Short time non-destructive evaluation of thermal performances of building walls by studying transient heat transfer

Accepted Manuscript

Short time non-destructive evaluation of thermal performances of building walls by studying transient heat transfer Yingying Yang , Tingting Vogt Wu , Alain Sempey , Jean Dumoulin , Jean-Christophe Batsale PII: DOI: Reference:

S0378-7788(18)32427-7 https://doi.org/10.1016/j.enbuild.2018.12.002 ENB 8931

To appear in:

Energy & Buildings

Received date: Revised date: Accepted date:

6 August 2018 7 October 2018 2 December 2018

Please cite this article as: Yingying Yang , Tingting Vogt Wu , Alain Sempey , Jean Dumoulin , Jean-Christophe Batsale , Short time non-destructive evaluation of thermal performances of building walls by studying transient heat transfer, Energy & Buildings (2018), doi: https://doi.org/10.1016/j.enbuild.2018.12.002

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ACCEPTED MANUSCRIPT Highlights 

Thermal quadrupoles formalism is applied for modelling transient heat transfers in building walls with a semi-infinite assumption.



Front face response curves of multi-layered walls are analysed to estimate the thermal properties of the wall. Experiments are carried out on two classical multi-layered building walls using

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

artificial thermal excitations.

The proposed method reduces the evaluation time less than 10 hours.

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Short time non-destructive evaluation of thermal performances of building walls by studying transient heat transfer Yingying YANGa, Tingting Vogt WUb*, Alain SEMPEYb, Jean DUMOULINc, JeanChristophe BATSALEb School of Energy and Power Engineering, University of Shanghai for Science and Technology, 516 Jungong

Road, Shanghai 200093, China b

Institute of mechanics and engineering (I2M), UMR CNRS 5295, University of Bordeaux, Arts et Métiers

ParisTech, Bordeaux INP, INRA, Talence 33400, France c

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a

IFSTTAR, COSYS-SII, Bouguenais, F-44344, France, and Inria, I4S Team, Rennes, F-35042, France

* Corresponding author: [email protected], Esplanade des Arts et Métiers, Talence 33400,

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France

Abstract

Thermal performances of building walls are significant for energy conservation. However, very few non-destructive evaluation methods exist to quantitatively diagnose the

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building walls in situ due to the walls’ large thickness. Moreover, most of the existing

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methods are inconvenient to implement in situ and take a long characterization time. This paper studies transient heat transfer to estimate the wall’s thermal properties based on the

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thermal quadrupoles modelling. Semi-infinite boundary condition is assumed at the rear face of the wall. With this assumption, only the front face response of the wall is considered. The

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evaluation time is then effectively reduced within a few hours, and the diagnosis in situ is

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simplified without the measurement on the rear face of the wall. Experiments are carried out on two traditional multi-layered building wall cases using heating lamps. With the measured surface temperatures and heat fluxes, the unit-pulse response and unit-step response at the front surface of the investigated wall are reconstructed through a deconvolution approach and a TSVD (Truncated Singular Value Decomposition) inversion. The unit-step response curve is directly characterized by the thermal resistance, thermal effusivity and heat capacity of the wall, thus allowing us to estimate the wall properties. The characterization time for the two 2

ACCEPTED MANUSCRIPT cases is less than 10 hours. Keywords: short time NDE, thick building walls, unit-step response, thermal quadrupoles modelling Nomenclature

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r2

⁄

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p

Thermal effusivity, Specific heat capacity, Heat capacity, ⁄ or Unit response, Thickness, Laplace transformed time Heat flux, Pulse signal, Thermal resistance, Coefficient of determination Temperature, or °C Time, s or h

Greek alphabet Thermal diffusivity, Thermal conductivity, Laplace transformed temperature Laplace transformed Heat flux Density, Subscript exp Experimental data Truncation parameter for TSVD pulse Pulse response ref Reference sim Simulated data step Step response s,out Surface temperature of external of wall box s,in Surface temperature of internal of wall box wall Parameters for wall wall,1/2/3/4 Internal face temperatures of wall 1 Front surface of wall 2 Rear surface of wall

1. Introduction

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t x Location inside medium Abbreviation HFM Heat fluxmeter method NDE Non-destructive evaluation OLS Ordinary Least Square SVD Singular Value Decomposition TSVD Truncated Singular Value Decomposition

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In the composition of energy consumption, buildings consume the largest part (more than industry, transport and others). Moreover, buildings are also responsible for about 17%

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of total direct energy-related CO2 emissions from final energy consumers [1]. Climate controlling (space heating and cooling) occupies more than half of the building’s

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consumption [2]. Building envelops with good thermal performances can reduce this consumption and improve the building energy efficiency. So the thermal parameters of building envelops are essential information for building energy simulation, economic optimization and retrofitting energy efficiency of existing buildings. Though the wall’s performances of a new building have been designed, once built, they may not reach the designed values because of faults during construction management, or 3

ACCEPTED MANUSCRIPT humidity presence, compaction or expansion of the thermal insulation, material defects and so on. Considering this performance gap, the wall properties are recommended to be verified when the building is achieved. Especially during the construction stage, the diagnosis work is necessary to reduce this energy performance gap between a building’s designed and as-built values. In other cases, such as building resale and renting, the thermal diagnosis on building

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envelopes is also required. Therefore, the quantitative thermal non-destructive evaluation (NDE) on building walls is of great importance. However, there is still a lack of NDE methods for the thermal characterization of thick building walls that are widely used in situ. Some of the existing methods need a very long time for the measurement, some others are

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useful only for particular structures of building walls, such as only for homogenous construction, and some methods have to be used only during a limited period, such as only in winter or during the night.

