Numerical Evaluation of a muon tomography system for imaging defects in concrete structures
Sridhar Tripathy, Jaydeep Datta, Nayana Majumdar, Supratik Mukhopadhyay
PPrepared for submission to JINST
Numerical Evaluation of a muon tomography system forimaging defects in concrete structures
Sridhar Tripathy 𝑎,𝑏, Jaydeep Datta 𝑎,𝑏
Nayana Majumdar 𝑎,𝑏 and Supratik Mukhopadhyay 𝑎,𝑏 𝑎 Saha Institute of Nuclear Physics,AF Block, Sector 1, Salt Lake, Kolkata 700064, India 𝑏 Homi Bhabha National Institute,Training School Complex, Anushaktinagar, Mumbai 400094, India
E-mail: [email protected]
Abstract: Among its numerous applications, deployment in civil structures has caught attractionsof many recently. The detection of defects based on inherent physical quantities such as density andatomic number by probing naturally available cosmic muons makes MST a novel idea suitable forinexpensive and non-destructive imaging. In this work, capability of MST to detect concrete defectshas been tested and evaluated in terms of two-dimensional imaging and statistical calculations. Theimaging has been done on unique and critical defects causing degradation in civil structures. Thecapability and limitation of MST in this avenue has also been studied.Keywords: Particle tracking detectors (Gaseous detectors), GEANT4, Portal imaging, Simulations,muon tomography Corresponding author a r X i v : . [ h e p - e x ] F e b ontents t -statistics. 63.2 Discrimination capability using PRM-score 7 Cosmic ray muons are high-energy charged particles with high penetration power. Their invasivenature and omnipresent property inspires to exploit its scattering phenomenon for portal imaging.Muon Scattering Tomography (MST) exploits the deviation of cosmic muons from their path due totheir interaction with atomic nuclei and electrons of the target material whose physical properties onewants to probe. Cosmic muons with their large rest mass (105 MeV/c ), and with large momentum(mean ≈ 𝜎 = . 𝛽 𝑝 √︂ 𝐿𝑋 (cid:16) + . 𝑙𝑛 𝐿𝑋 (cid:17) (1.1) 𝑋 = . 𝐴𝜌𝑍 ( 𝑍 + ) 𝑙𝑛 (cid:16) √ 𝑍 (cid:17) (1.2)where 𝑝 is the momentum of muon, 𝐿 is the distance traversed by it in the object and 𝛽 is the ratiobetween velocity of muon ( 𝑣 ) to velocity of light ( 𝑐 ). The radiation length, 𝑋 , is a property of– 1 –he object material which is related to its atomic weight, 𝐴 , atomic number, 𝑍 , and density, 𝜌 , asshown in equation 1.2. The equations 1.1 and 1.2 suggest that the stopping length of the muonmostly depends on 𝑍 and 𝜌 . Therefore while traversing through high- 𝑍 and high- 𝜌 matter suchas lead, uranium muons slow down and eventually stop whereas they can pass a moderately largerdistance through low- 𝑍 and low- 𝜌 matter like concrete, aluminum, etc. Based on this property wehad shown in the previous work [13], that it is possible to distinguish high- 𝑍 , mid- 𝑍 and low- 𝑍 materials.Most experimental / computational works have used MST for imaging high- 𝑍 / 𝜌 and mid- 𝑍 / 𝜌 materials [4, 6–8]. It has been observed that, for carrying out imaging of large concrete structures,muon transmission radiography is the preferred option [11, 14]. In this method, images are producedbased on muon hit-intensity map, with and without the target. After passing through the target thehit-intensity is reduced because many muons under go through heavy scattering, energy loss andstopping; which helps produce the tomographic image. In [15], muon-induced secondary radiationshave been used for imaging organic soft tissue, polymethyl methacrylate and water. ConclusivelyMST has been utilized for distinguish relatively dense and high-Z/mid-Z material from low-Zbackground, and not heavily exploited for imaging low-density materials.In this computational work, MST has been studied as an option to be applied in severalcivil engineering problems. The less-interacting and high-penetrating power of muon makes ita viable candidate of Non-Destructive