Uncertainty Estimation for Ultrasonic Inspection of Composite Aerial Structures
Abstract
Components made of polymeric composite materials, such as wings and stabilizers of aircrafts, are periodically inspected using nondestructive testing methods. Ultrasonic testing is one of the primary inspection methods applied in the aircraft/aerospace industry. Image processing methods have been developed for the purpose of ultrasonic data analysis and increasing the inspection efficiency. A critically important factor in damage sizing is appropriate processing of ultrasonic data in order to extract the damage region properly before calculation of its extent. The paper presents a comparative analysis of various image segmentation methods in the light of accuracy of damage detection in ultrasonic CScans of composite structures. A brief review of image segmentation methods is presented and their usefulness in the ultrasonic testing applications is discussed. The selected methods, namely the threshold, edge, region, and clusteringbased ones, were tested using ultrasonic CScans of a specimen with barely visible impact damage and aircraft panels with delamination, all made of CFRP composites. A problem with the selection of appropriate input parameters using most of the segmentation methods is discussed, and nonparametric histogrambased approaches are proposed. A quantitative analysis of the accuracy of damage detection using the segmentation methods is presented and the most suitable approaches are introduced. The proposed processing procedures may significantly improve the objectivity of inspections of composite elements and structures using ultrasonic testing.
Keywords
Ultrasonic testing Damage quantification Composite structures Aircraft structures Image segmentation Image processing1 Introduction
Due to the complex nature of polymeric composite materials, including the presence of interfaces and inherent anisotropy, they have drawbacks which cover poorer performance at high temperature, poor throughthethickness properties and poor resistance to transverse impact loadings [13]. From among the inservice damage types, delamination, bond failure, cracking, moisture ingress, fibre buckling or fracture, failure of the interface between the matrix and fibres, and impact damage can be distinguished. Low energy impacts are the source of common problems, since they cause the socalled barely visible impact damage (BVID), which may cause extensive internal damage with simultaneous very limited visible marks on the impacted surface.
Modern nondestructive testing (NDT) methods allow for the effective diagnostics of composite structures. Commonly used damage tolerance philosophy allows composite components with existing damage to be operated under certain conditions. A structure is considered to be damage tolerant if the existing damage does not weaken the structural integrity. Therefore, such structures are included in a maintenance program, the aim of which is to identify damage before its development reduces the residual strength of the structure below an acceptable limit. The damage tolerance approach assumes necessity of damage extent identification and monitoring of its growth by periodic inspections using NDT methods. This procedure is very important because of a very complex nature of composite damaging and its propagation. In a general scenario, microcracks develop in the composite matrix due to cyclic loading, continuation of loading causes development of the microcracks into macroscopic cracks, which, in turn, spread through the composite plies, and finally, develop into local delamination due to stress concentrations. When delamination is formed, the damage may increase rapidly up to failure [20]. In view of this progressive damage behaviour, composite elements are periodically inspected to monitor the damage progression.
1.1 Ultrasonic Testing of Composite Materials
One of the most commonly applied NDT methods for composite elements is ultrasonic testing (UT). During ultrasonic inspections, two fundamental parameters of the received energy are observed: the amplitude and TimeofFlight (ToF). The socalled CScan presentation mode of UT results, presenting damage as from the top side of the tested element, is used for the purpose of damage sizing. Appropriate processing of ultrasonic CScans allows for damage detection, localisation, and calculation of its extent. However, there are numerous factors influencing on the damage detectability and the occurrence of measurement errors during performing ultrasonic inspections. In the paper [64], the authors presented a study on the uncertainty assessment connected with the selection of techniques and parameters of ultrasonic testing that affects the damage size estimation significantly. This paper is focused on the uncertainty assessment connected with the postprocessing of ultrasonic data obtained after the inspection.
1.2 Ultrasonic CScan Processing