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2. State of the art

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The existing well-developed in situ methods and standards, such as the Heat Fluxmeter Method (HFM) [3] (ISO 9869:2014 [4]) and Hot Box Method [5] (ASTM С236 [6]), are

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based on steady state heat transfer. The thermal resistance of the wall (R) is calculated with the temperature difference between the two surfaces of the wall (

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passing through the wall (q), that is

) and the heat flux

. However, these methods need data from

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several days’ measurement [4], sometimes several weeks [7], and the steady state heat transfer regime is difficult to achieve at in situ conditions. In addition, these techniques need a large temperature difference between indoor and outdoor environment. Ahmad et al [3] applied the HFM to the measurement of the thermal transmittance and thermal resistance of hollow reinforced precast concrete walls. Two exterior walls of a building were characterized in situ. The trial lasted for about two months in the summer. The results show that a measurement period of six days is needed to obtain in situ thermal properties of reinforced 4

ACCEPTED MANUSCRIPT precast concrete walls. Desogus et al [8] implemented a similar measurement on two chambers, and proposed that the thermal resistance value is reliable when the temperature difference between cold chamber and warm chamber is equal to or higher than 10oC. R. Bouthié et al [9] proposed the ISABELE (In Situ Assessment of Building EnveLope performancEs) method which can achieve a good accuracy of the heat loss coefficient

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estimation by transmission. But this method can only be used in unoccupied buildings, and several days’ measurements are still needed.

To overcome these drawbacks and explore a shorter time NDE approach, transient heat transfer techniques should be considered with several suitable assumptions in classical

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conditions. Generally, there are active techniques and passive techniques to study such transient methods. Active techniques use an artificial thermal excitation to build a transient heat transfer field, while passive techniques just depend on the natural thermal source (such

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as solar radiation). The active techniques are considered in our work for the primary investigation. The pulse (flash) method [10] has been popularly used for NDE of thin

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materials in laboratory. Responses at the front and rear faces of the investigated sample are

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analysed to estimate the properties when a pulse is applied to one surface of this sample. However, it is very difficult to implement this active technology on the building walls

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because the walls are thick and formed by multi-layers. Moreover, in situ measurement conditions and influence of surroundings should be considered, which makes the

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characterization approach more complex. Chaffar et al. [11] used a flat heating resistance instead of an optical excitation to perform a heat pulse. The thermal conductivity and heat capacity were estimated with rear face temperatures by finite difference numerical modelling and inverse method. However, this method is proposed for homogeneous walls and is unavailable for the multi-layered walls. In addition,

the

heating resistance

and

the

insulating plate on the surface of the investigated wall would be inconvenient for the in

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ACCEPTED MANUSCRIPT situ trials, especially for the high buildings. Derbal et al. [12] applied a sandwiched structure to simultaneously determining the thermal conductivity and heat capacity of a construction material by using finite difference numerical modelling. The material to be characterized is placed between two layers of materials with known thermal properties. This method is also particularly appropriate for materials presenting good homogeneity and is not adapted at in

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situ due to its complex setups. Some tomography technologies, such as terahertz NDE [13], have also been studied, but these technologies generally take a high cost and need complex setups. P. Gori et al.[14] studied the multi-layered wall cases by using the thermal quadrupoles model to estimate the equivalent thermophysical properties. Z. Petojević et al.

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[15] presented a novel numerical framework for estimation of TIR functions and dynamic thermal characteristics for multi-layered building walls, which still need a very long evaluation time.

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Our work aims to explore innovative NDE methods which are fast, adapted to thick multi-layered building walls and convenient for in situ conditions. Firstly, the thermal

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quadrupoles formalism is introduced for modelling transient heat transfer in multi-layered

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building walls. Semi-infinite boundary condition is assumed in the modelling, so only the front face response of the wall is needed in a short characterization time. Then a

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deconvolution approach is utilised to reconstruct the unit-pulse and unit-step responses at the front face with the measured heat fluxes and temperatures. Thus the wall properties are

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estimated from the reconstructed unit-step response curve. Two building wall cases are investigated: one is studied in the laboratory by applying several periodic heating signals (case A), the other is tested in situ using the step heating signals (case B). The experimental results of the two cases are analysed based on the proposed estimation approach.

3. Numerical study 3.1 Modelling analyses 6

ACCEPTED MANUSCRIPT The quadrupoles formalism [16] is an analytical method for solving linear partial differential equations in simple geometries. It relies on the classical analytical tools such as Laplace integral transforms (in time) or space integral transforms (Fourier) related to the method of separation of variables. With the application of this quadrupoles formalism to the heat transfer system, the thermal solution may be expressed in terms of linear matrix

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relationships between the transformed temperature and heat flux vectors at the boundaries of the system. This analytical solution is independent on the boundary conditions. The quadrupoles method makes the construction of heat transfer modelling in a very simple way. This thermal quadrupoles formalism can allow us to apply a semi-infinite assumption

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on the investigated walls. This assumption is adapted to reduce the measurement time without waiting the response of the rear face. It also allows us to obtain intrinsic approximated expressions, then we can clearly choose out suitable parameters to estimate from these

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approximated solutions and physically analyse the response curves. These are the advantages of quadrupoles formalism compared to other numerical tools, such as finite difference

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building walls [17,18].