Evaluation (NDE) technique. Various NDE techniquessuch as, ultrasonic tomography [16, 17], infrared (IR) tomography [20], ground penetrating radar(GPR) [21], thermography [22], impact-echo [46] etc. have been used to image and hence monitorand maintain civil structure such as buildings, bridges, highways and tunnels. Removing a samplerebar from a structure and inspecting it for defects is not a viable solution. Moreover, it doesnot assure the fitness of the other rebars in the adjoining structures. The speciality of these NDEtechniques is detection of abnormalities in concrete structures without causing physical damage tothe materials. These methods have some advantages and disadvantages depending on the types ofdefects they are probing, hence always a room for improvement or alternate solution exists. HenceMST can be considered as a possible candidate.The conventional NDE methods have been used toidentify several possible defects in concrete structures such as air/liquid voids, cracks, corrosionof steel rebars, etc. There are other elaborate reports, in which MST has been used for imagingreinforced cement concrete (RCC) structures by computation as well as experiment [24, 25]. In thiswork, we have tried go one step beyond to use MST for health monitoring of concrete structuresbased on portal imaging. The problem has been simulated in GEANT4 environment [26].Details of the detector dimensions, placement, target specification have been given in section 2.The algorithm for defect identification and evaluation of degree of discrimination has been narratedin section 3. The imaging results and their analysis has been given in section 4. The articleconcludes with a study on the limitations and capability of MST in imaging concrete structures. Two sets of three tracking detectors have been placed sandwiching a region of interest (ROI), wherethe targets are placed. Gaseous ionization detectors, having gas thicknesses of 2mm each, have beenconsidered for the following numerical studies. The area of the detectors governs the acceptance– 2 –
Upper detector layersLowerdetector layersROI marked by the shaded regionExample of a target: A rusted rebar inside concrete block
Figure 1 . Schematic of the simulated setup solid angle of the setup geometry, and hence has to be optimized for uniform exposure across theROI [13]. Therefore, the area of the detectors has been varied according to the target size. Cosmicmuon exposure equivalent of 30 days has been used for the simulations. A schematic diagram ofGEANT4 simulation setup has been shown in figure 1. x-axis (mm)300 - - - y - a x i s ( mm ) - - - (a) x-axis (mm)300 - - - y - a x i s ( mm ) - - - (b) x-axis (mm)300 - - - y - a x i s ( mm ) - - - (c) Figure 2 . Images obtained for blocks of Steel, Concrete, Rust for no minimum threshold , 𝜃 𝑡ℎ =5 mrad, 10mrad. Although stopping is not an issue while using MST to image low- 𝑍 / 𝜌 matter, feeble scatteringmakes it difficult to distinguish the target from the background. Hence it is important to choseevents which scatter more than a minimum threshold. This threshold has been decided based onrepeated observation of scattering distribution of concrete and background to be 10 mrad. Figure 2shows results obtained based on scattered image plots of three blocks of Steel, Concrete, Rust forscattering angle threshold ( 𝜃 𝑡ℎ )= 10 mrad, 5 mrad and no minimum threshold.Three commonly occurring defects in concrete structures [20, 22, 23] have been consideredas test cases for imaging. These defects are chosen as they are very common to appear in civilstructures and are key problems causing degradation. Each of the deformities is unique and servesdifferent challenges for imaging. The target, dimension, defect dimension and other simulationparameters have been listed in table 1. – 3 – arameter Rusted Rebar CFST Void in Concrete DetectorSide 60 cm 100 cm 140 cmDimensionof theVolume
