Sky temperature modelisation and applications in building simulation

Sky temperature modelisation and applications in building simulation

PERGAMON SKY TEMPERATURE Renewable Energy I5 (I 998) 418430 MODELISATION AND APPLICATIONS IN BUILDING SIMULATION. L. ADELARD, F. PIGNOLET-TARDA...

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PERGAMON

SKY TEMPERATURE

Renewable

Energy

I5

(I 998) 418430

MODELISATION AND APPLICATIONS IN BUILDING SIMULATION.

L. ADELARD, F. PIGNOLET-TARDAN, T. MARA, P. LAURET, F. GARDE, H. BOYER Chercheurs au Laboratoire de Genie Industriel, Universite de la Reunion, 15 av. RenC Cassin 97705 Saint Denis Messag Cedex 9, Reunion Island Tel : (262 ) 93 82 16 ; Fax : (262) 93 8166; Email : [email protected]

ABSTRACT - The sky temperature is an important parameter for simulation codes in building studies. A preliminary campaign of validation of a simulation software CODYRUN has demonstrated the misinterpretation of the radiative exchanges of long waves between the building and its environment. A bibliographical research has then led to the use models using dry air temperature to estimate sky temperature. However, these models has not been completely satisfactory as far as night clear sky are concerned. In this case, sky temperature remains overestimated. A research of a non linear model has been undertaken, leading to the use of neural networks with satisfactory results. Sky temperature is then calculated and reinjected into the simulation code. Comparison between simulated temperature and measures has turned to be acceptable. c; 1998 Published by Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION The account of radiative exchanges with the sky lays a problem that is common to various fields of solar energy applications, as solar collectors, thermal behaviour of outer walls or greenhouse. Sky temperature is a fictitious temperature, introduced to model the long wave radiation exchanges with the sky. Often taken as equal to the dry air temperature of the external air, this model is faulty, especially in temperate climates during very clear nights. Several authors offered various relations and take into consideration the external dry air temperature (Swinbank, 1963), the dew temperature (Berger and a1.,1984), or the degree of cloud cover (Roulet, 1987). Nonetheless, this procedure remains problematic, correlations being only acceptable in certain weather conditions or for a specific site. The interest in the precise definition of this parameter has become clear during the experimental validation phase of a thermal building simulation CODYRUN, during the experiments on light weight 0960-1481/98/%see front matter PII: SO960-1481(98)00198-0

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buildings with low emissivity roofs. The empirical models found in literature are specific to one area and need to be readapted to a tropical humid climate. A campaign of measures was then undertaken to find a more accurate model for Reunion Island in the Indian Ocean [2 1’ S.,55” E]. After a comparison between several traditional models, we decided to use non linear methods with neural networks techniques (Grondin Perez, 1994). These new techniques led to a black box model which can be used with noisy data. Besides, its capacity to take into account several inputs and interpret very complicated relations allows it to be more and more used into meteorological studies, and even in tornadoes forecast (Marzban and al., 1996). Results presented in this article show the performances of this black box model and the improvements made at the level of the simulations.

2. AN OVERVIEW OF CODYRUN SOFTWARE. CODYRUN is a thermal multizone software integrating both natural ventilation and moisture transfers. Its main characteristics is to be a multiple model structure, allowing the choice between a wide range of models of heat transfer and meteorological data reconstitution. Concerning the calculation, the main parts are the airflow model (pressure model taking into account wind, thermal buoyancy and large openings), the thermal model and the moisture transfer model. The thermal model relies on usual assumptions as monodimensional heat conduction in walls, well mixed air volumes, and linearized superficial exchanges. Lumped capacities analysis leads to an electrical network representative of the building model. Thus, the principle of energy conservation applied to each concerned wall node, associated with the sensible balance of the air volume, constitute a set of equations, solved by finite differences. During a simulation, one of the most interesting aspects is to offer the expert thermician a wide range of choices between different heat transfer models and meteorological reconstitution parameter models. For the study presented in this paper, different models of sky temperature proposed in literature were tested thanks to this multiple model aspect. More information can be obtained about the software concerning multiple model aspect in (Boyer and al, 1993,1997), building description in (Boyer and a1.,1994), thermal model constitution in (Boyer and al., 1999) and preliminary software validation in (Garde and al., 1995).

