1 Introduction

Structural health monitoring of nuclear power plants is crucial for ensuring public and environmental safety. Almost all nuclear power plants are covered by concrete with a carbon steel plate base layer with a thickness of 6 mm, which is called CLP. Corrosion affects the CLP during its operation. Inspection and maintenance are critical to prevent wall thinning in the corroded area of the CLP. Otherwise, there is the possibility of diminishing the CLP’s protection capability, resulting in a reduction in safety and operational lifespan. Corrosion defects appear between the CLP and the thick concrete layer, and visual inspection of the CLP is physically not possible. Due to the large dimensions and operating environment of nuclear power plants, an ultrasonic guided wave-based inspection of the CLP is the most suitable technique among all other nondestructive methods (Basu et al. 2021). A Lamb wave is a type of guided wave that can propagate for a long distance as well as its sensitivity to various types of defects. The Lamb wave can be used for the inspection of plate corrosion, flaws, debonding, and other kinds of defects (Zhang et al. 2023; Malikov et al. 2023). In addition, Lamb waves can propagate along curved structures as well, making them useful for monitoring the structural health of curved structures. Using the waveform propagation pattern, an ultrasonic image of the hidden defects can be reconstructed using a set of ultrasound probes arranged around the specimen. Ultrasonic tomography of CLP is the most effective method of inspecting and detecting localized defects. The main limitation of ultrasonic testing is that sufficient experimental skills are required for the ultrasonic NDT technician, because of the nonlinearities introduced due to the instrument and variation in the sensitivity of the ultrasonic elements, etc. These nonlinear effects significantly reduce the accuracy of the ultrasonic tomographic images, thus increasing the risk of missing defects.

Most of the significant improvements in ultrasonic tomographic detection have occurred in the industrial and medical fields in recent years (Malikov et al. 2021). For instance, the application of the RAPID algorithm with variable shape functions for detecting multiple defects in space (Martucci et al. 2021). Variable shape factors to improve ultrasonic tomography's reconstruction of images and microdamage in space (Basu et al. 2021). The Westervelt equation is employed to scan the surface structure using pulse-echo scanning (Bao et al. 2022). A correlation between the shape function and the skew parameter of the ultrasound beam has been applied to improve tomographic imaging (Duan and Gan 2019). Furthermore, fast ultrasonic tomography has been employed for underwater samples, including non-contact ultrasonic samples (Hay et al. 2006; Zhang et al. 2021).

The increasing use of deep learning in computer vision applications is due to the advancements in deep learning architecture, including the popularly used U-Net (Siddique et al. 2021; Malikov et al. 2022). U-Net is mainly adopted within medical imaging and specifically created for image segmentation (Antonioli et al. 2021). The encoder and decoder architecture are used in the U-Net model and image segmentation allows automatically detecting the particular objects in the image (Wu et al. 2021). As previously stated, U-Net is largely employed in medical image analysis, not only for image segmentation but also for computed tomography image reconstruction (De Carvalho et al. 2022). In the area of nondestructive testing (NDT), the U-Net was also utilized by using image segmentation to extract the defect from X-ray images (Liu and Kim 2022), to locate the defect with step-heating thermography for composite laminates (Pedrayes et al. 2022), to reconstruct ultrasonic images for curved parts and ultrasound reflection tomography images (Almansouri et al. 2019; Mei et al. 2021). Moreover, the U-Net architecture is famous for the application of the ready frameworks model as an encoder and a decoder(Costa et al. 2021). Particularly EfficientNet is a convenient architecture that can be adopted as an encoder of the U-Net architecture and allows it to reach higher accuracy within the limited number of the dataset (Nguon et al. 2022; Sharma et al. 2023).

Meanwhile, transfer learning enables the enhancement of prediction accuracy by transferring information from different models with huge datasets (Mushtaq et al. 2021). Therefore, the purpose of transfer learning is to enhance accuracy while utilizing fewer computational resources (Hussain et al. 2019; Zhuang et al. 2021). In addition, transfer learning has been applied for classification and segmentation in computer vision. In the case of image segmentation, transfer learning allows getting better predictions. The transfer learning technique was implemented in U-Net deep learning architecture for breast tumor cell nuclei segmentation in histopathology images and segmentation of COVID-19 CT images (Le Dinh et al. 2021; Wang et al. 2021). In addition, transfer learning can be applied to a range of applications by using pre-built architectures like EfficientNet as the encoder in U-Net models (Wang et al. 2021). The application of transfer learning for segmentation purposes has extended beyond medical images and has been utilized for inspecting materials and detecting flaws in ultrasonic images (Medak et al. 2022), applying EfficientNet as an encoder of U-Net (Wu et al. 2019). The most popular database utilized to train models and extract the pre-trained parameters of these models is ImageNet (Jia Deng et al. 2009). ImageNet is a large-scale image database widely used for transfer learning in deep learning applications. In the context of U-Net architecture, ImageNet has been used to pre-train the encoder part of the U-Net model, resulting in improved segmentation performance for various types of images.