Concrete Volume: × ×
10 cm RebarDimension: length:24cm, diameter:3 cm
CFST diameter:
CFST length:
Steel Diameter:
Concrete Volume: × ×
15 cm Defect Size
Rust Thick-ness:
Defect Thickness:
10 mm and 7 mm
Void size:
Sphere diameter:6.74 cm and 5.64 cm.Cube side:6 cm and 5 cmDefect Per-cent (%)along 𝑍
30 and 15 12.5 and 8.75 40 and 33.33
Table 1 . The parameters of simulation of all three examples have been listed. The area of the detectors(side ) has been changed according to the increased target volume. Two thicknesses of each type of defect hasbeen simulated. The dimension of the defects have been shown. The Percentage of defects along 𝑍 -direction(the direction of cosmic muon exposure) has been shown for all the cases. Reinforced cement concrete (RCC) structures with steel-rebars have been used for a long time tobuild civil structures. The most common problem in such structures is the corrosion of rebars.Exposure to atmosphere, rainfall, concrete-metal contacts [30] cause corrosion and rusting inrebars. Various NDE techniques have been implemented to identify the corrosion in rebars, such aselectromagnetic induction [23], thermal imaging [31]. Muon tomography has also been used for thispurpose [24, 25]. In [23], quantitative measurement of corrosion has been done by thermographyusing electromagnetic induction. A schematic diagram of the problem as shown in [23] has beendisplayed in figure 3 (a). A similar geometry has been constructed in GEANT4. Three differentviews of the geometry has been shown in figure 3(b). The steel rebar has been placed along thecentral axis of the concrete volume in the 𝑋 -direction. The target volume has been placed at thecentre of the ROI. In GEANT4, Fe O composition has been used as rust with density 5.25 g/cc.Steel and concrete have been simulated with densities 7.87 g/cc and 2.3 g/cc respectively. Concrete-filled steel tube (CFST) are cost-effective solutions for implementing in large numbersin building truss elements and columns in high-rise buildings. The comprehensive strength ofconcrete and confinement, rigidity of steel can make the combination carry more load than indi-vidual elements [32]. However de-bonding can occur between concrete and steel which results into voids [33]. These voids and local cavities, de-bonding ring-gaps can also occur due to fluiditybefore initial setting and dry shrinking during use [34]. This phenomenon reduces the load carryingcapacity of the CFST, and is a critical problem. Due to shielding effect, high-density and low 𝑋 – 4 – a) RustedportionSteelConcrete
Side
View Cross-sectional
View3D
View (b)
Figure 3 . (a) Schematic diagram of a rebar with a portion corroded, reproduced from [23]. (b) Images ofGEANT4 simulation geometry. Portions of the rebar, shown in grey are partially corroded. The rebar hasbeen placed at the middle of the concrete column. The target has been lain on the central plane of the ROIalong the X-direction. of steel imaging defects of CFSTs is a difficult job for traditional NDE techniques such as electro-magnetic waves, impact echo technique, X-ray and gamma ray [35]. Several experimental workshave been done to identify and image the de-bonding occurring in CFSTs [17–19]. Similar to oneof the specimen structure described, an example case has been constructed in GEANT4. Geometrywith 50% circumferential void has been constructed, that is 50% part of the circumferential areanear the steel edge has been taken as void. Three different views of the scenario has been shownin figure 4(b). The CFST lies in the 𝑋 -direction inside the ROI, such that the defect faces the mostcosmic exposure. This can be realised by the ‘Side View’ image in the figure 4(b). SteelVoidConcrete View Side
View
Cross-sectionalView (a) (b)
Figure 4 . (a) An image of CFST constructed and used for imaging using ultrasonic by Dong et. al.Reproduced from [17] (b) Images of GEANT4 geometry, as simulated.