3. OVERVIEW OF THE INSTRUMENTED

SITES.

To validate the simulation code in indoor realistic cases, a real size test cell has been settled on the faculty roof It is composed of a single room. Its size is 3.0 x 3.0 x 2.30m ( see fig. 1). The test cell is made of sandwich panels consisting of two 7 mm layers of ciment-fiber boards with 6 cm of polyurethane foam between them. A layer of 5 cm of Styrofoam is put between the floor panel and the concrete. On the roof, there is an extra sandwich panel, made of aluminium sheets and polyurethane, about 5 cm thick. The inner floor is made of Scm concrete paving stones placed on 5 cm of polystyren.

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Fig 1: Figure of the test cell.

The other realistic case is an existing house located at ‘1’Hermitage’at Reunion Island, near the coast. The walls are built with heavy concrete of 15cm thick, recovered on the inner part with panelling of 3mm thick. The roof is made of two elements : sheet steel, and plywood, with a confined air layer between both. This type of roof is widely used in Reunion Island because of its low cost. The sheet steel is grey-coloured above bedroom 1 (fig. 2), and red for the rest of the house. The veranda roof is made of ordinary grey sheet metal. During our experimentations, we have measured exterior temperature, relative humidity, global and diffuse solar radiation, wind speed and surfaces temperature of the roof as meteorological inputs

Fia 2

: Plan of the house in exuerimentatron in situ, and captors settlement

Concerning internal parameters, we have measured, in each room, the dry air temperature by means of type T thermocouples, located at 150 meters high from the ground. We have also

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measured the surface temperatures of the ceilings, (including the veranda ceiling). The results obtained concerning comparison of model and measurements were fairly good (Garde, 1997), except for some particular sequences. In these cases, analysing one point after another, the main discrepancies were found on external roofs surfaces. Then, signal processing techniques (nowadays currently used in validation) (Mara, 1995). allows us to point this external temperature error to be mainly responsible of differences between indoor measurements and calculations. As long wave radiation measurements were not made at that time, the only thing we could do was to use models found in bibliography. Tc = Ta - K, with K= 6 was the best appropriate value (Tc and Ta stand respectively for sky and dry air temperatures) (Garde, 1997). However, the results were not satisfying for the case of clear sky, were the sky temperature is overestimated.

4. BIBLIOGRAPHY ON SKY TEMPERATURE

MODEL.

Each volume of atmosphere emits a long wave radiation, in all directions. Radiative requests of long waves mainly correspond to the spectral band [5um to lOOurn], with a maximum at 10um. When solar radiation go through the atmosphere, a part of it is absorbed or scattered by air molecules, sprays, clouds, water vapour, ozone and carbon dioxide. The atmosphere, assimilated to the sky vault gets two transparency windows into it emits long waves radiation. -The first window is situated between 3.5um and 4um. -The second window is situated between 9um and 12um in which a body can emit a radiation without receiving a counterpart. The atmosphere is assimilated to a grey body. Berger proposed two relations for the determination of sky emissivity using the dew point temperature: &, = 0.77 + 0.0038 r+ for daytime E, = 0.752 + 0.0048 T&

for night-time

Former studies made on Reunion Island (Tourrand, 1991) have led to the very first estimations concerning local sky temperatures. The results can be found in the following table. Table 1.