The objective of this research is to improve ultrasonic imaging by eliminating blurred zones in the reconstructed image by the RAPID algorithm. The application of the ultrasonic reconstruction algorithm leads to images with blurred which might cause misclassification presence of defects in structures and makes it difficult to define the real dimension of the defects. In this research, the most sensitive wave mode was chosen based on an analysis of the sensitivity of the Lamb wave to wall thinning. Moreover, the image was processed by a deep learning algorithm such as U-Net. Applied U-Net architecture was simplified by using a ready model such as EfficientNet as an encoder. Additionally, the weight of the U-Net architecture was initiated by using transfer learning techniques based on the ImageNet database, which allows for fast and accurate training of the U-Net model to high accuracy even though a limited number of data is present. Through the application of the selected methods, blurred zones of the ultrasonic tomography images were eliminated, and the boundaries of defective zones were clearly defined.

2 Materials and methods

2.1 Lamb waves

The Lamb wave is a guided wave that can propagate for a long distance, which has many advantages over pointwise bulk waves. In contrast to the Rayleigh surface wave, the Lamb wave can be applied to typical structures with a curved shape. Moreover, the Lamb wave has a dispersive property, and it is calculated according to the material properties of the specimen under inspection. The dispersions property of the Lamb waves depends on the material properties and they vary with direction. A CLP has isotropic properties, which means that its material property is independent of the inspection direction. Isotropic properties of materials simplify the Lamb wave dispersion equilibrium equations. The displacement component of a Lamb wave can be separated into symmetric and antisymmetric modes as it propagates through the structure. The characteristic equation of the symmetric mode can be written as follows (Shi et al. 2020):

$$\left( {J^{2} - k_{{}}^{2} } \right)^{2} \tan (Dh) + \left( {4k_{{}}^{2} DJ} \right)\tan (Jh) = 0$$
(1)

Symmetric modes are also known as quasi-extensional modes because they have a dominant wave polarization component along the propagation of the wave. In contrast, antisymmetric modes (or flexural modes) have quasi-flexural behavior, and they can be mathematically defined as follows (Šofer et al. 2021):

$$\left( {J^{2} - k_{{}}^{2} } \right)^{2} \cot (Dh) + \left( {4k_{{}}^{2} DJ} \right)\cot (Jh) = 0$$
(2)

The half thickness of the plate is defined by \(h\) and the wave number is assigned as \(k\) in Eqs. (1) and (2), whereas parameters \(D\) and \(J\) define as unitless quantities based on angular velocity (\(\omega\)). In the following equation \(C_{L}\) and \(C_{S}\) longitudinal and shear wave velocities correspondingly.

$$D = \sqrt {\left[ {\left( {\frac{\omega }{{C_{L} }}} \right)^{2} - k_{{}}^{2} } \right]} \;{\text{and}}\;J = \sqrt {\left[ {\left( {\frac{\omega }{{C_{s} }}} \right)^{2} - k_{{}}^{2} } \right]}$$
(3)

In the experiments, mock-up CLP specimens without concrete were used, and the main concern was the nondestructive detection of thickness reduction in the CLP. The Lamb wave constitutive equation is based on the assumption of uniform plate thickness and traction-free boundary conditions. This model is frequently employed in the detection of defects since variations in plate thickness or boundary conditions significantly alter wave propagation properties. In the case of CLP, the wall thinning occurs in the delaminated zone between CLP and the concrete layer. An important advantage of the Lamb wave is its ability to facilitate ultrasonic testing of large areas. As mentioned earlier, the CLP specimen was made of carbon steel and material property such as the longitudinal and transverse wave propagation speeds were measured as \(C_{L}\) = 5.9 mm/\(\upmu\)s and \(C_{S}\) = 3.2 mm/\(\upmu\)s respectively. Taking into consideration the material properties of the CLP, the phase velocity curve of the Lamb wave derived, and it is shown in Fig. 1.

Fig. 1
figure 1

Phase velocity dispersion curve of the carbon steel CLP

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Phase velocity represents the velocity of the crest of the wave, and its magnitude is defined as \(C_{P} = \omega /k.\) In the case of isotropic materials such as CLP, the magnitude of phase velocity depends only on the wave number. In Fig. 1, symmetric (or extensional) modes are labeled \(S_{n}\), and anti-symmetric (or flexural) modes are labeled \(A_{n}\).

In Fig. 2, the group velocity dispersion curve for the CLP is represented, which determines the propagation speed of wave packets. The Lamb dispersion curve can be classified as dispersive or non-dispersive. The dispersive region of the Lamb wave mode corresponds to the region where propagation speed varies with frequency. Generally, the region where Lamb wave speed does not depend on frequency is called non-dispersive. In the literature, it is often considered that Lamb waves with a lower frequency range are appropriate since only two modes coexist only. In contrast, a Lamb wave at a higher frequency has a multimodal dispersion property, making excitation more challenging.