Another common problem found in concrete structures is sub-surface voids and delaminationsin concrete decks. These defects make the bridge decks structurally deficient. Different NDEtechniques such as IR thermography, GPR, impact-echo is used to identify the delaminations, voidsin concrete decks. The detection of these sub-surface defects depends upon size, position inside theconcrete deck. In [20], IR imaging has been used to detect shallow defects inside concrete decks.There, few bridge decks have been constructed and several voids and delaminations have been– 5 –eliberately made inside deck. In this work, Similar scenario has been constructed in GEANT4 totest the capability of MST. In several research works carried out to identify such defect [20, 22], ithas been reported that the amount of concrete covering has a huge impact on imaging the defects.Therefore it is easier to image defects if they are not buried deep inside. The voids are placed inthree depths to preserve anonymity in concrete cover. In reality, however, defects in nature are notexpected to follow any prescribed pattern. In order to maintain randomness, two different shapes(spherical/cubical) of voids have been implemented. The spherical voids in concrete has diameter 𝑑 = × √︃ 𝑎 𝜋 ; where ‘ 𝑎 ’ is the length of the side of the cubical void. This way both types of voidsreceive equal areal exposure of cosmic muons. The schematic image used in [20] has been shownin figure 5 (a). The concrete deck is lain in the XY plane. Different images of GEANT4 geometryhave been shown in figure 5 (b). (a) (b) Side
View
Cross-sectionalView View
Figure 5 . (a) A schematic image of concrete deck used in [20] imaged using IR. (b) Images of GEANT4geometry, as simulated. The figure of cross-sectional view in (b), shows placement of the voids at differentdepths (4 cm from top, 8 cm from top, and 12 cm from top)
In MST, the incoming and outgoing tracks of cosmic muons are used to find scattering hit locationsin the ROI and scattering angle ( 𝜃 ). Various algorithms have been used to identify the scatteringlocations [4, 29, 36–38]. The Point of Closest Approach (PoCA) [4, 39, 45] has been implementedto determine scattering vertices in this work. Using the track selection criteria described in [13], andfollowing 𝜃 𝑡ℎ = 10 mrad, selected scattering vertices have been used to obtain the two-dimensionalmaps (XY-plot) of the ROI. The pixelised scattering map has been weighted by the parameter 𝑆 asdefined in equation 3.1. 𝑆 = 𝜌 𝑐 ∑︁ 𝑘 = 𝜃 𝑘 (3.1)where ‘ 𝜌 𝑐 ’ represents number of entries to the pixel. In general, 𝑆 is the sum of the scatteringangles of all valid events in the given pixel. The discrimination of defected and not-defected targetshas been done based on a statistical test and a Pattern Recognition Method (PRM) described below. t -statistics. The 𝑡 -statistics is a widely accepted test for checking if means of two distributions are equal [40].The 𝑡 -value has been calculated in each case using equation 3.2.– 6 – = 𝜇 − 𝜇 𝑠 𝑣 (cid:104) 𝑛 + 𝑛 (cid:105) with 𝑠 𝑣 = √︄(cid:20) ( 𝑛 − ) 𝑠 + ( 𝑛 − ) 𝑠 𝑛 + 𝑛 − (cid:21) (3.2)where 𝜇 , 𝑛 and 𝑠 are the sample mean, sample size and standard deviation of the referencedistribution while 𝜇 , 𝑛 and 𝑠 are the corresponding parameters of the test data set. The testbegins with assuming the null hypothesis that the data from the two images are identical. The 𝑝 -value, which is the probability of finding the observed 𝑡 -value or more extreme given the nullhypothesis is true; has been estimated. The 𝑡 -value and corresponding 𝑝 -value have been used asdecisive quantity to evaluate the discrimination capability of the technique. 𝑝 = .
05 has beentaken as the maximum threshold to declare presence of void in test data.
