operation data of the building werealso collected to assess the accuracy and stability of the building model with the identified parameters of thebuilding internal mass model to estimate the cooling load and the indoor air temperature in other operationconditions.

5.1. Identified parameters of 2R2C building internal mass model

For the concerned building, the basic structure of the floor layer is 150 mm high density concrete. Becausethe internal mass includes the basic structure of the floor layer, the partitions, the internal walls, furniture etc.,the searching scopes of the parameters of the building internal mass with the GA estimator should be muchlarger than the capacitance and resistance of the basic structure of the floor layer. The searching scope of thetwo resistances of the building internal mass was assumed as the resistance of the indoor air film plus threetimes the resistance of the floor basic structure. The searching scope of the two capacitances of the buildinginternal mass was assumed as three times the capacitance of the floor basic structure.

The operation data of the building for fourteen consecutive days (two weeks) in the typical summer seasonwere used to identify the parameters of the 2R2C building internal mass model. The outdoor air temperatureand the horizontal global solar radiation for the parameter identification case are shown in Fig. 5. Most of thedays were sunny and cloudy. Some days were in sunny periods with a few showers.

The air conditioning systems in the offices were shut down except from 8:00 am to 18:00 pm of office hours.The air conditioning systems in the restaurants and shopping centers were shut down a little later. Almost eachoffice floor has fan coil units to supply the cooling load of communication or computation rooms for non-office hours, such as night time and holidays. The cooling load in these hours was only a very small partof the total building cooling load in normal office hours. The temperatures measured in non-office hours can-not represent the indoor air temperature because the sensors installed in the air chamber (in the core of thebuilding) and the air in the offices is stagnant. Therefore, only the operation data during office hours were used

Time (h)

Out

door

air

tem

pera

ture

(o C)

Hor

izon

talg

loba

lsol

arra

diat

ion

(MJ/

h)

0 24 48 72 96 120 144 168 192 216 240 264 288 312 33615.0

20.0

25.0

30.0

35.0

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00Outdoor air temperatureHorizontal global solar radiation

Fig. 5. Outdoor air temperature and horizontal global solar radiation (parameter identification case).


to identify the parameters of the building internal mass model. It is worth noting that the operation data innon-office hours are preferably used in the regression fittings for parameter identification when reliable mea-surements in that period are available.

The identified parameters using the GA estimator are: Cim,1 = 648,729 J/(m2K), Cim,2 = 73,793 J/(m2K),Rim,1 = 0.299 m2K/W, Rim,2 = 0.0282 m2K/W.

Fig. 6 presents a comparison between the model predicted cooling load with the identified parameters of thebuilding internal mass model and the actual measured cooling load. It shows that the model predicted coolingload followed the dynamic profile of the actual measured cooling load well. The average error (average ofabsolute deviation) was 7.8% for the data points during office hours from 8:00 am to 18:00 pm. If all the datapoints, including those in office hours and non-office hours, were used for model validation, the error wasslightly higher, 18.5%, because the model tended to over predict the cooling load for non-office hours. Itcan be explained that the ‘‘measured’’ uniform indoor air temperature, as Eq. (11), is higher than the actualtemperature in non-office hours, which is described as follows.

Fig. 7 presents the model predicted uniform indoor air temperature with the identified parameters of thebuilding internal mass model and the measured cooling load in the period used for the parameter identifica-tion. It shows that the identified model predicted well the trends of the indoor air temperature. At the begin-ning of office hours, the indoor air was cooled by the air handling systems. In contrast, when the air handlingsystems were shut down in non-office hours, the indoor air was warmed by heat transfer through the buildingenvelopes and released heat from the building internal mass, which absorbed amounts of radiant heat fromsolar radiation, occupancy etc. The comparison shows that the model predicted indoor air temperature inthe office hours agreed well with the ‘‘measured’’ uniform indoor air temperature, which was ‘‘measured’’using the measured return air temperatures as shown in Eq. (11). In non-office hours, the model predicted

Time (h)

Coo

ling

Load

(Kw

)

0 48 96 144 192 240 288 3360

3000

6000

9000

12000

15000Actual measured cooling loadModel predicted cooling load

Fig. 6. Actual measured cooling load vs model predicted cooling load (parameter identification case).

Time (h)

Indo

orai

rtem

pera

ture

(o C)

0 48 96 144 192 240 288 33615.0

18.0

21.0

24.0

27.0

30.0"Measured" uniform indoor air temperatureModel predicted indoor air temperature

Fig. 7. ‘‘Measured’’ uniform indoor air temperature vs model predicted indoor air temperature (parameter identification case).


indoor air temperature was higher than the ‘‘measured’’ uniform indoor air temperature. It is because, in officehours, the air was circulating, and the measured return air temperature in the return air chamber could wellrepresent the indoor air temperature. However, in non-office hours, the measured return air temperature wasobviously lower than the real indoor air temperatures in the summer season because the air was stagnant andthe measured return air temperature in the return air chamber (in core area) was not affected (i.e. heated) sig-nificantly by the outside weather condition. Therefore, the model predicted indoor air temperature could rep-resent the uniform indoor air temperature more accurately compared with the ‘‘measured’’ uniform indoor airtemperature in non-office hours.