In order to calculate the extent of damage detected in the ultrasonic CScan it is necessary to firstly separate the pixels representing damage from other pixel regions visible in the scan. Therefore, a very important factor in damage sizing is appropriate processing of ultrasonic scans in order to extract the damage region properly before calculation of its extent. The industrial inspections using UT techniques must be performed by a certified expert. In practice, damage size is usually calculated based on manually selected areas on the CScans. Due to the necessity of increasing the efficiency of ultrasonic inspections, i.e. shortening the duration of UT data analysis, the application of image processing methods is one of the presently undertaken goals.
In the literature, one can find certain approaches aimed at aiding the procedure of damage size assessment from CScans using image processing methods. The examples are, e.g., a method based on segmentation of ultrasonic scans by data clustering [49], segmentation based on statistical mean and standard deviation [33], or an algorithm based on image filtering, thresholding and morphological operations [59]. The latest studies of the authors of this paper in the area of application of image processing methods to UT data cover an interactive algorithm allowing for damage extraction from CScans and calculation of its extent [62], as well as development of damage segmentation with its 3D reconstruction approaches [63, 65, 66].
However, there is so far little work devoted to the development of a universal method of damage detection from CScans. Approaches found in the literature were adapted to specific tested cases and are not universal. Some methods that succeed in the case of inspection of simple structures, e.g. with a uniform thickness, may fail in the case of testing of more complex structures, e.g. with a varying thickness, and vice versa. There is a vast number of methods of image processing that may be helpful for the purpose of damage extraction from ultrasonic scans. The aim of this paper is to analyse various types of image segmentation methods in the light of their effectiveness in damage extraction, and select the most useful methods for the analysis of ultrasonic scans.
2 A Brief Review on Image Segmentation Methods
Image segmentation results in partitioning of an image into fragments (sets of pixels) corresponding to objects visible in the image. Main criteria considered in such procedure can be a colour, intensity or texture. Segmentation algorithms may either be applied to the images as originally recorded, or after the initial processing, e.g. application of filters. After segmentation, methods of mathematical morphology can be used to improve the results. Finally, the segmentation results are used to extract quantitative information from the images.
In the literature, there is a large number of surveys on image segmentation methods, from the former general overviews (e.g. [17, 22, 53]) and those focused on thresholdbased methods [47, 60] to more recent surveys—from the overall (see e.g. [11, 32, 56, 68, 69]), to those focused on image binarization [9, 58], thresholding [21, 52], or colour image segmentation [55].
The mentioned surveys and comparative studies found in the literature are mainly based on object detection from photographs, where problems have a different character than in the case of ultrasonic scans. These are, for instance, the noise content in the photograph or the influence of the uniformity of the illumination. Moreover, many studies are dedicated to problems related to a text/background separation (see e.g. [29, 58]) for the optical character recognition (OCR) systems. Surveys of image segmentation found in the area of UT relate mainly to medical applications (e.g. [36, 48, 57]). In the survey considering segmentation of Xray and CScan images of composite materials performed by Jain and Dubuisson [25] only four methods, mainly adaptive thresholding, were tested and compared. The authors of [52] compared more image thresholding methods for NDT applications. There seems to be a lack of comprehensive analyses of image segmentation methods in the context of processing of ultrasonic images in industrial applications, such as diagnostics of composite materials. As mentioned earlier, performing such the analysis is the aim of this paper.
Short descriptions of the most common segmentation methods, within the following categories, are presented below. Considering the introductory character of this section, full descriptions are omitted here, however, a reader can find the details in cited literature.
2.1 ThresholdBased Segmentation
Thresholding is the simplest and one of the most commonly used segmentation methods. The pixels are divided depending on their intensity value. In a basic approach, a threshold value is selected from a greyscale image and used to separate the foreground of the image from its background. This approach is also called a bimodal segmentation, since it assumes that the image contains two classes. The threshold can be chosen manually or automatically using one of many methods developed for this purpose, which are described below. Thresholding can be categorized into global, variable, and multiple methods.
2.1.1 Global Thresholding

