- Email: [email protected]
Improving the detection of thermal bridges in buildings via on-site infrared thermography: The potentialities of innovative mathematical tools
Accepted Manuscript
Improving the detection of thermal bridges in buildings via on-site infrared thermography: the potentialities of innovative mathematical tools Stefano Sfarra , Antonio Cicone , Bardia Yousefi , Clemente Ibarra-Castanedo , Stefano Perilli , Xavier Maldague PII: DOI: Reference:
S0378-7788(18)32380-6 https://doi.org/10.1016/j.enbuild.2018.10.017 ENB 8846
To appear in:
Energy & Buildings
Received date: Revised date: Accepted date:
30 July 2018 13 October 2018 16 October 2018
Please cite this article as: Stefano Sfarra , Antonio Cicone , Bardia Yousefi , Clemente Ibarra-Castanedo , Stefano Perilli , Xavier Maldague , Improving the detection of thermal bridges in buildings via on-site infrared thermography: the potentialities of innovative mathematical tools, Energy & Buildings (2018), doi: https://doi.org/10.1016/j.enbuild.2018.10.017
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Highlights The solar loading was used as thermal stimulus
Unoccupied buildings without any heating systems were analyzed
Iterative filtering minimized the influence of the shadows projected on the facade
Sparse principal component thermography was used to detect thermal bridges
The measurement accuracy improved after the application of the iterative filtering
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Improving the detection of thermal bridges in buildings via on-site infrared
thermography:
the
potentialities
of
innovative
mathematical tools
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Stefano Sfarraa,b*, Antonio Ciconec,d,e, Bardia Yousefif, Clemente Ibarra-Castanedof, Stefano Perillia and Xavier Maldaguef
a
Department of Industrial and Information Engineering and Economics (DIIIE), University of
b
c
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L‟Aquila, Piazzale E. Pontieri no. 1, I-67100, L‟Aquila (AQ), Italy
Tomsk Polytechnic University, Lenin Av., 30, Tomsk 634050, Russia
Department of Information Engineering, Computer Science and Mathematics (DISIM),
University of L‟Aquila, Via Vetoio, I-67100, L‟Aquila (AQ), Italy Istituto Nazionale di Alta Matematica, I-00185, Rome, Italy
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d
e
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Gran Sasso Science Institute, I-67100, L‟Aquila (AQ), Italy
f
Computer Vision and Systems Laboratory, Department of Electrical and Computer
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Engineering, Université Laval, 1065, av. de la Médecine, Quebec City, Quebec G1V 0A6,
*
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Canada
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email: [email protected] ; telephone number: +39 340 6151350
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ACCEPTED MANUSCRIPT Abstract: The detection of thermal bridges in buildings is one of the key points to be taken into account in energy saving procedures during refurbishment works. Passive infrared thermography (IRT) has been applied for years to detect thermal bridges by referring to the International Organization for Standardization (ISO) 6781:1983. However, the successfulness of this norm is strongly affected by the detection accuracy of the thermal imprint produced on the facade by a conductive material called as “defect” in this work. The drop shadow effect, also produced by the surrounding environment on the
mask/modify the natural thermal evolution due to diffusion.
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facade under inspection, plays indeed an important role during the defect evaluation procedure since it can
Many real-life signals acting in the space physics domain exhibit variations across different temporal
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scales. This work presents an application of a new multiscale data analysis technique, the Iterative Filtering (IF), which allows to describe the multiscale nature of an electromagnetic signal working in the long-wave infrared (LWIR) region. IF appears to be a promising technique minimizing the influence of the shadows projected on the facade under inspection; subsequently, it allows the optimization of the detection
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of thermal bridges via sparse principal component thermography (SPCT) technique. The latter inherits the
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advantages of PCT allowing more flexibility by introducing a penalization term. Here is shown how the accuracy of the defect detection increases after the application of the IF
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mathematical procedure. Results are discussed on the basis of a couple of case studies referring to dissimilar buildings. Finally, a signal-to-noise-ratio (SNR) comparison with raw data is added to the
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discussion of the results.
Keywords: thermal bridge; solar loading; iterative filtering; sparse principal component thermography; quantitative analysis; building.
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ACCEPTED MANUSCRIPT 1. Introduction A thermal bridge is a localised area of the building envelop where the thermal conductivity is bigger than in the surrounding structures. The heat energy moves from molecules to other molecules allowing heat to flow through the path created. The larger the difference is between exterior and interior temperature in the building, the faster the building gains or losses heat. The most obvious locations for
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thermal bridges are where there are geometrical changes, deliberate penetrations, or places with structural changes. The material properties are affecting the heat transfer as well.
A useful method to detect thermal bridges in buildings is infrared thermography (IRT) [1]. Several years ago Grot [2] provided an interpretation of thermographic data for the identification of building heat
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loss. On this basis, Fang et al. [3] described the difficulties in the application of the above-mentioned method on buildings having large thermal inertia. One year later, Zücher [4] extended the research to localize insulation defects, by-passes, points of air leakage and areas of moisture damage. A quantification of the sizes of thermal bridges in buildings by means of IRT was for the first time introduced by Groet et
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al. in 1985 [5]. The heat loss was then calculated using field data recorded via heat flux transducers.
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Vavilov et al. introduced the use of “maxigram” and “timegram” images containing information needed for the characterization of defects (i.e., insulation deficiencies, air leaks, moist areas and thermal
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bridges) in building envelopes [6].
One year later, the same authors studied a methodology based on the solution of the inverse heat
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transfer problem, for the detection and evaluation of flaws in buildings. The building envelope was
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examined mainly in transient thermal regime [7]. A couple of years later, Kauppinen et al. on the basis of thermographic campaigns conducted in Laboratory studied a test wall using relatively low energy pulses and short heating-up times in order to detect defects and thermal bridges [8]. Kauppinen also performed in 2001 over 200 thermal scanning tests of one-family and detached houses affected by air tightness in a historic moment in which air tightness requirements were not created yet in Finland [9]. Subsequently,
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ACCEPTED MANUSCRIPT Colantonio and Desroches outlined the various types of thermal patterns created by both positive and negative building pressures during exterior inspection of various types of masonry clad buildings [10]. Moreover, the influence of thermal bridges caused by the presence of anchoring systems was studied in [11]. The evaluation of surface temperature and heat flow pattern at the four corner walls of a building envelope having thermal bridges was broadened by Jeong et al. in 2007 [12]. The mathematical models for
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estimating the thermal bridge effect at the corner walls per boundary condition were studied too. In [13], a technique to evaluate the thermal transient behaviour of buildings combining thermographic measurements and computer simulation using the software tool TRNSYS 16 was
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developed.
An IRT method combined to a simplified thermal model for evaluating thermal performance of insulated containers was studied in [14]. The proposed thermographic method allowed also determining the thermal bridges magnitude and the air leakages location. The research was further deepened later [15].
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Condensation problems in buildings retrieved via IRT were studied in [16], while the effects of
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direct solar loading on the detection of subsurface targets in a concrete test block were analysed by Washer et al. [17]. Zalewski et al. presented a contribution to the characterization of the thermal efficiency of
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complex walls of buildings with respect to the ever increasing requirements in thermal insulation. A genuine complementary experimental method allowing for the determination of the quantitative aspects of
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the heat losses through the envelope was introduced. A three-dimensional numerical method useful for
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parametric studies was also added to the discussion of the results [18]. Asdrubali et al. proposed a methodology to perform a quantitative analysis of some types of thermal
bridges, through simple thermographic surveys and subsequent analytical processing. From the measurement of the air temperature and the analysis of the thermogram, the thermal bridge effect was estimated as a percentage increase of the homogeneous wall thermal transmittance [19].
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ACCEPTED MANUSCRIPT In the same year, Hopper et al. discussed the methodology and results of using IRT for pre-retrofit and post-retrofit surveys undertaken to qualitatively assess retrofitted external wall insulation on before the 1919 existing dwellings with solid exterior walls. Evidences of potential thermal bridges were provided [20]. An example of a thermal bridge in a standard building detail and an alternate design were analysed by Kleinfeld in 2012 [21] to predict the energy impact of the bridge and of its removal.
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An interesting work which developed thermal imaging for the detection of subsurface deterioration in the soffit areas of bridges was written by Washer et al. [22]. The paper discussed via an on-site inspection the rates of change in ambient temperature needed to ensure the detection of subsurface damage
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in shaded conditions.
Previtali et al. integrated building geometrical models automatically derived from laser scanning technology with thermal images by providing metric information to thermographic analyses [23]. Instead, a low-cost, portable technology called “HeatWave” which allows non-experts to generate detailed 3D
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surface temperature models for energy auditing was developed in [24]. The presence of surface
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temperature data in the generated 3D model enabled the operator to easily identify and measure thermal irregularities such as thermal bridges, insulation leaks, moisture build-up and HVAC faults.
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An investigation of the scope for testing the thermal performance of the building envelope during the construction process using IRT was performed in [25]. The scope for four types of “in-construction” test
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was identified in: a) early stage checks on the installation of insulation, b) identifying air leakage through
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the building envelope, c) assessing insulation continuity and the severity of thermal bridges, and d) investigating the performance of building services. Thermal images acquired by an Unmanned Aerial Vehicle (UAV) to determine energy efficiency
and to detect defects like thermal bridges and heat losses were used by Previtali et al. in [26]. The developed methodology allowed also fusion of thermal data acquired from different cameras and platforms.
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ACCEPTED MANUSCRIPT In [27], in-field experimental measurements were carried out with the purpose of evaluating the energy losses through the envelope of a test room experimental field. Each element was characterized by its own thermal insulation capability. The proposed methodology coupled with IRT method were applied to assess the energy losses due to thermal bridges. IRT was also applied in the experimental detection and evaluation of the thermal defects of modern farm biogas plant envelope. Indeed, the unsuitable structural design of the biogas plant can lead to
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existence of thermal bridges and high heat losses of the building and degradation of structures [28]. In the same year, a review concerning the IRT applications for building diagnostics was published [29]. Instead, the blower door and IRT results of measured air test in historical buildings renovated by using natural
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materials were presented in [30].
In [31] a quantitative method using IRT to measure the thermal performance of complete building envelope elements that were subjected to non-steady state heat flow was described. It was found that IRT could provide a more representative result with respect to heat flux meters (HFM) measurements as it
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captures areas of imperfections, point and linear thermal bridges. One year later, Sviták et al. focused the
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attention on thermal bridges in case of wooden panel structures, both in case of low-energy and passive structure-standard. IRT was used for localization of critical areas of structures, i.e., details of corner joints
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of external walls and ceiling connections [32]. Contextually, Pagan-Vazquez et al. studied architectural details thermal bridge modelling values, and schematics of good construction practices to improve the
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building envelope performance of typical Army facilities. They also suggested examples to be used by the
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construction practitioner for the assembly of a properly mitigated thermal bridge detail in the building envelope [33]. IRT method was also used in this case. Ferrarini et al. investigated the possibilities and limitations of spot thermographic surveys coupled
with contact probes able to acquire continuously the thermal signal for days and evaluating the thermal bridges of buildings. Numerical simulations were performed to determine the reference value of an
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ACCEPTED MANUSCRIPT experimental case, while a long term thermographic survey was performed and integrated with the contact probe measurement assessing the feasibility of the method [34]. Junga and Trávníček focused the attention on a case study of a solid-state biogas plant. In particular, the work specifically concerned the qualitative evaluation of envelope construction details by IRT and quantitative evaluation of thermal defects by calculation. A significant numbers of thermal bridges caused by uninsulated bearing steel frames of the facades system, gates, doors and windows were detected [35].