First estimations of the sky temperature for Reunion Island site. Night

Dav Average on 23 Days Average on 14 Summer Days Average on 9 Winter Days Maximum Minimum

21.9”C 22°C 21.8OC 29.5”C

17.5”C 17.5OC 17.5”C ____ 10.5oC

The correlation allowing the sky temperature determination are usually done according to the meteorological parameters which are measured at the ground surface (air temperature, air water vapor tension and sky cloud cover). The most simple formulations of sky temperature Tc depend on dry air temperature Ta:

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T, = T,

(Dreyfus, 1960)

T,=0.0552 T, ‘.5

(Swinbank,l963)

T,” = T (1- 0.261 exp(-7.77

lo-‘) (T, - 273)*)

(Daguenet,1985)

Others formulations take into account the water vapor tension P, of the air to which the sky temperature is more correlated, with a regression coefficient equal to 0.914 in comparison with the regression coefficient equal to 0.776 for air temperature. r, = r, (0.56+0.08p,“~5)025

(Melchor,1982)

r, = r, (0.55 + 3.85 lo-’ ,“.5)o.25

(Daguenet,1985)

Presence of clouds slightly increases the importance of atmospheric emission. Some predictive, more complete correlations are done with three parameters: air temperature (T,), water vapor tension (PJ and cloud cover (N,). Daguenet, (Daguenet, 1985), established a correlation for nightly data, without solar radiation.

T, =(T,(a+b.p,O.5)(1-

VN, VNe 8 )+,)

025

Ne = 8 for a clear sky and Ne = 0 for a cover sky. a and b are according to the altitude and the situation. v = 0.9 for low altitude cloud and v = 0 for cirrus. v = 0.8 as average value is recommended. The following formulation, proposed by Roulet (Roulet, 1987), is used for daily data:

r, = (i),;!with:

L=L,(l+O.Ol

A)+

BC (8-N,) 8

Lo=3.6(T,-273)+231 A = 10.1 ln(P,) - 12.3 B=1,7(T,-273)+

107

C = -0.22 ln(PV) + 1.25 The correlation established by Aubinet, (Aubinet,l994) use the clearness index K, (which is the ratio between extraterrestrial radiation and global solar radiation) : T,= 94 + 12.6 ln(PV) - 13 K,+ 0.341 T, For Donnet and Berger (Donet and al.,1983), the various formulations proposed give large dispersion for sky temperature values because of their relative simplicity. Therefore, all of these models use ground level measures that can be hardly linked to Tc. Therefore sky temperature model using radiosounding measures were made taking account of the multiple layer transmission in the atmosphere. Determination of the multiple transmittances is made with Low&an 3D. However this model is very sophisticated, but needs a great computation time.

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5. WEATHER DATA ACOUISITION

FOR SKY TEMPERATURE

MODELLING

The Campaign of measures took began at August 15’i’1997, i.e in the dry season on the roof of the faculty. A pyrgeometer CGI (of Kipp & Zonen) is added to the previous instruments used for meteorology measures. This instrument is used to measure the radiation between 5 and 25um. This probe gives a signal proportional to the long wave radiation taking account of its temperature. This instrument has a limited vision (about 1500). This tends to limit the measure precision (about 10%). The sampling time lasts 10 minutes. Thus, a moving average for one hour (6 points), is applied in order to reduce disturbances caused by the measures. The atmospheric radiation allows sky temperature calculation. Wind direction is not taken into account. As a first observation, we can say that the sky temperature is really overestimated for a clear sky. Figures 4 and 5 present the data for a cloudy day and a clear day. For a clear sky, the difference between the air temperature and the sky temperature is about 15”. Evolutions

of sky and dry air temperature

for a sequence

of the fresh season

r

I

200

400

600

800

1000

;ig. 3: Descriutron of air temDerature and skv temperature

1200

1400

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Measured temperatures

l

3

5

7

9

11

Measured temperatures

for a clear

13 15 17

19 21

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23

0

3

6

Hours -Sky

temperature

-Air

( -Sky

temperature;

1

3

5

and the sky temperature

7

9

ill;

15 17

19 21

a cloudy

9 12 15 18 21 H0U-S

temperature

-Air

temperature

Difference between air temperature and sky temperature

Difference between the air temperature

for

23

0

2

4

6

8

10

12

14 16

HOUS

big. 4 and 5 : Description of skv temperature evolution for clear and clouds skies.

