Crack detection using modified spectral clustering method assisted with FE analysis for distress anticipation in cement-based composites


 The present work aimed to develop an efficient way of capturing real-time crack propagation in concrete structures. The image processing was utilized for crack detection, while finite element modeling (FEM) and scanning electron microscopy (SEM) were used for quantitative and qualitative analysis of crack propagation. A green cement-based composite (CBC) containing saw dust was compared to a reference M20 grade concrete under compressive loading. Crack propagation during compression tests was captured using an 8-megapixel mobile phone camera. The randomly selected images showing crack initiation and propagation in CBCs were used to assess the crack capturing capability of a spectral analysis based algorithm. A measure of oriented energy was provided at crack edges to develop a similarity spatial relationship among the pairwise pixels. FE modelling was used for distress anticipation, by analyzing stresses during the compressive test in constituents of CBCs. SEM analyses were also done to evaluate cracked samples. It was found that FE modeling could predict the crack prone regions that can be used jointly with the image analysis algorithm, providing real-time inputs from the crack-prone areas. Green CBC were compared to reference concrete samples, showing reliable results. The replacement of OPC with wood dust reduced compression strength and produced a different fracture pattern regarding reference concrete. The results of the study can be used for distress anticipation and early crack detection of concrete structures for preventive support and management.


Introduction
Cracks and distress in concrete structures are generally due to restrained shrinkage, improper load balancing or material degradation. Their early detection and repair is a priority for proper maintenance as their development might lead to fatal damage and structural collapse.
Before image processing techniques were developed, man-made inspection was the only crack inspection technique, but it is dreggy and requires considerable time dedication and skilled staff [1][2]. Image processing is cheap, accurate, and can be automated, becoming the alternative of this manual approach for structural inspection.
Image processing methods can provide a highly precise crack detection results based on local features of the crack image [3]. There are many powerful techniques in image processing for crack detection and takes a different form of images captured through the digital camera, Infra-red (IR) camera, ultrasonic imaging, laser imaging, time of flight diffraction (TOFD) and various other imaging technologies. The generalized process of crack detection using image processing involves image pre-processing and then utilize the preprocessed picture for the feature extraction and parameter estimation required for the determination of crack length and direction of propagation [4].
The images captured using a digital camera for concrete crack detection is frequently reported [5][6][7]. These studies have attempted to explain the role of camera imaging for crack detection through threshold segmentation, neural network, image stitching, and acoustic emission. The crack detection using the structural feature (morphological and multidirectional shape of the crack) based algorithm on camera images has been developed and tested in a few studies [8,9]. Different filters based on region, edge and contrast features of the crack images have been used to find cracks in the multi-step model [10][11][12][13]. Some authors developed an artificial intelligence-based depth analysis model for the crack depth calculation [6,[14][15][16].
However, a cost-effective, reliable commercial application of the image processing technologies for crack detection in the structures still requires significant research efforts.
Many researchers are working in this direction; Fernandez et al. [1] proposed a method to minimize the cost of crack repair by developing an early crack detection system utilizing logarithmic transformation, bilateral filter, canny, and morphological filter. Oliveira et al. [2] proposed a fully integrated system based on unsupervised learning for automatic detection and characterization of cracks, which doesn't require the manual labeling of the samples.
