Coating Thickness Estimation Using a CNN-Enhanced Ultrasound Echo-Based Deconvolution

Academic Editors: Miguel Ángel García Izquierdo and Margarita González Hernández Received: 8 September 2025 Revised: 26 September 2025 Accepted: 1 October 2025 Published: 8 October 2025 Citation: Perez-Diego, M.; Thibbotuwa, U.C.; Cortés, A.; Irizar, A. Coating Thickness Estimation Using a CNN-Enhanced Ultrasound Echo-Based Deconvolution. Sensors 2025,25, 6234. https://doi.org/ 10.3390/s25196234 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article Coating Thickness Estimation Using a CNN-Enhanced Ultrasound Echo-Based Deconvolution Marina Perez-Diego 1,2,* , Upeksha Chathurani Thibbotuwa 1, Ainhoa Cortés 1,2,* and Andoni Irizar 1,2 1 CEIT-Basque Research and Technology Alliance (BRTA), Manuel Lardizabal 15, 20018 Donostia-San Sebastián, Spain; [email protected] (U.C.T.); [email protected] (A.I.) 2 Department of Electrical and Electronic Engineering, Tecnun, Universidad de Navarra, Manuel Lardizabal 13, 20018 Donostia-San Sebastián, Spain *Correspondence: [email protected] (M.P.-D.); [email protected] (A.C.); Tel.: +34-943212800 (M.P.-D. & A.C.) Abstract Coating degradation monitoring is increasingly important in offshore industries, where protective layers ensure corrosion prevention and structural integrity. In this context, coating thickness estimation provides critical information. The ultrasound pulse-echo technique is widely used for non-destructive testing (NDT), but closely spaced acoustic interfaces often produce overlapping echoes, which complicates detection and accurate isolation of each layer’s thickness. In this study, analysis of the pulse-echo signal from a coated sample has shown that the front-coating reflection affects each main backwall echo differently; by comparing two consecutive backwall echoes, we can cancel the acquisition system’s impulse response and isolate the propagation path-related information between the echoes. This work introduces an ultrasound echo-based methodology for estimating coating thickness by first obtaining the impulse response of the test medium (reflectivity sequence) through a deconvolution model, developed using two consecutive backwall echoes. This is followed by an enhanced detection of coating layer thickness in the reflectivity function using a 1D convolutional neural network (1D-CNN) trained with synthetic signals obtained from finite-difference time-domain (FDTD) simulations with k-Wave MATLAB toolbox (v1.4.0). The proposed approach estimates the front-side coating thickness in steel samples coated on both sides, with coating layers ranging from 60 µ m to 740 µ m applied over 5 mm substrates and under varying coating and steel properties. The minimum detectable thickness corresponds to approximately λ/ 5 for an 8 MHz ultrasonic transducer. On synthetic signals, where the true coating thickness and speed of sound are known, the model achieves an accuracy of approximately 8 µ m. These findings highlight the strong potential of the model for reliably monitoring relative thickness changes across a wide range of coatings in real samples. Keywords: coating thickness estimation; deconvolution modelling; CNN; ultrasound pulse-echo 1. Introduction The rapid expansion of offshore wind energy, which foresees an increase in capacity of 380 GW over the next ten years [ 1 ], has intensified the demand for reliable corrosion protection systems capable of withstanding harsh marine environments. Protective coatings applied to steel turbine structures serve as essential barriers against corrosion; however, they are subject to accelerated degradation from prolonged exposure to ultraviolet (UV) Sensors 2025,25, 6234 https://doi.org/10.3390/s25196234 Sensors 2025,25, 6234 2 of 26 radiation, saltwater immersion, and mechanical stress in the marine environment. As a result, the offshore energy sector is increasingly prioritising coating integrity monitoring as an emerging research focus, particularly for detecting early-stage degradation or failure where the coating remains visibly intact but has lost its protective functionality. Even when coatings are well adhered to the substrate, environmental exposure can gradually compromise their effectiveness [2,3]. Monitoring coating degradation is important across various industries, particularly those exposed to harsh and demanding environments. This challenge becomes even more complex when coatings are applied to hard-to-access locations, such as offshore structures, where continuous and reliable monitoring is critical. Current non-destructive testing (NDT) techniques such as ultrasonic, eddy current, magnetic, and optical methods are widely used for coating thickness measurement in industrial settings [ 4 – 6 ]. These established methods reliably assess whether a protective coating meets design specifications in terms of uniformity and applied thickness. However, monitoring coating degradation over time presents a more complex challenge. Early-stage degradation often involves subtle changes in material properties, surface conditions, or barrier integrity that may not immediately affect thickness or be detectable by conventional means. In particular, changes in coating properties caused by exposure to harsh environments—for example, marine or industrial conditions—can alter acoustic properties, including the speed of sound, or lead to partial breakdown of the coating. These changes can be detected indirectly through thickness-related measurements. Tracking such relative changes in coating thickness and acoustic response over time can therefore provide valuable insights into the onset and progression of degradation. However, this line of research is still emerging, and more field-relevant experimental data are needed to understand how coatings physically evolve in challenging environments and how these changes affect the assessment of material properties via ultrasonic or other NDT methods. To address this, more advanced and sensitive approaches are needed, which are capable of observing subtle relative changes in signals over time, where recurring or evolving patterns can reveal the earliest indications of coating degradation. This paper presents our work investigating the potential of ultrasound-based nondestructive testing (NDT) to address the challenge of coating thickness detection for monitoring purposes by offering a reliable and non-invasive means of evaluating the condition of protective coatings and the underlying steel. The motivation for our study is to estimate the thickness of the coating layer applied on the opposite side of the sensor in a three-layer structure, where a steel substrate is coated on both sides. The proposed method uses an ultrasound pulse-echo approach that first obtains the reflectivity sequence of the test medium through a deconvolution model developed from two consecutive backwall echoes, followed by enhanced detection of the coating layer thickness in the reflectivity sequence using a 1D convolutional neural network (1D-CNN). 