Keywords

1 Introduction

The thermal performance of buildings is largely dependent on the thermal transmittance or U-value of their walls. The theoretical U-value of a building’s wall is calculated as the reciprocal of the summation of thermal resistance values of different layers of the wall, where thermal resistance is a function of thermal conductivity and thickness of the layers [1].

$$ U = \frac{1}{{R_{i} + \frac{{d_{1} }}{{k_{1} }} + \frac{{d_{2} }}{{k_{2} }} + \cdots + R_{e} }} $$
(5.1)

Equation (5.1) represents the theoretical U value of the wall where, \( k \) is the thermal conductivity of the materials in different layers of the wall, \( d \) is the thickness of the wall’s layers. \( R_{i} \) and \( R_{e} \) are the thermal resistance of air at internal surface and external surface respectively. The U-value of an existing building’s wall often differs from its theoretical U-value because of the degradation of the wall materials, deviation of the layers’ thicknesses from their designed values, presence of voids between two layers resulting from poor craftmanship and so on [2]. Also, in some countries the quality of materials used and type are not well-characterised in terms of thermal performance and consistency. There are different approaches exist for determining the U-value of existing buildings; however, they have some limitations [3]. One of the approaches, for example, requires collecting samples of wall materials for laboratory test by drilling holes through walls [3]. Two other non-invasive methods, namely: Heat Flux Meter (HFM) method and Infrared Thermovision Technique (ITT), are limited to be performed in winter only, as they require over 10°C temperature gradient between indoor and outdoor environment [4, 5]. Another approach of estimating U-value from external and internal wall temperatures is by using noncontact infrared sensors; this technique shows better performance over HFM method; however, it is restricted to use during night only and it requires the measurement to be conducted over a few days [6]. The reliable estimation of in situ U-value is difficult in real buildings because of many constraints such as, installing instruments, extended period of monitoring time, dependency on season, dependency on weather condition and presence of sunlight [4,5,6]. Furthermore, nonlinear and complex relationship among different parameters need to be considered for accurate estimation of U-value. Artificial Neural Network (ANN) could form a very strong tool to analyse nonlinear and complex relationship among input and output parameters and a previous research work shows successful use of infrared thermography and ANN with application of point heat for categorising walls with different U-values [3]. ANN can be trained to learn the relationship between inputs and outputs in a data set and apply the learning process to estimate the outputs from a similar unknown data set. The thermal profile that is generated from infrared images of walls with known U-value can be used to train ANN which later will be able to determine the U-value of an unknown wall. This paper presents a study with a novel product designed to estimate the U-value of a real building’s wall from infrared images with application of point heat source using ANN, where the product is calibrated by training the ANN in laboratory environment with different wall samples.

2 Methodology

Wall sections with different U-values have been monitored with an infrared camera during the application of a point heat in the internal side of the walls. The thermal profiles generated from the monitored infrared images are used as the inputs for the ANN and theoretical U-values of those wall sections as the outputs to train ANN. Later, the thermal response of a real building’s wall during the application of a similar point-heat in the internal side of the wall is monitored using infrared camera and the thermal profiles generated from the infrared image are analysed with the ANN to estimate the U-value of the wall. The flow chart in Fig. 5.1 represents the methodology of this study. The ANN performance has been evaluated against the absolute deviation using Eq. (5.2).

Fig. 5.1
figure 1

Flow chart of the suggested methodology

Full size image
$$ {\text{Absolute Deviation}} = \frac{{\left| {U_{\text{predicted}} - U_{\text{calculated}} } \right|}}{{U_{\text{calculated}} }} \times 100\% $$
(5.2)

where \( U_{\text{predicted}} \) is the ANN estimated U-value and \( U_{\text{calculated}} \) is the theoretical U-value of real building’s wall using Eq. (5.1). The training and evaluation of ANN have been performed 25 times to generalise the solution and the average value of them is considered as final outcome from the ANN.

3 Experimental Work

In this study six walls, indexed as A, B, C, D, E and F respectively, are monitored using infrared camera with the application of point heat source form internal side. Sample A is a concrete block wall without any internal or external mortar layers. Samples C and E are solid brick walls without any internal or external mortar layers. Samples B and D are concrete block and solid brick walls respectively with external insulation of 100 mm thick Ecotherm. Infrared images are captured using CHINO TP-L0260EN thermal camera at five seconds interval for about an hour resulting in around 720 images per set up of the experiment. Figure 5.2 shows the experimental work on one of the lab samples. The infrared camera is fitted into a plastic box which contains a diesel engine glow plug (Fig. 5.2). The glow plug acts as a point heat source and it is fitted within a plastic box in such a way that it always stays in touch with the internal wall surface. Two K-type thermocouples connected to NIUSB-TC01 data acquisition system are used to measure the glow plug’s tip temperature and the ambient temperature respectively.

Fig. 5.2
figure 2

The setup configuration of the experimental work

Full size image

Experiments on samples A-E are conducted in lab environment and infrared images obtained from the experiments are used for the calibration process by training the ANN. The experiment on sample F is done inside a real building and infrared images captured during the experiment are used to estimate the U-value of the wall with the help of the calibrated ANN. The properties of the wall samples are listed in Table-1, where the U-values are calculated using Eq. (5.1). The values of \( R_{i} \) and \( R_{e} \) is taken as 0.13 and 0.04 respectively [7]. The thermal conductivity of concrete block in samples A and B are considered as 1.5 W/mK [8] and the thermal conductivity of the Ecotherm is 0.022 W/mK [9]. The thermal conductivity of brick in samples C and D are taken as 0.27 W/mK [10] and the thermal conductivity of the brick in samples E and F are taken as 0.56 for inner leave and 0.77 for outer leave W/mK [7] as the brick in the samples E and F are different than brick in the samples C and D.