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modelling. Some researchers have applied this quadrupoles model to the characterization of

(a) Thermal quadrupoles modelling

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For a homogeneous and isotropic solid medium without internal heat source (Fig. 1(a)), the one dimensional heat transfer is expressed as Eq.(1). The heat flux (q) at any location (x)

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inside the medium is defined by the Fourier’s law as Eq.(2). A unit area (1 m2) is considered in this paper.

(1)

(2) Where

is the thermal diffusivity, T is the temperature, t is the time,

is the thermal

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is the initial temperature of the medium. Then the temperature and heat flux

in Laplace domain are: θ(x,p)=

(T(x,t)), Φ(x,p)=

(q(x,t)), where p is the Laplace

transformation of time; θ1 and θ2 are respectively the transformed temperatures at front face (x=0) and rear face (x=L, L is the thickness of the medium),

and

are the corresponding

transformed heat fluxes, as shown in Fig. 1(b). Then the heat transfer equations become

[

]

*

+[

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Eq.(3) [16]: ]

(3)

( √ ⁄ )

( √ ⁄ )

√ ⁄

√ ⁄

( √ ⁄ )

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The matrix with four coefficients A, B, C, D completely characterizes the surface responses to the heat flux, marked as coefficient matrix. Front face

Medium

Φ1

Rear face

q1 T1

q2 T2 x

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0

θ1

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L

Medium

𝐴 * 𝐶

𝐵 + 𝐷

Φ2 θ2

(b)

(a)

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Fig. 1: Transient heat transfer in a homogeneous medium: (a) geometry; (b) matrix representation in Laplace domain

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Semi-infinite boundary condition at the rear face is assumed in this quadrupoles

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modelling. When a sample becomes semi-infinite, one face of the sample goes to infinite. For an infinite value of the thickness L, the corresponding quadrupoles expression Eq.(3) can reduce to:

√ Using a pulse signal

(

(4)

, independent with time) to excite a semi-infinite sample,

the front face temperature of this sample Eq.(4) is then expressed:

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ACCEPTED MANUSCRIPT (5) The relationship between the pulse ( ) and the front face temperature ( ) is defined as the unit-pulse response, given by Eq.(6). (

√

)

⁄

√

(6)

This unit-pulse response at semi-infinite condition is characterized by the thermal

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effusivity (b). Generally, the unit-pulse response curve is plotted in the logarithmic scale, which can amplify the characterization and make it easier to estimate the thermal parameters. This is the classical NDE method that used for thin samples at laboratory condition.

) is used, the front face temperature of the sample is obtained

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If a step signal q (

by the inverse Laplace of Eq.(4), given in Eq.(7). Then the unit-step response of front face is expressed by Eq.(8). Clearly, this unit-step response performs a linear relationship with the square root of time for this homogenous sample at semi-infinite condition.

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√

(7)

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√

√

⁄

√

(8)

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The obtained response expressions above (Eq. (6) and Eq. (8)) are only suitable for one

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homogenous layer. However, for multi-layered walls with different structures, the response curves perform differently. The global equivalent coefficient matrix is obtained by

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multiplying the coefficient matrices from each layer medium, as given in Eq.(9). The contact resistance between each layer has been ignored hereby because this contact resistance is much smaller than the resistance of building materials. [

]

[

][

]

[

][

]

[

][

]

(9)

Basing on Eq. (9), the front face temperature is then given by Eq.(10). This is the exact expression from the quadrupoles modelling. 9

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(10) In order to intrinsically analyse the front face response curves, the previous exact expression Eq.(9) is approximately represented by Eq.(11) in terms of the electrical network shown in Fig. 2. This approximated expression is a quite simple approach to fundamentally

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show the heat transfer behaviour at semi-infinite condition only with a few lumped-parameter representations, which has been reviewed and discussed by P. Gori et al.[19]. Such expressions provide physical insight into the phenomenon of heat transfer.

[

[

]*

+[

(J/K) is the heat capacity, R (

]

(11)

) is the thermal resistance. Then the

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where

]

approximated expression of front face temperature is obtained, given by Eq.(12).

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𝛷

𝐶𝑡

R

𝑧

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𝜃

(12)

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Fig. 2: Electrical analogy for approximated expression at semi-infinite condition (b) Simulations for three diagnosis cases

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Unit-step response curves for three diagnosis cases are simulated. As shown in Fig. 3, in case 1, the concrete layer (dense layer) is heated firstly. In case 2, an insulation layer (resistance-dominated layer) is located in the front of the concrete layer. In case 3, a plaster layer (capacity-dominated layer) is added as the first layer based on case 2. The concrete layer is supposed as a semi-infinite layer in these three cases. The thermal properties of concrete, insulation and plaster used in the simulation are given in Table 1. Assuming that the insulation materials are completely resistant and the dense building 10

ACCEPTED MANUSCRIPT materials are completely capacitive in the three diagnosis cases, based on Eq.(11) and Eq.(12), the front face temperature is then reduced to the simple expressions in time domain (Eq.(13)). √ √ √

(13)

(

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√ )

These reduced expressions allow us to obtain the simplified unit-step response

Case 1

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expressions, then we can analyse the exact response curves intrinsically and intuitively. Case 3