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In the same year, Troppová et al. created a numerical model of thermal bridges in a wooden structure discovering differences between factual values of linear thermal transmittance utilized in the finite-element (FE) modelling and values given by the European normative method (EN ISO 14683).
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Thermal bridges of wooden structures were detected using a thermal camera. These measurements allow displaying the temperature distribution of the thermal scan and proving the positive correlation between heat flux and change in the evaluated temperatures of a thermal bridge [36]. A new methodology to detect the most significant sectors in energy transmission through IRT and
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the thermal intensity assessment of each opaque area, building element or thermal bridge, taking into
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account different values of wind speed has been proposed in [37]. Building elements or zones of a thermal envelope were selected according to their energy losses; this, in order to avoid an indiscriminate
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intervention on the opaque parts of envelopes.
O‟Grady et al. showed how the IRT method can be used as a non-invasive and easy-to-use method
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to provide quantitative measures of the actual thermal bridging performance. The novelty of their approach
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included evaluation of the actual heat flow rate caused by thermal bridge qTB and Ψ-value by means of the IRT solely, without any supporting methods. The methodology was tested under laboratory conditions in a steady state in a hot box [38].
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ACCEPTED MANUSCRIPT Lei et al. focused the attention on the detection of defects and thermal bridges in insulated truck box panels, utilising IRT. The research used both heating and cooling methods in active IRT configurations. Numerical simulations were also conducted [39]. A quantification of the wind velocity impact on the Ψ-value is reported in [40]. In fact, wind velocity significantly influences the heat losses through the building envelope. This was assessed by undertaking IRT of the same thermal bridge at various wind velocities, in a controlled environment, in a hot box device.
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The results showed that the Ψ-value is highly dependent on wind velocity.
Garrido et al. presented a procedure for the automation of thermographic building inspections mainly focused on thermal bridges. The procedure, in addition to detecting the thermal bridges by their
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geometric characteristics and their temperature differences with the surroundings, includes the computation of the thermophysical property of linear thermal transmittance of each candidate to thermal bridge, thus implying their characterization in addition to their detection. The accuracy of the detection of thermal bridges regarding existing methodologies was improved in 15% considering false positives and
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negatives obtained in each methodology [41].
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The development and validation of an innovative mathematical algorithm to enhance the image resolution and the consequent accuracy of energy losses assessment has been introduced in [42]. An
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experimental campaign was conducted in a controlled environment (hot box apparatus) on three typologies of thermal bridge, firstly performing the thermographic survey and then applying the enhancement
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algorithm to the infrared images. Results showed that the proposed methodology could bring to an
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accuracy improvement up to 2% of the total buildings envelope energy losses evaluated by quantitative IRT. Moreover, the proposed algorithm allowed the implementation of a further process applicable to the images, in order to extract the physical boundaries of the hidden materials causing the thermal bridge. In [43], the joint use between quantitative IRT and ultrasonic pulse velocity (UPV) methods has been introduced into the energy saving field by Tavukçuoğlu et al. because they are both useful for
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ACCEPTED MANUSCRIPT detection of visible and invisible cracks, thermal bridges and damp zones in building materials, as well as for thermal performance assessment of building components. Tavukçuoğlu was also involved in [44] in which the combined use of blower test method and IRT was useful for non-destructive assessment of airtightness features of building envelopes. O‟Grady et al. also demonstrated an application of the quantitative IRT method to evaluate the heat loss via multiple thermal bridging. It is shown that, using IRT, the heat loss via multiple thermal bridges
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can be easily estimated in an existing building envelope, without any knowledge of its internal structure or material properties. The methodology was validated against experimental measurements taken on different specimens in a hot box device. Results from the thermographic analysis also co-related well with results
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from finite element heat transfer and computational fluid dynamics simulations [45].
In [46], the effects of clouds and radiative cooling were underlined for the first time; it was found that the clear sky is a preferable condition for IRT. In addition, the effect of obstacles on a vertical surface that bring additional challenges to IRT was experimentally evaluated, too.
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The present research continues the idea started in [46] by focusing the attention on two case studies.
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In particular, selected parts of facades of two condemned buildings due to the 2009 earthquake which hit L‟Aquila city (Italy) and its surroundings [47] were inspected by IRT using the solar diurnal cycle [48].
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Applications of mathematical methods on raw thermograms explain how a useful and simple protocol based on a thermal camera (working into the long-wave infrared spectrum) coupled with a PC help to
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obtain interesting results.
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Segmentation methods were applied on smoothed and non-smoothed thermograms in order to explain how the accuracy of thermal bridges detection improves after the initial mathematical treatment. The latter tends to minimize the drop shadow effect on the recorded facades and, therefore, provide accurate thermal imprints to be segmented.
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ACCEPTED MANUSCRIPT The signal-to-noise-ratio (SNR) technique was applied to a case study of the two treated herein; this, with the aim to quantitatively evaluate the image enhancement obtained thanks to the implementation of the innovative filtering procedure. The result confirms the ability of the smoothing method in removing the high frequency oscillations due to the noise. Further studies will be focused on the evaluation of heat loss studying occupied buildings.
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2. Brief recap concerning IRT IRT is a well-known non-destructive testing (NDT) method able to analyse the thermal information obtained from an object having a temperature above –273.15 °C. This method detects the energy emitted by a surface and converts it into temperature variation. The output is an image (or a series of images
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collected over time) named thermogram(s). Infrared refers to the radiations located between visible and microwave in electromagnetic bands [1].
Usually, IRT is applied for the evaluation of electrical components [49] and thermal comfort [50], as
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well as for the inspection of buildings [51], artworks [52], materials [53] and composites [54], without forgetting medical [55] and surveillance [56] applications.
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Generally, infrared bands are divided into five parts, near infrared (NIR), short-wave infrared (SWIR), mid-wave-infrared (MWIR), long-wave infrared (LWIR), and far-infrared (FIR), which are
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respectively from 0.75 to 1 µm, 1 to 2.5 µm, 3 to 5 µm, 7.5 to 14.5 µm, and 50 to 1000 µm. MWIR and
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LWIR are more appropriate for the buildings‟ inspection [57]. A series of thermograms forms a 3D (x-y-t) data set that can be analyse by advanced techniques,
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such as [58–60] in order to improve contrast, e.g., the signal-to-noise (SNR) ratio. In particular, sparse principal component thermography (SPCT) technique [60] has recently been proposed in the NDT field, and its main features will be discussed in section 4. In this study, the external energy source (approach: passive) was an optical thermal stimulus (source: thermal radiation), i.e., the Sun, therefore, the source was in motion (configuration: dynamic), and the
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ACCEPTED MANUSCRIPT energy was transferred in reflection (mode: reflection) on a surface (scanning: surface) via a modulated excitation (waveform: modulated) due to the solar cycle. The physics of periodic heating/cooling by solar radiation was described in [61]. Interested readers can refer to this work in order to understand the general theory inherent to a thermally stratified slab illuminated by a periodic changing solar radiation and bathed in an atmospheric temperature. These conditions are the basis of the case studies analysed in this work. The temperature variation in time on the
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surfaces of the two buildings was recorded by an infrared camera working in the LWIR spectrum, connected to a PC sequentially storing the thermograms. The thermal camera was mounted on a tripod. The latter was positioned in two rooms located each one in front of the inspected facades. The centre of
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the external lens was adjusted to be perpendicular at each inspected facade. This, in order to avoid rectification processes of the thermal images analysed [41]. A telephoto was also used in both case studies; this, taking into account the distance to the target, as explained in the next section. In both case studies, the wind speed was measured by a digital anemometer installed near to the
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calm, according to Beaufort‟s scale.
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facades. In all cases, the measured wind speed (< 1 km/h) corresponded to a Beaufort number = 0, that is,
3. The Iterative Filtering (IF) Method as a pre-processing tool
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In order to understand the reason why the authors use in this work the Iterative Filtering (IF) method
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as a pre-processing tool and how it works in details, we need to briefly go back to the origin of this method showing why it was developed and presenting the so called Empirical Mode Decomposition (EMD)
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algorithm from which IF inherits its structure and good properties. In our digital era we are surrounded by instruments which allow to measure and record any kind of
signal. Such signals are in general produced by nonlinear systems and, therefore, are inherently non stationary.
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ACCEPTED MANUSCRIPT Over the years many methods have been devised to study and analyze all kinds of signals. However, all of these methods proved to be limited. Either because they were based on the assumption that the signal is stationary, like the Fourier transform and analogous techniques, or because they assumed the phenomenon was linear in nature, like the wavelet transform (WT) [62] and equivalent methods. Furthermore, all the standard methods require an a priori selection of a basis for the decomposition and analysis of a signal. Several ideas have been proposed and developed to improve the ability of such
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methods to deal with the non-stationarities of the signals under study, like the Short Time Fourier Transform (STFT) [63], or the Synchrosqueezing WT [64]. However, these further developments of the original approaches only partially alleviate the inherent limitations of such techniques.
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Two decades ago [65] a group of researchers at NASA leaded by Huang proposed a new technique, first algorithm of its kind, called EMD method which is able to decompose non stationary signals into simple components called Intrinsic Mode Functions (IMFs). Each IMF is an oscillatory signal which fulfills two properties:
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respect to the horizontal axis, and
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1) the envelope connecting its maxima and the envelope connecting the minima are symmetric with
2) the number of zero crossing equals the number of its extrema
.
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The idea behind the EMD algorithm is simple but powerful. Is the so called sifting process: to extract the highest frequency oscillatory component from a signal by computing and subtracting its
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moving average. The algorithm works as follows: given a signal , its maxima is computed and connected
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to all other signal maxima using an envelope, produced using cubic splines for instance, and then the same is done for the minima. The point by point average of these two envelopes is the curve
, which
represents an approximation of the so called moving average of . A first rough approximation of the highest frequency component contained in computing now the moving average of
is now computed as: which is called
as:
. The procedure is repeated . An iteration procedure
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has a moving average
, which is small enough in some chosen norm. Hence,
represents the first IMF that is subtracted from the original signal , and the entire sifting procedure is iterated on the remainder
. In this way, all the IMFs contained in a given signal can be extracted
until the remainder until a significant trend is observed. The EMD decomposition of a signal
into IMFs together with the calculation of the instantaneous
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frequency of each IMF via the Hilbert transform allows to compute the time frequency representation of and as a whole is known as the Hilbert Huang Transform (HHT) method [63].
Thanks to the HHT algorithm several breakthroughs have been achieved in several research fields ranging from Physics to Engineering, Finance and Medicine and many others, the interested reader can
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find a list of the main contributions in [66]. However, from a mathematical standpoint the EMD remains still a black box.
The repeated usage of envelopes specifically tailored at each iteration for the signal under analysis it makes impossible to perform any kind of convergence analysis on the method. In practice, the algorithm
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just described is still completely empirical and the only thing that researchers have been able to show so
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far is that it does decompose known signals as the authors would expect them to be decomposed. However, in doing this kind of studies they discovered that the method is unstable in this form: a small perturbation
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in the original signal can lead to a drastic change in the decomposition. To solve this issue Huang and his
[67].
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collaborators devised in 2009 the so called Ensemble Empirical Mode Decomposition (EEMD) method
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The idea is to perturb a given signal (to be decomposed) with an ensemble of noise realizations. Then each perturbed version of the original signal is decomposed using EMD and the average among all the decompositions is derived. The greater is the number or noise realizations in the ensemble the more the method is stabilized. This solution clearly impacts drastically the computational time needed for the
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ACCEPTED MANUSCRIPT decomposition. Furthermore, the problem of showing the a priori convergence of the method remains unsolved. For these reasons, in the last years several research groups have devised alternative methods able to produce results similar to the EEMD algorithm, such as the Empirical WT developed by Gilles [68], the Sparse time–frequency representation method developed by Hou et al. [69], using the multicomponent amplitude modulation and frequency modulation (AM–FM) representation [70], and several others [71, 72,
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73]. All these alternative methods make use of optimization techniques in order to produce the decomposition of a given non-stationary and non-linear signal, and they require the a priori selection of a suitable basis for the decomposition.