Fig. 2
figure 2

Group velocity dispersion curve of the Lamb wave

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2.2 Sensitivity

As mentioned previously, the Lamb wave has multimodal and dispersive properties. As a result, determining proper mode selection is crucial for ultrasonic inspection. Depending on the field of the application the different Lamb modes can be selected since each mode has a different level of sensitivity to a certain kind of defect. The sensitivity of the selected Lamb wave mode to wall thinning is essential to obtain precise ultrasonic tomography image of the CLPs. Also, direct evaluation of each mode's sensitivity from the dispersion curve is relatively difficult. Sensitivity analysis allows us to compare the level of sensitivity of different modes to wall thinning. It is obvious from the dispersion curve that wall thinning will affect wave propagation speed. This is because the product of frequency and thickness will be reduced in case of wall thinning. The variation in the time of flight due to wall thinning can be written as follows (Gao and Rose 2010):

$$\Delta t = \int_{0}^{L} {\left( {\frac{1}{{C_{g} + dC_{g} }} - \frac{1}{{C_{g} }}} \right)} {\text{d}}x = \int_{0}^{L} {\int {\frac{{ - dC_{g} }}{{(C_{g} + dC_{g} )C_{g} }}} } {\text{d}}x$$
(4)

From Eq. 4, the expression of the time of flight shifts \((\Delta t)\) is due to the change of the wave propagation speed \((dC_{g} )\) caused by the wall thinning \((dh)\) of the plate as the wave propagates the distance \(L\). Considering the time of flight variation the sensitivity of the Lamb wave mode can be derived (Cheng et al. 2019):

$$S = \frac{ - 1}{{C_{g}^{2} }}\left( {\frac{{{\text{d}}C_{g} }}{{ {\text{d}}h}}} \right)$$
(5)

Considering the dispersion property of the Lamb wave, the sensitivity curve of each mode was derived as a function of the frequency. The sensitivity curve of the Lamb wave modes is nonlinearly proportional to the value of the magnitude of the group velocity and inversely proportional to the amount of wall thinning. Figure 3 shows the sensitivity plots of the Lamb wave modes. As can be observed from the graph, each mode of the Lamb wave has a different level of sensitivity.

Fig. 3
figure 3

Sensitivity curve of the Lamb wave modes

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From the sensitivity plots in Fig. 3, it is shown that the low-frequency range of the mode S0 mode of the Lamb wave for the CLP does not show very high sensitivity due to the fact that it has nondispersive properties. Nevertheless, the sensitivity of the S0 mode increases rapidly as the frequency increases, and the mode dispersion property becomes more noticeable. The sensitivity of the S0 mode reaches its peak at 2.25 MHz*mm. In terms of sensitivity, the S0 mode was the most appropriate for detecting wall thinning on the CLP because it was the most sensitive among the other modes. The excited waveform has a certain frequency band, so concentrating at a single point of the dispersion curve would not be possible. Considering the frequency band of the excited Lamb wave, the 2.35 MHz*mm mode was used in the experiments. Furthermore, in many similar studies, it was found that waveforms with a low group velocity and dispersive properties were most suitable for evaluating wall thinning (Gao and Rose 2010). Ultrasonic tomographic algorithms were performed to analyze the CLP using the sensitive frequency of the S0 mode. In the next section, we will discuss the ultrasonic tomographic algorithm in more detail.

2.3 Ultrasonic tomography algorithms

The main idea behind the RAPID algorithm is that the waveform parameters such as time of flight, phase, and amplitude vary as the defect is present in the structure. In ultrasonic tomographic imaging, sets of pulser and receiver are implemented. Probabilistic reconstruction algorithms are based on the signal difference coefficient \((SDC_{ij} )\) between the measured waveform and the reference signal (measured from an intact specimen). The SDC value can be determined as follows (Li et al. 2019):

$$SDC_{ij} = 1 - \left| {\frac{{\sum\limits_{p = 1}^{n} {[w_{ij} (p) - \mu_{{w_{ij} }} ][m_{ij} (p) - \mu_{{m_{ij} }} ]} }}{{\sqrt {\sum\limits_{p = 1}^{n} {[w_{ij} (p) - \mu_{{w_{ij} }} ]^{2} \sum\limits_{p = 1}^{n} {[m_{ij} (p) - \mu_{{m_{ij} }} ]^{2} } } } }}} \right|$$
(6)