Case 2

C

P

C

I

C

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I

Fig. 3 Three diagnosis cases, C is concrete layer; I is insulation layer; P is plaster layer

Materials

10-6(m2/s)

L (m)

0.893

1

Infinite

Insulation

0.038

1.2

0.1

Plaster

0.25

0.63

0.0125

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Concrete

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Table 1 Materials’ parameters used in the simulation

Fig. 4 shows the exact unit-step response curves simulated by Eq.(10). The three

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formulas are the simplified expressions obtained from Eq.(13). Clearly, these unit-step response curves are directly characterized by thermal effusivity (b), thermal resistance (R) and heat capacity (Ct). The behaviours of the three curves are obviously different. For case 1, the slope of the curve is low and keeps at a constant value of

√ , which is determined by

the thermal effusivity of concrete. For case 2, the response values increase sharply at beginning in a short time, and then this increase rate slows down and the slope of this curve

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ACCEPTED MANUSCRIPT becomes constant quickly. The value of this constant-slope is the same with that in case 1, namely

√ . The intercept of the curve in this constant-slope period is characterized by

the thermal resistance of the insulating layer (R). For case 3, the curve performs as a middle behaviour between case 1 and case 2, it takes a longer time to attain the constant-slope period than that in case 2. This transition time is determined by the heat capacity of plaster and

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thermal resistance of insulating layer (R Ct).

Therefore, the thermal resistance of insulation layer and thermal effusivity of concrete layer will be easily estimated by the intercepts or the slopes of these unit-step response curves. The analysis of these response curves at a semi-infinite condition can also make it

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possible to identify the order of different layers: the first layer (layer near the front face) is light insulating, or insulating and slightly capacitive, or contrarily highly effusive. Exact response curves: Case 1 Case1 2 Case 3

4.0

𝒈𝒔𝒊𝒎,𝒔𝒕𝒆𝒑 =

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3.5

Simplified expressions:

3.0 2.5

𝟐√𝒕

𝒃√𝝅

+𝑹

Constant-slope period

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Unit-step response (Km2/W)

4.5

2.0 1.5 1.0

𝒈𝒔𝒊𝒎,𝒔𝒕𝒆𝒑 =

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1

𝟐√ 𝒕 +𝑹 𝒃√𝝅

0.5

0

1

2

3

4

5

6

7

8

9

10

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0.0

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Fig. 4 Simulated unit-step responses and the analytical simplified expressions for three diagnosis cases at semi-infinite boundary condition

3.2 Experimental data processing (deconvolution approach) However, in real cases, the response and step response cannot be achieved directly because it is almost impossible to apply a known high pulse signal nor a strict signal on the building walls at in situ condition, thus a deconvolution approach is applied hereby to reconstruct the unit-pulse response from the arbitrarily varying signals using a TSVD 12

ACCEPTED MANUSCRIPT (Truncated Singular Value Decomposition) inversion [20]. Then the unit-step response will be calculated by the integration of the unit-pulse response. According to Duhamel’s theorem [21] for zero initial condition, any arbitrarily varying excitation can be regarded as a superposition of a series of pulses, then the overall response of this excitation can also be broken down into the superposition of a series of pulse

unit-pulse response (

) and the input heat flux (

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responses. Thus the front face temperature ( ) is represented by the convolution of front face ), expressed by Eq.(14).

∫

∫

(14)

is discretized as the vector

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This integral is then discretized by time (t=1,2,3,…,n). (

),

is discretized as (

(

). So discretized expression of Eq.(14) is described by Eq.(15): 𝑞

𝑇

𝑞

𝑞

=

𝑞 .. .

𝑇𝑛

𝑞𝑛

0

0

𝑞

0

0

0

𝑞

0

0 .. .

𝑔

𝑞

𝑔𝑛

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𝑻

.. .

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.. .

0

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𝑇

𝑞

𝑞 𝒒

is discretized as

𝑔 𝑔

.. .

𝑇

) and

(15)

.. .

𝒈

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The three matrices are represented by T, , 𝒈 respectively, then Eq.(15) becomes:

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(16)

𝒈 is linear, we use the SVD (Singular Value Decomposition) on the

If the model matrix

𝒈

, that is

, then the Ordinary Least Square (OLS) [22]

estimation equation is written as: 𝒈 As we known, W is a square diagonal matrix of dimensions singular values of matrix , ordered according to decreasing values:

(17) , which contains the . If

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ACCEPTED MANUSCRIPT no noise is present in the data , the full rank of the matrix

is needed. However, in the

practical cases, because of the presence of noise, the larger n, the larger the condition number of the inversion and the larger the standard deviations of the estimated parameters due to the smaller singular value. So one of the solution is to use the TSVD. In TSVD regularization, items containing these small singular values are discarded to maintain the stability of the

matrix

) is then replaced by its truncated inverse

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solution, the inverse of singular values matrix ( :

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(18)

[

]

With a proper truncation parameter j, items containing singular values smaller than

expressed as: 𝒑 𝒑𝒖 𝒔𝒆

𝒈

(19)

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𝒈𝒆

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are discarded. Thus, the amplification will be restrained. The new regularized TSVD is

In order to find this proper j-value, the discrepancy principle [23] is used. The standard ) of residuals between the measured temperature (T) and the estimated 𝒈

) is considered, expressed by Eq.(20).