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In 2009, Lin et al. developed an alternative algorithm for the decomposition of a signal called IF [74]. Unlike all the aforementioned methods, which are based on optimization, the IF algorithm has an iterative structure exactly like the EMD technique. Hence, like the EMD, it does not require any initial
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assumption on the signal, and it is able to produce decompositions that are completely data driven.
Figure 1. Two examples of Fokker-Planck filters that can be used in the IF algorithm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article)
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ACCEPTED MANUSCRIPT IF method is structured exactly like the EMD with its sifting process. The only difference is that now the moving average filter
is derived by convolution of the given signal
with a chosen compactly supported
such as, for instance, a double average filter or a Fokker-Planck filter. An example of this last
kind of filters is shown in Figure 1, and is formally defined in [75]. Hence, (1)
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∫
The convolution with a filter represents the most natural way to compute the moving average from a mathematical standpoint: it is the average of the values of values of the filter
around the point
using as weights the
. The fact that this average is local is ensured by the fact that
is a compactly
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supported function. This new way of computing the moving averages opens the door to a rigorous analysis of this technique [75, 76, 77] and to an extension of this method to higher dimensions of the signals [78, 79].
In particular, from the numerical analysis of IF it follows that the method is convergent and stable
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and it can be sped up by means of the FFT [76]. In [80] the author compares the results produced using
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EEMD versus the ones derived using IF on a couple of well know geophysical signals and provides a detailed explanation on how to use the IF code, which is available at www.cicone.com.
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In this work, the authors use the IF method as a preprocessing tool. Given the measurements collected using a telephoto mounted on the external lens of a FLIR S65 HS thermal camera.
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Two case studies are considered herein. In the first one, the authors recorded from the area of
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interest shown in Figure 2, left panel, 900 thermograms from July 29, 2015 at 5:30 p.m. to July 30, 2015 at 11:30 p.m., with a frame rate of 1 thermogram every 2 minutes. The distance of the thermal camera from the area of interest was around 80 m. Each pixel recorded over time represents a nonstationary signal that can be decomposed using IF.
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ACCEPTED MANUSCRIPT After decomposing in IMFs each one of these signals, all the components relative to frequencies higher roughly than 1/700, which represents the natural frequency due to the solar cycles in our time window, were removed. The authors add together all the leftover IMFs to produce a new postprocessed signal. Figure 2 (right panel) shows an example of this preprocessing applied to the values of the pixel in position row 120 and column 160 of the area of interest measured over time. The original raw signal is
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plotted in blue, whereas the postprocessed result is plotted in red.
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Figure 2. Left panel (a), picture of the area of interest surrounded by a dotted red rectangle. Right panel (b), example of preprocessing by means of IF applied to row 120 column 160 of the area of interest recording over time. In blue, the original
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signal and in red the post processed one. (For interpretation of the references to colour in this figure legend, the reader is
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referred to the web version of this article)
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As a second example, a Church Bell Tower was inspected using the same thermal camera and similar procedure. In Figure 3 on the left, the building with the area of interest is highlighted in red. On the
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right panel, the original signal corresponding to the pixel in row 160 and column 120 is compared with the same signal after preprocessing with IF. In Figure 4, the authors plot the components, the so called IMFs, produced in the decomposition. The last function plotted in the bottom right is the remainder, which is the very same curve plotted in red in the right panel of Figure 3. It should be noted that the original signal can be reproduced summing all together these IMFs including, of course, the remainder.
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(a)
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Figure 3. Left panel (a), the scheme of our experimental setup is shown for Bell Tower along with thermography and visible
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image. Right panel (b), example of preprocessing by means of IF applied to row 160 column 120 of the area of interest recording over time. In blue, the original signal and in red the post processed one. (For interpretation of the references to colour
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in this figure legend, the reader is referred to the web version of this article)
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Figure 4. Decomposition produced using IF applied to the nonstationary signal corresponding to pixel in row 160 column 120 of the area of interest of the Bell Tower‟s case study: Left panel (a) highest frequency IMFs with frequencies decreasing from
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top to bottom, and Right panel (b) lowest frequency IMFs with frequencies decreasing from top to bottom and the trend. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article)
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ACCEPTED MANUSCRIPT Such pre-processing allows to remove high frequency oscillations in a smart way. In particular, low frequency non-stationarity are fully preserved meanwhile temporary effects, like the shadow of a tree moving due to wind or simply do to the rotation of the earth are removed. In Figure 5 the authors compare the pre-processing filtering obtained using IF, in dot-dash magenta, with the ones produced using the well-known Discrete Wavelet Transform (DWT) [62], solid red, and the EEMD, green dots when applied to the pixel in row 160 and column 120 of the Bell Tower‟s case study.
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For the EEMD [67], 200 ensembles were used whereas for the DWT the authors used in Matlab the wavedec function with level seven and wname set to „db4‟, as well as the wden function with soft thresholding rule 'rigrsure' and rescaling based on a level-dependent estimates of the noise. The DWT is
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the fastest approach; it requires just 0.016 seconds to pre-process the signal associated with the chosen pixel using Matlab R2018a run on a Windows 10 Intel Core i7-8550U CPU 1.80 GHz 16 GB RAM personal computer. However, the DWT cannot remove completely the high frequency oscillations contained in the signal due to its limitation in the scales which can only be powers of two. If, in fact, the
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level in the DWT is increased, significant information are lost.
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The EEMD proves to be a reasonable filtering technique. There are small problems at the boundaries that can be easily fixed. However, the ensemble approach to stabilize the EMD method makes this
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technique really slow as stated before. In particular, the EEMD pre-processing requires 80.2 seconds of computational time for the single pixel pre-processing making it 5000 times slower than the DWT
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approach. The authors point out that the number of ensembles should be chosen in general higher than 200,
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as suggested in [67], to ensure a complete stability of the approach, making the method further slow. Finally, the IF requires 0.13 seconds. The outcome produced by IF, shown in Figure 5 in dot-dash
magenta, is definitely better than the one produced with the DWT and comparable with the one produced by EEMD. However, the IF is more than 600 times faster than the EEMD.
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Figure 5. Comparison of three different pre-processing filtering techniques applied to denoise the pixel in row 160 and column 120 of the Bell Tower‟s case study. In solid blue, the original signal is shown. In dot-dash magenta, the IF filtering is plotted. In solid red, the DWT is charted, while by green dots the EEMD filtering is identified. (For interpretation of the references to
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colour in this figure legend, the reader is referred to the web version of this article)
4. Sparse principal component analysis (SPCA) / thermography (SPCT)
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The application of Principal Component Analysis (PCA) [81, 82] in thermography (PCT) [58]
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provides a significant contribution to post-analysis of thermal images concerning several different applications, such as detection of defects for Infrared Non-Destructive Testing (INDT) [83–87], and Art
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and archeological investigations [88, 89]. PCT is used for many applications such as dimension reduction, noise elimination, classification, etc. PCT calculation can be performed by using covariance matrix
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calculation, Singular Value Decomposition (SVD), or Candid Covariance-Free Incremental Principal Component Thermography (CCIPCT) [90, 91]. Summarizing, PCT is the application of PCA to thermographic data. The decomposition matrix is performed for the input matrix (heat matrix) X which is
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ACCEPTED MANUSCRIPT p×n, where n is the vectorized thermal image in every sequence and p corresponds to the number of observations, and decomposes to (2) where, p > n and
is a diagonal matrix with a dimension of n×n and either zero or positive elements.
It is considered as the singular value of matrix X and
denotes the transpose of the n×n matrix
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(eigenvector or basis matrix) and U is the p×n matrix. The data is arranged column-wise based on the observation variation. Spatial variations are mapped in the row direction (input data located in columns and rows show the observations). The columns of matrix U represent the input matrix (frame here) [58]. PCT in general is a linear transformation method which applies a decomposition of the input zeroand coefficient matrix . The basis matrix carries the orthonormal
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mean data matrix into the basis
property that also maximizes the variance of projected data, which leads to the Principal Components (PCs) of the input matrix. The optimal property of PCT cannot be achieved through a linear transformation due to the compact representation of the input data by a limited number of basis vectors which is sometimes
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very good for noise reduction. This problem exists in all types of PCT calculations even for CCIPCT
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where the iterative computation leads to eigenvalues and eigenvectors which might benefit from low computational complexity as compared to PCT (for high-dimensional data). To alleviate this problem in
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PCT, and uphold some or all good properties of PCT, Sparse-PCT (SPCT) is used. In a few words is a PCT together with two penalty terms,
and
, in the formulation. Additional regularization parameters
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in SPCT not only turn PCT into a nonlinear transformation, but also maximize variance of uncorrelated
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PCs [93–96]. If the empirical covariance matrix of maximization of variance in the direction of vector
is presented by for
, SPCT [97] is a
. (3)
such that ‖ ‖
‖ ‖
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ACCEPTED MANUSCRIPT Let
be
norm of v, which is the non-zero components. This is a NP-hard problem and
several alternative methods have been proposed to solve it [92]. SPCT maximizes the variance of uncorrelated PCs and is independent of loading vectors, thus providing the linear combination from a few original variables. The algorithm follows Zou et al. (2006) and Elastic Net in a regression-like framework for PCT [95,
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96]. The following theorem concerns an approximation of PCT in two stages. From [96], the first part performs PCT, which is mentioned as follows:
the
principal components, let a and
row vector of the matrix X. For any ( ̅ ̅)
, let ∑|
such that Then, ̅
. For
|
∑|
be
matrices.
denotes
|
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Theorem Considering the first
(4)
.
(this is taken from [96]). It converts the PCT from a linear
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problem into a regression-type problem. The exact PCT answer can be obtained by
penalty term (Least Absolute Shrinkage
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formulation, and having the ridge penalty terms. The additional
in the
and Selection Operator - LASSO) is added to the previous portion to obtain the sparse loading and
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( ̅ ̅)
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changes the previous formulation into the following optimization problem [96]:
where,
applied for all
∑|
|
∑|
|
∑|
| (5)
such that components and
, for every j controls the variation of PCs.
In synthesis, since in PCT each PC is calculated as a linear combination of all of the pixel values
(i.e., all the entries in the loading vectors are typically nonzero), the result is that the loading images may
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ACCEPTED MANUSCRIPT be sometimes difficult to interpret. This stimulated the development of SPCT [60] which introduces SPCA [96] into the thermographic field. 5. Main information about defects, results of sparse analysis on thermal imagery and discussion The experimental set-up used in the present work is shown in Figure 3a. Although it refers to the
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case of the Bell Tower, the case of the Faculty of Engineering is based on the same experimental setup. Concerning the Bell Tower‟s case, the defects we are talking about are a buried window and three beams (1., 2. and 3.) in the wall. They are briefly summarized in Fig. 6. In the latter it is possible to see how photographs were captured in the course of time (both from the interior and the exterior part of the
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façade of the Bell Tower). The defects were measured, and the processed thermogram acquired once the window under inspection was covered by bricks and plaster is compared and linked with the snapshots. The region of interest (ROI) on which the authors focused the attention will be later clarified. On it, the
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SNR was calculated in order to demonstrate the effectiveness of the smoothing process by means of IF. In
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fact, a comparison with the raw data is provided before the discussion of the Faculty of Engineering‟s case.