2. State of the Art This section reviews state-of-the-art developments and ongoing research aimed at improving the detection and monitoring of coating deterioration over time. While not all studies focus specifically on coating degradation, deconvolution model approaches have been widely explored in the literature, and more recently, deep learning (DL) frameworks have emerged as promising tools to address the problem of overlapping echoes in ultrasonic NDT. Traditional deconvolution methods, including least squares, Wiener filtering, and minimum variance deconvolution [ 7 ], rely on prior knowledge of the second-order statistics of both the noise and the input signal. Wiener deconvolution is one of the methods com- Sensors 2025,25, 6234 3 of 26 monly used in the literature for analysing ultrasound backscattered signals, particularly to extract the reflectivity sequence that reveals material flaws. Different works were found in the literature that have applied this convolution-based system modelling and Wiener deconvolution in the scope of ultrasound NDT for materials. For example, Wiener filterbased approaches have been applied for detecting crack-like defects, as discussed in [ 8 , 9 ]. Following Wiener filtering, autoregressive spectral extrapolation was applied to extend the system response beyond the inherent bandwidth limitations of piezoelectric sensors to improve the sparse resolution further. The results of these experiments demonstrated the effectiveness of this combined approach in enhancing the interpretability of ultrasonic signals, allowing features that would otherwise be difficult to discern in the unprocessed data to be more clearly resolved. Acoustic noise resulting from scattering by the grains within the propagation medium does not have readily known statistics, and conventional Wiener deconvolution, which is based on second-order statistics, could struggle to accurately estimate the flaw impulse response under poor signal-to-noise ratio (SNR) conditions. Addressing this limitation, the authors of [ 7 ] proposed a deconvolution technique based on higher-order statistics, which has proven to be more effective in such low SNR environments. This ultrasonic model was applied for defect identification using both synthesised ultrasonic signals and real signals obtained from artificial defects. As computational resources become increasingly accessible, CNNs and similar architectures are expected to play a significant role in advancing ultrasonic signal interpretation. To address the challenge of overlapping ultrasonic echoes, several recent studies have explored deep learning (DL) frameworks, aiming to perform deconvolution of overlapping echoes through data-driven learning. However, to the best of our knowledge, the integration of explicit deconvolution models with CNNs remains unexplored in the existing literature. One of the key aspects of a CNN is the training process. To enable accurate learning of a CNN, a large and varied training dataset is essential. This dataset is often generated through finite element (FE) simulations [ 10 – 13 ] that replicate a realistic propagation of ultrasonic waves in a given medium. Simulated A-scans are augmented with realistic experimental noise, extracted from initial calibration scans, to ensure robustness against variability in measurement conditions. Another common way to generate synthetic A-scan signals is to use sparse spike trains [ 14 ], where reflections from different interfaces are modelled as a sequence of discrete impulse events. These signals are then convolved with representative pulse-echo wavelets and added noise conditions approximating real material inspection conditions. To achieve more realistic conditions in synthetic signals, amplitude attenuation, echo dispersion, and phase conversion are incorporated into the modelling process. A few recent studies have explored the use of convolutional neural networks (CNNs) as end-to-end models for deconvolution in ultrasonic signal processing. In [ 13 ], authors proposed to improve axial resolution in ultrasonic testing by using a CNN to separate overlapping echoes, allowing for more accurate estimation of time-of-flight (ToF) and amplitude. The framework was validated experimentally to detect flat bottom holes in an aluminum block with a minimum depth corresponding to λ/ 4 at 2.25 MHz. A CNN-based approach was proposed in [ 14 ] for detecting overlapping ultrasonic echoes trained on simulated data derived from a physics-based echo model. Experimental validation on both simulated datasets and physical phantom samples demonstrated that the proposed network outperforms traditional sparse approximation algorithms, providing significantly improved resolution in layer thickness estimations and exhibiting promising results across various echo overlap scenarios. Notably, the method was demonstrated to detect layer Sensors 2025,25, 6234 4 of 26 thicknesses as thin as 0.1 mm. In [ 12 ], a CNN-based approach was introduced for embedded crack detection within a material. Validation experiments on physical specimens, using A-scan measurements, demonstrated prediction accuracy with average errors of 5.7%, 5.6%, and 8.4% for crack length, location, and orientation, respectively. The evaluated crack sizes, primarily characterised by their length, ranged from 1 mm to 5 mm, representing typical penny-shaped cracks. Sendra et al. (2025) [ 11 ] introduced a novel hybrid architecture combining convolutional neural networks (CNNs) with Transformer neural networks (TNNs) for ultrasonic signal deconvolution. The CNN-TNN architecture outperformed the CNN by a 1.81% success rate and exceeded thresholding methods by 17.5% for detecting minimal depths at 0.5 λ , corresponding to resolutions of approximately 1.32 mm (2.25 MHz) and 0.59 mm (5 MHz) on experimental datasets. A key objective in the proposed methodology is to eliminate the dependency on a reference signal in the deconvolution process—typically required in conventional approaches such as Wiener filter approach for enhancing the sparse resolution of ultrasound responses. To this end, we propose a novel deconvolution model that operates on two consecutive backwall echoes to extract the reflectivity function of the tested medium. The outputs of this model are then processed with a 1D convolutional neural network (1D-CNN) to detect closely spaced reflected impulses within the reflectivity function. The CNN follows the input–output design proposed in [ 14 ], where a one-dimensional input vector encoding overlap information is mapped to an output vector of the same size with smoothed spikes, although with key changes in the synthetic signal generation and with the filters of the architecture adapted to capture the local overlap patterns across the wide range of coating thicknesses in our dataset. In the reference method, synthetic signals consist of a single main backwall echo that sums the contributions from internal layers. They were generated as spike trains with echoes spaced to produce varying degrees of overlap and amplitudes drawn from a controlled range, including both well-separated