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temperature (

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deviation (

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‖

𝒈

‖

‖

𝒈

‖

(20)

is chosen in our study cases. With the optimal j-value, the unit-pulse

response vector 𝒈 is then obtained with the experimental heat flux q1 and temperature T1. The unit-step response curve is determined by the surface temperature response when using a known step heating signal, referred to Eq.(8). In fact, the input heat flux of the wall may not be a step signal due to the influence of surroundings’ convection and radiation heat transfer, the unit-step response curve should be reconstructed through the integral of the 14

ACCEPTED MANUSCRIPT experimental pulse response, expressed by Eq.(21). ∫

(21)

4. Experimental study Two multi-layered wall cases formed by mortar, concrete block, insulation material and

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plaster board are investigated in our work. One is studied in the laboratory (case A) and the other is tested in situ (case B). The investigated walls are heated on one surface by using several thermal excitation signals. The temperature and heat flux at the same surface are measured by sensors.

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4.1 Case A

The measurement instruments used in our cases are listed in Table 2. Thermoelectric modules (Fig. 5 (a)) are used as the heat fluxmeter in this case thanks to their high sensitivity

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and low cost. Based on the Seebeck effect, when the module is heated by a given heat flux, it can convert this heat signal directly into electricity at the junction of different types of wire.

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This electrical signal will be detected as an output voltage. The heat flux is then estimated by the relationship between the output voltage and input heat flux (usually called sensitivity). In

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addition, the flat plate heat flux sensor (Fig. 5 (b)), a widely used heat fluxmeter made by

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Captec manufacture [24], is also utilised. The sensitivity of these heat fluxmeters are calibrated in Laboratory. With the calibration tests, when the heat flux is less than 500 W/m2,

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the uncertainty of thermoelectric module is 4.15 W/m2, and the uncertainty of flat plate heat flux sensor is 3.56 W/m2. When the heat flux is less than 20 W/m2, the uncertainty of thermoelectric module is 0.17 W/m2, and the uncertainty of flat plate heat flux sensor is 0.56 W/m2.

Table 2 Specifications of instruments Instruments Thermoelectric module

Specifications European Thermodynamics (30×30×3.5 mm)

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ACCEPTED MANUSCRIPT Captec manufacture (50×50×0.4 mm) Type T (copper–constantan) GRAPHTEC GL840 FLIR A325

Flat plate heat flux sensor Thermocouple Data logger

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IR camera

(b)

(a)

Fig. 5 Heat flux sensors: (a) thermoelectric module: 30×30×3.5 mm; (b) flat plate heat flux

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sensor (Captec heat fluxmeter): 50×50×0.4 mm

The differences of emissivity and absorptivity between the heat fluxmeter sensors and the investigated wall cause the differences of absorbed heat flux of each surface. One solution is to calculate the wall heat flux based on the heat flux balance law by using two heat

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flux sensors: one is covered by an aluminium film (shiny heat flux sensor) and the other is

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painted black (black heat flux sensor). This approach has been described by Y. YANG [25]. Type T (copper–constantan) thermocouples are used in our work. All the thermocouples have

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been calibrated in advance in the laboratory. Accuracy of thermocouple is 0.1 °C. The investigated wall, size of 100×70×26.3 cm (height × width × thickness), is formed

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by mortar, concrete block, insulation material and plaster board, as shown in Fig. 6. The red

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points are the positions of the installed thermocouples. Table 3 gives the parameters of each layer referred to the ASHRAE handbook and French national thermal regulation [26,27]. Twall,3

Twall,2

Twall,4

Twall,1

Ts,out

Ts,in

Concrete block (20cm) Mortar (1cm)

Insulation (4cm) Plaster (1.25cm)

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ACCEPTED MANUSCRIPT Fig. 6 Structure of the wall and the positions of thermocouples in case A Table 3 Thermal properties of each layer of the wall in case A L (m)

Mortar cement

0.01 0.2

Concrete block Insulation Plaster

R (

0.04

1.15

1.7x106

0.87

6

0.9x10

0.038

0.0125

0.03x10

0.25

0.9x10

6

6

b (√

)

) 0.009

1398

0.23

885

1.05

34

0.05

474

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Layers

As shown in Fig. 7 (a), this investigated wall (located at IFSTTAR Nantes) is installed against a caisson (named wall box) with insulation materials at the top and bottom to reduce

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the heat losses in the vertical direction. The size of the wall box is 200 195.8 85.2 cm.

Six halogen lamps placed in front of the wall are used as heating source. The input voltage of the heating lamps is regulated by a program ranging from 0 V to 10 V, resulting in the heat flux at the wall surface ranging from 0 to 1380 W/m2. The IR camera, FLIR A325

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whose spectrum ranges from 7.5 to 13 m, is also fixed in front of the wall to measure the

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surface emissivities of the wall and the sensors, and to provide a global thermography to avoid anomalous thermal behaviours. A heater is installed inside the wall box to regulate the

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internal temperature.

The test area (Fig. 7 (b)) is located at the center of the wall. The IR camera and the

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center of lamps are fixed at the same height with this test area. Both the shiny and black heat

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flux sensors are installed on the test area for the wall heat flux calculation. The measurements are collected by a data logger GL840.