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Figure 6. Main defects of the Bell Tower‟s case: their thermal imprints can be easily recognized in the processed
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thermogram. The Bell Tower was photographed in the course of time and recorded into the long-wave IR spectrum once the window below the clock was covered by bricks and plaster. As can be seen, the clock was installed subsequently with respect to
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the edification of the Bell Tower [57]. The position of the inspected beams (size: 15 x 15 [cm]) are signaled by the numbers 1., 2. and 3. both in the processed thermogram (PCT – EOF5) and in the snapshot captured from the interior part of the Bell Tower.
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(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article)
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Although Fig. 6 is just to describe the defects after a combined visual and thermographic inspection, the information that provided were useful to quantitatively analyze the defects themselves. It is possible to see how the buried window was not covered for the entire depth of the wall. This explains why it acts as a thermal bridge.
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ACCEPTED MANUSCRIPT The defects detected on the wall of the Faculty of Engineering are inherent to recursive horizontal and parallel stripes (width: 20 [cm]), and based on the application of flax fiber-reinforced polymers (FFRP) fabrics (FIDFLAX UNIDIR 300 HS50®) impregnated with epoxy resin. They were applied on bars made by double stranded basalt fibers passing through the thickness of the wall. On the one hand, they increased the load and deformation capabilities of the building, while preserving its stiffness and dynamic properties. On the other hand, they act as thermal bridges by considering the remaining part of the external opaque
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wall constituted by a uniform material similar to tuff and arranged by means of bricks. Sometimes, indeed, the double stranded basalt fibers arrive to the slabs by locally interrupting the continuity of the external wall. This, for earthquake-proof reasons [98].
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With the description of the defects, it is possible now to describe first the segmentation algorithm and then the results obtained by using it. The authors also compared the computational results for SPCT decomposition techniques in the algorithm to analyze the performance by segmenting the defects. To quantitatively evaluate the accuracy of the proposed algorithm, a ground truth (GT) is required.
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For that, an image that is manually labeled has been used. The photographic evidence performed before
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the thermographic inspections helped in this respect. Having the GT available, automatic labeled pixels and GT points could be compared and led to both a raw accuracy (ACC) and two types of errors, named
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False Negative (FN) and False Positive (FP). The latter is an error which represents a region instead of another one (i.e., a defect is detected due to an error), while FN is an error that reveals no detection at all
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(although there was a defect that had to be detected). In particular, the general accuracy of the proposed
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method was computed using the following equations: Total accuracy = ACC (%) – FN (%) – FP (%)
(6)
where, ACC was calculated by means of Eq. 7): (7)
As above-mentioned, FN stands for the FN error. It was estimated using Eq. 8):
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ACCEPTED MANUSCRIPT (8) while, the FP error was calculated by following Eq. 9). (9)
From Tab. 1a it is possible to see how the computational complexity increases for the smoothed data;
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contextually, the accuracy of defect detection increases, too. The graph shown in Tab. 1b sums up very nicely the latter result obtained on the basis of the real images containing the defects previously mentioned. The algorithm was run in a PC (Intel(R) Core(TM) i7 CPU, 930, 2.2.80GHz, RAM 12.00GB, 64 bit
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Operating System) and the processing was conducted using the MATLAB computer program.
Table 1.a The accuracy and computational complexity of the proposed approach is shown in the table.
Building
Pre-processing
Accuracy of defect detection (%)
Computational complexity (second)
51.09
27.19
Smoothed data
57.37
33.21
Non-smoothed data
20.21
86.45
Smoothed data
43.73
115.04
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Non-smoothed data Faculty of Engineering (AQ)
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Bell Tower
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Table 1.b The accuracy difference between the smoothed and non-smoothed data is represented in the bar-chart graph.
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Smoothing effect on precision Non-smoothed data
51.09
Smoothed data
57.37 43.73
Faculty of Engineering (AQ)
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20.21
Bell Tower
Regarding the Faculty of Engineering, the accuracy of defect detection was 51.09%. It is linked to a
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computational complexity of 27.19 seconds. The accuracy was improved by around 7%, i.e., up to 57.37%, although the computational time increased up to 33.21 seconds. Instead, the accuracy of the defects found in the Bell Tower increased from 20.21% to 43.73%. In practice, a significant improvement was obtained. Contextually, the computational cost grew 28.59 seconds.
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Figure 7f and Figure 7v show by means of red solid rectangles the ROIs for the Faculty of
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Engineering and the Bell Tower case, respectively. On them our analyses have been focused.
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Figure 7. The results of SPCT marked by red rectangles (f, v) to show thermal bridges for both the Faculty of Engineering of the University of L‟Aquila (d, e, j, k) and a Bell Tower (o, p, t, u). The infrared image set come from before and after the smoothing procedure. Please note that a, b and g, h are better results for the Faculty of Engineering in non-smoothed and
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smoothed results, respectively. The same can be said about l, m and q, r inherent to the Bell Tower. In particular, f, v are representing the region of interest (ROI) for the Faculty of Engineering and Bell-Tower, respectively. c, i, n, s are lower
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accuracy examples of SPCT for both cases analyzed in smoothed and non-smoothed conditions. (For interpretation of the
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references to colour, the reader is referred to the web version of this article)
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In particular, Figs. 7t, u show a square zone at the centre of the image that is undetectable in the nonsmoothed results (Figs. 7o, p). It is inherent to the buried window covered by bricks and plaster in the
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course of time. In addition, three square zones were detected below the buried window. They are well segmented only in Figs. 7t, u, i.e., after the application of the IF. This result emphasises the usefulness of the preventive application of IF. The three square zones correspond to beams used in the past to build the structure [57]. They are indicated by means of three arrows in Fig. 8b, although already described in Fig. 6. In the latter, see the numbers 1., 2. and 3..
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ACCEPTED MANUSCRIPT The proof of the thermal bridge comes from a photograph collected from the interior part along with the thermal behaviour in time of an area (defective) selected on it, and another area (defect-free) selected close to it (Fig. 8a – below). It is possible to see how a reduction in section exists in the wall (Fig. 8a – above), exactly in the position in which the window was. The proof of thermal bridge by IRT is linked to the thermographic footprint visible via PCT analysis in Fig. 8b. In this case, the second Empirical Orthogonal Function (EOF2), i.e., an eigenvector of the data covariance matrix, well summarize the
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thermal imprints projected on the plaster layer.
2012-07-18 6:30 pm peak positive contrast
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20 2012-07-18 1:30 pm start 15
0
6
2012-07-21 12:00 am 3rd day
2012-07-18 6:30 pm peak negative contrast 12
18
24
Defective area
30
36
42
Defect-free area
2012-07-23 1:30 end
2012-07-20 12:00 2nd day
2012-07-19 12:00 am 1st day
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100
Hidden window Sound area
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Temperature [ oC]
35
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50
48
54
60
150
2012-07-22 12:00 am 4th day 66
72
78
200 84
90
96
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Time [hours after start]
250
20
(a)
40
60
(b)
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Figure 8. (a) Thermal profiles of the two areas highlighted in (b) with a black (window) and white (defect-free area) cross, and (b) non-smoothed PCT-EOF2 of the Bell Tower [57]. Part of the real image captured from the interior of the Bell Tower useful for the computational approach is shown in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article)
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ACCEPTED MANUSCRIPT At this point, the SNR was applied as an example on the ROI of the Bell Tower to compare smoothed and non-smoothed (raw) thermograms (data), in order to evaluate quantitatively the IF image enhancement. The SNR was computed as the ratio between the mean and the standard daviation
of our
signal: (10)
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Its value moved from roughly 45.1 before smoothing to 46.4 after smoothing, confirming the ability of the smoothing method in removing the high frequency oscillations due to the noise.
Instead, the proof of the different nature of the materials in the case of the Faculty of Engineering [98] is understandable from Fig. 9a. The acquisition started on July 29th 2015 at 5:30 pm and ended on
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July 30th 2015 at 11:45 pm. The blue colour profile correspond to a part of the FFRP, while the red colour profile correspond to a part of the wall in bricks. The FFRP areas acting as a thermal bridges correspond to the recursive horizontal and parallel stripes that are light in color with respect to the brownish bricks (Fig.
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9a – above).
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305
295 290
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clouds
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300
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Temperature [oC]
310
6PM
12AM
Reinforcement area Sound area 6AM 12PM Time [s]
6PM
12AM
(a)
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(b)
(c)
Figure 9. (a) Temperature evolution through time covering the average temperature over the two selected areas (see Fig. 2a): the blue colour correspond to the FFRP, while the red colour correspond to the wall in bricks, (b) fourth thermogram recorded
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from the starting of the sequence (without the application of the IF method): the drop shadow is indicated by the arrow, and (c) fourth thermogram recorded from the starting of the sequence (with the application of the IF method): the drop shadow disappears [98]. Part of the real image captured from the exterior of the Faculty of Engineering useful for the computational approach is shown in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web
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version of this article)
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The areas corresponding to these thermal profiles are shown in Fig. 2a. As can be seen, both areas
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follow more or less the same thermal behavior during the first several hours after starting the survey, while the building is still heated by the sun (from 5:30 pm to 8:00 pm) and then for some hours while cooling
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down (from 8:00 pm to 12:00 am of the next day). Around midnight though, the profiles from these two areas start to diverge, reaching a maximum difference around 6:00 am, that is right after sunrise. From that
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point, the facade starts heating up again and the profiles approach to each other until no significant difference can be perceived in the early evening, similar to the day before. The sudden temperature variation in the profiles at around 7:00 pm (about an hour before sunset, ~8:00 pm) of the second day is due to the presence of clouds [99].
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ACCEPTED MANUSCRIPT The difference in temperature between these two areas is due to the presence of the FFRP reinforcement structure having a thermal diffusivity of 1.5x10-7 m2/s [100], which is slight different from the thermal diffusivity of tuff (5.0x10-7 m2/s) [101]. The potentiality of the IF method illustrated in section 3 is here visualized by comparing the same thermogram before (Fig. 9b) and after (Fig. 9c) its application. It is possible to see how the effect of clouds
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before the image processing is pointed out on a part of the wall by means of an arrow; this effect disappears after the image processing (Fig. 9c) thanks to the IF. The drop shadow is a high frequency oscillation, i.e., a temporary effect that can be indeed removed. 6. Conclusions
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The work starts with a brief review of the previous manuscripts centered on the thermographic analysis of thermal bridges in buildings. The work is focused on two case studies in which no internal heat input is present. Indeed, the damaged buildings were delimited inside a red zone due to the earthquake
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which seriously affected L‟Aquila city and its surroundings in 2009. In addition, the wind effect on the facades can be considered negligible, taking into account the anemometric campaign conducted during the
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thermographic inspections. Finally, it is important to underline how an increased non-defective
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surrounding region aids the lateral diffusion of heat. Hence, thermal waves over a small defect area surrounded by a large non-defective surrounding region diffuse very quickly [102]. Since the defective
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areas cannot be considered as small with respect to the inspected ROIs (Fig. 7), the projected defect size on the facade is only affected by the shadow effect. The latter can be minimized by using the IF method
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during the pre-processing of the thermograms. On the one hand, this step helps to improve the accuracy of the defect detection via SPCT technique, as can be gathered from the comparison between smoothed and non-smoothed data shown in Tab. 1. On the other hand, the computational complexity increase with increasing the accuracy.
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ACCEPTED MANUSCRIPT In addition, taking into account the example of the Bell Tower selected as representative of the two ones here treated, it is possible to say that the SNR values before and after smoothing confirm the ability of the proposed method in reducing the noise level. Finally, the use of numerical simulation computer programs will be explored as future perspective in order to foresee/evaluate the possible detection of thermal imprints on recorded facades, by imposing the
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real geographical coordinates of the sites under inspection to the model [103]. Acknowledgments
The authors would like to thank the mother tongue English Prof. Agnese Anna Aureli for the spell checked, technical checked and grammar checked of the sentences written in the article.