In [13], the PRM method to identify target objects in the ROI has been explained in details. Theentire two-dimensional map of the ROI is converted to a numerical matrix ‘ 𝑅 ’ of the parameter‘ 𝑆 ’. A filter sub-matrix ‘ 𝐾 ’ obtained from a given sample (non-defected target) is convoluted withthe test matrix ‘ 𝑅 ’ to check if the probed region has similarity. The PRM method rejects the partsof image-map, ‘ 𝑅 ’, which are less intense in terms of the given parameter ‘ 𝑆 ’ and identifies targetpixels. This way the PRM discriminates signal region and background region in ROI filled withseveral materials. To numerically understand the degree of distinction, a PRM-score has beenintroduced which evaluates the similarity and quality of imaging. The PRM-score for a givencase is the ratio of the number of pixels found void in the defected case (test case), ‘ 𝑚 ’ to thetotal pixels found in the non-defected case (sample), ‘ 𝑛 ’ in terms of the step ( 𝛿𝑛 ). The same hasbeen given mathematically in equation 3.3. The step ( 𝛿𝑛 ) is a random error which arises whenrepeated application of PRM on the same target and considered as 𝑓 𝑟𝑎𝑐 √︁ ( 𝑛 ) according to Poissionstatistics. Higher value of PRM-score indicates, the test image is less likely the same as the sample.Whereas PRM-score < 𝛿𝑛 indicates the test image and sample are not distinct. To identify thedefect in the concrete structures, 2 𝛿𝑛 is set as the benchmark. In other words a test image is saidto have defects if the PRM-score between it and a sample is found to be greater than 2 𝛿𝑛 . Thecalculation technique can be followed from the example shown in figure 6. The non-defected casehas been shown figure 6 (a), and the defected case has been shown in figure 6 (b).PRM-score = 𝑚𝑛 × 𝛿𝑛 (3.3) The imaging results for the above scenarios described in section 2, have been shown here. Thedegree of different defects obtained using 𝑡 -value and PRM-score has been listed in the table 2.– 7 – a) Whole Sample (b) Defected Sample n pixels (n-m) pixels Figure 6 . Comparison of defect and non-defect case based on PRM-score.
The figure 7 shows the scattering hit-images and PRM reconstructed outputs for a whole rebar(rebar without rust), and two rebars with rusted part 15% and 30% respectively. The color-axisshows the 𝑆 parameter accumulated in different bins. The concrete volume is clearly segregatedfrom the background, and the steel rebars have been discriminated from concrete volume. Thedefected part (rusted part) can be seen with low 𝑆 parameter in comparison to the steel rebar.The PRM positive bins have been shown in red pixels. For the case of 30% rust, the defect ismuch clearer than the case of 15% rust. The same is reflected from the parameters displayed intable 2. It is apparent that, the location of exact defect identification is not precise, nonetheless, theability of defect identification of PRM is practicable. With 15% the defect rust thickness becomes2.25 mm and becomes smaller than the image pixel size. Hence the discrimination deterioratesand this sets the upper limit of the technique. The same can be realised from 𝑝 -value of 0.011 andcorresponding statistical significance 2.29 which is barely above 2 𝜎 . The PRM score is also lessthan the discrimination threshold 2 𝛿𝑛 .Figure 8, displays the scatter hit-images and corresponding PRM reconstructed images forCFSTs. The figure 8 (a), displays the whole CFST, that is without any defect. Scattering images forCFSTs with 7 mm defect and 10 mm defect have been shown in figure 8 (c) and (e) respectively.The corresponding PRM reconstructed images have been shown in (b),(d) and (f). The images forboth 10 mm defect and 7 mm defect display the voids distinctly, but the recognised defect spreadis different from the actual defect. It implies, the void at the edge are identified whereas from thecentral part it is not identified. This happens because of the extended concrete covering at the centralpart. In addition to that, the steel covering with higher 𝜌 and 𝑋 accounts for the underestimationof the defect spread. By all accounts, the PRM has distinguished the whole CFST from both thedefected cases convincingly.Figure 9, shows the scattering hit-images and PRM reconstructed images for concrete deckas described in section 