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Crumped aluminum

Surface with known emissivity

Wall Box

Captec fluxmeter

Shiny heat flux sensor

Objective wall Test Area IR camera

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Lamps Black heat flux sensor

(a)

Thermocouple

(b)

Fig. 7 Experimental setup in case A: (a) global view; (b) test Area

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To confirm the reference parameters of the investigated wall and verify the measurements of temperatures and heat fluxes in this experimental system, a pre-testing is carried out firstly based on steady state heat transfer. The internal temperature of the wall box

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is set at 27°C (regulated by the heater). This wall box is placed in the chamber whose

heat transfer in the wall.

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temperature keeps at about 18°C. This pre-testing lasts for 91 hours to ensure a steady state

Then four transient tests are conducted with different periodic square-wave heating

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signals. Four periods are chosen: 24 hours (4 cycles) for test 1, 48 hours (1 cycles) for test 2,

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96 hours (1 cycles) for test 3, and 2 hours (10 cycles) for test 4. For example, Fig. 8 shows the shape of lamps stimulation in test 1. In this case, the heating lamps are placed near the

Square-wave signals: period of 24 hours Lamps stimulation

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concrete layer.

One cycle

0

12

24

36

48

60

72

84

96

Time (h)

18

ACCEPTED MANUSCRIPT Fig. 8 Shape of lamps stimulation for test 1 (period of 24 hours) in case A

4.2 Case B In case B, a real wall of a demonstration building in Bordeaux is diagnosed using the same measurement methods used in case A. The orientation of this investigated wall is northfacing. Tests are carried out in March, whose average indoor temperature is about 19.5 °C

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and average outdoor temperature is about 8 °C during the tests.

The wall composition is shown in Fig. 9 and its parameters are given in Table 4 referred to the ASHRAE handbook and French national regulations. This wall also has four

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layers with total thickness of 0.37m. Indoor

Outdoor Rear face

Front face

q 2 T2

q 1 T1

Concrete block (25cm)

Insulation (10cm)

Mortar (1cm)

M

Plaster (1cm)

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Fig. 9 Structure of the investigated wall in case B Table 4 Thermal properties of each layer of the wall in case B

Mortar cement

0.01 0.25

CE

Concrete block

L (m)

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Layers

Insulation

0.01

( 1.15 0.893 0.038 0.25

b (√ )

1.7x10

6

0.009

1398

0.9x10

6

0.28

897

2.63

32

0.04

474

0.03x10 0.9x10

6

6

)

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Plaster

0.1

R

16 artificial solar lamps were placed indoor to heat the wall, as shown in Fig. 10 (a). In

this case, the heating source is placed near the insulation layer. Shiny and black Captec fluxmeters are installed on the test areas to estimate the heat flux of wall, as shown in Fig. 10 (b).

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Shiny heat flux sensor Thermocouples Black heat flux sensor

Lamps

Test area

(b)

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(a)

Fig. 10 Experimental setup in case B: (a) global view; (b) test area

Three transient tests are carried out using the step heating signal (Fig. 11). All the tests

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last for about 10 hours.

0

M

Lamps stimulation

Step signal

2

4

6

8

10

12

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Time (h)

Fig. 11 Shape of lamps stimulation in case B

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The two walls in case A and case B have been widely used in the concrete-supporting walls with insulation materials built-in. The concrete block and insulation materials are the

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effective layers in the wall, while the mortar and plaster board are the layers that provide

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protection, which have weak influence on the thermal performance of the wall. The indoor heat stimulation is chosen to simplify the diagnosis setup, especially for high buildings. Case A and case B then represent the two most common diagnosis situations for building walls: external wall insulation and internal wall insulation. The results will be analysed in both situations.

5 Thermal properties estimation

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5.1 Results in case A As previously described, a steady state heat transfer test (pre-testing) is carried out firstly, the thermal resistance of each layer is obtained and compared with the reference value. Then the thermal effusivity is estimated by the 4 transient heat transfer tests. Results for the pre-testing

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Fig. 12 shows the temperatures measured by thermocouples at different positions (referred to Fig. 6). The insulation and plaster layer causes the largest temperature difference ( ). 29 28

Ts,in

Twall,4

26

 Tinsulation/plaster

25

Twall,2

M

24

Twall,3

23

Twall,1 Ts,out

 Tblock

22

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Temperature (℃)

27

21 20

PT

19

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(

), while the concrete block layer causes a temperature difference of 1 °C

1

2

3

4

5

Time (h)

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0

 Tmortar

Fig. 12 Measured temperatures during the pre-testing in case A

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The thermal resistance of each layer is calculated by Eq.(22) with the heat flux passing through the wall and temperature differences between the surfaces. The wall heat flux is calculated from the measurements of heat flux sensors. (22) Fig. 13 shows the thermal resistance results of each layer at each time step. In Fig. 13, the R-values are fluctuant because of the instability of heat fluxes and temperatures. The average R-values and its standard deviations are calculated, as given in Table 5. The R-values 21

ACCEPTED MANUSCRIPT of concrete block and insulate-plaster match well with the reference values given in Table 3, while the result of mortar layer has a very large uncertainty and relative error. The R-value of mortar layer is too low to be measured precisely because of the limitation of instruments’ accuracy. However, this mortar layer affects very slightly on the overall performance of this wall. The overall thermal resistance of this wall is achieved by using the temperature difference between front and rear surfaces, namely Roverall=1.35± 6%

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also very close to the reference value.