Methods based on using a Gaussianmixture distribution. Otsu’s method [39] aims at finding the optimal value for the global T. It is based on the interclass variance maximization (or the intraclass variance minimization) between dark and light regions, through the assumption that well thresholded classes have well discriminated intensity values. This method is also categorised as clusteringbased thresholding. Riddler and Calvard [45] proposed an iterative version of the Otsu’s method. Kittler and Illingworth [31] presented a minimumerrorthresholding method based on fitting of the mixture of Gaussian distributions.

Methods based on a histogram shape, where, for example, the peaks, valleys and curvatures of the histogram are analysed. One of the examples is an approach proposed by Prewitt and Mendelsohn [42], where the histogram is smoothed iteratively until it has only two local maxima.

Methods based on maximizing the entropy of the histogram of grey levels of the resulting classes, e.g. proposed by Pun [43], and modified by Kapur et al. [26] or by Pal and Pal [40]. A faster, twostage approach based on entropy was proposed by Chen et al. [10].
2.1.2 Variable Thresholding

Niblack’s algorithm [35] calculates a local threshold by sliding a rectangular window over the greylevel image. The computation of the threshold is based on the local mean and the local standard deviation of all the pixels in the window. This approach is the parent of many local image thresholding methods.

Sauvola’s algorithm [50] is the modification of the Niblack’s algorithm, also based on the local mean value and the local standard deviation, but the threshold is computed with the dynamic range of standard deviation.

Wolf’s algorithm [61] addresses a problem in Sauvola’s method when the grey level of the background and the foreground are close. The authors proposed to normalize the contrast and the mean grey value of the image before computing the threshold.

Feng’s algorithm [16] introduced the notion of two local windows, one contained within the other. This method can qualitatively outperform the Sauvola’s thresholding, however, many parameters have to be determined empirically, which makes this method reluctantly used.

Nick’s algorithm [30] derives the thresholding formula from the original Niblack’s algorithm. The method was developed for the OCR applications, especially for low quality ancient documents. The major advantage of this method is that it improves binarization for light page images by shifting down the threshold.

Mean and median thresholding algorithm. The meanbased method calculates the mean value in a local window and if the pixel’s intensity is below the mean the pixel is set to black, otherwise the pixel is set to white. In the medianbased algorithm the threshold is selected as the median of the local greyscale distribution.

Bernsen’s algorithm [2] is a method using a userdefined contrast threshold. When the local contrast is above or equal to the contrast threshold, the threshold is set as the mean value of the minimum and maximum values within the local window. When the local contrast is below the contrast threshold, the neighbourhood is set to only one class (an object or background) depending on the mean value.

Bradley’s algorithm [7] is an adaptive method, where each pixel is set to black if its value is t percent lower than the average of the surrounding pixels in the local window, otherwise it is set to white.

Triangle algorithm [67] calculates the threshold based on a line constructed between the global maximum of the histogram and a grey level near the end of the histogram. The threshold value is set as the histogram level from which the normal distance to the line is maximal.
2.1.3 Multiple Thresholding

A method of Reddi et al. [44] can be considered as an iterative form of Otsu’s original method, which is faster and generalized to multilevel thresholding.

Another extension of the Otsu’s method to multilevel thresholding is referred to as the multi Otsu method of Liao et al. [34].

A method proposed by Sezan [51] consists in detection of peaks of the histogram using zerocrossings and image data quantization based on thresholds set between the peaks.
2.2 EdgeBased Segmentation
In an ideal scenario, regions are bounded by closed boundaries and by filling the boundaries we can obtain the regions (objects). This assumption was the foundation to develop the edgebased segmentation methods. They are based on detection of rapid changes (discontinuities) of an intensity value in an image.

the first derivative of the intensity is greater in magnitude than a given threshold. Using this method, the input image is convolved by a mask to generate a gradient image. The most popular edge detectors (filters) are based on Sobel, Prewitt, and Roberts operators;

the second derivative of the intensity has a zero crossing. This approach is based on smoothing of the image and extraction of zero crossing points, which indicates the presence of maxima in the image. A popular approach is based on a Laplacian of Gaussian (LoG) operator.
There are also many other methods aimed at finding straight lines and other parametrized shapes in images. The original Hough transform [24] was developed for detection of straight lines. This method was later generalized to the detection of analytically described shapes, such as circles [14], and to the detection of any shape [1]. These methods, however, are not useful for the problem undertaken in this study, since the general assumption is the baselinefree approach, i.e. damage needed to be detected is of unknown shapes.
2.3 RegionBased Segmentation

Region growing is a method, in which an initial pixel (a seed) is selected and the region grows by merging the neighbouring pixels of the seed until the similarity criteria (colour, intensity value) are met.