2.3. Due to distinction between only two types of materials (concreteand void), this example is comparatively simpler than previously described cases. Evidently, theconcrete decks with voids have been significantly distinguished from the no void case. The images– 8 – a) (b)(c) (d)(e) (f) Figure 7 . (a),(b) display the scattering hit-image and PRM reconstructed image for the whole rebar. (c) and(d) display the same for rebar with 15% thicknesses rusted and (e) and (f) display the same for rebar with30% defect. The ‘ 𝑆 ’ parameter has been shown in the color scale for each image. for 6 cm voids are clearer than those of 5 cm voids. As described in section 2.3, the voids wereplaced at different depth inside the concrete deck. The image for the top-most void (at 4 cm) ismuch clearer than the other two. However, MST has been able to identify the defects at differentdepths which was a deficiency of other NDE techniques like thermography [20]. This is due to theless-interacting and penetrating nature of the muons. The limit discrimination capability of MST in case of imaging concrete structures has been studied.For the study the rusted rebar problem has been chosen due to its diverse scenario with three– 9 – a) (b)(c) (d)(e) (f)
Figure 8 . (a),(b) display the scattering hit-image and PRM reconstructed image for the whole CFST. (c) and(d) display the same for CFST with 7 mm void and (e) and (f) display the same for CFST with 10 mm void.‘ 𝑆 ’ parameters of the pixels have been shown in the color scale. different materials (concrete,rust and steel). The study has been done based on two parameters.First, the capability of this technique to identify the rusted part of the rebar with varying thicknesshas been studied. The thickness of the rust has been varied between 15% to 50%. Second, thesame set of defects have been calculated for 90 days data and compared to that obtained in 30 days.The corresponding results have been compared to the image of whole rebar. The 𝑡 -value, hencecalculated has been shown in figure 10 (b). The PRM-score has been shown in figure 10 (a). Fromthe figures it can be said that the 15% and 20% defect is hardly distinguishable with PRM-score< 2 𝛿𝑛 in terms of PRM analysis, whereas their discrimination has more than 2 𝜎 significance interms of 𝑡 -statistics. The detection of void also improves with increased exposure. Moreover, with– 10 – a) (b) (c) (d) (e) (f) Figure 9 . (a),(c),(e) display the scattering image obtained for non-defected concrete slab, concrete slab with5 cm void and 6 cm defect respectively. Figures (b),(d),(f) display the corresponding PRM output results.
90 days data the discrimination results are more precise; that is, each fraction of defect is easilydistinguishable from the other.
It is in great demand to use NDE techniques to monitor civil structures. It not only helps tomaintain and repair those structures but also can improve building engineering techniques. Thecapability of the MST approach, has been tested to identify defects inside several concrete structures.Corresponding scattering images have been produced and a statistical test, as well as the PRMmethod have been utilized to rate the detection capability in terms of 𝑡 -values, 𝑝 -values and PRM-– 11 –arget type DefectDimension (mm) t -score p -value StatisticalSignificance PRM-scoreRebar 2.25 -2.28 1e-2 2.29 1.484.5 -4.76 1e-6 4.75 4.45CFST 7 -3.83 6e-5 3.83 19.1110 -6.5 4e-11 6.48 25.20Void 50 -4.07 2e-5 4.2 5.6260 -4.88 5e-7 4.89 7.98 Table 2 . The identification metrics t-value and corresponding p-value and significance has been provided.The PRM-scores have also been listed.
Figure 10 . The 𝑡 -value, 𝑝 -value and PRM-score calculated for different defects. scores. The images for defects in all the three examples are are encouraging for deployment ofMST portals for civil engineering problems. It has been found that the MST can identify defects aslow as 2.25 mm in thickness. Reliability of MST studied on the basis of several attributes such aspresence of variable materials, different defect size and shape, depth of the defect and exposure. Acknowledgments
The author, Sridhar Tripathy, acknowledges the support and cooperation extended by INSPIREDivision, Department of Science and Technology, Govt. of India.