Whenever the specimen is free of defects, the SDC value is zero, while as defect size increases, the SDC value also increases. As we can see in Eq. (6), the SDC value is computed for each set of pulser \(i\) and receiver \(j\). Reference signal from the intact section of the CLP is denoted by \(w_{ij}\), whereas \(m_{ij}\) is waveform from the examining specimen, and the \(\mu\) is the corresponding mean value of the signal. The number \(\begin{gathered} p \hfill \\ \hfill \\ \end{gathered}\) corresponds to the order of an element in the signal vector, which has a length of \(n\). The signal difference coefficients are distributed along the surface in an elliptical shape as shown in Fig. 4. In order to define the ultrasonic tomographic image, the estimated numerical coefficient \(SDC_{ij}\) must be distributed over the plane. This is done by the spatial distribution parameter \((s_{ij} )\) is calculated by:

$$\left\{ \begin{gathered} s_{ij} = \frac{{\beta - R_{ij}^{{}} }}{1 - \beta } \, \quad {\text{for}}\; \, \beta > R_{ij} \hfill \\ s_{ij} = 0 \, \quad {\text{for}}\; \, \beta \le R_{ij} \end{gathered} \right.$$
(7)
Fig. 4
figure 4

Shape parameter’s (\(\beta\)) geometrical interpretation

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In Eq. (7), the \(\begin{gathered} R_{ij} \left( {x,y} \right) \end{gathered}\) is a unitless parameter determined by the ratio of the sum of distances among the pulser (with coordinates \(\left( {x_{i} ,y_{i} } \right)\) and receiver \(\left( {x_{j} ,y_{j} } \right)\) and a point with coordinates \(\left( {x,y} \right)\)). This unitless parameter \(\begin{gathered} \left( {R_{ij} \left( {x,y} \right)} \right) \end{gathered}\) can be expressed as (Wang et al. 2020):

$$R_{ij} (x,y) = \frac{{\sqrt {(x - x_{i} )^{2} + (y - y_{i} )^{2} } + \sqrt {(x - x_{j} )^{2} + (y - y_{j} )^{2} } }}{{\sqrt {(x_{i} - x_{j} )^{2} + (y_{i} - y_{j} )^{2} } }}$$
(8)

Using the calculated \(SDC_{ij}\) parameters, the damage of the sample can be reconstructed by adding local probability values from each pulser-receiver pair. The number of pulser-receiver pairs required depends on the scanning area and the properties of the ultrasonic probe. The \(SDC_{ij}\) is distributed in an elliptical shape over the tomographic image, based on the spatial distribution described in Eq. (7). The dimension of the ellipse is determined by a single coefficient called the shape parameter, which is illustrated graphically in Fig. 4 and expressed numerically in Eq. (9).

$$\beta = \frac{a + b}{c}$$
(9)

According to the literature, there is no predefined method for determining the shape parameter \((\beta )\). It is common for ultrasonic tomography imaging to set the shape parameter at around 1.05 (Zhao et al. 2007). A given value of the shape parameter might cover a wide range of defects because the expression of the shape parameter possesses degrees of freedom. It is also useful to note that the values \(\begin{gathered} R_{ij} \left( {x,y} \right) \end{gathered}\) vary for each pulser and receiver position, whereas the shape parameter is constant and it determines the distribution of the spatial distribution values as expressed in Eq. (7) (Guo et al. 2022).

$$P_{ij} (x,y) = \sum\limits_{i = 1}^{M - 1} {\sum\limits_{j = i + 1}^{M} {SDC_{ij} } s_{ij} }$$
(10)

Damage reconstruction image can be obtained by adding all probability distributions of all pulser receiver sets. With Eq. (10), the reconstruction of tomographic images is possible by summing the probability distribution of the defect from each pulser and receiver. In Eq. (10) the \(SDC_{ij} s_{ij}\) corresponds to the defect probability for a single pulser and receiver pair and \(M\) is the total number of pulser and receiver sets (Hay et al. 2006) so that the reconstructed image pixels are the linear summation of the probabilities.

2.4 Instrumental setup

In the experimental analysis of the ultrasonic inspection of the CLP, the conventional ultrasonic testing setup was applied. The schematic diagram of the ultrasonic instruments can be observed in Fig. 5. The wave signal is excited and received by tone burst (Hay et al. 2006), which enables the setting of several parameters including the center frequency, the number of cycles of the excited waveform, and also the power of the signal. The maximum sampling frequency of the oscilloscope was 40 GHz.

Fig. 5
figure 5

Schematic representation of the instrumental setup for ultrasonic scanning, (a) indicates the CLP and position of the ultrasonic probes, (b) is an ultrasonic wedge, and (c) an image of the wedge and ultrasonic probe