and closely overlapping reflections, with additive Gaussian noise to achieve a target SNR. However, the methodology proposed by Shpigler et al. [ 14 ] showed limited performance across the wide coating thickness range considered in our study (60 µ m–740 µ m). Furthermore, the synthetic signals generated based on their approach did not provide a good representation of the signals measured on real samples—a limitation successfully addressed in our method using the k-Wave MATLAB toolbox (v1.4.0). On top of that, the synthetic signals generated in our method explicitly contain multiple echoes within the considered sampling window and simulate acoustic wave propagation through three-layer media. Amplitude attenuation is considered by accounting for reflection, transmission, and material-dependent attenuation coefficients in each layer. These multiple backwall echoes, closely resembling real echoes, are important because the CNN is trained to predict the impulses in the reflectivity function derived from two consecutive echoes rather than directly from time-domain signals with overlapping echoes. Furthermore, the proposed deconvolution model isolates the reflectivity sequence of the tested medium corresponding to the coating layer of interest, improving the detection of reflections with enhanced sparse resolution and without relying on a reference signal. Building on this, we propose a hybrid framework that integrates the deconvolution model with a CNN for coating thickness estimation. 3. Proposed Modelling Approach In the pulse-echo mode of ultrasonic testing, the reflected signal y(t) can be modelled in the time domain as a convolution of the measurement system impulse response function to an electrical excitation x(t) (assuming the excitation approximates a delta function), Sensors 2025,25, 6234 5 of 26 the medium’s impulse response h(t) , and with additive noise n(t) [ 7 , 15 , 16 ]. This can be expressed as follows: y(t) = x(t)∗h(t) + n(t)(1) Deconvolution can then be employed to reverse the effect of convolution and obtain an estimate of the impulse response of the medium, h(t) . This impulse response h(t) is a function of time, that represents the characteristics related to the reflections that occur as the sound propagates through the test material in the propagation direction. We refer to this as the reflectivity sequence. If the medium is made up of homogeneous, lossless layers, h(t) will be a sum of impulses, with each impulse’s amplitude determined by the relative change in acoustic impedance between adjacent layers [ 16 ]. The underlying assumption is that the measured pulse-echo signal results from the linear convolution of the reflectivity sequence of the material interfaces with the ultrasonic system’s response. Once we model the system response, considering both the transducer characteristics and wave propagation, the deconvolution operation can be applied to reverse the effects of convolution and extract the reflection impulse response from the material interfaces. In the ultrasound responses from a multilayer material, strong echoes primarily occur at interfaces with significant acoustic impedance differences—the greater the difference, the stronger the reflection. In our study, we focus on steel coated on both sides, as in offshore wind turbine towers, where the relevant interfaces are steel–coating and coating–air. Unlike a bare steel sample, which produces distinct echoes from the steel–air interface, coated samples generate more complex backwall echoes due to overlapping reflections within the layered structure. The degree of overlap depends on coating thickness, sound speed in the coatings, reflection amplitudes, and ultrasonic pulse characteristics such as duration and frequency. Since our goal is to estimate the coating thickness, we apply deconvolution to resolve the partially overlapping steel–coating and coating–air reflections within the main backwall echoes. To do this, we model two consecutive backscattered echoes using a convolution approach (Equation (1)), assuming the measurement system with a single longitudinal transducer is linear and time-invariant. The model establishes a relationship between the two consecutive echoes by incorporating the impulse responses of each echo’s propagation path and the measurement system, treating successive echoes as delayed and attenuated versions of the transmitted signal. We then apply deconvolution to recover the reflectivity function. To our knowledge, this approach has not been previously applied to model two consecutive backwall echoes and estimate the medium’s impulse response without a known reference signal, forming the basis of our deconvolution model for coating thickness estimation. Our experience in ultrasonic testing shows that the measured ultrasonic response can be affected by sensor positioning and contact quality. Factors such as couplant thickness, local surface roughness, and coating application variations can affect the signal. Therefore, each sensor–object contact is treated as an independent measurement channel, and deconvolution is performed on this channel basis without relying on reference signals or baselines from other samples. Therefore, any advanced processing applied to achieve our objectives should account for these channel-specific variations, as reflected in the model we present. 3.1. Model of the Reflection Response of the Medium To establish a theoretical basis for analysing back-scattered echoes from a highly reverberant discrete structure, we first studied the simplest case: a single-layer medium representing a bare steel sample. Figure 1illustrates the reverberation process, showing incident, transmitted, and reflected beams over time. The model assumes a linear, timeinvariant system and a flawless, homogeneous material. Sensors 2025,25, 6234 6 of 26 Figure 1. Ultrasound reflection profile for bare steel. A simplified breakdown of echo generation is as follows: 1. Incident Wave: The transducer emits an ultrasonic pulse into the material. 