Post-doctoral proposition CSC (China Scholarship Council)

Title: Multicriteria tool to enhance thermal building renovation

Topic CSC : VI-4 Intelligent construction Supervisor: Stéphane Ginestet, Assistant Professor E-mail address: stephane.ginestet@insa-toulouse.fr Phone: +33 5 61 55 99 14 Fax: +33 5 61 55 99 00 http://www-lmdc.insa-toulouse.fr/presentation/fiches/ginestet.php Laboratory: LMDC Laboratoire Matériaux et Durabilité des Constructions Institutions : INSA Toulouse, Institut National des Sciences Appliquées Detailed subject: Buildings renovation is a major issue in the international context of the reduction of consumption and of greenhouse gas emissions.

In France, the office buildings energy retrofit challenge represents between 165 and 197 million m2 for entire investments, reaching 190 billion euros. Spread out until 2022 it represents an annual expenditure of about 19 billion euros. This change would represent the creation of approximately 330.000 jobs (on a basis of an average of 60.000 €/an). This challenge would forecast important economic consequences, revenues from taxes and social contributions.

However, so that the projects of thermal renovation technically have a measurable impact on energy consumptions, and indoor comfort, it appears necessary to make studies upstream (in design phase) allowing:

• to identify and treat on a hierarchical basis the solutions to be implemented (opaque glazing, walls, ventilation…)

• to study the interest of any materials and the impact of their implementation (thermal inertia, phase change materials…)

To make these studies, the recourse to simulation is unavoidable. The use of traditional tools for direct simulation (TRNSYS, Energy +, Comfie) runs up here against the difficulty in working on an existing building.

The proposed work within the framework of the proposition is to develop a multicriteria tool for energy renovation of old buildings.

Methodology will be based on work already carried out (in numerical simulation) within the framework of project ANR-HABISOL (2009-2012) AMMIS (Multicriteria analyses and

inverse method in energy simulation for buildings), in particular the use of algorithms based on the reflective Newton method.

The idea is here to propose to engineers and architects a tool that will allow establishing a hierarchy of several improvements to consider, according to energy, but also comfort criteria.

The study will focus primarily on improvements to the building envelope and its materials. From experimental data, an inverse method will be used to come across the characteristics of the building walls again. Based on a consumption target, improvements will be identified on various items (windows, insulation, and ventilation). A study will bring out a multi-criteria tool to assess the impact of these solutions.

Candidate profile:

• Thermal modeling • Numerical analysis • Inverse problems • Building technology notions

Related publications and communications:

• S. Ginestet, D. Marchio « Control tuning of a simplified Variable Air Volume system: methodology and impact on energy consumption and indoor air quality », Energy and Buildings, 2010, vol. 8, p. 1205-1214

• S. Ginestet, D. Marchio « Retro and on-going commissioning tool applied to an existing building: operability and results of IPMVP », Energy, 2010, vol. 35, p.1717–1723

• T. Bouache, S. Ginestet, « Identification des caractéristiques thermiques d’une paroi de bâtiment par optimisation sous contrainte basée sur un modèle simplifié », Conférence IBPSA France 2010 : Fiabilisation de la performance énergétique du bâtiment : simulation et expérimentation. novembre 2010, EDF, Moret-sur-Loing ;

• T. Bouache, S. Ginestet, « Identification des caractéristiques thermiques d’un modèle simplifié de bâtiment », Conférence SFT 2011 : Énergie solaire et thermique. mai 2011, Perpignan ;

Related publication (reviewing in process)

Building multilayer walls thermal identification:

reflective-Newton algorithm applied to electrical analogy

T. Bouachea

, S. Ginestet b,*

a Université Bordeaux1-ENSAM-ENSCPB-CNRS, Laboratoire TREFLE UMR 8508, Talence, France

b Université de Toulouse, INSA-Université Paul Sabatier,

Laboratoire Matériaux et Durabilité des Constructions, Toulouse, France

ABSTRACT. The design of low-energy buildings becomes nowadays necessary, encouraged

by thermal regulations, energy savings, and environmental realization. Thermal computer-

aided design of building is a current problem, investigated in many studies, using the latest

optimization algorithms. This paper deals with the coupling of a direct thermal model with a

particular optimization algorithm, applied to building multilayer walls identification. The

resolution of the thermal problem is based on a direct representation equivalent electrical

circuit, that can be found in many commercial or official building software, and then a

numerical solution is obtained by finite difference method. The optimization model

minimises a “least squares” criterion, between intended indoor temperatures and direct

response model. The objective of this work consists in optimising thermal insulation and heat

thermal capacity of the several layers of the wall, and further heating loads of the building.