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In the ultrasonic inspection of the CLP, a piezoelectric transducer was used to convert electrical energy to mechanical vibration and vice versa. Piezoelectric elements are known for their high-power transformation efficiency and low acoustic impedance, making them suitable for material inspection (Pramanik and Arockiarajan 2019). In the experiment, three sets of ultrasonic piezoelectric probes were utilized: HAGISONICS M501-SB, Technisonic ABS-000408-GP, and Panametrics NDT A413S. Different probe types were used to account for any variations introduced by the ultrasonic probes and to increase the dataset for the training of the deep learning model. The probes were all piezoelectric and exhibited both wideband and narrowband characteristics. The HAGISONICS M501-SB 0.5 MHz and Technisonic ABS-000408-GP were narrowband probes, and the Panamsetrics NDT A413S was a broadband probe. Despite the use of different probe types, the experimental setup remained without changes for all ultrasonic probes. To obtain a maximum resolution of the ultrasonic tomographic reconstruction algorithm, 16 transducer positions were used to scan each of the sections of the CLP, as shown in Fig. 5a. In each scanned zone of the plate, 160 waveforms were obtained from ultrasonic scanning. The excitation frequency was set to 0.39 MHz, which corresponds to the fundamental symmetric mode (S0) of the Lamb wave. The selected Lamb wave phase velocity was determined using the dispersion curve (as shown in Fig. 1), which was found to be 4.3 mm/μs, while its group velocity was 1.9 mm/μs (derived from Fig. 2). An acrylic angle wedge was adopted to excite the selected Lamb wave mode, and wave propagation speed in the wedge was 2.7 mm/μs. Based on Snell’s law, the wedge angle was calculated, and a 40˚ wedge angle was used during all experiments, as shown in Fig. 5b and c.

3 Results

3.1 Experimental results

Experimental investigations were conducted using the instrumental setup shown in Fig. 5. Ultrasonic tomography imaging was performed over a section of the mock-up CLP specimen shown in Fig. 6, which had dimensions of 2500 × 1400 × 6 millimeters. The specimen contained ten defects of different shapes, but because they occur between the concrete and CLP layers, they cannot be visually detected in real applications. Only one side of the CLP plate had defects, while the backside was defect-free. Ultrasonic scanning of the CLP was performed from the backside, which was free of any structural defects. Additionally, the defects cannot be recognized visually in a real inspection of the CLP because they are located between the concrete structure and the CLP. The S0 mode of the Lamb wave at 2.35 MHz*mm was used in the experiment, and details of the Lamb wave mode selection are described in Sect. 2.1, while the details of the instrumental setup are in Sect. 2.3. To obtain good time–frequency resolution, the exciting wave signal was set to five cycles. When an ultrasonic signal has fewer cycles, it will have a wider band of frequencies in the frequency domain, which increases the chance of exciting nearby modes.

Fig. 6
figure 6

CLP specimen image from the defective side

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The ultrasonic inspection of the CLP specimen was conducted in sections, and defects were identified using the ultrasonic tomographic reconstruction (RAPID) algorithm. The ultrasonic tomographic reconstruction algorithm provides an approximate image of the defects (wall thinning). Waveforms were processed by the method described in Sect. 2.2. For all reconstructed images, the value of the shape parameter was set to 1.05, which is very common for the ultrasonic reconstruction method.

The ultrasonic image of the CLP specimen is shown in Fig. 7, whereas the original image of the CLP specimen is in Fig. 6. The coincidence between the image of the defect and the ultrasonic tomographic image can be obtained by comparing those two figures. As can see in Fig. 7, the ultrasonic tomography image does not clearly illustrate the borders of the defect. This makes it very difficult to determine its size and evaluate its severity. In some fields of application, the size of the defect might have an impact on the decision regarding the condition (whether intact or defected) of the CLP. The defect's shape and dimension become critical since there exists a particular dimension threshold below which the defect is considered as not significant. The blurred part in the ultrasonic tomographic image in Fig. 7 corresponds to an intact area, but the exact shape of the defects cannot be seen from the image due to the gradual change of color. NDT technicians who lack sufficient skill might misclassify blurred zones as defects in the real testing environment. Image processing is necessary to avoid the misdetection of CLP defects. In this case, conventional image processing methods such as binarization may not provide sufficient precision. This is because these blurred zones are caused by nonlinearities regarding the ultrasonic tomographic procedure as well as the experimental instrumentation. Due to the presence of multiple sources of nonlinearity in the system of ultrasonic tomographic imaging methods, the only way to increase accuracy in defect detection is by using artificial intelligence systems. One such method is the U-Net model. In the next section of this chapter, the details of applying the U-Net model for defect segmentation will be described.

Fig. 7
figure 7

Ultrasonic tomographic image of the CLP specimen

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3.2 U-Net architecture

Image segmentation can be used to improve ultrasonic tomographic imaging and to eliminate blurred zones caused by nonlinearity in the ultrasonic inspection method. The U-Net architecture is a powerful technique used for image processing in many fields. There is a wide application of deep learning approaches, such as U-Net in ultrasonic tomographic imaging processing (Lyu et al. 2020). In contrast to other conventional fully connected neural networks, U-Net trains faster and achieves higher accuracy, thereby revolutionizing deep learning for image segmentation. Image segmentation allows the filtering of the image pixels by classifying them into certain groups or segments. In the case of CLP, the tomographic image pixels can be classified as intact and defective areas.