Wavelet-based crack image decomposition into different frequency sub-band was demonstrated by Zhou et al. [17] for the detection of cracks in a different direction. Zhong et al. used an ultra-efficient crack detection algorithm with a second percolation model to address the issue of unclear and tiny cracks to be detected effectively [18]. Many other authors have raised the issue of detection of non-crack parts such as image shadow and stains, which alternatively affect the accuracy of the system and solve the problem by using various types of noise removal filters [19,20]. Hoang et al. [21] demonstrated a program for surface crack investigation using Min-Max Gray Level Discrimination by adjusting the gray intensity for accurate crack detection. Sheerin et al. [22] reported a study of Otsu's based thresholding method for the classification of the different types of cracks. Arun et al. [23] presented an analysis based on multiple features for the measurement of length, width, and direction of propagation of the crack. Kaur et al. [24] reported a comparative study for extracting curves, edges, and other features of the crack and pointed out that no single method is sufficient for every image type.
Compared to other methods available for image segmentation, thresholding is the simplest and fastest amongst all. Pal et al. [25] studied the impact of thresholding and its associated methods such as hidden Markov random field (HMRF), Markov Random Field, and K-means Clustering for accurate crack detection. Clustering is a powerful technique [26], and Sathya et al. [27] discussed some important clustering methods such as k-means, improved k means, fuzzy c-mean (FCM), and improved fuzzy c-mean algorithm (IFCM) to determine the even small crack in the concrete structure. Jorden et al. [28] presented two algorithms, one for spectral clustering and another for similarity matrix, to derive a new cost function for spectral clustering based on error measurement.
Minimizing this cost function concerning the partition leads to a new spectral clustering algorithm. In this way, Ng et al. [29] reported modifications in spectral clustering as the clustering method has unresolved issues related to the eigenvalues and eigenvectors. Luxburg et al. [30] investigated the consistency of spectral clustering by analyzing the convergence of eigenvectors of the normalized and un-normalized Laplacian matrices on random samples under standard assumptions. Tung et al. [31] suggested a modified form of spectral clustering, which includes a combination of block-wise processing and stochastic ensemble consensus for solving the most common challenge faced in image segmentation methods based on spectral clustering viz. scalability. Rohe [32] examined spectral clustering under the more general latent space model in which the eigenvectors of the normalized graph Laplacian asymptotically converge to the eigenvectors of a "population" normalized graph Laplacian.
Noise, illumination conditions and macrotexture are some factors that can weaken crack information in captured images. Jin et al. [33] developed a crack detection method based on spectral clustering. The proposed method worked not only on the local features (gray features) but also considered the step edge, roof, and line profile to improve the accuracy of the crack detection.
Although various methods have been proposed on crack detection using image processing, their accuracy still requires improvement, especially if the noise is present in the image acquisition environment. Thus, the first objective of the study was to develop an image processing algorithm for crack detection based on the modifications in the spectral clustering method to overcome stated challenges. However, this algorithm needs to take into account concrete composition, as it has ben reported that the fracture initiation and crack propagation of concrete depend on the type of Supplementary cementitious material (SCM) incorporated [4,[7][8][9][10][11][12][13].
Waste wood dust is readily available as SCM at no cost in India [53,54]. Thus, the second objective of this study was to define the crack propagation pattern of CBC under compressive strength analyzed combining FE quantitative analyses and SEM qualitative assessment.
Finally, the effect of wood dust inclusion as SCM on the cracking pattern of a green CBC was also studied. Collectively, investigating these multidisciplinary aspects propose a novel way for unmanned inspection of the damage in the structure for appropriate maintenance.