Region splitting and merging methods. Splitting operation stands for iteratively dividing of an image into homogeneous regions, whereas merging contributes to joining of the adjacent similar regions. There are approaches using one of these operations solely (e.g. a statistical region merging (SRM) algorithm of Nock and Nielsen [37], a region splitting method of Ohlander et al. [38]), or both of them.
The main disadvantage of the regionbased approaches is that they are computational time and memoryconsuming.
2.4 ClusteringBased Segmentation

Hard clustering is a simple clustering technique dividing an image into a set of clusters, which is best applicable to data sets that have a significant difference (sharp boundaries) between groups. The most popular algorithm of hard clustering is a kmeans clustering algorithm [23], which simultaneously belongs to unsupervised classification methods. In this method, initial centroids of a given number k of clusters are computed, and each pixel is assigned to the nearest centroid. Then, the centroids of clusters are recomputed by taking the mean of pixel intensity values within each cluster, and the pixels are reassigned. This process is repeated iteratively until the centroids stabilize. In this method, k must be determined, which is its main disadvantage. Moreover, it may lead to different results for each execution, which depends on the computation of initial cluster centroids.

Soft clustering is applicable to noisy data sets, where the difference between groups is not sharp. An example of such a method is a fuzzy cmeans clustering, developed by Dunn [15] and later improved by Bezdek [4]. The algorithm steps in the fuzzy cmeans clustering are very similar to the kmeans clustering. The main difference in this method is that pixels are partitioned into clusters based on partial membership, i.e. one pixel can belong to more than one cluster and this degree of belonging is described by membership values.

A mean shift clustering (appeared first in [19]) is another clusteringbased method. It seeks modes or local maxima of density in the feature space. Mean shift defines a window around each data point and calculates the mean of data point. Then, it shifts the centre of the window to the mean and repeats the algorithm step till it converges. This method does not need prior knowledge of a number of clusters but it needs a mean shift bandwidth parameter.

Expectation Maximization (EM) algorithm [12] is used to estimate the parameters of the Gaussian Mixture Model (GMM) of an image. The method consists in recursive finding of the means and variances of each Gaussian distribution and finding the best solutions for the means and variances. The EM algorithm can be efficient when analysed data is incomplete, e.g. there are missing data points. However, the method is computationally expensive, and prior knowledge of a number of clusters is needed. Exemplary studies on segmentation using the GMM and EM algorithm are presented in [18].
2.5 Other Segmentation Methods

Texturebased segmentation approaches are useful when objects that are needed to be detected have a distinguishable texture. These approaches are often based on making use of texture measures, such as cooccurrence matrices or wavelet transforms. By applying the appropriate filters together with morphological operations, an object of a given texture can be identified in the image.

Template matching methods (see for instance [8]) are used when an object looking exactly like a template is expected to be found in images. In such a method, a template is compared to all regions in the analysed image and if the match between the template and the region is close enough, this region is labelled as the template object.

Artificial neural networkbased segmentation methods simulate the learning strategies of human brain for the purpose of decision making. A neural network is made of a large number of connected nodes and each connection has a particular weight. A wellknown example of neural networks used for data clustering is a Kohonen selforganising map (SOM) [41].