The conventional U-Net architecture is composed of an encoder. Usually, in the encoder part, an input image passes through to the convolution layers, which contain a set of filters or kernels for performing a convolution operation. After the convolution layers, batch normalization is usually performed, and then the activation function is computed. Batch normalization is commonly utilized in order to eliminate noise that may occur after the convolution layers and also provides faster and more stable training results. Moreover, the pooling layer is applied in order to downsize the dimension of the feature maps output from the convolutional layer. The U-Net architecture relies on pooling layers to extract significant structural features from an image.

The second half of the U-Net architecture consists of the decoder, which is used to restore and enhance the spatial resolution of the feature maps. The decoder consists of a set of convolutional blocks that perform up-sampling convolution operations. The up-sampling process doubles the dimensions of all the encoder outputs. Additionally, concatenation can be used to combine the feature maps from the encoder to the decoder. Concatenation plays an important role in preserving information from previous layers, which reflects more strongly on overall values and accelerates model convergence.

Overall, the performance of the U-Net architecture is extremely dependent on the values of its hyperparameters. Hyperparameters are variables that are set by the user to tune and optimize the performance of the U-Net architecture. These hyperparameters include the number of encoder and decoder stages, the number and size of filters, the type of activation function and its values, the learning rate, the batch size, and other parameters that strictly affect the performance of the U-Net architecture. However, tuning the hyperparameters of the U-Net architecture becomes challenging when there is a limited amount of training data. Additionally, tuning the hyperparameters is time-consuming and requires significant computational resources.

The process of building a U-Net model from scratch is very time-consuming and requires sufficient data to guarantee high accuracy. However, as a rule of thumb in literature, there are off-the-shelf architectures that balance the accuracy of segmentation, computational efficiency, and model size. There is a wide range of neural network architectures that can be implemented for this purpose, and in this research, we implement the Efficient Net framework as the encoder of the U-Net model. Efficient Net is a cutting-edge neural network architecture that has achieved exceptional performance on various computer vision tasks, utilizing fewer parameters and computation resources than earlier architectures. The main motivation for selecting the EfficientNet is its flexibility and capability to reach higher accuracy with a limited number of epochs or iterations. Along with Efficient Net, there are many kinds of ready neural network architectures. However, in comparison to other architectures, Efficient Net's training requires less computational resources and is faster. Moreover, many research studies have found that EfficientNet is more effective and accurate than others. This has been observed in various fields such as medical (Zhou et al. 2022; Sharma et al. 2023) as well as engineering (Nguon et al. 2022; Jin et al. 2022).

EfficientNet is employed as an encoder module in the proposed U-Net architecture, as depicted in Fig. 8. The EfficientNet structure can be divided into seven blocks depending on the size of the filters, and different values of channels. The core of each encoder block relies on the Mobile Inverter Bottleneck Convolution (MBConv) layers and that layer can be implemented in different values. It can be seen from Table 1 that the number of the MBConv layer in each block is not the same. Table 1 displays the specifications for each block of the EfficientNet model. Each block has different input and output resolution, different input and output channel dimensions, and a different number of MBConv blocks. The input resolution of the input image is decreased as it moves from block 1 to block 7, while the number of output channels is increased. The number of MBConv blocks also varies among the blocks. Blocks 1, 2, and 7 have 4 MBConv blocks each, while block 3 has 7 MBConv blocks. Blocks 4, 5, and 6 have the most MBConv blocks, with 10 each.

Fig. 8
figure 8

U-Net architecture for image segmentation using transfer learning

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Table 1 EfficientNet encoder part’s blocks structure
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The MBConv block can be decomposed into pointwise and depthwise convolutional layers, as well as squeeze and excitation layers. Figure 9a shows the layer of the MBConv block, where the input data pass through the pointwise convolutional layer, which expands the channels. Then, the channels are reduced in the depthwise convolutional layer. The squeeze and excitation layer focuses on the most important features of the channel. The pointwise convolutional layer is used to reduce the dimensionality of the feature space (Nayak et al. 2022).

Fig. 9
figure 9

a Single MBConv block of the encoder b a “Stage” of the decoder

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The U-Net decoder is composed of multiple stages and utilizes a concentration connection mechanism (as shown in Fig. 8) to transfer features from the encoder to the decoder, which helps to improve the accuracy of the segmentation process. The concentration connection allows the decoder to access features from the corresponding level of the encoder. In other words, this connection enables the decoder to concentrate on and extract relevant information from the encoder's output, which it then uses to generate its own output. The proposed U-Net decoder consists of five stages, and at each stage, up-sampling, convolution 2D, batch normalization, and ReLU operations are performed to refine the feature maps (Fig. 9b).