The aim of our study is to identify building walls composition assuming these conditions,

using inverse resolution based on reflective-Newton algorithm.

KEYWORDS: Identification; thermal modelling; reflective-Newton method

* Corresponding author : Tel : +33-5-56-84-63-84 ; fax : +33-5-56-84-58-29. E-mail address : stephane.ginestet@insa-toulouse.fr

1. Introduction

Many scientific works have already been carried out on the optimization of the thermal

insulation of building walls. Recently, [1] have established a correlation between thermal

conductivity of the thermal insulation and this optimal thickness through a second order

polynomial equation. Previously, [2] have determined the optimal thickness of the insulation

of an external wall, working on building cycle-life, in Turkish coldest cities. From an economic

point of view, [3] have identified for each kind of insulating material, the best thickness,

using both whole energy and insulating material costs in hottest countries. Using a dynamic

thermal modelling, [4] have pointed out the effect of electricity prices on the optimal

thickness of the insulating material in Saudi Arabia. [5] have run a new approach to

determine the best insulation level for new buildings, from an energetic, economic and

environmental point of view, using… approach. All the studies cited before are based on the

insulation definition and optimisation, the thermal inertia is often neglected, whereas it

appears as a crucial point to study dynamic behaviour of such systems as buildings.

The impact of thermal inertia in buildings daily or seasonal behaviour is a current topic,

developed in many publications. For instance, [6] underlined and improved the knowledge

about the impact of thermal inertia on cooling loads. In this paper, he also reviewed and

classified several simulation tools assuming cooling loads calculation and indoor air

temperature prediction, considering thermal inertia.

[7] have described and quantified the major effect of the thermophysical properties of

the wall materials on magnitude and phase of a thermal wave applied to a building wall . [8]

has completed this approach, carrying out a theoretical and experimental study on the

effects of the thermal properties of the material on magnitude and phase of the whole

building response. He finally suggested using multilayer insulated walls for buildings

occupied all the year, and monolayer walls for specified occupied buildings.

To describe the dynamic behaviour of a building, [9] introduced an apparent capacitance

and an effective capacitance. Others authors have investigated the impact of the position of

the insulating material in the multilayer wall on the dynamic behaviour of the building ([10-

12]). In [12], the influence of the relative position of insulation/masonry for a three layer

wall on heating and refrigerating consumption has been quantified.

[13] have used an original procedure to optimize thermal parameters of a classical

building which are thermal resistance and thermal inertia. The direct model is numerically

solved and the optimisation is achieved using « interior - Reflective-Newton » algorithm.

Coleman et al [14 -15]. have proposed a reflective Newton method, for solving nonlinear

minimization problems where some of the variables have upper and/or lower bounds. They

have established strong convergence properties. In particular, reflective Newton methods

can achieve global and quadratic convergence. Experimental results for the case when the

objective function is quadratic are provided in [14]. These computational results are

extremely encouraging and indicate that reflective Newton methods have strong potential

for large-scale computations. A remarkable feature of this type of algorithm, illustrated by a

typical example, is the very slow growth in required number of iterations. Given a class of

problems and a "natural" way to increase the problem dimension, reflective Newton

methods appear for Coleman to be strikingly insensitive to problem size.

Our model was limited to studying the structure of a building with a single window

located in Gironde (South West of France), subject on all exterior walls to a temperature and

heat flux over a period of one year. Representation by an equivalent electric circuit was

proposed and then solved numerically by the finite difference method. The interest of our

study is the use of an optimization method to determine thermal wall characteristics

(thermal resistance, thermal capacity). The method involves minimizing a criterion such as

"least squares" between the wished indoor temperatures and the model response.

2. Assessment of a thermal building model based on electrical analogy modelling

The considered thermal zone (building room, e.g.), made up of six homogenous walls,

separates an outdoor environment (temperature TE(t)) from an isothermal indoor

environment (thermal capacity of the media, indoor air CIn). The walls exchange with the

outdoor environment by convection (thermal outdoor resistance RE=1/hE) and absorb

radiative thermal flux coming from sun (ΦS(t)). On the other side, the walls exchange with

the indoor environment by convection (thermal indoor resistance RIn=1/hIn) and absorbs a

thermal flux coming from heating systems (ΦC(t)). So it is possible to calculate the evolution

of the indoor air temperature TIn(t)) (Figure. 1).