Genetic algorithms are randomised search and optimization methods guided by the principles of evolution and natural genetics. A study concerning the application of image segmentation using the genetic algorithms was broadly presented in a book of Bhanu and Lee [5]. Besides the genetic algorithms, there are many other optimisation approaches that can provide similar results of image segmentation.
3 Experimental Data
The comparative analysis of image segmentation methods, presented in Sect. 4, was performed based on exemplary CScans acquired during UT of two real composite structures. The testing of both elements was performed using a \(\text {MAUS}{\textregistered }\) automated system of the Boeing\({\textregistered }\) company (see Fig. 1), which is widely used for the inspections of aircraft structures. For this purpose, a 5 MHz single transducer was selected and a resolution of 0.01” (0.254 mm per pixel) was set.
The first tested element is a specimen (see its fragment in Fig. 2a) made of a CFRP composite with an impact damage of a BVID type. The BVID was introduced artificially using a test rig for the drop weight impact tests (described in [28]), i.e. the specimen was impacted with the energy of 20 J, using the impactor with a rounded ending (see the impactor E presented in Fig. 1 in [27]). As it can be noticed, there are only barely visible marks of impact damage on the specimen’s surface, in the middle of the image.
The second element is a fragment of an aircraft panel made of a CFRP composite, with delamination formed during the aircraft operation. A demonstrative fragment of this element is presented in Fig. 2b. The delaminated areas developed around a flap of an elliptic shape as well as in the area of openings for the rivets. This more complicated structure was intentionally chosen for this study since the performed analysis aims at selecting universal segmentation methods that are suitable for both simple and more difficult tested cases.
Additionally, a verification of potentially the best segmentation methods (selected based on the results presented in Sect. 4) was performed with the use of 5 other CScans of composite aircraft panels, presented in Sect. 5.
4 Comparative Analysis of Image Segmentation Algorithms
In order to consider a segmentation method as a candidate for the analysis of ultrasonic CScans during inspections of composite materials, the method should not require setting of many input parameters, thus it should be universal. Based on the performed review of image segmentation methods and taking into consideration their advantages, disadvantages and limitations, appropriate methods were selected for the comparative analysis. The obtained CScans were processed using Matlab\({\textregistered }\) environment.
Two main criteria should be taken into consideration when analysing accuracy of damage detection in ultrasonic CScans: a segmentation accuracy, and a number of the resulting classes. The accuracy was calculated as a correlation between the resulting binary image and the reference groundtruth image, given in the range of 0–1. The resulting number of classes obtained as a result of image segmentation is also very important since, for instance, obtaining high accuracy but through detection of a large number of little segments that perfectly cover the area of the ground truth object is not desirable.
4.1 Analysis of Bimodal ThresholdBased Segmentation Methods
From these results one can notice that bimodal segmentation did not bring the expected results in any case. It can be observed that such approaches are not appropriate for the UT applications, since CScans should not be respected as having only two classes, i.e. the damaged and undamaged regions. It is especially visible in the case of the aircraft panel that beyond damage and the healthy structure there are also other regions, such as stiffeners, openings, or just noise, which should be segmented separately. This fact entirely eliminates the bimodal segmentation methods from further considerations.
4.2 Analysis of EdgeBased Segmentation Methods
It can be noticed that the assumption of edgebased segmentation methods that regions are bounded by closed boundaries is not met. In many cases, the produced edges do not have closed contours and a significant part of these edges does not represent contours of damage only. Using this approach, similarly as in the case of the bimodal thresholding, it is not easily possible to extract damage regions only (i.e. clearly separate them from other elements or noise), thus the edge detection methods are regarded as not suitable for the considered problem.
The abovementioned observations lead to the conclusion that multimodal segmentation approaches are needed to be applied, i.e. the methods that enable obtaining more than two classes.
4.3 Analysis of ClusteringBased Segmentation Methods
In the case of the impacted specimen, the segmentation accuracy using the kmeans clustering and multilevel Otsu thresholding is in most cases very high, whereas using the cmeans clustering and GMMEM clustering it is changeable with the k variation. However, when analysed more complicated data, i.e. the CScan of the aircraft panel, the segmentation accuracy is very changeable for all the tested segmentation methods. These observations prove that selection of the number of classes k strongly affects the segmentation accuracy. Although the accuracy is in many cases very high, the necessity of the k selection makes these methods nonuniversal and inappropriate for the NDT applications.
4.4 Analysis of RegionBased Segmentation Methods
4.5 Analysis of Other HistogramBased Segmentation Approaches
Since all of the tested methods described above have some disadvantages, i.e. the main problem is the necessity of selection of input parameters, and thus, the lack of universality, the authors decided to test several nonparametric histogrambased approaches based on owndeveloped algorithms.
The second approach is based on the MBP algorithm with the difference that the histogram is smoothed before the minima detection step. Remarkably the elimination of some local noisy maxima in the histogram produces sharper distinction between the relevant segments. For the smoothing purpose, the onedimensional median filters of a 2nd, 3rd, and 4th order were tested. The exemplary results, i.e. the smoothed histograms with indication on the thresholds’ locations, and the corresponding segmented images are presented in Fig. 14c, d, for the impacted specimen, and in Fig. 15c, d, for the aircraft panel.
Filtering of the input CScans before processing of their histograms was also tested. Various types of twodimensional filters, such as the averaging, or Gaussian lowpass filters, and variable scenarios of their sizes were tested. However, this approach did not bring satisfying results, since the segmented images have too large number of classes (for the CScan of the aircraft panel it is in the range of 37–54). Interestingly the postfiltering (smoothing the histogram) appears to be more efficient than applying filters on the physical image itself.
The proposed approaches have a main significant advantage over other segmentation methods tested in this study, that they do not require setting any input parameters, such as a number of classes k. The resulting k value is selected automatically and the algorithms are universal for both simple and more complicated tested cases.
5 Verification of the Proposed HistogramBased Segmentation Approaches
Segmentation accuracy obtained using histogrambased approaches for the additional test cases
Method  CScan case  