Rmortar; Rinsulation/plaster;

Rconcrete block Roverall

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2.0

1.5

1.0

M

0.5

0.0

-0.5 0

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Thermal resistance (Km2/W)

3.0

2.5

, which is

1

2

Time (h)

3

4

5

PT

Fig. 13 Thermal resistance results calculated at each time step during the pre-testing in case A

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Table 5 Thermal resistance results of each layer for the pre-testing in case A Layers

Rref

Rexp ( 6 ±

%

0.009

Concrete block

0.23

± 6%

Insulate-plaster

1.10

±

Overall (4 layers)

1.34

1.35±16%

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Mortar

%

Relative errors to Rref 622.2% -17.4% 1.0% 0.8%

Generally, the evaluation on building walls in situ has a large uncertainty because of the complex structure of wall and the uncontrolled ambient conditions. For example, the uncertainty of Standard ISO9869 [4] ranges from 14% to 28%. The results of pre-testing confirm the reference parameters of the investigated wall and indicate that the measurements 22

ACCEPTED MANUSCRIPT of temperatures and heat fluxes in this experimental system are credible. Results for the transient tests Fig. 14 shows the experimental surface temperature (T1) and heat flux (q1) at the front face of the wall during test 1. The heat flux of the wall is different with the stimulation of lamps shown in Fig. 8 due to the impact of the convection heat transfer and surroundings’

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radiation. 55

300

T1

50

q1

250

150

40 35 30

20

0

12

M

25

24

36

48

60

72

84

100 50 0

Heat flux(W/m2)

45

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Temperature (℃)

200

-50 -100 -150 -200 96

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Time (h)

Fig. 14 Surface temperature and heat flux obtained in test 1 (period of 24 hours) in case A

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The experimental unit-pulse response is calculated by the deconvolution approach

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described in section 2.2.1, results of the four transient tests are shown in Fig. 15. The simulated curve in Fig. 15 is obtained basing on the thermal quadrupoles modelling (Eq.(9))

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using the reference properties (given by Table 3), the concrete layer is assumed to be semiinfinite as for the simulation. As shown in Fig. 15, though the heating signal of each test is different, the similar unit-

pulse responses are achieved. In fact, the heat stimulation makes no effects on the unit-pulse response, which is only characterized by the thermal properties of the wall. The experimental curves have a good agreement with the simulated curve in the semi-infinite period except for a few data at the beginning (in 0.1 h). These undesirable data may be caused by the wall 23

ACCEPTED MANUSCRIPT inertia. The noise observed from these experimental curves is still very obvious even a TSVD inversion is used, especially at the long time. In fact, the investigated walls cannot be semi-infinite during the tests because the wall may be penetrated through and heat losses presence at the rear face. Variations of temperature and heat flux at the rear face of the wall have been observed during our tests.

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This gap between the reality and the assumption will lead to the difference between the experimental and simulated curves, especially in the long time. The longer time, the more obvious the difference will be. In Fig. 15, the experimental curves trend to go down quickly and perform differently with the simulated curve in the long time.

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1E-05

1E-06

M

1E-07

Test 1 Test 2 Simulation

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Unit-pulse response (Km2/J)

1E-04

0.1

1

10

100

1000

10

100

1000

Time (h)

(a)

PT

1E-08 0.01

AC

CE

Unit-pulse response (Km2/J)

1E-04

1E-05

1E-06

Test 3 Test 4 Simulation

1E-07

1E-08 0.01

0.1

1

Time (h)

(b) Fig. 15 Experimental unit-pulse response results in case A: (a) Test 1 and Test 2; (b) Test 3

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ACCEPTED MANUSCRIPT and Test 4 Based on Eq.(21), the unit-step response curves are achieved through the integral of the experimental unit-pulse response results, as shown in Fig. 16 (a). These curves are clearer and have less data noise than the unit-pulse response curves. The four curves are very close. The data the arrow pointed represents that the time t is 10 hours. In this case, the concrete

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layer is heated firstly, linear trends are obvious in this figure except at the short beginning, corresponding to the curve of case 1 in Fig. 4, whose slope is determined by

√ . For the

practical case, it needs some time to be in the response of the stimulation regularly, the bvalues are then estimated by linear fitting the data during a linear trend period (1 to 9 hours). should be transformed to

(multiply by 60). For example, Fig.

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It notes hereby the unit

16 (b) shows the linear fitting result for test 1. The slope of this fitting curve is 0.051 with good coefficient of determination r2=0.997. Hence b=1328

. Similarly, the b-

M

values of the other 3 tests are calculated, the results are given in Table 6. The coefficients of determination (r2) are quite good for each test.

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Actually, this achieved b-value is a global effusivity of the mortar layer and the

Table 3, that is

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concrete block layer. This global effusivity is predicted with the reference values given in . The relative errors between the experimental b-

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values and this reference values are also shown in Table 3. The four experimental b-values are higher than this reference value but are very similar themselves. As previously shown in

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the pre-testing results, the experimental R-value of concrete block is lower than the reference value. Errors of the two results are corresponding, which may be caused by the degradation of concrete’s thermal performances or the water infiltration.