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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declarations of interest: None.
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Graphical abstract
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Improving the detection of thermal bridges in buildings via on-site infrared thermography: the potentialities of innovative mathematical tools Stefano Sfarra , Antonio Cicone , Bardia Yousefi , Clemente Ibarra-Castanedo , Stefano Perilli , Xavier Maldague PII: DOI: Reference:
S0378-7788(18)32380-6 https://doi.org/10.1016/j.enbuild.2018.10.017 ENB 8846
To appear in:
Energy & Buildings
Received date: Revised date: Accepted date:
30 July 2018 13 October 2018 16 October 2018
Please cite this article as: Stefano Sfarra , Antonio Cicone , Bardia Yousefi , Clemente Ibarra-Castanedo , Stefano Perilli , Xavier Maldague , Improving the detection of thermal bridges in buildings via on-site infrared thermography: the potentialities of innovative mathematical tools, Energy & Buildings (2018), doi: https://doi.org/10.1016/j.enbuild.2018.10.017
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Highlights The solar loading was used as thermal stimulus
Unoccupied buildings without any heating systems were analyzed
Iterative filtering minimized the influence of the shadows projected on the facade
Sparse principal component thermography was used to detect thermal bridges
The measurement accuracy improved after the application of the iterative filtering
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Improving the detection of thermal bridges in buildings via on-site infrared
thermography:
the
potentialities
of
innovative
mathematical tools
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Stefano Sfarraa,b*, Antonio Ciconec,d,e, Bardia Yousefif, Clemente Ibarra-Castanedof, Stefano Perillia and Xavier Maldaguef
a
Department of Industrial and Information Engineering and Economics (DIIIE), University of
b
c
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L‟Aquila, Piazzale E. Pontieri no. 1, I-67100, L‟Aquila (AQ), Italy
Tomsk Polytechnic University, Lenin Av., 30, Tomsk 634050, Russia
Department of Information Engineering, Computer Science and Mathematics (DISIM),
University of L‟Aquila, Via Vetoio, I-67100, L‟Aquila (AQ), Italy Istituto Nazionale di Alta Matematica, I-00185, Rome, Italy
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d
e
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Gran Sasso Science Institute, I-67100, L‟Aquila (AQ), Italy
f
Computer Vision and Systems Laboratory, Department of Electrical and Computer
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Engineering, Université Laval, 1065, av. de la Médecine, Quebec City, Quebec G1V 0A6,
*
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Canada
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email: [email protected] ; telephone number: +39 340 6151350
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ACCEPTED MANUSCRIPT Abstract: The detection of thermal bridges in buildings is one of the key points to be taken into account in energy saving procedures during refurbishment works. Passive infrared thermography (IRT) has been applied for years to detect thermal bridges by referring to the International Organization for Standardization (ISO) 6781:1983. However, the successfulness of this norm is strongly affected by the detection accuracy of the thermal imprint produced on the facade by a conductive material called as “defect” in this work. The drop shadow effect, also produced by the surrounding environment on the
mask/modify the natural thermal evolution due to diffusion.
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facade under inspection, plays indeed an important role during the defect evaluation procedure since it can
Many real-life signals acting in the space physics domain exhibit variations across different temporal
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scales. This work presents an application of a new multiscale data analysis technique, the Iterative Filtering (IF), which allows to describe the multiscale nature of an electromagnetic signal working in the long-wave infrared (LWIR) region. IF appears to be a promising technique minimizing the influence of the shadows projected on the facade under inspection; subsequently, it allows the optimization of the detection
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of thermal bridges via sparse principal component thermography (SPCT) technique. The latter inherits the
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advantages of PCT allowing more flexibility by introducing a penalization term. Here is shown how the accuracy of the defect detection increases after the application of the IF
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mathematical procedure. Results are discussed on the basis of a couple of case studies referring to dissimilar buildings. Finally, a signal-to-noise-ratio (SNR) comparison with raw data is added to the
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discussion of the results.
Keywords: thermal bridge; solar loading; iterative filtering; sparse principal component thermography; quantitative analysis; building.
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ACCEPTED MANUSCRIPT 1. Introduction A thermal bridge is a localised area of the building envelop where the thermal conductivity is bigger than in the surrounding structures. The heat energy moves from molecules to other molecules allowing heat to flow through the path created. The larger the difference is between exterior and interior temperature in the building, the faster the building gains or losses heat. The most obvious locations for
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thermal bridges are where there are geometrical changes, deliberate penetrations, or places with structural changes. The material properties are affecting the heat transfer as well.
A useful method to detect thermal bridges in buildings is infrared thermography (IRT) [1]. Several years ago Grot [2] provided an interpretation of thermographic data for the identification of building heat
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loss. On this basis, Fang et al. [3] described the difficulties in the application of the above-mentioned method on buildings having large thermal inertia. One year later, Zücher [4] extended the research to localize insulation defects, by-passes, points of air leakage and areas of moisture damage. A quantification of the sizes of thermal bridges in buildings by means of IRT was for the first time introduced by Groet et
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al. in 1985 [5]. The heat loss was then calculated using field data recorded via heat flux transducers.
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Vavilov et al. introduced the use of “maxigram” and “timegram” images containing information needed for the characterization of defects (i.e., insulation deficiencies, air leaks, moist areas and thermal
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bridges) in building envelopes [6].
One year later, the same authors studied a methodology based on the solution of the inverse heat
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transfer problem, for the detection and evaluation of flaws in buildings. The building envelope was
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examined mainly in transient thermal regime [7]. A couple of years later, Kauppinen et al. on the basis of thermographic campaigns conducted in Laboratory studied a test wall using relatively low energy pulses and short heating-up times in order to detect defects and thermal bridges [8]. Kauppinen also performed in 2001 over 200 thermal scanning tests of one-family and detached houses affected by air tightness in a historic moment in which air tightness requirements were not created yet in Finland [9]. Subsequently,
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ACCEPTED MANUSCRIPT Colantonio and Desroches outlined the various types of thermal patterns created by both positive and negative building pressures during exterior inspection of various types of masonry clad buildings [10]. Moreover, the influence of thermal bridges caused by the presence of anchoring systems was studied in [11]. The evaluation of surface temperature and heat flow pattern at the four corner walls of a building envelope having thermal bridges was broadened by Jeong et al. in 2007 [12]. The mathematical models for
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estimating the thermal bridge effect at the corner walls per boundary condition were studied too. In [13], a technique to evaluate the thermal transient behaviour of buildings combining thermographic measurements and computer simulation using the software tool TRNSYS 16 was
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developed.
An IRT method combined to a simplified thermal model for evaluating thermal performance of insulated containers was studied in [14]. The proposed thermographic method allowed also determining the thermal bridges magnitude and the air leakages location. The research was further deepened later [15].
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Condensation problems in buildings retrieved via IRT were studied in [16], while the effects of
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direct solar loading on the detection of subsurface targets in a concrete test block were analysed by Washer et al. [17]. Zalewski et al. presented a contribution to the characterization of the thermal efficiency of
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complex walls of buildings with respect to the ever increasing requirements in thermal insulation. A genuine complementary experimental method allowing for the determination of the quantitative aspects of
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the heat losses through the envelope was introduced. A three-dimensional numerical method useful for
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parametric studies was also added to the discussion of the results [18]. Asdrubali et al. proposed a methodology to perform a quantitative analysis of some types of thermal
bridges, through simple thermographic surveys and subsequent analytical processing. From the measurement of the air temperature and the analysis of the thermogram, the thermal bridge effect was estimated as a percentage increase of the homogeneous wall thermal transmittance [19].
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ACCEPTED MANUSCRIPT In the same year, Hopper et al. discussed the methodology and results of using IRT for pre-retrofit and post-retrofit surveys undertaken to qualitatively assess retrofitted external wall insulation on before the 1919 existing dwellings with solid exterior walls. Evidences of potential thermal bridges were provided [20]. An example of a thermal bridge in a standard building detail and an alternate design were analysed by Kleinfeld in 2012 [21] to predict the energy impact of the bridge and of its removal.
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An interesting work which developed thermal imaging for the detection of subsurface deterioration in the soffit areas of bridges was written by Washer et al. [22]. The paper discussed via an on-site inspection the rates of change in ambient temperature needed to ensure the detection of subsurface damage
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in shaded conditions.
Previtali et al. integrated building geometrical models automatically derived from laser scanning technology with thermal images by providing metric information to thermographic analyses [23]. Instead, a low-cost, portable technology called “HeatWave” which allows non-experts to generate detailed 3D
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surface temperature models for energy auditing was developed in [24]. The presence of surface
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temperature data in the generated 3D model enabled the operator to easily identify and measure thermal irregularities such as thermal bridges, insulation leaks, moisture build-up and HVAC faults.
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An investigation of the scope for testing the thermal performance of the building envelope during the construction process using IRT was performed in [25]. The scope for four types of “in-construction” test
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was identified in: a) early stage checks on the installation of insulation, b) identifying air leakage through
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the building envelope, c) assessing insulation continuity and the severity of thermal bridges, and d) investigating the performance of building services. Thermal images acquired by an Unmanned Aerial Vehicle (UAV) to determine energy efficiency
and to detect defects like thermal bridges and heat losses were used by Previtali et al. in [26]. The developed methodology allowed also fusion of thermal data acquired from different cameras and platforms.
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ACCEPTED MANUSCRIPT In [27], in-field experimental measurements were carried out with the purpose of evaluating the energy losses through the envelope of a test room experimental field. Each element was characterized by its own thermal insulation capability. The proposed methodology coupled with IRT method were applied to assess the energy losses due to thermal bridges. IRT was also applied in the experimental detection and evaluation of the thermal defects of modern farm biogas plant envelope. Indeed, the unsuitable structural design of the biogas plant can lead to
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existence of thermal bridges and high heat losses of the building and degradation of structures [28]. In the same year, a review concerning the IRT applications for building diagnostics was published [29]. Instead, the blower door and IRT results of measured air test in historical buildings renovated by using natural
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materials were presented in [30].
In [31] a quantitative method using IRT to measure the thermal performance of complete building envelope elements that were subjected to non-steady state heat flow was described. It was found that IRT could provide a more representative result with respect to heat flux meters (HFM) measurements as it
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captures areas of imperfections, point and linear thermal bridges. One year later, Sviták et al. focused the
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attention on thermal bridges in case of wooden panel structures, both in case of low-energy and passive structure-standard. IRT was used for localization of critical areas of structures, i.e., details of corner joints
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of external walls and ceiling connections [32]. Contextually, Pagan-Vazquez et al. studied architectural details thermal bridge modelling values, and schematics of good construction practices to improve the
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building envelope performance of typical Army facilities. They also suggested examples to be used by the
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construction practitioner for the assembly of a properly mitigated thermal bridge detail in the building envelope [33]. IRT method was also used in this case. Ferrarini et al. investigated the possibilities and limitations of spot thermographic surveys coupled
with contact probes able to acquire continuously the thermal signal for days and evaluating the thermal bridges of buildings. Numerical simulations were performed to determine the reference value of an
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ACCEPTED MANUSCRIPT experimental case, while a long term thermographic survey was performed and integrated with the contact probe measurement assessing the feasibility of the method [34]. Junga and Trávníček focused the attention on a case study of a solid-state biogas plant. In particular, the work specifically concerned the qualitative evaluation of envelope construction details by IRT and quantitative evaluation of thermal defects by calculation. A significant numbers of thermal bridges caused by uninsulated bearing steel frames of the facades system, gates, doors and windows were detected [35].
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In the same year, Troppová et al. created a numerical model of thermal bridges in a wooden structure discovering differences between factual values of linear thermal transmittance utilized in the finite-element (FE) modelling and values given by the European normative method (EN ISO 14683).