Sample preparation and compression testing
The concrete cube samples and green CBC samples of 150 mm × 150 mm × 150 mm were

Crack Detection using modified spectral clustering
A survey of crack detection algorithms including image processing, neural network, machine and deep learning based methods is available in the literature [55]. An 8-Mega Pixel mobile phone camera has captured crack initiation and propagation in green CBC samples during the compression test. The ordinary camera contributes to the lower cost requirement for the developed system. The images of the crack developed during the compression test were captured. Further, the spectral clustering method was used to detect the crack edges. For accurate crack detection, features for differentiating the cracks from the background were selected.
In general, the gray features for crack are derived from its roof, step change, and line profile [33]. The shape, contour, and texture information along with the gray features were used for modeling a global descriptor required for high accuracy in crack detection. This allows the detection of gray features on points where sharp intensity change occurs. The pattern of orders in-phase component present at edges was studied using Fourier transform. The phase component obtained thus used for oriented energy calculation for crack edge pixels in the image.
The phase congruency is basic building block for the spectral clustering. In general, the phase congruency is calibrated through local energy oriented for edge detection. One of the major drawback with phase congruency based edge detection is their sensitive to the noise. In the present work, for reducing the sensitivity to noise present in the image, a differential phase congruency was utilised instead of phase congruency. Inclusion of differential phase has improved the accuracy of the spectral clustering. The images for concrete structure may have considerable noise, thus, this modification in spectral clustering method is useful for improving the accuracy in crack detection. Further, a pairwise comparison on pixels performed through spectral clustering to divide the pixels into two clusters. These clusters are organized by oriented energy through phase congruency associated with crack edge pixels.
The differential phase congruency based method takes the signal as a gray scale image and scales it at s=0.5 for all the test images to be used in clustering through Poisson filtering. For an image ( , ) and for the phase vector ( , ) the differential phase vectors are calculated using equation 1: The process of phase congruency to calculate the oriented energy cannot be directly implemented over an image which a 2-dimension set of discrete values (pixels). Thus, the Gaussian function (eqution 2) was used for local energy calculation in a 2-Dimensional point spread distribution, and this was accomplished through convolution.
The value of x and y are chosen concerning the 2-D image where x is the distance from the origin in the horizontal axis, y is the distance from the origin in the vertical axis, and σ is the standard deviation of the Gaussian distribution. The illustration of the Gaussian filter is shown as the integer-valued kernel in Fig.1 with respect to every pixel value p(i, j). The values of the mask defined such that it approximates the distribution of the Gaussian with a standard deviation of 1. with crack image Cimg. Therefore, the local energy (LE) function is given by: The oriented energy (OE φ,σ ) at angle φ and neighborhood radius σ around the crack image pixel (x,y) is given by:   2 gives an illustration of dissimilarity between pixel p(i,j) and q(m,n) and it accords to: Dedg (pi, j, qm,n) = OEcon(x �, y �)-avg{OEcon(pi,j) + OEcon (qi,j) The elements of the similarity matrix are calculated as: The spectral clustering is different from spatial analysis, which directly works on sample space. It is a graph theory-based method used to describe the belongingness of one object to the other. However, spectral clustering converts the spatial sample classification to the global optimal solution of graph theory. The Ncut algorithm was used as a final element of the spectral clustering to detect the crack edges. The essential terms used in Ncut method involves the assumption of graph theory such that: 1. Image is considered as a weighted graph 2. Nodes are considered as pixels in the image and, 3. An Adjacency matrix is considered as a similarity matrix W.
The adjacency matrix as a similarity matrix has been calculated on oriented energy associated with the crack edge. The similarity matrix has the form in graph theory as: The elements of the diagonal matrix D is defined from the similarity matrix whose (i,i)th elements are taken as the sum of the ith row.
From the definition of the Adjacency and Diagonal matrix the Laplacian matrix is then given by: Alternatively, the elements of the Laplacian matrix are defined as: The characteristics of the Laplacian matrix are then implemented through eigenvalues and eigenvectors. The gradient of the eigenvector was used to determine the crack edge as eigenvector contains the vital information of the crack. The coding for the algorithm was executed using MATLAB.

Finite Element Model
The 3D FE based numerical model was constituted using COMSOL 5.4 for analyzing stresses and deformation in concrete and green CBC during compressive loading. The representative volume method (RVM) was employed for making the model computationally inexpensive [56,57]. The geometry of the representative volume was constituted considering the volume proportion of each element for concrete and the green CBC separately. a b. Figure 3 (a-d). Different zone of Green cement-based composites.
For example, Fig. 3 shows a representative volume element of green CBC having the mix ratio of wood dust, cement, fine aggregate and coarse aggregate 0.1: 0.9: 1.5: 3 by volume.  (Fig. 4). The material properties used for modeling are given in Table 1 [58]. The linear elastic material model was selected for the study. For a linear elastic material, Hooke's law relates the stress tensor to the elastic strain tensor: Where C is the 4th order elasticity tensor, double-dot denotes tensor product (or double contraction). The elastic strain ε el is the difference between the total strain ε and all inelastic strains ε inel . c d Fig. 4. Meshing of a representative volume of green CBC After meshing, the average failure load obtained during the experimentation was applied to concrete and green CBC. The loading and boundary conditions were taken from the experiments during the simulation. The stresses and deformations were obtained for different constituents, interfaces, and zones of the representative volumes of concrete and green CBC.

Crack Detection using modified spectral clustering
The capability of the developed algorithm for detecting cracks was demonstrated by analyzing photographs of the samples during compression testing. The first photograph considered for the study was the concrete cube sample fitted in the CTM (Fig. 7) at no load.
The different steps include the localization for crack examination followed by the crack segmentation, contrast stretched imaging, gray scaled imaging which produces noisy spectral clustered image and finally the image with no crack detected was obtained after removal of noise by morphological examination.   Fig. 9(a) shows the sample photographs reporting the crack initiation and propagated crack, respectively. Fig. 8(d), (e) and Fig. 9(d), (e) are the pre-processed image for the image contrast stretching and RGB to gray conversion. The noisy and noise-free images of the crack have been shown in Fig. 8(f), (g) and Fig. 9(f), (g) for the smaller and larger crack, respectively. The algorithm is capable of capturing multiple cracks propagating simultaneously and report the size of crack (Annexure 1) useful for highlighting the requirement of maintenance.