References [1] https://pdg.lbl.gov/2020/reviews/rpp2020-rev-cosmic-rays.pdf [2] H. Miyadera, et. al.
Imaging Fukushima Daiichi reactors with muons , AIP Advances , , (2013),052133-0521337. – 12 –
3] Konstantin N. Borozdin, et al.
Radiographic imaging with cosmic-ray muons , Nature , , (2003),277.[4] L.J. Schultz, et al. Image reconstruction and material Z discrimination via cosmic ray muonradiography , Nuclear Instruments and Methods in Physics Research A (2004) 687.[5] Harel, A. et. al.
Lingacom muography , Philosophical transactions. Series A, Mathematical, physical,and engineering sciences , (2018), 20180133.[6] Baesso P. et. al. Toward a RPC-based muon tomography system for cargo containers. , Journal ofInstrumentation , (2014), C10041–C10041[7] G Jonkmans, et al. Nuclear waste imaging and spent fuel verification by muon tomography , Annals ofNuclear Energy , , (2013), 267.[8] Chatzidakis S., et. al. Analysis of Spent Nuclear Fuel Imaging Using Multiple Coulomb Scattering ofCosmic Muons , IEEE Transactions on Nuclear Science Muons tomography applied to geosciences and volcanology , Nuclear Instrumentsand Methods in Physics Research A (2012) 23-28.[10] Nagamine K., et. al.
Method of probing inner-structure of geophysical substance with the horizontalcosmic-ray muons and possible application to volcanic eruption prediction , Nuclear Instruments andMethods in Physics Research A
Discovery of a big void in Khufu’s Pyramid by observation of cosmic-ray muons , Nature , (2017) 386-390.[12] Bethe H. A. , Molière’s theory of multiple scattering , Phys. Rev. Material discrimination in cosmic muon imaging using Pattern RecognitionMethod , Journal of Instrumentation , (2020) P06029.[14] Alvarez L. W., et. al. Search for hidden chambers in the pyramids using cosmic rays , Science , (1970) 832[15] Mrdja D. et. al., First cosmic-ray images of bone and soft tissue , Epl , (2016) 48003.[16] Lorenzi A., et al.
3D Ultrasonic Tomography Technique as a tool to Evaluate Concrete Structures , e-Journal of Nondestructive Testing (NDT) (2017).[17] Dong W., et. al. Experimental studies on void detection in concrete-filled steel tubes using ultrasoundConstruction and Building Materials , (2016) 154-162.[18] Xu B., et. al. Active interface debonding detection of a concrete-filled steel tube with piezoelectrictechnologies using wavelet packet analysis Mechanical Systems and Signal Processing , (2013)7-17.[19] Dongdong C., et. al. Detection of subsurface voids in concrete-filled steel tubular (CFST) structureusing percussion approach Construction and Building Materials (2020) 119761.[20] I. Abdel-Qader et. al.
Segmentation of thermal images for non-destructive evaluation of bridge decks , NDT and E International , , (2008), 395-405.[21] Bungey J. H., et. al. Sub-surface radar testing of concrete: a review , Construction and BuildingMaterials , (2004) 1–8.[22] Maierhofer C., et. al. Active thermography for evaluation of reinforced concrete structures.Non-Destructive Evaluation of Reinforced Concrete Structures: Non-Destructive Testing Methods ,(2010) 370-402. – 13 –
23] Oshita H.,
Quantitative estimation of rebar corrosion in reinforced concrete by thermography , Acoustic Emission and Related Non-Destructive Evaluation Techniques in the Fracture Mechanics ofConcrete , (2015), 177-203.[24] Guardincerri E. et.al.,
Imaging the inside of thick structures using cosmic rays , AIP Advances , (2016), 015213.[25] Dobrowolska M. et. al., Towards an application of muon scattering tomography as a technique fordetecting rebars in concrete , Smart Materials and Structures , (2020) 055015.[26] GEANT4 Collaboration, GEANT4 - a simulation toolkit , Nuclear Instruments and Methods in PhysicsResearch A
A 506 (2003) 250.[27] C. Hagmann, et al.