Figure. 1 : building outline Figure.2 : electrical analogy outline

Heat conduction transfer inside windows are solved in steady-state case, they are

depicted with only one resistance. It is an analogical 1R model. The others conductive heat

transfers inside the others opaque walls are assumed in variable case and leads to a 1R2C

analogical model.

At nodes InT , 1T and 0T the heat conduction transfer equations can be written as follows.

( ) ( ) ( )tdt

dTCTT

RTT

RC

InInEIn

T

In

In

φ=+−+− 111 (1)

( ) ( ) ( )tTTR

TTRdt

dTC TIn

InM

M φ=−+−+ 1011 11

(2)

( ) ( ) ( )tTTR

TTRdt

dTC S

M

E

E

E φ=−+−+ 1000 11

(3)

Using finite difference scheme, it leads to :

n

C

n

E

nnn dTcTbTaTInIn

φ1111

1 1+++= − (4)

n

T

nnnn dTcTbTaTIN

φ2221

121 0+++= − (5)

MR

ΦS ΦT

ΦC

ECMC InC

ER InR

TR

ET 0T 1T InT

n

S

nn

E

nn dTcTbTaT φ31331

030 +++= − (6)

ia , ib , ic et 3,..,1=id are coefficients depending on geometrical and thermophysical

properties of the building, as mentioned in Annex 1.

The thermal outdoor solicitations most often have a quasi-periodic character, dry bulb

temperature, solar radiation and heating of the local follow a diurnal variation. They are

here generated by TRNSYS for the Gironde region in France.

Figure 3 : hourly solar flux variation for the considered building (1st

January to 31st

December)

Figure 4 : hourly heating/cooling flux for the considered building

(1st

January to 31st

December)

0

200

400

600

0 50 100 150 200 250 300 350

Jours

ΦS (

kW)

-20

-10

0

10

20

30

0 50 100 150 200 250 300 350

Jours

ΦC (

kW)

3. Model validation using TRNSYS

The simplified building model proposed here consists in the concept of "single area"

considered with uniform temperature. In order to compare then validate the model with

TRNSYS, we assumed a local with a similar volume than in our case. TRNSYS is considered as

a world reference in building simulation tools for decades and has been benchmarked many

times. All walls are composed of a layer of brick, 30 cm-thick and an outside insulation layer.

The exterior walls of the room are subjected to a constant temperature and flow of

respectively C 20 ° and 1000 W/m². Convective and radiative transfers are combined in the

overall transfer coefficients with hE = 20 W/m²K for outdoor air and with hA = 20 W/m²K for

air inside the room.

The comparison between the simplified model and TRNSYS is performed for two thicknesses

of insulation: 2 then 5 cm. The results of this comparison are shown in Figure 5. We observe

that the results of both models converge in terms of time constant and temperatures values,

for several thickness insulation cases. The observed differences are too small to be

considered as not representative in a building case study.

Fig. 5: comparison with TRNSYS

4. Introduction to the optimization method

0

10

20

30

40

0 100 200 300 400 500

Time (hours)

T (

°C)

quadripol model

TRNSYS

einsulation=2 cm

einsulation=5 cm

Building thermal optimisation consists generally in the search of an optimal solution

in terms of thermal comfort, for a set of variables satisfying several constraints. The word

“optimal” suggests that several conceptions are suitable. In an optimisation process,

variables are selected to describe the system (size, form, materials, work, and e.g.). An

objective consists in minimizing or maximizing a function (indoor air temperature difference

in our study), and the constraints are linked to a working domain, which indicates a

restriction or a limitation about a technological capacity of the system.

Generally, an optimisation problem consists in minimizing one or several “objective

functions”, on the conditions that many constraints are respected. It can be written as

follow:

( ) ( ) ( )[ ]xfxfxf mDx ,....,,minimize 21∈ (18)

Where ( )mifi ,...,1= is an objective function. x is the parameter vector to identify in the D

domain. In the case of only one objective is searched (m = 1), the function to minimize (Eq.

18) becomes:

( )xfxminimize , uxl ≤≤ (19)

The Eq. 19 is solved using here the Reflective Newton algorithm. It is an iterative

algorithm applied to non-linear multivariable functions, on the conditions that the upper and

lower limits of the variables. Each iteration aims to find a quasi solution of a higher linear

system using preconditioned conjugated gradients method. More details can be found in

Coleman et al [14 -15]. The authors have proposed a reflective Newton method, for solving

nonlinear minimization problems where some of the variables have upper and/or lower

bounds. They have established strong convergence properties. In particular, reflective

Newton methods can achieve global and quadratic convergence. Experimental results for

the case when the objective function is quadratic are provided in [14]. These computational

results are extremely encouraging and indicate that reflective Newton methods have strong

potential for large-scale computations. A feature of this type of algorithm, illustrated by a

typical example, is the very slow growth in required number of iterations. Given a class of

problems and a "natural" way to increase the problem dimension, reflective Newton

methods appear for Coleman to be strikingly insensitive to problem size.