2. First Echo ( ec1 ): The pulse reaches the back surface of the material, where a greater portion of the energy is reflected back (due to impedance difference), creating the first echo. 3. Subsequent Echoes ( ec2 ): The remaining energy of the original pulse continues to propagate through the material. With each round trip (transmit–receive cycle), additional portions of energy are reflected at the back surface, resulting in successive echoes. In the ultrasound response from a bare steel sample, successive echoes result from multiple reflections at the same interface (steel backwall–air). Each echo represents a round trip of the ultrasonic wave between the transducer and the backwall. Two consecutive received echoes can be expressed using a convolution formulation as follows. First Echo: ec1(t) = x(t)∗hec1(t) + n1(t) Here, ec1(t) represents the first backwall echo reflected in the received signal as a convolution of the measurement system impulse response x(t) with the impulse response of the total propagation path for the first echo hec1(t) , with n1(t) accounting for additive noise. Assuming that the second echo is simply a further propagated and attenuated version of the transmitted signal, and considering x(t) , the measurement system impulse response, hec1(t) , the impulse response of the total propagation path for the first echo, and hec2(t) as the propagation path traversed by the first echo to produce the second echo, we can model the second echo as follows: Second Echo: ec2(t) = x(t)∗hec1(t)∗hec2(t) + n2(t) where ec2(t) represents the second backwall echo as a convolution involving both hec1(t) and an additional term for its own propagation path hec2(t)with additive noise n2(t). Converting these representations into the frequency domain yields: EC1(f) = X(f)×Hec1(f) + N1(f) EC2(f) = X(f)×Hec1(f)×Hec2(f) + N2(f) Here, we assume that the signal has high SNR, meaning that the noise terms N1(f) and N2(f) are relatively small compared to the signal components. Therefore, they are not explicitly carried forward in the next step. Assuming our signal has high SNR, we can approximate the relationship between two consecutive echoes as EC2(f) = EC1(f)×Hec2(f)(2) Sensors 2025,25, 6234 7 of 26 This provides a direct relationship between the first and second echoes, with Hec2(f) representing the additional propagation path that the second echo travels relative to the first echo, and this leads us to: Hec2(f) = EC2(f)×EC∗ 1(f) |EC1(f)|2+K(3) Here, ∗ denotes the complex conjugate and K is a small regularisation term introduced to stabilise the deconvolution process, which implicitly accounts for noise effects. Its purpose is to prevent division by very small values of |EC1(f)|2 , which could otherwise amplify noise and lead to unstable estimates of Hec2(f) . The exact value of K is usually chosen experimentally, based on the noise level present in the measurements. The assumptions we made during this modelling are as follows: • The transducer is inherently band-limited. • Any type of noise present in the system is assumed to be additive. • The incident wave is modelled as a longitudinal plane wave. • The measurement system is assumed to be linear and time-invariant (LTI); therefore, deconvolution techniques can be applied. To obtain Hec2(t) in the time domain, an inverse fast Fourier transform (IFFT) is performed: hec2=IFFT(Hec2) For the bare steel sample, since all echoes propagate solely through the steel, the term hec2(t)corresponds to the medium’s reflectivity function. Next, we extend the analysis to a three-layer medium, with a coating layer on each side of the steel substrate, under the condition that the steel thickness is much greater than that of the coatings and therefore the main consecutive backwall echoes can be clearly separated. Figure 2shows the energy reflection paths for steel samples coated on both sides, where the first and third layers are coatings. The focus is on isolating the propagation paths of the first two main backwall echoes. It is important to note that reverberations within coating layers are not considered in this figure. Figure 2. First two reflecting echoes in a three-layer medium: representing a 5 mm steel sample coated on both sides (the reverberation effects within coating layers are neglected). For the coating media, ec1 and ec2 represent the main backwall echoes, each a composite signal formed by multiple reflections within the layered media. These reflections partially overlap, producing a single, complex event in the received signal. So as to account for transmission and reflection at the boundaries of the multilayered structure, two semiinfinite layers (couplant/transducer and air) are also defined: Sensors 2025,25, 6234 8 of 26 Layer 0: Couplant/Transducer Layer 1: Rear coating Layer 2: Steel Layer 3: Front coating Layer 4: Air The reflections are caused by impedance mismatches at the interfaces, where the impedance of the medium depends on the density and speed of sound: Zk=ρkck(4) where ρk: material’s density [kg/m3] in medium k; ck: speed of sound [m/s] in medium k. Reflection and transmission coefficients at normal incidence, when going from medium k to medium k+ 1, define how the amplitude of the stress or pressure of the elastic wave changes [17]: rk,k+1=Zk+1−Zk Zk+1+Zk , (5) tk,k+1=2Zk+1 Zk+1+Zk . (6) The reflection coefficient rk,k+1 is always less than 1 in magnitude, while the transmission coefficient tk,k+1 can exceed 1 when Zk+1>Zk , corresponding to an increase in the stress or pressure amplitude at the interface. Despite this, the transmitted energy remains physically consistent. The relevant approximate values of these coefficients [ 18 , 19 ] for the three-layer system are listed in Table 1. These coefficients were calculated using relevant acoustic impedance values of each layer. Table 1. Approximate reflection ( rk,k+1 ) and transmission ( tk,k+1 ) coefficients for interfaces between adjacent layers. Only the coefficients of layers that interact in the three-layered system have been considered. Reflection [rij]and Transmission [tij] klayer k+1 layer 0: Couplant/ Transducer 1: Rear Coating 2: Steel 3: Front Coating 4: Air 0: Couplant/ Transducer r01 =0.16 t01 =1.16 1: Rear Coating r10 =−0.16 t10 =0.84 r12 =0.83 t12 =1.83 2: Steel r21 =−0.83 t21 =0.17 r23 =−0.83 t23 =0.17 3: Front Coating r32 =0.83 t32 =1.83 r34 =−0.999 t34 =0.001 To understand the contribution of the ultrasound pulse propagation path to the consecutive echoes measured by the transducer at the top of the sample, we approximate the impulse response of each layer as an ideal delta, assuming linearity and neglecting any possible dispersion: pk=mkδ(t−tk), Sensors 2025,25, 6234 9 of 26 with mk being the mean attenuation in the k -th layer due to propagation, and tk the time it takes for the ultrasound pulse to traverse the layer. Furthermore, at each interface between layers, the pulse amplitude is modified according to the corresponding reflection or transmission coefficient of Equations (5) and (6), respectively. As illustrated in Figure 2, when the ultrasound pulse passes through the layered medium for the first time, the first backwall echo can be approximated as the convolution of the pk responses of all layers traversed by the ultrasound pulse, scaled by the corresponding reflection and transmission coefficients (refer to Equations (5) and (6)) at each layer interface: ec1=t01 t12 r23 t21 t10 p1∗p2∗p2∗p1+t01 t12 t23 r34 t32 t21 t10 p1∗p2∗p3∗p3∗p2∗p1 =t01 t10 t12 t21p1∗p1∗p2∗p2∗r23δ(t) + t23 r34 t32 p3∗p3 Approximate values of reflection and transmission coefficients for the acoustic interfaces in the layer medium are provided in Table 1. Each contribution to the first backwall echo can be approximated as the product of the reflection and transmission coefficients along the corresponding propagation path. Using the reflection and transmission coefficient values provided in Table 1, the two main paths for the first echo have approximate total coefficients: |t01 t12 r23 t21 t10| ≈ 0.266, |t01 t12 t23 r34 t32 t21 t10| ≈ 0.105. These values indicate the relative contribution of the main propagation