Cosmic-ray shower generator (CRY) for Monte Carlo transport codes , , (2007), 1143.[28] Ambrosio M., et. al., Muon energy estimate through multiple scattering with the MACRO detector , Nuclear Instruments and Methods in Physics Research A , (2002) 376-386.[29] Schultz L., et. al., Statistical Reconstruction for Cosmic Ray Muon Tomography IEEE TransactionsOn Image Processing , (2007) 1985-1993.[30] [31] Na S., et. al., Application of Thermal Image Data to Detect Rebar Corrosion in Concrete Structures , Applied Sciences , (2019), 10-12.[32] Shangumam N. E. et. al., State of the art report on steel–concrete composite columns. Journal ofConstructional Steel Research , (2001) 1041-1080.[33] Xue J. Q., Efects of debonding on circular CFST stub columns , Journal of Constructional SteelResearch , (2012) 64–76.[34] Lu Z., Air void and ring gap effect on CFST arch bridges dynamic performance , Journal ofConstructional Steel Research , (2020) 106418.[35] Chen H., Interfacial Debonding Detection for Rectangular CFST Using the MASW Method and ItsPhysical Mechanism Analysis at the Meso-Level , Sensors , (2019) 2778.[36] Chatzidakis S., et. al. A generalized muon trajectory estimation algorithm with energy loss forapplication to muon tomography , Journal of Applied Physics , (2018), 124903.[37] Thomay C. et al., A novel Markov random field-based clustering algorithm to detect high-Z objectswith cosmic rays , IEEE Nuclear Science Symposium and Medical Imaging Conference (2013), 1-3.[38] C. Thomay, et al.
A binned clustering algorithm to detect high-Z material using cosmic muons , Journal of Instrumentation (2013) P10013.[39] S. Tripathy, et al., Material identification with cosmic ray muons using RPCs , Journal ofInstrumentation (2019) C07007.[40] Cowan G., Statistical Data Analysis , Oxford University Press , (1998).[41] Riggi S.,
Muon tomography imaging algorithms for nuclear threat detection inside large volumecontainers with the Muon Portal detector , Nuclear Instruments and Methods in Physics Research A (2013) 59-68.[42] Wang Z. et. al.,
Image Quality Assessment: From Error Visibility to Structural Similarity , IEEETransactions on Image Processing , (2004) 600. – 14 –
43] Poirsonb A. B.,
Appearance of colored patterns: pattern-color separability, J. Opt. Soc. Amer. A:Opt. Image Sci. , , (1993), 2458-2470.[44] https://geant4-userdoc.web.cern.ch/UsersGuides/ForApplicationDeveloper/html/Appendix/materialNames.html. [45] Sunday. D. (2006). Distance between Lines and Segments with Their Closest Point of Approach. http://geometryalgorithms.com/Archive/algorithm_0106/algorithm_0106.htm [46] Sansalone M. and W. Streett, Impact-echo: Non-destructive Evaluation of Concrete and Masonry,Bullbrier Press, Ithaca, (1997).[47] Di Benedetti M. et. al.,
Acoustic Emission Monitoring of Reinforced Concrete under AcceleratedCorrosion , Journal of Materials in Civil Engineering , , (2008).[48] Feng M. et. al., Use of Microwaves for Damage Detection of Fiber Reinforced Polymer-WrappedConcrete Structures , Journal of Engineering Mechanics ,
128 (2) (2002).[49] Poston RW. et. al.,
Condition assessment using nondestructive evaluation. , Concr Int. Am Concr Inst (1995) 36–42.[50] Avdelidis NP. et. al.,
Applications of thermography in assessment of masonry, airport pavement andcomposite material . Insight , (2003), 836–841, (2003), 836–841