6.

SKY TEMPERATURE

18 20

22

J

AND NEURAL NETWORK.

All of the relations established to calculate the sky temperature in function of the other climatic variables did not take the past of the variables into account. So, the first step of our reseach consist in creating a single model taking not account of the past and leading to a single relation. This way didn’t give good results, at a second step 2, we tried to establish an ARMAX model: Y(t) = f(u(t - l), u(t - 2),.

, u(t - na >) + h(y(t - l), y(t - 2),

y(t - nb ))

y(t) stands for the sky temperature at the time t, y(t-1), stands for the sky temperature at the time (t-l). u(t) stands for the exogenous variables at time t. na and nb stand for the regressive order for the exogeneous variables and for y(t) f and h are functions which can be determined following a linear or a non linear method. The use of ARMAX models Concerning linear models, we (Rey-Chue Hang and al., 1996) to find simple linear relations, model described in figure 6.

is widespread in climatic variables modelisation studies. can quote Thianzhen Hong (Thianzhen and al, 1995), and for the use of non linear black box models. As it is quite hard we decided to use neural network as a non linear black box

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A neural network consists of several layers of interconnected neurones. Homick (Perez, 1994), mentionned the fact that just one hidden layer was sufficient for any neural network. The hidden layer is made of a varying number of neurones that will be defined during the learning phase. Each neuron can be defined as an activation function whom entry is a pondered sum of the several inputs. The network exit layer calculates the neural model outputs, So, there will be, in this layer, the same quantity of neurones and output variables, Each neuron of the hidden layer has got a network of connections (called synaptic connection) function of the input variables. Each connection has a different weight related to the importance of the connection. A neuron with an activation function equal to one is added to each neural layer. It is equal to the existence of a bias in the model. Creating a model with neural network needs a succession of stages listed below:

InOut Ta(t-l),(t-2),

Model ,___________________________ ‘1 Non linear activation I

Dh (t-1),(t-2),

OutDut I

J-sky(t) _______________~’

??

i_g.6 : Description of a neural network. Choice of the network inputs: We have studied, the most relevant variables concerning the modelisation of the sky temperature. From a physical point of view, radiative exchanges between soil and sky vault will depend upon global and diffuse solar radiation received, air temperature and humidity, and convection that will be linked to the wind intensity. Parameters estimation: The purpose of this stage is the determination of the different connections weights thanks to a learning stage. It is based upon the minimisation of a quadratic criterion J which is defined as the sum of the squares of the modelization errors : J = c [output signal - measured signal]’ The principle is to find the weights leading to a null gradient of the error prediction and a definite positive hessian. Multiples algorithms are then used to determine these weights using at first initial values, and adjusting them at each iteration of the learning phase. The optimisation algorithm used here is from Levenberg Marquardt (Norgaard, 1996). The advantage of this algorithm versus the traditional Gauss Newton method is that a search direction for determining the weights at each iteration step is calculated, leading to a best and faster convergence.

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Imnlementation: The number of hidden neurones necessary to the model is determined by various tests. Two criterions help to the evaluation of the model. The average quadratic error calculated between the measured output s(k) and the calculated output y(k) during the learning stage, and the same error calculated for a set of different data, allowing to check the network adaptability.