paths to the first backwall echo in the model. The first path, with a total coefficient of approximately 0.266, is the dominant contributor to the echo, while the second path, with a coefficient of approximately 0.105, contributes less. This indicates that most of the energy in the first backwall echo originates from the reflection at the steel–front coating interface. The impedance mismatch at the steel–rear coating interface is larger than at the rear coating–couplant/transducer interface. Therefore, it can be assumed that most of the energy in the second echo comes from the reflection of the elastic wave at the steel–rear coating interface, characterised by the reflection coefficient r21 (before receiving the first echo), which then propagates again through the layered medium. Consequently, the second echo can be approximated as: ec2=t01 t12 p1∗p2∗p2∗r23δ(t) + t23 r34 t32 p3∗p3 ∗r21 r23 t21 t10 p2∗p2∗p1+r21 t23 r34 t32 t21 t10 p2∗p3∗p3∗p2∗p1 As we can see, the second echo arises from multiple propagation paths, each involving a different sequence of reflections and transmissions. To compare their relative contributions, calculated total coefficients for each path are: C1=|t01 t12 r23 r21 r23 t21 t10|=0.183, C2=|t01 t12 r23 r21 t23 r34 t32 t21 t10|=0.072, C3=|t01 t12 t23 r34 t32 r21 r23 t21 t10|=0.072, C4=|t01 t12 t23 r34 t32 r21 t23 r34 t32 t21 t10|=0.028. The dominant contributor to the second echo is the path associated with C1 , which corresponds to the reflection from the steel–front coating interface without any prior propagation through the coating. The two paths associated with C2 and C3 involve propagation through the front coating and arrive at the transducer at the same time, so their contributions add constructively, enhancing the overall reflection from the front coating. Sensors 2025,25, 6234 16 of 26 the layered medium. Ideally, it should not matter which pair of echoes is selected. However, in practice, each echo may contain reverberation effects and overlapped reflections that are not consistently preserved throughout propagation, which can influence the resulting impulse response. The final synthetic reflectivity signal, consisting of 512 sample points, is used as the input to the CNN. 4.3.4. Ground Truth Definition The ground truth is defined as a spike train, or sparse vector, with two non-zero entries corresponding to the reflective interfaces steel–front coating and front coating–air, based on the impulse response of the test medium defined in Equation (7). For each simulation, the amplitudes are determined by the reflection, transmission, and attenuation coefficients, computed from the defined material properties. Although the incident US excitation pulse is broadband, the frequency dependent attenuation due to propagation is computed using a fixed central frequency of f=8MHz. Since the focus is on the relative amplitude and time separation between the two spikes, the common attenuation is omitted, and the common displacement due to the steel layer thickness is treated as a variable reference parameter from the post-processing stage, t2re f . Therefore, the ground truth is a normalised and displaced version of the theoretical impulse response: hnorm =δ(t−2t2re f ) + m2 3t23 r34 t32 r23 δ(t−2t2re f −2t3). (10) The resulting spike train is smoothed by convolving it with a Gaussian kernel. This transforms the sparse vector into a smoother curve, facilitating the CNN’s learning task while preserving the temporal positions of the echoes, as carried out in [ 14 ]. Finally, the ground truth signal is downsampled to match the 512-sample length of the synthetic signal, so that the spike separation of the ground truth in samples is given by: ToF3(samples) = ToF3(t)×fs=2t3×fs=2d3 c3×125MHz (11) 4.4. CNN-Network A 1D convolutional neural network (CNN) is implemented in Python 3.9.18 using TensorFlow/Keras and following an architecture inspired by [ 14 ]. Instead of explicitly modelling the physical system, the network is designed to implicitly learn the reflectivity response of layered media. All operations in the model are purely convolutional, and the parameters are learned through backpropagation. The output of the network is a smooth impulse train representing the location and amplitude of each echo event. The model is trained to learn the mapping between impulse responses and their corresponding smoothed spike trains, which represent reflection events within a three-layer medium. In this configuration, the rear coating is impedance-matched to the transducer through a couplant. The training dataset consists of synthetic signals generated using kWave simulations. Each sample includes an impulse response (i.e., the reflectivity function) and a smoothed spike train used as ground truth. Signals and targets are flattened, stacked, and reshaped into arrays of shape (N , T ,1 ) , where N is the number of samples, T the number of time steps, and the final dimension represents a single-channel input. The dataset is randomly split into a training set (80%) and a validation set (20%). The CNN architecture is summarised in Figure 6. It consists of six convolutional layers of 32 filters each, all using ReLU activation, followed by a dropout layer and a final convolutional layer. The network uses wide kernels in the early layers to capture Sensors 2025,25, 6234 17 of 26 broad temporal features, followed by progressively narrower kernels in the subsequent layers, with dilated convolutions to increase the receptive field without reducing temporal resolution. This design is important because the model must handle a wide variation of coating thicknesses, and the local patterns corresponding to different thicknesses are difficult to capture with a single filter size. A dropout layer with a rate of 0.2 is included to mitigate overfitting, and the final 1 × 1 convolutional layer maps the features to a one-dimensional smoothed spike train. Figure 6. CNN architecture used for smoothed spike reconstruction. The model is compiled using the Adam optimiser and a mean squared error (MSE) loss function, which is also used as a performance metric. Training is performed with a batch size of 100 and a maximum of 30 epochs. Two callback functions are employed: ReduceLROnPlateau , which reduces the learning rate by a factor of 0.2 if the validation loss plateaus for 12 epochs, and EarlyStopping , which halts training after 20 epochs of no improvement in validation loss, restoring the weights from the best-performing epoch. This architecture effectively captures both the global structure of the signal and localised spike events by combining wide and narrow convolutional receptive fields. The output is a sparse, smooth signal that preserves the temporal structure of reflection events in the simulated media. 