Crack length measurement
The crack length was measured by measuring the distance between the farthest pixel either in vertical or horizontal direction with certain angle. The end-point distance between pixel has been measured in present work by the following method: Step1: Detect the crack through spectral clustering.
Step2: Start from with the pixel f(0,0) of the crack image to determine the first pixel in the row and column through iterative process for rows and columns until first pixel found.
Step3: Find the starting point of the crack by comparing the adjacent pixel in horizontal and vertical direction to predict the crack propagation.
Step4: Find the last pixel through iterative process of the crack depending upon the propagation of the crack either in vertical or horizontal direction.
Step5: Now determine the longest geometrical distance between first and last pixel by considering the : Where OF is the distance perpendicular from the first pixel (F) to the line of the last pixel (at pixel O) and OL is the linear distance in direction till the last pixel (pixel L) from the point receiving the perpendicular(at pixel O) from pixel F.
Finally, the length of the crack is calculated and calibrated in mm through number pixel converted in to equivalent crack length. In Fig.9 (h) 652 pixles lengths, transform into actual length is 38.06 mm. For the image quality available in the present work, the crack of <5 mm size can be detected easily. with an additional experimental run with the specially prepared samples having higher wood dust content at the corners. This verification experiment has ensured the correctness of the model results. Fig. 11 shows the SEM micrographs of verification CBC samples. The sample

Finite Element Model
for SEM was prepared from the fractured edges. The presence of wood dust in a more significant amount is visible. SEM micrograph shows that the green CBC is comparatively heterogeneous to concrete. However, C-S-H was less developed because of unreacted particles. The dilution, agglomeration, and filler effect have resulted in lower compressive strength of green CBC [59]. The dilution due to partially replacing OPC with the wood dust leads to fewer hydration products and a weaker microstructure. Additionally, the wood dust agglomeration created a fragile zone in the microstructure, and lack of hydration of particles could take place in the hardened cement matrix. In order to support the theory that the FA-wood dust interface contributes to the fracture initiation, the difference between the stresses and displacement of concrete and green CBC was investigated. Fig. 13 clearly shows that the Von Mises stresses and total displacement along the upper edge of green CBC are considerably higher than the concrete. Thus, it is apparent that the broken edges of the green CBC are due to the high displacement resulted

Conclusion
The present work proposes an initial investigation for a methodology that will provide inputs for unmanned structure maintenance using a modified spectral clustering algorithm, FEM, and SEM investigation. The methodology was applied on conventional concrete and green composite based composites (CBCs) incorporating saw dust subjected to compressive strength tests. The main findings of the study were: • The developed image processing algorithm can effectively extract the crack features from the concrete crack images taken with an ordinary mobile phone camera. Some pre-processing steps are required for proving useful input to the spectral clustering algorithm.
• Cracks were detected by the dissimilarity between the surface energy of the pixel pairs. The algorithm is capable of overcoming the environmental noises, and any other noise appeared during image analysis.
• Damage-prone zones can be predicted effectively using the developed numerical model.
• The FE model and image processing collectively develop a framework for crack detection at an early age with continuous automated observation. The smaller, larger and multiple cracks in concrete and CBCs can be captured and measured in real-time.
Crack length can be measured through standard function in the image toolbox of the MATLAB.
• The replacement of OPC with wood dust reduced compression strength and produced different fracture pattern regarding reference concrete. Conventional concrete samples showed compressive strength 10.25 % higher than green CBC samples.
• The lower strength of green CBC and crack prone zone was determined through FE method and matched with SEM micrographs of fractured CBC samples.
• The method allows timely intimation about the damage in structure for appropriate action through images from inspected zones without requiring any expert from the same domain.
The implementation of developed methods for real time structural health monitoring requires additional efforts and considered as a future work.

Acknowledgement
This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 754382, GOT ENERGY TALENT. The content of this article does not reflect the official opinion of the European Union. Responsibility for the information and views expressed herein lies entirely with the author(s).

Declaration of Conflicting Interests
The authors declare that there is no conflict of interest.