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Thermal bridges of wooden structures were detected using a thermal camera. These measurements allow displaying the temperature distribution of the thermal scan and proving the positive correlation between heat flux and change in the evaluated temperatures of a thermal bridge [36]. A new methodology to detect the most significant sectors in energy transmission through IRT and
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the thermal intensity assessment of each opaque area, building element or thermal bridge, taking into
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account different values of wind speed has been proposed in [37]. Building elements or zones of a thermal envelope were selected according to their energy losses; this, in order to avoid an indiscriminate
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intervention on the opaque parts of envelopes.
O‟Grady et al. showed how the IRT method can be used as a non-invasive and easy-to-use method
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to provide quantitative measures of the actual thermal bridging performance. The novelty of their approach
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included evaluation of the actual heat flow rate caused by thermal bridge qTB and Ψ-value by means of the IRT solely, without any supporting methods. The methodology was tested under laboratory conditions in a steady state in a hot box [38].
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ACCEPTED MANUSCRIPT Lei et al. focused the attention on the detection of defects and thermal bridges in insulated truck box panels, utilising IRT. The research used both heating and cooling methods in active IRT configurations. Numerical simulations were also conducted [39]. A quantification of the wind velocity impact on the Ψ-value is reported in [40]. In fact, wind velocity significantly influences the heat losses through the building envelope. This was assessed by undertaking IRT of the same thermal bridge at various wind velocities, in a controlled environment, in a hot box device.
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The results showed that the Ψ-value is highly dependent on wind velocity.
Garrido et al. presented a procedure for the automation of thermographic building inspections mainly focused on thermal bridges. The procedure, in addition to detecting the thermal bridges by their
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geometric characteristics and their temperature differences with the surroundings, includes the computation of the thermophysical property of linear thermal transmittance of each candidate to thermal bridge, thus implying their characterization in addition to their detection. The accuracy of the detection of thermal bridges regarding existing methodologies was improved in 15% considering false positives and
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negatives obtained in each methodology [41].
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The development and validation of an innovative mathematical algorithm to enhance the image resolution and the consequent accuracy of energy losses assessment has been introduced in [42]. An
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experimental campaign was conducted in a controlled environment (hot box apparatus) on three typologies of thermal bridge, firstly performing the thermographic survey and then applying the enhancement
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algorithm to the infrared images. Results showed that the proposed methodology could bring to an
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accuracy improvement up to 2% of the total buildings envelope energy losses evaluated by quantitative IRT. Moreover, the proposed algorithm allowed the implementation of a further process applicable to the images, in order to extract the physical boundaries of the hidden materials causing the thermal bridge. In [43], the joint use between quantitative IRT and ultrasonic pulse velocity (UPV) methods has been introduced into the energy saving field by Tavukçuoğlu et al. because they are both useful for
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ACCEPTED MANUSCRIPT detection of visible and invisible cracks, thermal bridges and damp zones in building materials, as well as for thermal performance assessment of building components. Tavukçuoğlu was also involved in [44] in which the combined use of blower test method and IRT was useful for non-destructive assessment of airtightness features of building envelopes. O‟Grady et al. also demonstrated an application of the quantitative IRT method to evaluate the heat loss via multiple thermal bridging. It is shown that, using IRT, the heat loss via multiple thermal bridges
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can be easily estimated in an existing building envelope, without any knowledge of its internal structure or material properties. The methodology was validated against experimental measurements taken on different specimens in a hot box device. Results from the thermographic analysis also co-related well with results
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from finite element heat transfer and computational fluid dynamics simulations [45].
In [46], the effects of clouds and radiative cooling were underlined for the first time; it was found that the clear sky is a preferable condition for IRT. In addition, the effect of obstacles on a vertical surface that bring additional challenges to IRT was experimentally evaluated, too.
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The present research continues the idea started in [46] by focusing the attention on two case studies.
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In particular, selected parts of facades of two condemned buildings due to the 2009 earthquake which hit L‟Aquila city (Italy) and its surroundings [47] were inspected by IRT using the solar diurnal cycle [48].
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Applications of mathematical methods on raw thermograms explain how a useful and simple protocol based on a thermal camera (working into the long-wave infrared spectrum) coupled with a PC help to
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obtain interesting results.
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Segmentation methods were applied on smoothed and non-smoothed thermograms in order to explain how the accuracy of thermal bridges detection improves after the initial mathematical treatment. The latter tends to minimize the drop shadow effect on the recorded facades and, therefore, provide accurate thermal imprints to be segmented.
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ACCEPTED MANUSCRIPT The signal-to-noise-ratio (SNR) technique was applied to a case study of the two treated herein; this, with the aim to quantitatively evaluate the image enhancement obtained thanks to the implementation of the innovative filtering procedure. The result confirms the ability of the smoothing method in removing the high frequency oscillations due to the noise. Further studies will be focused on the evaluation of heat loss studying occupied buildings.
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2. Brief recap concerning IRT IRT is a well-known non-destructive testing (NDT) method able to analyse the thermal information obtained from an object having a temperature above –273.15 °C. This method detects the energy emitted by a surface and converts it into temperature variation. The output is an image (or a series of images
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collected over time) named thermogram(s). Infrared refers to the radiations located between visible and microwave in electromagnetic bands [1].
Usually, IRT is applied for the evaluation of electrical components [49] and thermal comfort [50], as
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well as for the inspection of buildings [51], artworks [52], materials [53] and composites [54], without forgetting medical [55] and surveillance [56] applications.
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Generally, infrared bands are divided into five parts, near infrared (NIR), short-wave infrared (SWIR), mid-wave-infrared (MWIR), long-wave infrared (LWIR), and far-infrared (FIR), which are
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respectively from 0.75 to 1 µm, 1 to 2.5 µm, 3 to 5 µm, 7.5 to 14.5 µm, and 50 to 1000 µm. MWIR and
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LWIR are more appropriate for the buildings‟ inspection [57]. A series of thermograms forms a 3D (x-y-t) data set that can be analyse by advanced techniques,
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such as [58–60] in order to improve contrast, e.g., the signal-to-noise (SNR) ratio. In particular, sparse principal component thermography (SPCT) technique [60] has recently been proposed in the NDT field, and its main features will be discussed in section 4. In this study, the external energy source (approach: passive) was an optical thermal stimulus (source: thermal radiation), i.e., the Sun, therefore, the source was in motion (configuration: dynamic), and the
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ACCEPTED MANUSCRIPT energy was transferred in reflection (mode: reflection) on a surface (scanning: surface) via a modulated excitation (waveform: modulated) due to the solar cycle. The physics of periodic heating/cooling by solar radiation was described in [61]. Interested readers can refer to this work in order to understand the general theory inherent to a thermally stratified slab illuminated by a periodic changing solar radiation and bathed in an atmospheric temperature. These conditions are the basis of the case studies analysed in this work. The temperature variation in time on the
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surfaces of the two buildings was recorded by an infrared camera working in the LWIR spectrum, connected to a PC sequentially storing the thermograms. The thermal camera was mounted on a tripod. The latter was positioned in two rooms located each one in front of the inspected facades. The centre of
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the external lens was adjusted to be perpendicular at each inspected facade. This, in order to avoid rectification processes of the thermal images analysed [41]. A telephoto was also used in both case studies; this, taking into account the distance to the target, as explained in the next section. In both case studies, the wind speed was measured by a digital anemometer installed near to the
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calm, according to Beaufort‟s scale.
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facades. In all cases, the measured wind speed (< 1 km/h) corresponded to a Beaufort number = 0, that is,
3. The Iterative Filtering (IF) Method as a pre-processing tool
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In order to understand the reason why the authors use in this work the Iterative Filtering (IF) method
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as a pre-processing tool and how it works in details, we need to briefly go back to the origin of this method showing why it was developed and presenting the so called Empirical Mode Decomposition (EMD)
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algorithm from which IF inherits its structure and good properties. In our digital era we are surrounded by instruments which allow to measure and record any kind of
signal. Such signals are in general produced by nonlinear systems and, therefore, are inherently non stationary.
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ACCEPTED MANUSCRIPT Over the years many methods have been devised to study and analyze all kinds of signals. However, all of these methods proved to be limited. Either because they were based on the assumption that the signal is stationary, like the Fourier transform and analogous techniques, or because they assumed the phenomenon was linear in nature, like the wavelet transform (WT) [62] and equivalent methods. Furthermore, all the standard methods require an a priori selection of a basis for the decomposition and analysis of a signal. Several ideas have been proposed and developed to improve the ability of such
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methods to deal with the non-stationarities of the signals under study, like the Short Time Fourier Transform (STFT) [63], or the Synchrosqueezing WT [64]. However, these further developments of the original approaches only partially alleviate the inherent limitations of such techniques.
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Two decades ago [65] a group of researchers at NASA leaded by Huang proposed a new technique, first algorithm of its kind, called EMD method which is able to decompose non stationary signals into simple components called Intrinsic Mode Functions (IMFs). Each IMF is an oscillatory signal which fulfills two properties:
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respect to the horizontal axis, and
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1) the envelope connecting its maxima and the envelope connecting the minima are symmetric with
2) the number of zero crossing equals the number of its extrema
.
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The idea behind the EMD algorithm is simple but powerful. Is the so called sifting process: to extract the highest frequency oscillatory component from a signal by computing and subtracting its
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moving average. The algorithm works as follows: given a signal , its maxima is computed and connected
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to all other signal maxima using an envelope, produced using cubic splines for instance, and then the same is done for the minima. The point by point average of these two envelopes is the curve
, which
represents an approximation of the so called moving average of . A first rough approximation of the highest frequency component contained in computing now the moving average of
is now computed as: which is called
as:
. The procedure is repeated . An iteration procedure
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has a moving average
, which is small enough in some chosen norm. Hence,
represents the first IMF that is subtracted from the original signal , and the entire sifting procedure is iterated on the remainder
. In this way, all the IMFs contained in a given signal can be extracted
until the remainder until a significant trend is observed. The EMD decomposition of a signal
into IMFs together with the calculation of the instantaneous
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frequency of each IMF via the Hilbert transform allows to compute the time frequency representation of and as a whole is known as the Hilbert Huang Transform (HHT) method [63].
Thanks to the HHT algorithm several breakthroughs have been achieved in several research fields ranging from Physics to Engineering, Finance and Medicine and many others, the interested reader can
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find a list of the main contributions in [66]. However, from a mathematical standpoint the EMD remains still a black box.
The repeated usage of envelopes specifically tailored at each iteration for the signal under analysis it makes impossible to perform any kind of convergence analysis on the method. In practice, the algorithm
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just described is still completely empirical and the only thing that researchers have been able to show so
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far is that it does decompose known signals as the authors would expect them to be decomposed. However, in doing this kind of studies they discovered that the method is unstable in this form: a small perturbation
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in the original signal can lead to a drastic change in the decomposition. To solve this issue Huang and his
[67].
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collaborators devised in 2009 the so called Ensemble Empirical Mode Decomposition (EEMD) method
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The idea is to perturb a given signal (to be decomposed) with an ensemble of noise realizations. Then each perturbed version of the original signal is decomposed using EMD and the average among all the decompositions is derived. The greater is the number or noise realizations in the ensemble the more the method is stabilized. This solution clearly impacts drastically the computational time needed for the
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ACCEPTED MANUSCRIPT decomposition. Furthermore, the problem of showing the a priori convergence of the method remains unsolved. For these reasons, in the last years several research groups have devised alternative methods able to produce results similar to the EEMD algorithm, such as the Empirical WT developed by Gilles [68], the Sparse time–frequency representation method developed by Hou et al. [69], using the multicomponent amplitude modulation and frequency modulation (AM–FM) representation [70], and several others [71, 72,
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73]. All these alternative methods make use of optimization techniques in order to produce the decomposition of a given non-stationary and non-linear signal, and they require the a priori selection of a suitable basis for the decomposition.