5. Results and Discussion The impulse response of the test medium is obtained by post-processing the simulated received pressure signal, which results from propagating the real ultrasound pulse through the material. Therefore, it is important to directly compare both the synthetic, filtered pulseecho signal and the impulse response with the real ones. Figure 7shows the synthetic signal that best matches the real one for that coating type, identified by maximising the crosscorrelation between the synthetic and real signals, as well as between their corresponding impulse responses. The similarity metric in each subfigure, ranging from 0 to 1 (with values closer to 1 indicating higher similarity), is calculated as the absolute maximum of the cross-correlation between the plotted real and synthetic reflection impulse response signals. For the signals plotted here, this metric ranged between 0.90 and 0.94. Sensors 2025,25, 6234 18 of 26 (a)d3(synth)=59.73µm, c3(synth)=2369.88 m/s →ToF3(synth)= 6.30samples |Similarity (real vs. synthetic) =0.94 (b)d3(synth)=88.49µm, c3(synth)=2223.24 m/s →ToF3(synth)= 9.95samples |Similarity (real vs. synthetic) =0.91 (c)d3(synth)=268.97µm, c3(synth)=2807.73 m/s →ToF3(synth)= 23.95samples |Similarity (real vs. synthetic) =0.91 (d)d3(synth)=263.03µm, c3(synth)=2499.41 m/s →ToF3(synth)= 26.31samples |Similarity (real vs. synthetic) =0.90 (e)d3(synth)=630.31µm, c3(synth)=2066.02 m/s →ToF3(synth)= 76.27samples |Similarity (real vs. synthetic) =0.93 Figure 7. Graphical comparison between the real and synthetic echo signals and impulse responses. Sensors 2025,25, 6234 19 of 26 Differences between the simulated and real signals may arise for the following reasons: • Measurement system impulse response and experimental noise. The non-ideal response of the transducer and measurement system cannot be explicitly modelled in k-Wave. In the simulations, the excitation is defined directly as a normal stress with a temporal waveform taken from the first backwall echo of bare steel measurements (one for each steel type, S235 and S355, randomly assigned in the simulations), and spatially modulated with a Gaussian kernel to mimic a focused aperture. Since this reference signal is obtained from pulse-echo measurements in bare steel performed with the same transducer used for the coated samples, it is assumed to capture the effect of the transducer’s impulse response. However, it is not strictly representative of the actual transmitted pulse, and thus remains a simplification. Experimental noise, which refers to random fluctuations in the measurement system—e.g., electrical noise, electronic jitter, and environmental vibrations—is also present in the real signals and cannot be incorporated into the simulation. • Frequency-dependent attenuation and dispersion. k-Wave accounts for frequencydependent attenuation and the corresponding dispersion using a quadratic power-law model ( α(f)∝f2 ). This corresponds to an ideal thermoviscous loss law, which does not always reflect the actual frequency-dependent absorption of real materials. •Homogeneity and isotropy. The simulations assume constant and isotropic material properties within each layer. This is a good approximation for steel, and although the coatings are intended to be uniform, their application process may lead to small variations in homogeneity that are not captured in the model. • 2D approximation. A 2D geometry is used primarily for computational efficiency, as full 3D simulations at the required resolution would be prohibitively expensive. The 2D assumption is a good approximation when the out-of-plane dimension is much larger than the propagation path, as in our case, where the sample thickness is small compared to its lateral area. However, 2D simulations cannot capture out-of-plane scattering, diffraction, or mode conversion, and they confine energy differently than in 3D, which may slightly alter attenuation and energy distribution. • Single-layer coating approximation. In the simulations, the front and rear coatings were modelled as single layers. In contrast, some of the real commercial coatings consist of multiple sublayers. However, the impedance mismatch between these sublayers is assumed to be small, so the dominant contribution to reflections arises from the last sublayer adjacent to air. It is possible that these internal sublayers introduce minor reverberations or phase shifts in the ultrasonic field, but such effects have not been incorporated at this stage. This gap between synthetic and experimental signals is difficult to avoid, as it arises from unknown or non-ideal aspects of the measurement setup that are challenging to emulate and incorporate into simulations. In spite of this, the synthetic signals are considered to contain oscillatory patterns sufficiently similar to those in the real signals, allowing the CNN to recognise these patterns and generalise effectively to unseen data. By closely analysing the synthetic signals in Figure 7, it can be observed that the ground truth does not always align with the most prominent peaks due to the close overlap of reflections or their physical characteristics. For very thin coatings, as in Figure 7a, the overlap is so close that the presence of the coating layer can be difficult to discern. Nevertheless, even for these thin coatings, the reflectivity signal is more oscillatory than that of bare steel, indicating a slight but noticeable overlap. In Figure 7b, for example, the overlap causes partial amplitude cancellation: the local maximum nearest the ground truth second spike is smaller than the subsequent oscillation maxima due to the additive nature of the overlapping reflections. Moreover, the limited bandwidth of the transducer Sensors 2025,25, 6234 20 of 26 and additional reverberations within both coatings create oscillations that make it difficult to extract the actual ground truth visually or with conventional signal processing methods. In contrast, the CNN can learn the local patterns corresponding to the subtle differences in peak amplitude, spacing, and oscillation frequency between the steel backwall and front-coating backwall reflections, enabling the extraction of spikes corresponding to the reflectivity function with higher accuracy. From now on in the manuscript, results are reported in samples, and for better understanding, the corresponding micrometre values are provided using a reference speed of sound of 2500 m/s, so that 1 sample corresponds to approximately 10 µ m, according to Equation (11). For model development, the CNN was trained on approximately 10,000 synthetic signals, with 80% of the data used for training and 20% reserved for validation. After thirty epochs, the model reached a validation mean squared error (MSE) of 5.61 × 10 −5 . The model was first evaluated on predicting the ground truth of 100 unseen synthetic signals, for which the exact thickness and speed of sound of the front coating are known. Some of the predictions are plotted in Figure 8. The ToF, corresponding to the separation between the two main reflection peaks, was computed by performing a parabolic interpolation around each maximum of the smoothed spike train to estimate their true locations, and then calculating the distance between them. The main peak prediction is very well aligned with the ground truth, while the second peak contributes