4 Results and Discussion

Figure 5.3 represents the temperature profile and infrared image of samples D, E and F. It is noted in Fig. 5.3 that sample D has the warmest wall surface. As sample D has the lowest U-value, most of the heat is spread on the wall surface. Sample E has higher U-value than sample F and therefore, sample F is expected to have warmer wall surface. However, the infrared images in Fig. 5.3 convey the opposite information. This is also observed in the temperature profiles in Fig. 5.3.

Fig. 5.3
figure 3

A comparison between temperature profiles: sample D, E and F

Full size image

This could happen due to the difference in ambient temperature during the time of experiments. Previous research work [3] also supports the fact and recommends three modified profiles as presented in Eqs. (5.3), (5.4) and (5.5).

$$ \varvec{T}_{{\left( {i,j,k} \right)}}^{a} = \varvec{T}_{{\left( {i,j,k} \right)}} - \varvec{T}_{k}^{ext} $$
(5.3)
$$ \varvec{T}_{{\left( {i,j,k} \right)}}^{b} = \mathop \sum \limits_{1}^{k} \left[ {\varvec{T}_{{\left( {i,j,k + 1} \right)}} - \varvec{T}_{{\left( {i,j,k} \right)}} } \right] $$
(5.4)
$$ \varvec{T}_{{\left( {i,j,k} \right)}}^{ab} = \mathop \sum \limits_{1}^{k} \left[ {\varvec{T}_{{\left( {i,j,k + 1} \right)}}^{a} - \varvec{T}_{{\left( {i,j,k} \right)}}^{a} } \right] $$
(5.5)

Here \( T_{{\left( {i,j,k} \right)}} \) is the original temperature value at pixel (i,j,k) on infrared image, \( T_{{\left( {i,j,k} \right)}}^{a} \) is the modified temperature value of pixel (i,j,k) on the infrared image, \( T_{{\left( {i,j,k} \right)}}^{b} \) is the cumulative temperature difference at pixel (i,j,k),\( T_{{\left( {i,j,k} \right)}}^{ab} \) is the cumulative temperature difference of profile Ta and \( T_{k}^{ext} \) is the external temperature at the time of capture of the corresponding infrared image. In Eqs. (5.3) to (5.5), i and j refer to the pixel indices of infrared image in x and y direction respectively, and k refers to the image index in the sequence of infrared images. A feed forward neural network with single hidden layer containing 20 neurons is developed using MATLAB. Sigmoid transfer function is used in the neurons of hidden layer and Levenberg-Marquardt backpropagation algorithm is used as the learning algorithm. The standard deviation of profile T, Ta Tb and Tab are selected as the input parameters to the neural network and the U-value listed in Table 5.1 as the output. The training data set contains 60 samples of each profile taken equally from the walls AE mentioned in Table 5.1. The test data set is composed of 12 samples from each profile of the wall F. Figure 5.4 shows the average training performance of ANN for profile T, Ta, Tb and Tab of samples A-E. The absolute deviation ranges between 5% to 15% with profile T having the lowest absolute deviation and profile Tab having the highest.

Table 5.1 Properties of wall samples used to train and test ANN
Full size table
Fig. 5.4
figure 4

Average training performance of ANN for different profiles of samples A-E

Full size image

Figure 5.5 represents the ANN’s performance regarding predicting the U-value of sample F. The theoretical U-values are the target for the ANN and the ANN predicted U-values are the achievement made. The bar chart in Fig. 5.5a compares the performance of ANN with the target values. It is found in Fig. 5.5a, that the ANN produces the closest prediction to the theoretical U-value in profile Tb. Profile Tb and Tab achieve the lowest absolute deviation which is around 20% (Fig. 5.5b). The training performance of ANN for profile T is found to be the best but the test performance is the worst among all profiles, which indicates that ANN overfits this profile. On the other hand, the difference between the training performance and the test performance are found to be the lowest for profile Tab, which indicates the best fit among all profiles. Similarly, for profile Tb, ANN shows a reasonable difference between training performance and test performance indicating a better fit than the two others. In profile Ta, the difference between training performance and test performance is significantly high indicating an overfit as well. The profiles Tab and Tb are developed considering the cumulative temperature difference; and thus, it generalises the thermal behaviour of walls more precisely. As a result, the ANN produces the best performance for those two profiles.

Fig. 5.5
figure 5

a A comparison between theoretical and predicted U-values; b The absolute deviations of different profiles

Full size image

5 Conclusion

The U-value of buildings’ walls signifies the thermal performance and the energy transferred via the envelop. There is a need to estimate the U value of buildings’ components in situ and in a rapid way. This paper presents a novel approach of determining U-value of a real building’s wall by designing a novel product that can be calibrated using the training process of an ANN with the help from material samples in the lab. The results signify the ability of ANN to estimate U-value of real building based on the analysis of infrared data captured during the application of a point heat. There is no general rule to decide on the optimum configuration of an ANN or the most efficient size of training data set required to perform successful ANN analysis; as this depends on the nature of the utilised data as input and target values. The results presented in this paper show that ANN is capable of estimating U-value of buildings’ wall with 80% accuracy, including multi-layered walls. Future work will be utilised to attempt to enhance the accuracy of the system using other ANN architectures, including more training data, and compare between the existing technologies and the this suggested one.