3.3 Training dataset

Building a U-Net architecture from scratch is very time-consuming and requires sufficient data to guarantee high accuracy. When there is a limited amount of training data, these tasks become even more challenging. Therefore, pre-trained neural networks are commonly used when there is a limited amount of data available as a starting point for a new task, rather than initializing the parameters to be trained from scratch. Moreover, a pre-trained model offers several advantages: The parameters are already optimally tuned based on the different datasets, and the number of layers and hyperparameters does not need to be modified. It is only required to update the weights of a pre-trained model for this particular application. In the literature, this approach is called transfer learning. Transfer learning was employed in the proposed U-Net architecture with the use of an ImageNet dataset. The ImageNet database is a widely used large-scale dataset that comprises over 14 million images, annotated with over 20,000 categories. Additionally, taking advantage of pre-trained models on large-scale datasets such as ImageNet, highly informative features can be extracted from images that can be effectively employed for various downstream tasks.

In the given case, the number of ultrasonic measurements has limited value because most ultrasonic scanning has confidentiality issues, and laboratory-made specimens are exceedingly costly. In this experiment, we employed three sets of ultrasonic piezoelectric probes used equally to scan the CLP specimen and 60 images of defects were captured. The details of the ultrasonic probes were described in Sect. 2.3. It should be noted that the CLP specimen which is shown in Fig. 6 had 10 different types of defects. Overall, 70% (42 out of 60) of the ultrasonic tomographic images of the CLP were used to train the deep learning model, and 30% (18 out of 60) of images were used to test the U-Net model. Due to the limited number of specimens, 70% of the dataset was used to train the U-net architecture. The distribution of the dataset might be analyzed with a larger dataset. Nevertheless, dataset distribution analysis was beyond the scope of this study. The dataset distribution for the U-Net model's training and testing processes is illustrated in Fig. 10, where a subset of the ultrasonic tomography images of the CLP was used for training, and the remaining images were analyzed for testing.

Fig. 10
figure 10

Dataset distribution for the training and testing of the U-Net model

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Figure 11a depicts a picture of a specimen, which measures 2500 mm by 1400 mm. Because the CLP has a large size, a segment of the plate has been used for the typical experiment. Moreover, the “Computer Vision Annotation Tool" was implemented to obtain ground truth images of defects (shown in Fig. 11b). This particular online platform was chosen due to personal preference, but other software options could be used for the same purpose. According to the literature, this strategy of preserving the original shape of the defect is effective in a variety of different fields (Liu and Kim 2022). Similarly, other specimens were utilized to train the U-Net architecture, along with the match of ultrasound tomography and ground truth.

Fig. 11
figure 11

Data processing for training U-Net architecture: a photo of mock-up CLP specimen with the defect; b the ground truth image of Fig. 11a

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3.4 Image processing with U-Net

The proposed U-Net architecture was built on the Google Colab cloud simulation platform, due to sufficient computational resources provided for free. However, in some cases, the U-Net model can also be designed with other conventional IDEs (Integrated Development Environments). The specification of the simulation platform is shown in Table 2.

Table 2 Software specification
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Using the GPU provided by Google Colab, the developed U-Net model was trained using the transfer learning method as well as using real experimental images obtained from ultrasonic tomography. The number of CUDA Cores is also helpful to reduce computation time. In this study, 400 epochs were needed to train the model, and its learning rate was 0.001.

The result of the U-Net segmentation is shown in Fig. 12, where the first column corresponds to the ultrasonic tomographic images from the experimental analysis, and the second column shows the ground truth images (obtained by the image annotation method), which corresponds to the original defect shape. Finally, the third column is associated with the segmented images by the U-Net architecture. It should be noted that the images for testing of the U-Net model were taken from the "Testing dataset" shown in Fig. 10 and were not used to train the U-Net model. The main limitation of the research method is the limited number of datasets for testing and validation. For this purpose, we selected sections of images with single defects as well as with multiple defects from the testing dataset. As a result, different shapes and dimensions of images are produced. Images with large or non-square shapes were compressed to a uniform square view to fit the fixed input size of the U-Net model, which was set at 300 × 300 pixels. In other words, all images in Fig. 12 correspond to the images from the “Testing dataset” in Fig. 10.

Fig. 12
figure 12

Predictions of the test image dataset

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As can be seen from the segmented tomographic images in Fig. 12c, there are no blurred ones, and the edge of the defect can be clearly distinguished. In the case of the ultrasonic tomographic image (Fig. 12a), the gradually varying color makes it difficult to detect the clear location of the defects. Moreover, the segmented image closely resembles the shape of the ground truth image, indicating that the segmentation model has successfully localized the defects in the images with a high degree of accuracy. Despite variations in the shapes of the defects, the segmented images exhibit a high degree of similarity to the original defective images. To assess the accuracy of the segmented tomographic images, we calculated their intersection over union (IoU) metrics (Eq. 11). IoU is a common evaluation metric in image segmentation tasks, and it measures how well the predicted image segmentation map matches the ground truth segmentation map. To calculate IoU, we need to first calculate the intersection \(G \cap P\) and union of the ground truth and predicted image segmentations \(G \cup P\). The intersection is the area where the ground truth and predicted segmentations overlap, and the union is the area where either the ground truth or predicted segmentation exists.

$${\text{IoU}} = \frac{G \cap P}{{G \cup P}}$$
(11)

where G is the ground truth image (Fig. 12b), and P is the predicted segmentation (Fig. 12c). We calculated the IoU for each image in the testing dataset to gain a better evaluation of the performance of our trained model. In this research, the IoU value was determined for each image, and the average of all tested images was taken, which resulted in a prediction of 83.5% for the U-Net architecture.