more significantly to the prediction error of the ToF. To illustrate this, the second peak prediction is zoomed in the subfigures. We observe that the model has learned to identify local patterns and avoids detecting the reflection spike corresponding to the coating at local maxima locations when this is not defined in the ground truth. Conversely, when the ground truth defines a reflection at those positions, the model is able to detect it correctly. For example, in Figure 8a, where the overlap is particularly close, the second ground-truth spike does not align with any local maxima of the synthetic signal. Nevertheless, the model predicts it accurately, thanks to training on synthetic signals with similar features and a ground truth capturing the overlap. Table 4summarises the statistical metrics of the ToF prediction errors for the 100 unseen synthetic signals, including absolute mean error (MAE), median, standard deviation (of the MAE), root mean square error (RMSE), minimum, maximum, skewness, and kurtosis. The metrics are computed from the absolute errors, as the distribution of errors shows no systematic positive or negative bias. The positive skewness indicates that most of the prediction errors are concentrated toward the lower end of the range, while the few larger errors appear as outliers. The kurtosis above three suggests a peaked distribution, meaning that the majority of errors are clustered near the median (0.62 samples), and extreme deviations toward the maximum are relatively rare. The model accuracy is reported as RMSE (0.8 samples), which provides a single metric that accounts for both the magnitude and variability of the prediction errors, corresponding to an equivalent thickness error of approximately 8µm (assuming a front-coating speed of sound of 2500m/s). Also, for a clearer visualisation of the prediction errors, the synthetic signals were grouped according to their coating thickness into defined intervals, and the mean absolute errors for each interval are plotted in Figure 9, with the number of signals in each interval indicated above the bars. The results show that the errors are consistent across intervals, reflecting a systematic predictive behaviour across different thicknesses. Only in the penultimate interval is a slightly higher mean error and standard deviation observed; however, since this analysis is based on a set of 100 synthetic signals with 10–15 signals per interval, this variation lies within the expected range. Sensors 2025,25, 6234 21 of 26 (a) ToF3=5.6 samples (∼56 µm) Prediction error = 0.9 samples (∼9µm) (b) ToF3=9.5 samples (∼95 µm) Prediction error = 0.6 samples (∼6µm) (c) ToF3=15.0 samples (∼150 µm) Prediction error = −0.4 samples (∼−4µm) (d) ToF3=23.0 samples (∼23 µm) Prediction error = 1.0 samples (∼10 µm) (e) ToF3=68.8 samples (∼688 µm) Prediction error = 0.2 samples (∼2µm) (f) ToF3=79.0 samples (∼79 µm) Prediction error = 0.7 samples (∼7µm) Figure 8. Ground truth prediction of some synthetic reflectivity signals. Table 4. Statistical metrics of the CNN’s ToF3 prediction errors (in samples), evaluated on 100 synthetic signals not seen during training. MAE Median Std. Dev. (MAE) RMSE Min Max Skewness Kurtosis ToF3error (samples) 0.67 0.62 0.46 0.81 (⇒∼8µm) 0.02 2.40 0.85 3.84 The model’s prediction on synthetic signals constitutes the best-case scenario, as these synthetic signals—although unseen during training—originate from the same simulation process as the training data, unlike the real signals, which are acquired through laboratory measurements. After this evaluation, the model was applied to estimate the unknown front coating thicknesses in nearly 100 real signals. Sensors 2025,25, 6234 22 of 26 Figure 9. Bar plot of the mean absolute prediction error of synthetic signals, grouped by coating thickness intervals. The number above each bar indicates the number of signals in that interval. In the case of real signals, additional small spikes are sometimes predicted, originated from minor reflections that the model cannot consolidate into just two main spikes. However, two main maxima are predicted in all cases. As with the synthetic signal predictions, to compute ToF3 , a parabolic interpolation was applied to the two maxima to refine their locations, and the distance between these points was calculated. This provides an estimated value with subsample resolution, overcoming the limitation imposed by the 125 MHz sampling frequency of the real measurement system. Figure 10 shows the predictions made by the network for one sample from each set, including the ground truth spike train and the ToF3 derived from the spike separation. Correspondingly, Table 5shows the mean predicted front coating thicknesses for all the samples from the different sets. In the laboratory, measurements were performed at different positions on each sample, since the coating thickness may vary along the surface due to non-uniform application. The results are therefore grouped by sample position, with each set–position group including 5 to 11 measurements performed on the same area (top or bottom) of each sample. The values in the table are given in samples and cannot be directly converted to thickness, since the exact speed of sound in the real coatings is unknown. However, assuming a reference coating speed of sound of 2500 m/s, an equivalence of 1 sample ≈ 10 µ m has been applied for comparison with the nominal thickness values provided by the manufacturers. Taking into account that the actual conversion from samples to thickness depends on the coating’s speed of sound, and that the nominal thickness values themselves exhibit some tolerance due to the coating application process, the predictions are well-aligned with expectations. Nonetheless, the actual prediction error cannot be computed as was done for the synthetic signals, because the true thickness of each real sample and the speed of sound in its coating are not precisely known. In some cases, variation in thickness across measurements at the same position of a sample is observed. This was previously noted in the real signals, where differences between reflections in the impulse responses were visually noticeable. Such variation occurs because the signals were collected after measuring the same area multiple times, and the measurement spot may not have been exactly identical each time, meaning that the actual front coating thickness could genuinely differ. Therefore, these variations cannot be attributed to the prediction model’s precision. Sensors 2025,25, 6234 23 of 26 (a) S235-06.02 coupon Predicted ToF3=6.0 samples (∼60 µm) (b) S235-06.03 coupon Predicted ToF3=9.4 samples (∼94 µm) (c) S235-06.04 coupon Predicted ToF3=32.1 samples (∼321 µm) (d) S235-01.04 coupon Predicted ToF3=24.9 samples (∼249 µm) (e) S355-03.02 coupon Predicted ToF3=70.3 samples (∼703 µm) Figure 10. Ground truth prediction of real reflectivity signals from each sample type. The model successfully estimates the coating thicknesses within the expected value range, demonstrating good generalisation to unseen data. This