Results for the skv temperature modelisation. We tried to elaborate two models: - The model 1 is made for a time step of ten minutes. - The model 2 is made for a time step of one hour. This will be the most useful model because building simulation codes use generally this time step. We chose to create an ARX model, so it is necessary to determine the order of recursivity for each input. After a phase of multiple simulations, we chose the recursive order for each input variables (table 2). The optimal number of neurone of the hidden layer for the two models has been fixed to 2. Table 2: Different order for the input of the model Variables: Order for model 1 Order for model 2

Tc 2 2

Ta 2 2

Dh 1 1

dh 2 2

Rh 2 2

Ws 2 2

The mean square error was about 6.10” for the first model, and 3.10” for the second model. It appears then that the fist model is better than the second. This can be explained by the fact that there is far more data for the first model for learning stage, than for the second model where the size of the database is divided into six. So the hourly model will be improved later with more data. ompar~son

I

between

I

It11‘..-._. 0

the simulated

and the measured

sky temperature

forten

minutes

Measured

sky

temperature

1

I

Simulated

ski temperature 500

1

cl 1500

1000

data

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between

the measured

and the simulated

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sky temperature

for 10 minutes data

-I 200

400

600

600

1000

1200

1400

i Fig 7 and 8: Results of the modelisation of Tc for the model I

Reading the different weights for each neurone, we can establish a hierarchy for the different predictors. For the first model, The diffuse solar radiation, the relative humidity and the wind speed are the best predictors. For the second model, the air dry temperature becomes the preponderant predictor.

Table 3: Different weights for the two neural models for the hidden layer for the variables.

Variables Bias Tc(t-1) Tc(t-2) Ta(t- 1) Ta(t-2) Dh(t-1) dh(t-1) dh(t-2) Rh(t-1) Rh(&2) Ws(t- 1) Ws(t-2)

Model 1 Model 1 1St 2 nd hidden hidden neuron neuron 3.47 1.08 6.85 -0.5 -1.39 0.02 0.63 -0.02 0.25 0 0.32 0.01 -1.2 -0.01 -7.4 0.02 5.84 -0.02 3.87 0 -3.09 0 -1.07 -0.37

Model 2 Model 2 2nd 1St hidden hidden neuron neuron 0.54 0.98 -0.10 1.72 -0.25 23 -24 -0.25 9.21 0.04 8.94 -8.94 -0.86 0.89 -1.53

0.40 -0.04 -0.04 -0.03 0.01 0.06 0.02 -0.02 0.20

Neuron number of Model 1 Model 2 the hidden layer Bias 0.01 0.08 1 1.70 1.45 0.62 2 0.32

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1 Comparison

between the calculated

----

Simulated Measured

and the measured

Difference

between

for hourly data

sky temperature sky temperature

-5 0

sky temperature

50

100

the calculated

and

150 the

measured

200 sky

temperature

6 4 2 P v 2 3 8 s z2

0 -2 -4 -6 0

50

100

150

200

FIN 9 and 10: Results of the modelisation of Tc for the model 2

7. PEED BACK ON PREVIOUS SIMULATIONS.

To test the model 2, we made some simulations with CODYRUN using two models for the calculation of sky temperature. The first model was Tc=Tad, and the second model was the neural network for hourly data. The studied building in this case was the experimental cell on the roof of the faculty. We compare the resultant temperature measured in the’cell to this determinated by simulations. Results are shown in figure 11. We can see that the model (Ta6) is the best model. The neural network gives good results in the day, but gives too low temperatures for the night-time. However, as a first approach of the problem, we can say that

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it is satisfying. However, the neural network needs improvement. daytime, and one for the night-time can be considered. Resultant air temDerature for two skv temperature

Two networks, one for the

model

-

-Simulation

with neural

network -Simulation wth Air temperature - 6

-----Tam&d

fig. 11 : Resultant temperatureJor

. . ^. the two models of 12 and experlmental studies (la mea). 3

1.

_

9,

8. CONCLUSION This paper showed applications of neural network for the sky temperature determination for building simulations applications. A black box ARX model can be elaborated by using an experimental database. Therefore, the size of the database must be important to have good results. Results for the simulations are relatively satisfying. An extrapolation to another site (this of I’Hermitage’) have been proceed giving good results. As the models needs improvement, the campaign of measure is going on. Two networks can then be considered separately for daytime and night-time.