25

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Unit-step response (Km2/W)

0.20

Test 1 Test 2 Test 3 Test 4

0.15

t=10 h 0.10

0.00

0

1

2

3

(a)

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4

Test 1 Linear fitting curve

y=0.051x-0.021 (r2=0.997)

M

0.10

0.05

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Unit-step response (Km2/W)

0.15

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0.05

PT

0.00

1

CE

0

2

3

(b)

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Fig. 16 Unit-step response in case A: (a) experimental results for the four transient tests; (b) linear fitting result for test 1 Table 6 Estimation results of b-values in case A Test

r2

Test 1

0.997

1328

43.1%

Test 2

1

1233

32.9%

Test 3

0.998

1241

33.7%

Test 4

0.992

1276

37.5%

Relative errors to

b

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5.2 Results in case B In case B, the insulation layer is heated firstly. Three transient tests are carried out using the step heating signal. Though the heating signals are constant (Fig. 11), the heat flux of the wall is non-constant due to the influence of convection and surroundings’ radiation. The previous deconvolution approach is applied for each test. Fig. 17 shows the experimental

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unit-pulse response curve in test 1 and the simulated curve. This simulated curve is achieved with the modelling Eq.(9) using the reference properties given in Table 4. The experimental curve matches well with the simulated curve. Similar unit-pulse response curves are achieved

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Test 1 Simulation

M

1E-04

ED

Unit-pulse response (Km2/J)

for test 2 and test 3 as well.

0.1

1

10

100

Time (h)

PT

1E-05 0.01

Fig. 17 Experimental unit-pulse response results for test 1 in case B

CE

With the integral (Eq.(21)), the experimental unit-step response are calculated. Fig. 18

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shows the unit-step response curve for test 1 and the results of linear fitting at the constantslope period, referring to the previous analysis in Fig. 4. The coefficients of determination (r2) are good. The intercept of this linear fitting curve equals the thermal resistance of insulation layer, namely R=2.07 m2 K/W, 21.3% relative error compared with the reference value (Rref=2.63 m2 K/W). Similarly, the R-values for the other two tests are also estimated, results are given in Table 7. The experimental thermal resistance values are lower than the reference values, but the results of these three tests are roughly similar. The decrease of 27

ACCEPTED MANUSCRIPT thermal resistance may be caused by the aging of the insulation layer or the water infiltration. Actually we are unable to know the true thermal resistance of this in situ building wall. The results obtained by the response curves are reasonable and repeatable.

Experimental step response curve Fitting curve

3.0 2.5

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Unit-step response (Km2/W)

3.5

2.0

y=0.231 x+2.07 1.5

r2=0.99

1.0

0.0 0.0

0.5

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0.5

1.0

1.5

2.0

2.5

3.0

Fig. 18 Experimental unit-step response and its linear fitting for test 1 in case B

Test 1 Test 2

r2

Relative error to Rref

0.99

-21.3%

2.02

0.95

-23.2%

2.16

0.93

-17.9%

PT

Test 3

R (m2 K/W) 2.07

ED

Test

M

Table 7 Estimated R-values in case B

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6 Conclusions

This paper studied the front face response curves to estimate the thermal performances

AC

of thick building walls based on the thermal quadrupoles formalism, the measurement only needs a few hours in transient heat transfer regime. Two classical multi-layered wall cases are studied by heating one surface using the artificial lamps. In case A, the heating lamps are placed at the concrete side, while the insulation layer is near the heating lamps in case B. The thermal quadrupoles modelling with semi-infinite boundary assumption is adapted for multi-layered thick building walls and convenient for in situ diagnosis, it reduces the 28

ACCEPTED MANUSCRIPT characterization time and simplifies the measurement parameters in situ (only the heat flux and temperature at the front face of wall are needed). A deconvolution approach is used to reconstruct the unit-pulse and unit-step responses using the measured varying heat flux and temperature at the front face. However, the obtained unit-pulse response curve has obvious data noise, and it is difficult to estimate the thermal properties of multi-layered walls in a

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short time. Actually, the pulse response curve method is more adapted for the characterizations of thin homogenous materials under laboratory condition.

There are fewer data noises for the unit-step response curves, even in a long time. The authors propose to use the unit-step response curve for thermal diagnosis of thick building

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walls in situ. Two typical diagnosis cases are studied in our work: the dense layer is heated firstly, the thermal effusivity may be estimated; the insulation layer is heated firstly, the thermal resistance may be calculated. When the information of the wall structure is unknown,

M

the unit-step response curve also has a large potentiality to distinguish the first layer (layer near the front face) is light insulating, or insulating and slightly capacitive, or contrarily

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highly effusive, thus to roughly identify the wall structures.

PT

In summary, this paper proposes an innovative estimation approach and shows the primary investigation results. The proposed method is fast, adapted to thick building walls

CE

and convenient to be implemented on a building in situ, and has the large possibility to be widely applied to more building walls with different structures. The analysis in this work

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only considers 1D heat transfer in the walls. 2D heat transfer modelling should be considered and analysed in the future. Building materials presented in our study cases are complex, such as the hollow concrete block, which can cause the unnecessary uncertainty. Thus homogenous materials should be used to construct multi-layered samples to further study on this proposed approach, such as analysing the sensitivities of front face response and the uncertainty factors during the diagnosis.

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Acknowledgement This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 637221. The sole responsibility for the content of this paper lies with the authors. It does not necessarily reflect the opinion of the

that may be made of the information contained therein.

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European Union. Neither the EACI nor the European Commission is responsible for any use

Conflict of interest statement

M

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled "short time nondestructive evaluation of thermal performances of building walls by studying transient heat transfer" .

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Reference

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