5.2. Validation of building model

To validate the building model and the parameter identification method, the building model was used topredict the cooling load with the ‘‘measured’’ uniform indoor air temperature in two other operation periods.One was also in the summer season, lasting for two weeks, and the other was in the winter season, lasting forone week. The same building model was also used to predict the uniform indoor air temperature with the givencooling load. The internal heat gains were kept unchanged in the two cases.

In the summer case, the weather condition was similar to that used for the training process as shown inFig. 5. Fig. 8 presents the model predicted cooling load profile using the building model and the actual mea-sured cooling load profile. It shows that the predicted cooling load could follow the trends of actual energyconsumption well. The average error between the predicted and measured cooling loads was 9.7% when thedata points in non-office hours were excluded. The average error was 22.0% if all the data points (both innon-office hours and office hours) were included. It shows that the building model can predict the cooling loadwith acceptable accuracy for practical application.

The predicted uniform indoor air temperatures in the office hours were close to the ‘‘measured’’ indoor airtemperatures based on the measured return air temperatures as shown in Fig. 9. The model predicted temper-ature well matched the actual indoor air temperature and its dynamic trend. Fig. 9 also displayed the ‘‘mea-sured’’ indoor air temperatures in the non-office hours (at night and weekend days), which were much lowerthan the predicted uniform indoor air temperatures. The situation was similar to that stated in Section 5.1.

The building model was also validated with a week long operation data in a winter case in Hong Kong.Fig. 10 shows the outdoor air temperature profile and horizontal global solar radiation profile. The outdoorair temperature was much low than that in the summer season. Most of the days were sunny, and the inten-sities of the solar radiation are a little lower than that used for the training process. Fig. 11 presents the actualmeasured cooling load and model predicted cooling load. The model predicted cooling load agreed with theactual measured cooling load in office hours with a corresponding average error of 12.0%. The total error,including all the data points, was higher, at 20.1%, because there was significant deviation in the 7th day(Sunday).

Time (h)

Coo

ling

Load

(Kw

)

0 48 96 144 192 240 288 3360

3000

6000

9000

12000


Fig. 8. Actual measured cooling load vs model predicted cooling load (validation–summer case).

Time (h)

Indo

orai

rte

mpe

ratu

re(o C

)

0 48 96 144 192 240 288 33615.0

18.0

21.0

24.0

27.0

30.0"Measured" uniform indoor air temperatureModel predicted indoor air temperature

Fig. 9. ‘‘Measured’’ uniform indoor air temperature vs model predicted indoor air temperature (validation–summer case).

Time (h)

Out

door

air

tem

pera

ture

(o C)

Hor

izon

talg

loba

lsol

arra

diat

ion

(MJ/

h)

0 24 48 72 96 120 144 16810.0

15.0

20.0

25.0

0.00

0.50

1.00

1.50

2.00

2.50

3.00Outdoor air temperatureHorizontal global solar radiation

Fig. 10. Outdoor air temperature and horizontal global solar radiation (validation–winter case).

Time (h)

Coo

ling

Load

(Kw

)

0 24 48 72 96 120 144 1680

2500

5000

7500


Fig. 11. Actual measured cooling load vs model predicted cooling load (validation–winter case).


6. Conclusion

Simplified models, which can represent the physical properties of a building system are desired for diagno-sis, control strategy analysis etc. The simplified thermal network model describes all the heat storage materialsinside the building, including the floors, internal walls etc., as a simplified lumped thermal network model with2R2C structure. The procedure to estimate the lumped thermal parameters of the building internal massmodel (2R2C) with the genetic algorithm presented in the study can be effectively used to identify the param-eters using short term operation data.


The parameters of the internal thermal network model of a commercial office building were identified usingoperation data of two weeks in the summer season. The results show that the trained model can predict thecooling load and average indoor air temperature in office hours with good accuracy. The entire building ther-mal network model, consisting of building envelope models and internal thermal model, can also be extrap-olated well to other operating conditions. The predicted cooling load in office hours in other operatingconditions using the building thermal network model shows the average error was about 10% compared tothe actual measured cooling load in the other two test conditions. The model can also predict average indoorair temperature in office hours with good accuracy.

In summary, the model has good robustness to predict the thermal performance under different operationconditions by capturing the dynamic characteristics of the building system correctly. The good robustness ofthe model is due to the parameters of the building internal mass model (2R2C) and the model structure, whichnot only describes the behavior or performance of the building internal mass but also represents the buildinginternal mass physically. The model can be used to predict building thermal performance for practical appli-cations with acceptable accuracy and good reliability.

Acknowledgements

The research presented in this paper was financially supported by a research grant of the Research GrantsCouncil (RGC) of the Hong Kong SAR and a research grant of The Hong Kong Polytechnic University.

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