NOMENCLATURE Tc : Sky temperature Dh : Beam solar radiation Ws : Wind speed

Ta : Dry air temperature dh : Diffuse solar radiation Rh : Relative humidity

REFERENCES W.C. SwinBank (1963), Long wave radiation from clear skies, Quart. J. Roy. Meteorol. sot., 89 R.A. Bliss (1961), Athmospheric radiation near the surface of the ground. Solar Enera, 5, 103. V. Melchior Centeno (1982), New formulae for the equivalent night sky emissivity, Solar &ergy, 28,489.

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4. H. Boyer, F. Garde, J.C. Gatina J. Brau (1997), A multi model approach of thermal building simulation for design and research approach, Accepted at Energy and Building. 5. Boyer H., Brau J., Gatina J.C.(1993), Multiple model software for airflow and thermal building simulation. A case study under tropical humid climate, in Reunion Island In Proceedings of Building Simulation 93, (IBPSA, Adelaide, Aug.), 11 l-l 17. 6. Boyer H., Chabriat J.P., Grondin-Perez B., Tourrand C., Brau J. (1996), Thermal Building Simulation and Computer Generation of Nodal Models. Building and Environment, Vol. 31,3,207-214. 7. Boyer H., Gatina J.C., Pignolet-Tardan F., Brau J. (1994), Modelisation methods and data structuration induced for building thermal simulation codes. In proceedings of the Conference of international Simulation Societies, (Zurich, Switzerland), p 729-733. 8. Garde F., Boyer H., Brau J., Gatina J.C. (1995), Validation experimentale dun code de modelisation thermique de batiments (CODYRUN). Une application en climat tropical humide. In proceedings of 2Pme Colloque interuniversitaire panco-quebecois, Thermique des systemes a temperature mode’re’e.Sherbrooke, Montreal, Canada, p. 197-202. 9. Garde F (1997), Validation et developpement dun modele thermo-aeraulique de batiments en climatisation passive et active. Integration multimodtles‘de systtmes. These de I’Universitt de la Reunion. 10. Grondin Perez B. (1994), Les reseaux de neuronnes pour la modelisation et la conduite des reacteurs chimiques : simulations et experimentations. These de doctorat, Universite de Bordeaux. 11. Tourrand C. (1991), Caracterisation thermique de parois complexes. These de doctorat, Universite de Paris 7. 12. Norgaard M.(1996), System identification and control with neural networks, Thesis, Department of Automation , Technical Universiv of Denmark. 13. Marzdan C. and Stumpf G.J.(1996), A neural network for tornado prediction based on doppler radar-derived attributes, Journal of applied meteorology, 35 ,pp 617-626. 14. Mara T. (1996) , Validation experimentale d’un code de calcul thermique de batiments, DEA Mecanique et Energetique, Reunion Island University. 15. Rey Hue Chang, Sy-Ruen Huang, Shyh-Jier Huang, Huang-Chu Huang, Wen-Yea-Tsai (1996), Short term weather forecasting by an artificial recurrent neural network technology, Department of Electrical Engineering, Kaohsiung Polytechnic Institute, Taiwan, R. 0. C. 16. Berger, Buriot, Gamier (1984), About the equivalent radiative temperature for clear skies, Solar Energy, 32, 5. 17. Aubinet, Long wave sky radiation parametrization, Solar Energy, 53 ,2,pp 147-154, 1994 18. Donnet I, Berger X., (1984), La temperature de rayonnement du ciel dtduites des radiosondages atmospheriques, et de la temperature de sol. Programmation et utilisation du modele d’atmosphere Lowtran, Colloque Meteorologie et Energies renouvelables, Valbonnes. 19. Daguenet M.(1985), Les sechoirs solaires, theorie et pratique, Unesco. 20. Thianzhen H., Jiang Y. (1995) Stochastic weather model for building HVAC systems, Building and environment, 30,4, ~~521-532.