In this paper optimisation method aims to determine the set of building physical

parameters which are unknown, minimising a quadratic criteria between estimated

temperatures by the electrical analogy model, and whished temperatures (“experimental

data”).

( ) ( )[ ]∑ −=N

mesA tTtTJ1

2)(,ββ (20)

β is the vector computing all the parameters to be estimated. The minimisation of

J leads to an identification of the parameters thanks to « Reflective Newton » algorithm.

Identification of the parameters is achieved in two steps (Figure. 4). Firstly, random errors

are simulated adding to exact temperatures a Gaussian noise ξ of nil mean and unitary

variance. The deviation of the noise is σ (Equation 19). The second step consists in the use

of the identification algorithm to minimise the quadratic function (Equation. 18).

( ) ( ) ξσ+= tTtT exactmes (21)

Fig. 6 : Solving algorithm

minimization

No

Yes

Numerical inversion (Fourier) Algorithm

»

Figure 7-a : hourly outdoor temperature variation for the considered climate

(1st

January to 31st

December)

Figure. 7-b : indoor air simulated temperatures

5. Results and discussion

The objective here is to identify both thermal resistance ( )kWKRi and thermal

capacitances ( )KkJCi of the several walls constituting the outdoor envelope of the studied

building. All the unknown parameters are group together in the following vector

( )EMTM CCRR ,,,β . iR values are ranking form 0.01 to K/kW 102 , and iC values are

circumscribed by 100 and KkJ 106 . The algorithm is initialized from ( ) 10,10,10,10 44220β .

-5

5

15

25

35

0 50 100 150 200 250 300 350

Jours T

ext (

°C)

-5

5

15

25

35

0 50 100 150 200 250 300 350

Jours

T (

°C)

σ= 0,5 σ =0,1 σ = 0 Text (°C)

For a null noise ( 0=σ ), R and C identified values (Figures 8 and 9) are very closed to

target values, with a quasi-null relative error. In the case of stronger noises ( 1.0=σ and

5.0 ), and despite the oscillatory behavior of the simulated temperatures, due to the added

noise, identified parameters values keep closed to exact target values, except for thermal

capacitance EC (70 % of relative error for a noise of 5.0=σ ). Therefore and as expectable,

identification errors occurred for higher noises: we noticed a maximum error of %9 on

thermal resistance.

Figure. 8: thermal resistances identification

0,1

1

10

Log

(H)

Exact

Initial

σ=0σ=0,1σ=0,5Exact 0,286 1,227

Initial 10,000 10,000

s=0 0,286 1,227

s=0,1 0,286 1,227

s=0,5 0,287 1,226

HM (kW/K) HT (kW/K)

σ = 0

σ = 0,5

σ = 0,1

Figure. 9 : thermal conductance identification

To better understand the influence of thermal conductance on indoor air temperature,

we led a study on sensibility analysis. Results are presented on Figure 7, to show the

transitory evolution of the following reduced sensibilities ( )( )MM HtTH ∂∂ , ( )( )TT HtTH ∂∂

, ( )( )MM CtTC ∂∂ and ( )( )EE CtTC ∂∂ int . It can be noticed that indoor air temperature is

strongly affected by EC and also but lightly by MH , and MC , that can explain the

difficulties for the algorithm to converge to EC .

0

50000

100000

150000

Exact

Initial

σ=0

σ=0,1

σ=0,5Exact 122317 15830

Initial 100000 100000

s=0 122317 15830

s=0,1 122432 15884

s=0,5 123086 14627

CM (kJ/K) CE (kJ/K)

σ = 0

σ = 0,5

σ = 0,1

Figure. 10 : indoor air temperature sensibility to HM, HT, CM and CE

6. Conclusion

In this paper, a temperature calculation module for simple buildings is presented,

based on the coupling of two models: direct model based on the electrical analogy and

an inverse model based on the method of "reflective newton method" applied for

nonlinear functions. The module can estimate the thermal parameters of the walls and

heating needs of the building. The interest of the module presented in this paper is to

identify technical solutions that can meet the requirements. Direct simulation involved a

large number of trials to achieve results (RT2005, [19]). The inverse simulation used in

our module can quickly give a first guidance of the composition of the walls (design

phase), which can then be taken up by direct simulations (TRNSYS, Energyplus, COMFIE,

e.g.) to refine solutions. The module will be used by architects as an artifice of

calculation, to understand and define in advance the better insulation in new

construction. Further work will lead to initially identify more complex walls involving

windows for instance. The longer-term objectives of the project are to optimize the

design of the envelope to limit the consumption of heating while respecting the

traditional criteria of thermal comfort.