4 Discussions

This research investigates the method to improve ultrasonic tomographic images by using the deep learning algorithm and selecting the most suitable Lamb wave mode. In CLP, wall thinning is primarily the result of the surrounding environment. Sensitivity curves were used to determine the Lamb wave mode with the highest sensitivity to the defect. Based on the sensitivity curve in Fig. 3, it was found that the S0 mode had the highest sensitivity to wall thinning, particularly at a frequency of 2.35 MHz*mm. Therefore, this mode was used for the experiment, as any change in wall thickness would affect the time of flight of the waveform.

Ultrasonic tomographic imaging algorithm (RAPID) was employed to scan the mock-up CLP specimen from the defect-free side. Although the Lamb wave mode has been optimally selected, a tomographic image shows some blurred zones near defects, as can be seen in Fig. 7. In the case of a blurred ultrasonic image, it is not possible to evaluate the actual shape, and the intact section of the CLP will likely be misclassified as a defective zone or vice versa. Therefore, there is an increased risk of missing the CLP defect. To eliminate the blurred zone of the ultrasonic image, we implemented a U-Net-based segmentation method.

Due to the limited number of available datasets, we used the transfer learning technique using the ImageNet database. Moreover, experimental tomographic images were used to train U-Net, and datasets were collected by using three different kinds of ultrasonic probes with broadband and narrowband properties. The application of three different kinds of ultrasonic probes allowed us to collect 60 images from a mock-up CLP plate. The overall surface of the mock-up CLP specimen was divided into sections and an overall 60 ultrasonic tomographic images were collected, 42 of which were from the “Training dataset” subsection of the mock-up CLP specimen (as shown in Fig. 10) and the remaining 18 images from the “Testing dataset” subsection of the specimen (Fig. 10). Images were divided into a 70% (42 images) and 30% (18 images) ratio, and those image sets were used for training and testing of the proposed U-Net architecture. The photo of the mock-up CLP specimen was processed by an image annotation tool to obtain a ground truth image, as can be seen in Fig. 11b. The performance of the U-Net model was checked with the proposed data distribution by taking images of single, double, and 3 defects. It should be noted that the input image dimension for the U-Net architecture was 300 × 300 pixels. The predicted image by the U-Net architecture was represented in Fig. 11 by comparing the ultrasonic image with ground truth and segmented image by the U-Net architecture. To evaluate the accuracy of the segmentation result, we compared the ground truth and segmented images of the defect using IoU. Despite the limited training data implemented for the U-Net architecture, we achieved high accuracy with an IoU parameter, showing 83.5% accuracy.

5 Conclusions

A method of enhancing the ultrasonic tomographic image was investigated by selecting both the most sensitive Lamb wave mode and by applying the U-Net image segmentation method. According to the experimental results, the following conclusions can be drawn:

  1. 1.

    The CLP's main structural defect is corrosion caused by harsh conditions between concrete and carbon steel plates, resulting in thinning of the walls. The sensitive curve was applied to select the optimal Lamb wave mode for detecting wall thinning, and the S0 mode at 2.35 MHz*mm was found to be the most suitable one.

  2. 2.

    The ultrasonic tomographic image segmentation method is used to process ultrasonic tomographic images that have been reconstructed by applying the optimal Lamb wave mode. This method allows for the achievement of ultrasonic tomographic images without any blurred zones, which are more accurate than images obtained through conventional ultrasonic tomographic scanning methods. These combined techniques can be implemented as an assistant during the ultrasonic tomographic scanning process.

  3. 3.

    An image annotation tool was applied to obtain the ground-truth image of the defects in a mock-up CLP specimen. The ground-truth image of the defects was obtained by image annotation tool using the photo of the mock-up CLP specimen and those images further used to train the U-Net model. Application of the image annotation tool is an effective technique to obtain the ground truth images of defects when a specimen of CLP is available.

  4. 4.

    The U-Net architecture with transfer learning was used for tomographic image segmentation, and EfficientNet was used as the encoder module to achieve high ultrasonic tomography image resolution for better flaw identification. Despite the limited training data used in the U-Net model, relatively high accuracy was achieved. The segmentation accuracy was evaluated using the IoU technique, achieving an average accuracy of 83.5%.