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In 2009, Lin et al. developed an alternative algorithm for the decomposition of a signal called IF [74]. Unlike all the aforementioned methods, which are based on optimization, the IF algorithm has an iterative structure exactly like the EMD technique. Hence, like the EMD, it does not require any initial
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assumption on the signal, and it is able to produce decompositions that are completely data driven.
Figure 1. Two examples of Fokker-Planck filters that can be used in the IF algorithm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article)
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ACCEPTED MANUSCRIPT IF method is structured exactly like the EMD with its sifting process. The only difference is that now the moving average filter
is derived by convolution of the given signal
with a chosen compactly supported
such as, for instance, a double average filter or a Fokker-Planck filter. An example of this last
kind of filters is shown in Figure 1, and is formally defined in [75]. Hence, (1)
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∫
The convolution with a filter represents the most natural way to compute the moving average from a mathematical standpoint: it is the average of the values of values of the filter
around the point
using as weights the
. The fact that this average is local is ensured by the fact that
is a compactly
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supported function. This new way of computing the moving averages opens the door to a rigorous analysis of this technique [75, 76, 77] and to an extension of this method to higher dimensions of the signals [78, 79].
In particular, from the numerical analysis of IF it follows that the method is convergent and stable
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and it can be sped up by means of the FFT [76]. In [80] the author compares the results produced using
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EEMD versus the ones derived using IF on a couple of well know geophysical signals and provides a detailed explanation on how to use the IF code, which is available at www.cicone.com.
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In this work, the authors use the IF method as a preprocessing tool. Given the measurements collected using a telephoto mounted on the external lens of a FLIR S65 HS thermal camera.
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Two case studies are considered herein. In the first one, the authors recorded from the area of
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interest shown in Figure 2, left panel, 900 thermograms from July 29, 2015 at 5:30 p.m. to July 30, 2015 at 11:30 p.m., with a frame rate of 1 thermogram every 2 minutes. The distance of the thermal camera from the area of interest was around 80 m. Each pixel recorded over time represents a nonstationary signal that can be decomposed using IF.
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ACCEPTED MANUSCRIPT After decomposing in IMFs each one of these signals, all the components relative to frequencies higher roughly than 1/700, which represents the natural frequency due to the solar cycles in our time window, were removed. The authors add together all the leftover IMFs to produce a new postprocessed signal. Figure 2 (right panel) shows an example of this preprocessing applied to the values of the pixel in position row 120 and column 160 of the area of interest measured over time. The original raw signal is
310 308 306 304 302 300 298 296
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plotted in blue, whereas the postprocessed result is plotted in red.
292 290
(a)
0
100
200
300
400
500
600
700
800
900
(b)
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Figure 2. Left panel (a), picture of the area of interest surrounded by a dotted red rectangle. Right panel (b), example of preprocessing by means of IF applied to row 120 column 160 of the area of interest recording over time. In blue, the original
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signal and in red the post processed one. (For interpretation of the references to colour in this figure legend, the reader is
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referred to the web version of this article)
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As a second example, a Church Bell Tower was inspected using the same thermal camera and similar procedure. In Figure 3 on the left, the building with the area of interest is highlighted in red. On the
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right panel, the original signal corresponding to the pixel in row 160 and column 120 is compared with the same signal after preprocessing with IF. In Figure 4, the authors plot the components, the so called IMFs, produced in the decomposition. The last function plotted in the bottom right is the remainder, which is the very same curve plotted in red in the right panel of Figure 3. It should be noted that the original signal can be reproduced summing all together these IMFs including, of course, the remainder.
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(a)
(b)
Figure 3. Left panel (a), the scheme of our experimental setup is shown for Bell Tower along with thermography and visible
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image. Right panel (b), example of preprocessing by means of IF applied to row 160 column 120 of the area of interest recording over time. In blue, the original signal and in red the post processed one. (For interpretation of the references to colour
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in this figure legend, the reader is referred to the web version of this article)
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Figure 4. Decomposition produced using IF applied to the nonstationary signal corresponding to pixel in row 160 column 120 of the area of interest of the Bell Tower‟s case study: Left panel (a) highest frequency IMFs with frequencies decreasing from
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top to bottom, and Right panel (b) lowest frequency IMFs with frequencies decreasing from top to bottom and the trend. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article)
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ACCEPTED MANUSCRIPT Such pre-processing allows to remove high frequency oscillations in a smart way. In particular, low frequency non-stationarity are fully preserved meanwhile temporary effects, like the shadow of a tree moving due to wind or simply do to the rotation of the earth are removed. In Figure 5 the authors compare the pre-processing filtering obtained using IF, in dot-dash magenta, with the ones produced using the well-known Discrete Wavelet Transform (DWT) [62], solid red, and the EEMD, green dots when applied to the pixel in row 160 and column 120 of the Bell Tower‟s case study.
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For the EEMD [67], 200 ensembles were used whereas for the DWT the authors used in Matlab the wavedec function with level seven and wname set to „db4‟, as well as the wden function with soft thresholding rule 'rigrsure' and rescaling based on a level-dependent estimates of the noise. The DWT is
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the fastest approach; it requires just 0.016 seconds to pre-process the signal associated with the chosen pixel using Matlab R2018a run on a Windows 10 Intel Core i7-8550U CPU 1.80 GHz 16 GB RAM personal computer. However, the DWT cannot remove completely the high frequency oscillations contained in the signal due to its limitation in the scales which can only be powers of two. If, in fact, the
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level in the DWT is increased, significant information are lost.
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The EEMD proves to be a reasonable filtering technique. There are small problems at the boundaries that can be easily fixed. However, the ensemble approach to stabilize the EMD method makes this
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technique really slow as stated before. In particular, the EEMD pre-processing requires 80.2 seconds of computational time for the single pixel pre-processing making it 5000 times slower than the DWT
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approach. The authors point out that the number of ensembles should be chosen in general higher than 200,
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as suggested in [67], to ensure a complete stability of the approach, making the method further slow. Finally, the IF requires 0.13 seconds. The outcome produced by IF, shown in Figure 5 in dot-dash
magenta, is definitely better than the one produced with the DWT and comparable with the one produced by EEMD. However, the IF is more than 600 times faster than the EEMD.
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Figure 5. Comparison of three different pre-processing filtering techniques applied to denoise the pixel in row 160 and column 120 of the Bell Tower‟s case study. In solid blue, the original signal is shown. In dot-dash magenta, the IF filtering is plotted. In solid red, the DWT is charted, while by green dots the EEMD filtering is identified. (For interpretation of the references to
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colour in this figure legend, the reader is referred to the web version of this article)
4. Sparse principal component analysis (SPCA) / thermography (SPCT)
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The application of Principal Component Analysis (PCA) [81, 82] in thermography (PCT) [58]
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provides a significant contribution to post-analysis of thermal images concerning several different applications, such as detection of defects for Infrared Non-Destructive Testing (INDT) [83–87], and Art
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and archeological investigations [88, 89]. PCT is used for many applications such as dimension reduction, noise elimination, classification, etc. PCT calculation can be performed by using covariance matrix
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calculation, Singular Value Decomposition (SVD), or Candid Covariance-Free Incremental Principal Component Thermography (CCIPCT) [90, 91]. Summarizing, PCT is the application of PCA to thermographic data. The decomposition matrix is performed for the input matrix (heat matrix) X which is
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ACCEPTED MANUSCRIPT p×n, where n is the vectorized thermal image in every sequence and p corresponds to the number of observations, and decomposes to (2) where, p > n and
is a diagonal matrix with a dimension of n×n and either zero or positive elements.
It is considered as the singular value of matrix X and
denotes the transpose of the n×n matrix
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(eigenvector or basis matrix) and U is the p×n matrix. The data is arranged column-wise based on the observation variation. Spatial variations are mapped in the row direction (input data located in columns and rows show the observations). The columns of matrix U represent the input matrix (frame here) [58]. PCT in general is a linear transformation method which applies a decomposition of the input zeroand coefficient matrix . The basis matrix carries the orthonormal
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mean data matrix into the basis
property that also maximizes the variance of projected data, which leads to the Principal Components (PCs) of the input matrix. The optimal property of PCT cannot be achieved through a linear transformation due to the compact representation of the input data by a limited number of basis vectors which is sometimes
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very good for noise reduction. This problem exists in all types of PCT calculations even for CCIPCT
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where the iterative computation leads to eigenvalues and eigenvectors which might benefit from low computational complexity as compared to PCT (for high-dimensional data). To alleviate this problem in
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PCT, and uphold some or all good properties of PCT, Sparse-PCT (SPCT) is used. In a few words is a PCT together with two penalty terms,
and
, in the formulation. Additional regularization parameters
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in SPCT not only turn PCT into a nonlinear transformation, but also maximize variance of uncorrelated
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PCs [93–96]. If the empirical covariance matrix of maximization of variance in the direction of vector
is presented by for
, SPCT [97] is a
. (3)
such that ‖ ‖
‖ ‖
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ACCEPTED MANUSCRIPT Let
be
norm of v, which is the non-zero components. This is a NP-hard problem and
several alternative methods have been proposed to solve it [92]. SPCT maximizes the variance of uncorrelated PCs and is independent of loading vectors, thus providing the linear combination from a few original variables. The algorithm follows Zou et al. (2006) and Elastic Net in a regression-like framework for PCT [95,
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96]. The following theorem concerns an approximation of PCT in two stages. From [96], the first part performs PCT, which is mentioned as follows:
the
principal components, let a and
row vector of the matrix X. For any ( ̅ ̅)
, let ∑|
such that Then, ̅
. For
|
∑|
be
matrices.
denotes
|
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Theorem Considering the first
(4)
.
(this is taken from [96]). It converts the PCT from a linear
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problem into a regression-type problem. The exact PCT answer can be obtained by
penalty term (Least Absolute Shrinkage
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formulation, and having the ridge penalty terms. The additional
in the
and Selection Operator - LASSO) is added to the previous portion to obtain the sparse loading and
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( ̅ ̅)
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changes the previous formulation into the following optimization problem [96]:
where,
applied for all
∑|
|
∑|
|
∑|
| (5)
such that components and
, for every j controls the variation of PCs.
In synthesis, since in PCT each PC is calculated as a linear combination of all of the pixel values
(i.e., all the entries in the loading vectors are typically nonzero), the result is that the loading images may
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ACCEPTED MANUSCRIPT be sometimes difficult to interpret. This stimulated the development of SPCT [60] which introduces SPCA [96] into the thermographic field. 5. Main information about defects, results of sparse analysis on thermal imagery and discussion The experimental set-up used in the present work is shown in Figure 3a. Although it refers to the
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case of the Bell Tower, the case of the Faculty of Engineering is based on the same experimental setup. Concerning the Bell Tower‟s case, the defects we are talking about are a buried window and three beams (1., 2. and 3.) in the wall. They are briefly summarized in Fig. 6. In the latter it is possible to see how photographs were captured in the course of time (both from the interior and the exterior part of the
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façade of the Bell Tower). The defects were measured, and the processed thermogram acquired once the window under inspection was covered by bricks and plaster is compared and linked with the snapshots. The region of interest (ROI) on which the authors focused the attention will be later clarified. On it, the
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SNR was calculated in order to demonstrate the effectiveness of the smoothing process by means of IF. In
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fact, a comparison with the raw data is provided before the discussion of the Faculty of Engineering‟s case.