Case 1  Case 2  Case 3  Case 4  Case 5  
Original CScan  No. of classes  127  124  117  128  93 
MBPunfiltered  No. of classes  27  23  23  28  19 
Correlation  1.0000  1.0000  1.0000  1.0000  1.0000  
MBPmedfilt,2  No. of classes  18  21  17  21  13 
Correlation  0.9913  0.9995  0.9997  0.9993  1.0000  
MBPmedfilt,3  No. of classes  13  13  9  11  9 
Correlation  0.9905  0.9943  0.9959  0.9986  1.0000  
MBPmedfilt,4  No. of classes  13  12  6  13  10 
Correlation  0.9913  0.9931  0.9986  1.0000  1.0000  
GaussianMBP  No. of classes  27  23  23  28  19 
Correlation  0.9943  0.9965  0.9992  0.9993  0.9985 
The analysis of these results indicated that the MBP algorithm without filtering brought the best results with a total correlation for all the test cases. For the rest approaches there is, in most cases, a very little loss of accuracy (a correlation decrease by 0.003 on average) that corresponds to discrepancies in single pixel amounts. Therefore, it can be concluded that the best method selected from the experiments presented in this paper is the MBP algorithm without filtering, which allowed for the data reduction by approx. 80
The results of image segmentation using the MBP algorithm without filtering as well as the resulting binary images obtained for the 5 test cases are presented in Fig. 18.
6 Conclusions
The presented study was aimed at performing a comparative analysis of various types of image segmentation methods in the light of accuracy of damage detection in ultrasonic CScans of composite structures. A brief review of image segmentation approaches and their short description was introduced. A vast majority of surveys and comparative analyses found in the literature concerns mainly the problems of segmentation of photographs and documents. Processing of ultrasonic images is mainly addressed to issues connected with medical imaging. Due to the lack of comprehensive analyses in relation to segmentation of ultrasonic images in industrial applications, the authors presented the results of analysis of accuracy of damage extraction in CScans of CFRP structures with different level of complexity. The accuracy was determined based on the correlation between the resulting binary images and the groundtruth images, but also the resulting numer of classes in the segmented images was taken into consideration. Several threshold, edge, clustering, regionbased, as well as proposed nonparametric histogrambased segmentation approaches were tested and the quantitative analysis of the results was depicted.
The presented findings show several problems of many methods, mainly related to a necessity of selection of the input parameters or computation duration. The obtained results allow concluding that simple, very fast and nonparametric histogrambased methods are the most suitable for the aim of the analysis of ultrasonic scans of composite materials. Additional verification of the histogrambased segmentation methods based on more test cases indicated that the MBP algorithm without filtering brought the best results in all the test cases (the correlation equals 1) with the data reduction by approx. 80%.
The selected histogrambased segmentation method is universal and can be applied to CScans of composite elements of any type of material, thickness, or other geometrical properties. This versatility results from the fact that the method allows for proper sectioning of the ultrasonic scan into groups of colours (values), i.e. individual areas lying at different depths of the tested object, depending on the level of colour similarity, thus it is not dependent on the numerical values themselves. Therefore, the method can be applied not only for the CScan processing procedures but also in other applications related to image processing.
Notes
Acknowledgements
The authors would like to thank Adam Latoszek from the Air Force Institute of Technology for his assistance during the realisation of ultrasonic testing of the specimen used in this study and Andrzej Katunin from the Silesian University of Technology for preparing the specimen by introducing the impact damage.
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