also indicates that the synthetic signals are sufficiently representative of the real signals for accurately predicting the two main spikes from which the ToF3 can be extracted. The maximum tested coating thickness is approximately 740 µ m, while the minimum is around 60 µ m. Given the transducer’s central frequency of ∼ 8 MHz and the reference coating speed of sound 2500 m/s, this minimum corresponds to a detectable thickness slightly below λ/ 5. To further validate the model’s performance on real signals, it would be valuable to test samples with accurately calibrated thicknesses and known sound speeds for each layer. Sensors 2025,25, 6234 24 of 26 Table 5. Statistical metrics of the CNN’s predicted ToF3 values on nearly 100 real signals, grouped by sample ID, test piece, and measurement position. Mean and standard deviation are reported in samples, with the equivalent micrometre values given in parentheses (1 sample ≈ 10 µm ). Nominal coating thickness values are included for reference. Sample ID Test Piece Bottom Top Nominal Mean Std Mean Std (Samples) (Samples) (Samples) (Samples) S235-06.02 021 6.37 (∼64 µm) 0.28 (∼3µm) 6.65 (∼67 µm) 0.09 (∼1µm) 60 µm S235-06.03 031 9.43 (∼94 µm) 0.39 (∼4µm) 9.34 (∼93 µm) 0.48 (∼5µm) 80 µm 039 9.77 (∼98 µm) 0.59 (∼6µm) 10.71 (∼107 µm) 1.08 (∼11 µm) S235-06.04 041 25.62 (∼256 µm) 0.32 (∼3µm) 32.29 (∼323 µm) 0.80 (∼8µm) 278 µm 042 36.59 (∼366 µm) 1.02 (∼10 µm) 34.06 (∼341 µm) 1.59 (∼16 µm) S235-01.04 04 25.12 (∼251 µm) 1.97 (∼20 µm) 24.90 (∼249 µm) 1.79 (∼18 µm) 300 µm S355-03.02 02 70.39 (∼704 µm) 0.60 (∼6µm) 73.88 (∼739 µm) 1.45 (∼15 µm) 630–740 µm 6. Conclusions and Future Work In this paper, a novel CNN-enhanced ultrasound echo-based deconvolution model was developed to estimate the front-side coating thickness in three-layer coated steel samples. By deconvolving two consecutive backwall echoes, the method removes the dependency on the incident ultrasound pulse and provides an estimated reflectivity function that highlights the two main interfaces of interest: the steel–front coating interface and the front coating–air interface. To generate signals with known coating properties and to train the network, 2D k-Wave elastic simulations were used to create synthetic signals. Finally, a 1D-CNN was designed to discriminate the reflections of the steel backwall and the front-coating backwall within the impulse response of the test medium. The model is able to estimate coating thicknesses between 60 µm and 740 µm, with a minimum detectable thickness of about λ/ 5 for an 8 MHz transducer—surpassing resolution levels typically reported in the literature for this frequency. While the exact performance on real signals cannot be precisely quantified due to unknown coating properties, results on synthetic signals demonstrate a thickness prediction accuracy of ± 0.8 samples ( ≈ 8 µ m). Overall, these findings highlight the potential of the model to generalise to experimental data and to serve as a reliable tool for monitoring relative changes in coating thickness. The current model has been validated on 5 mm thick steel, but its principle is expected to extend to thicker substrates, provided sufficient transducer energy compensates for material absorption. Future work could also incorporate multilayer coatings in simulations to account for additional reflections between sublayers, as well as explore different coating properties to enhance the model’s applicability. Moreover, while all signals in this study were obtained with an 8 MHz transducer, extending the model to different centre frequencies and frequency bands would enhance generalisation. Using higher-frequency transducers would improve axial resolution in the micrometre range but reduce penetration depth due to higher material absorption, potentially diminishing the contribution of the coating to the received pulse-echo signal. In addition, the regularisation term in the deconvolution model could be further refined in future work to better suppress the ringing artefacts around the reflectivity impulses in the reflectivity function. This would be particularly beneficial for improving the reliability of detecting impulses in the reflec- Sensors 2025,25, 6234 25 of 26 tivity function for thinner coatings, or when reflections from individual sublayers become somewhat significant in the main ultrasound response. Author Contributions: Conceptualisation, A.C. and A.I.; Formal Analysis, A.I., U.C.T. and M.P.-D.; Funding Acquisition, A.C.; Investigation, A.C., A.I., M.P.-D. and U.C.T.; Methodology, A.C., A.I., M.P.-D. and U.C.T.; Project Administration, A.C.; Software, A.I., M.P.-D. and U.C.T.; Supervision, A.C. and A.I.; Validation, A.C., A.I., M.P.-D. and U.C.T.; Writing—Original Draft, M.P.-D. and U.C.T.; Writing—Review and Editing, A.C., A.I., M.P.-D. and U.C.T. All authors have read and agreed to the published version of the manuscript. Funding: The present research work is part of the WILLOW project, funded by the European Union with GA No. 1011122184. Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union. Neither the European Union nor the granting authority can be held responsible for them. Data Availability Statement: The data supporting the conclusions of this article will be made available by the authors on request. Acknowledgments: The experimental measurements carried out in this research work were possible thanks to the samples produced by Lurederra and by Sintef in the scope of other research projects such as HarshMoP and Watereye, respectively. Conflicts of Interest: The authors declare no conflicts of interest. Abbreviations The following abbreviations are used in this manuscript: NDT Non-destructive testing FDTD Finite-difference time-domain ML Machine learning DL Deep learning ToF Time-of-flight LTI Linear and time-invariant FFT Fast Fourier transform IFFT Inverse fast Fourier transform CNN Convolutional neural network UTB Ultrasound testbed GT Ground truth MSE Mean square error RMSE Root mean square error MAE Mean absolute error References 1. Global Wind Energy Council (GWEC). Global Offshore Wind Report. 2023. Available online: https://www.apren.pt/contents/ publicationsothers/gwec-global-offshore-wind-report-2023.pdf (accessed on 4 April 2025). 2. Song, G.L.; Feng, Z. Modification, degradation and evaluation of a few organic coatings for some marine applications. Corros. Mater. Degrad. 2020,1, 408–442. [CrossRef] 3. Chen, W.; Ma, L.; Li, Y.; Wu, D.; Zhou, K.; Wang, J.; Chen, Z.; Guo, X.; Li, Z.; Chowwanonthapunya, T.; et al. Prediction of coating degradation based on “Environmental Factors–Physical Property–Corrosion Failure” two-stage machine learning. npj Mater. Degrad. 2025,9, 67. [CrossRef] 4. Linshang Technology. Five Measuring Methods of Coating Thickness Gauge. Available online: https://www.linshangtech.com/ tech/tech376.html (accessed on 29 August 2025). 5. Aimil. The Importance of Coating Thickness Gauge in Industrial Applications. Available online: https://www.aimil.com/blog/ importance-of-coating-thickness-gauge-in-industrial-applications/ (accessed on 29 August 2025).