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Figure 6. Main defects of the Bell Tower‟s case: their thermal imprints can be easily recognized in the processed
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thermogram. The Bell Tower was photographed in the course of time and recorded into the long-wave IR spectrum once the window below the clock was covered by bricks and plaster. As can be seen, the clock was installed subsequently with respect to
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the edification of the Bell Tower [57]. The position of the inspected beams (size: 15 x 15 [cm]) are signaled by the numbers 1., 2. and 3. both in the processed thermogram (PCT – EOF5) and in the snapshot captured from the interior part of the Bell Tower.
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(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article)
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Although Fig. 6 is just to describe the defects after a combined visual and thermographic inspection, the information that provided were useful to quantitatively analyze the defects themselves. It is possible to see how the buried window was not covered for the entire depth of the wall. This explains why it acts as a thermal bridge.
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ACCEPTED MANUSCRIPT The defects detected on the wall of the Faculty of Engineering are inherent to recursive horizontal and parallel stripes (width: 20 [cm]), and based on the application of flax fiber-reinforced polymers (FFRP) fabrics (FIDFLAX UNIDIR 300 HS50®) impregnated with epoxy resin. They were applied on bars made by double stranded basalt fibers passing through the thickness of the wall. On the one hand, they increased the load and deformation capabilities of the building, while preserving its stiffness and dynamic properties. On the other hand, they act as thermal bridges by considering the remaining part of the external opaque
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wall constituted by a uniform material similar to tuff and arranged by means of bricks. Sometimes, indeed, the double stranded basalt fibers arrive to the slabs by locally interrupting the continuity of the external wall. This, for earthquake-proof reasons [98].
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With the description of the defects, it is possible now to describe first the segmentation algorithm and then the results obtained by using it. The authors also compared the computational results for SPCT decomposition techniques in the algorithm to analyze the performance by segmenting the defects. To quantitatively evaluate the accuracy of the proposed algorithm, a ground truth (GT) is required.
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For that, an image that is manually labeled has been used. The photographic evidence performed before
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the thermographic inspections helped in this respect. Having the GT available, automatic labeled pixels and GT points could be compared and led to both a raw accuracy (ACC) and two types of errors, named
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False Negative (FN) and False Positive (FP). The latter is an error which represents a region instead of another one (i.e., a defect is detected due to an error), while FN is an error that reveals no detection at all
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(although there was a defect that had to be detected). In particular, the general accuracy of the proposed
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method was computed using the following equations: Total accuracy = ACC (%) – FN (%) – FP (%)
(6)
where, ACC was calculated by means of Eq. 7): (7)
As above-mentioned, FN stands for the FN error. It was estimated using Eq. 8):
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ACCEPTED MANUSCRIPT (8) while, the FP error was calculated by following Eq. 9). (9)
From Tab. 1a it is possible to see how the computational complexity increases for the smoothed data;
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contextually, the accuracy of defect detection increases, too. The graph shown in Tab. 1b sums up very nicely the latter result obtained on the basis of the real images containing the defects previously mentioned. The algorithm was run in a PC (Intel(R) Core(TM) i7 CPU, 930, 2.2.80GHz, RAM 12.00GB, 64 bit
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Operating System) and the processing was conducted using the MATLAB computer program.
Table 1.a The accuracy and computational complexity of the proposed approach is shown in the table.
Building
Pre-processing
Accuracy of defect detection (%)
Computational complexity (second)
51.09
27.19
Smoothed data
57.37
33.21
Non-smoothed data
20.21
86.45
Smoothed data
43.73
115.04
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Non-smoothed data Faculty of Engineering (AQ)
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Bell Tower
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Table 1.b The accuracy difference between the smoothed and non-smoothed data is represented in the bar-chart graph.
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Smoothing effect on precision Non-smoothed data
51.09
Smoothed data
57.37 43.73
Faculty of Engineering (AQ)
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20.21
Bell Tower
Regarding the Faculty of Engineering, the accuracy of defect detection was 51.09%. It is linked to a
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computational complexity of 27.19 seconds. The accuracy was improved by around 7%, i.e., up to 57.37%, although the computational time increased up to 33.21 seconds. Instead, the accuracy of the defects found in the Bell Tower increased from 20.21% to 43.73%. In practice, a significant improvement was obtained. Contextually, the computational cost grew 28.59 seconds.
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Figure 7f and Figure 7v show by means of red solid rectangles the ROIs for the Faculty of
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Engineering and the Bell Tower case, respectively. On them our analyses have been focused.
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Figure 7. The results of SPCT marked by red rectangles (f, v) to show thermal bridges for both the Faculty of Engineering of the University of L‟Aquila (d, e, j, k) and a Bell Tower (o, p, t, u). The infrared image set come from before and after the smoothing procedure. Please note that a, b and g, h are better results for the Faculty of Engineering in non-smoothed and
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smoothed results, respectively. The same can be said about l, m and q, r inherent to the Bell Tower. In particular, f, v are representing the region of interest (ROI) for the Faculty of Engineering and Bell-Tower, respectively. c, i, n, s are lower
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accuracy examples of SPCT for both cases analyzed in smoothed and non-smoothed conditions. (For interpretation of the
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references to colour, the reader is referred to the web version of this article)
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In particular, Figs. 7t, u show a square zone at the centre of the image that is undetectable in the nonsmoothed results (Figs. 7o, p). It is inherent to the buried window covered by bricks and plaster in the
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course of time. In addition, three square zones were detected below the buried window. They are well segmented only in Figs. 7t, u, i.e., after the application of the IF. This result emphasises the usefulness of the preventive application of IF. The three square zones correspond to beams used in the past to build the structure [57]. They are indicated by means of three arrows in Fig. 8b, although already described in Fig. 6. In the latter, see the numbers 1., 2. and 3..
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ACCEPTED MANUSCRIPT The proof of the thermal bridge comes from a photograph collected from the interior part along with the thermal behaviour in time of an area (defective) selected on it, and another area (defect-free) selected close to it (Fig. 8a – below). It is possible to see how a reduction in section exists in the wall (Fig. 8a – above), exactly in the position in which the window was. The proof of thermal bridge by IRT is linked to the thermographic footprint visible via PCT analysis in Fig. 8b. In this case, the second Empirical Orthogonal Function (EOF2), i.e., an eigenvector of the data covariance matrix, well summarize the
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thermal imprints projected on the plaster layer.
2012-07-18 6:30 pm peak positive contrast
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0
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2012-07-21 12:00 am 3rd day
2012-07-18 6:30 pm peak negative contrast 12
18
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Defective area
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Defect-free area
2012-07-23 1:30 end
2012-07-20 12:00 2nd day
2012-07-19 12:00 am 1st day
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Hidden window Sound area
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Temperature [ oC]
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2012-07-22 12:00 am 4th day 66
72
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200 84
90
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Time [hours after start]
250
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(a)
40
60
(b)
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Figure 8. (a) Thermal profiles of the two areas highlighted in (b) with a black (window) and white (defect-free area) cross, and (b) non-smoothed PCT-EOF2 of the Bell Tower [57]. Part of the real image captured from the interior of the Bell Tower useful for the computational approach is shown in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article)
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ACCEPTED MANUSCRIPT At this point, the SNR was applied as an example on the ROI of the Bell Tower to compare smoothed and non-smoothed (raw) thermograms (data), in order to evaluate quantitatively the IF image enhancement. The SNR was computed as the ratio between the mean and the standard daviation
of our
signal: (10)
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Its value moved from roughly 45.1 before smoothing to 46.4 after smoothing, confirming the ability of the smoothing method in removing the high frequency oscillations due to the noise.
Instead, the proof of the different nature of the materials in the case of the Faculty of Engineering [98] is understandable from Fig. 9a. The acquisition started on July 29th 2015 at 5:30 pm and ended on
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July 30th 2015 at 11:45 pm. The blue colour profile correspond to a part of the FFRP, while the red colour profile correspond to a part of the wall in bricks. The FFRP areas acting as a thermal bridges correspond to the recursive horizontal and parallel stripes that are light in color with respect to the brownish bricks (Fig.
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9a – above).
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305
295 290
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clouds
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6PM
12AM
Reinforcement area Sound area 6AM 12PM Time [s]
6PM
12AM
(a)
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(b)
(c)
Figure 9. (a) Temperature evolution through time covering the average temperature over the two selected areas (see Fig. 2a): the blue colour correspond to the FFRP, while the red colour correspond to the wall in bricks, (b) fourth thermogram recorded
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from the starting of the sequence (without the application of the IF method): the drop shadow is indicated by the arrow, and (c) fourth thermogram recorded from the starting of the sequence (with the application of the IF method): the drop shadow disappears [98]. Part of the real image captured from the exterior of the Faculty of Engineering useful for the computational approach is shown in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web
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version of this article)
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The areas corresponding to these thermal profiles are shown in Fig. 2a. As can be seen, both areas
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follow more or less the same thermal behavior during the first several hours after starting the survey, while the building is still heated by the sun (from 5:30 pm to 8:00 pm) and then for some hours while cooling
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down (from 8:00 pm to 12:00 am of the next day). Around midnight though, the profiles from these two areas start to diverge, reaching a maximum difference around 6:00 am, that is right after sunrise. From that
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point, the facade starts heating up again and the profiles approach to each other until no significant difference can be perceived in the early evening, similar to the day before. The sudden temperature variation in the profiles at around 7:00 pm (about an hour before sunset, ~8:00 pm) of the second day is due to the presence of clouds [99].
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ACCEPTED MANUSCRIPT The difference in temperature between these two areas is due to the presence of the FFRP reinforcement structure having a thermal diffusivity of 1.5x10-7 m2/s [100], which is slight different from the thermal diffusivity of tuff (5.0x10-7 m2/s) [101]. The potentiality of the IF method illustrated in section 3 is here visualized by comparing the same thermogram before (Fig. 9b) and after (Fig. 9c) its application. It is possible to see how the effect of clouds
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before the image processing is pointed out on a part of the wall by means of an arrow; this effect disappears after the image processing (Fig. 9c) thanks to the IF. The drop shadow is a high frequency oscillation, i.e., a temporary effect that can be indeed removed. 6. Conclusions
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The work starts with a brief review of the previous manuscripts centered on the thermographic analysis of thermal bridges in buildings. The work is focused on two case studies in which no internal heat input is present. Indeed, the damaged buildings were delimited inside a red zone due to the earthquake
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which seriously affected L‟Aquila city and its surroundings in 2009. In addition, the wind effect on the facades can be considered negligible, taking into account the anemometric campaign conducted during the
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thermographic inspections. Finally, it is important to underline how an increased non-defective
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surrounding region aids the lateral diffusion of heat. Hence, thermal waves over a small defect area surrounded by a large non-defective surrounding region diffuse very quickly [102]. Since the defective
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areas cannot be considered as small with respect to the inspected ROIs (Fig. 7), the projected defect size on the facade is only affected by the shadow effect. The latter can be minimized by using the IF method
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during the pre-processing of the thermograms. On the one hand, this step helps to improve the accuracy of the defect detection via SPCT technique, as can be gathered from the comparison between smoothed and non-smoothed data shown in Tab. 1. On the other hand, the computational complexity increase with increasing the accuracy.
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ACCEPTED MANUSCRIPT In addition, taking into account the example of the Bell Tower selected as representative of the two ones here treated, it is possible to say that the SNR values before and after smoothing confirm the ability of the proposed method in reducing the noise level. Finally, the use of numerical simulation computer programs will be explored as future perspective in order to foresee/evaluate the possible detection of thermal imprints on recorded facades, by imposing the
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real geographical coordinates of the sites under inspection to the model [103]. Acknowledgments
The authors would like to thank the mother tongue English Prof. Agnese Anna Aureli for the spell checked, technical checked and grammar checked of the sentences written in the article.
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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declarations of interest: None.
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Graphical abstract
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