Acknowledgments

This work has been supported by French Research National Agency (ANR) through “Habitat

intelligent et solaire photovoltaïque” program (project AMMIS n°ANR-08-HABISOL-001)

-20

-10

0

10

0 50 100 150 200 250 300 350

days

HM HT CM CE

Red

uced

sen

sibi

lity

Nomenclature

C thermal capacity (kJ.K-1

)

e thickness (m)

H thermal conductance (kW.K-1

)

J minimisation criteria

R thermal resistance (K.kW-1

)

t time (s)

T temperature (°C)

T0 outdoor wall temperature (°C)

T1 indoor wall temperature (°C)

TIn indoor air temperature (°C)

∆t time delay (s)

Greeks

β vector computing the parameters to be estimated

Φ heating flux (kW)

Subscripts and exponents

E outdoor layer of the wall

M indoor layer of the wall

In indoor air

C heating

N iteration subscript

S solar

T window

References

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conductivity and the thickness of selected insulation materials for building wall”. Energy and

Buildings, 2007, 39, pp. 182-187.

[2] Comakli, K., Yüksel, B. “Optimum insulation thickness of external walls for energy

saving”, Applied Thermal Engineering, 2003, 23, pp. 473-779.

[3] Al-Khawaja M.J, ”Determination and selecting the optimum thickness of insulation

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insulation-thickness in building walls as determined by a dynamic heat-transfer model”,

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decrement factor”, Energy and Buildings, 1998, 28, pp.159-166.

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pp. 273-278.

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buildings”, Energy, 1998, 23, 3, pp.183-192.

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decrement factor”, Energy and Buildings, 1998, 28, pp. 299-305.

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and minimum decrement factor point of view”, Energy and Buildings, 2000, 32, pp. 197–203.

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insulation/masonry distribution in a three-layered construction”, Energy and buildings, 1997,

26, pp. 153-157.

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parameters and loads using-on-site data logs”, Third National Conference of IBPSA-USA,

Berkeley, California, July 30 – August 1, 2008.

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walls using genetic algorithms », Energy and Buildings, 41, p. 1031–1036.

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1998.

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thermique des bâtiments. Thèse de Doctorat : INSA de Lyon. 1984, 201 p.

Annex 1.

Finite difference scheme coefficients.

( )( )tCRRs InTIn ∆++= 115.01 ,

( )( ) 11 115.0 sRRtCa TInIn +−∆= ,

11 1 sRb In= ,

11 1 sRc T= ,

11 1 sd =

( )( )InMM RRtCs 115.02 ++∆=

( )( ) 22 115.0 sRRtCa InMM +−∆= ,

22 1 sRb M= ,

22 1 sRc M= ,

22 1 sd =

( )( )EME RRtCs 115.03 ++∆=

( )( ) 33 115.0 sRRtCa EME +−∆= ,

33 1 sRb E= ,

33 1 sRc M= ,

33 1 sd = .

Annex 2.

The method used to calculate indoor thermal resistance MR and indoor (resp. outdoor)

thermal capacitance MC (resp. EC ) of a multilayer wall of N is detailed in [19].

1 ………. … j …..…..N

N couches

ie

iR

iC

iρ

iβ MR

EC MC

Figure A1.1 : analogie électrique 1R2C

The global resistance MR is the sum of the jR resistances of each layer j ,

= ∑

=

=

nj

i

jM RR1

The global conductance K is calculated as follows.

MR

K1=

The two capacitive nodes are located on the wall surface in order to limit equation number.

Indoor (resp. outdoor) thermal capacitance MC (resp. EC ) are defined as follows.

+×= ∑

−=

=

1

12

jk

k

k

j

j RR

Kβ

( )∑=

−=n

j

jjjjE eCC1

1 βρ

∑=

=n

j

jjjjM eCC1

βρ

iρ iC and ie are respectively the density, the specific heat and the thickness of the layer j.