Baseline-free defect detection in CFRP laminates via tri-planar blind-spot U-Nets and ultrasonic wavefields

Abstract

This study presents a baseline-free, self-supervised framework for defect detection in carbon fiber–reinforced polymer (CFRP) laminates using laser ultrasonic guided wave (LUGW) wavefield data. The experimental investigation involves two quasi-isotropic eight-ply laminates with a [0/45/90/−45]_S stacking sequence, each containing an artificial defect made by a centrally embedded square PTFE insert (10×10 mm² and 5×5 mm²) at the mid-plane to simulate local delamination. Data preprocessing includes narrowband temporal filtering centered on the dominant carrier frequency and frame-wise spatial detrending, followed by tri-planar decomposition of the spatiotemporal wavefield volume. Each orthogonal plane is processed independently using attention-assisted blind-spot U-Nets trained through masked-pixel restoration, producing per-pixel posterior means and log-variances. The three probabilistic estimates are fused using a product-of-experts (PoE) model, yielding a unified prediction with calibrated uncertainty. A standardized residual between the observed data and the fused prediction is used to drive adaptive thresholding and morphological post-processing, resulting in coherent delamination masks. The uncertainty-aware fusion strategy effectively down-weights low-information regions and mitigates boundary artifacts. A dual decision criterion based on the area fraction and the mean anomaly score enables robust detection. The proposed pipeline achieves accurate and interpretable delamination localization without reliance on prior knowledge of structural properties, defect presence, baseline measurements, or labeled training data.

Keywords

guided waves delamination ultrasonic imaging CFRP U-Nets

Introduction

Carbon fiber-reinforced polymer (CFRP) laminates are widely used in aerospace, automotive, and energy applications because of their high specific stiffness and strength, design flexibility, and chemical stability.¹ Their multilayered structure, however, makes them vulnerable to manufacturing defects.² Among the resulting damage mechanisms, delamination, that is the localized separation of adjacent plies, can markedly degrade stiffness,³ load-bearing capacity,⁴ and fatigue life,⁵ while generating local stress concentrations⁶ that promote further crack growth and may precipitate premature failure if not detected.

Non-destructive evaluation (NDE) methods are therefore an integral part of the structural health monitoring (SHM) of composites. Ultrasonic guided waves (UGWs) are particularly attractive because they can detect subsurface defects in large areas using relatively few transducers.^7,8 Nevertheless, conventional UGW setups require physical access and contact coupling, which makes inspections of complex geometries and restricted regions more difficult and time-consuming.⁹ In this context, laser ultrasonic guided waves (LUGWs), coupled with scanning wavefield acquisition, provide a contactless alternative. A pulsed laser generates UGWs and the out-of-plane surface response is recorded while the excitation point is raster-scanned across the structure. This approach is ideal for components that are difficult to access, have intricate shapes, or operate in harsh conditions, such as high temperatures, where contact-based methods are impractical.^10–12

Although LUGW scanning provides information-rich spatiotemporal datasets, manual interpretation is slow, costly, and operator dependent. The use of human-defined thresholds and ad hoc filtering introduces subjectivity, and the approach performs poorly when coverage and sampling rates increase.¹³ These constraints are incompatible with autonomous SHM deployments, which require timely and repeatable decisions without continuous human oversight. Automated, objective pipelines are therefore required to process wavefield data in real time and to deliver consistent defect detection. Deep Learning (DL) offers a way to achieve this automation by learning discriminative spatiotemporal patterns directly from the data, bypassing hand-crafted features.¹⁴

A central limitation in DL-based SHM is the limited availability of annotated defect data. Outside of controlled laboratory settings, it is rarely feasible to assemble large, balanced, labeled datasets, which limits the practicality of fully supervised DL pipelines to narrow scenarios involving synthetic or carefully curated labels.^15,16 Unsupervised anomaly detection mitigates this dependency by learning a model of the healthy baseline and flagging deviations as potential defects. However, its reliability depends on the availability of representative baseline data that capture environmental and operational variability.¹⁷ Self-supervised learning complements this approach by exploiting intrinsic data regularities to create pretext tasks that generate informative representations without manual labeling. This benefits downstream detection, localization, and prognostics when labeled defects are unavailable.^18–20

Within DL for image-like data, the U-Net is a seminal convolutional architecture designed to reconcile context and precise localization.²¹ Its encoder–decoder topology, augmented with skip connections, preserves high-resolution spatial information while aggregating multi-scale semantic features. This enables accurate segmentation even when data is limited. U-Net can also accommodate variable input sizes and supports efficient tiling strategies for large images, maintaining resolution without incurring excessive memory costs.²² Together with strong data-augmentation practices, these properties help the model remain effective when labeled samples are scarce.

U-Net was originally introduced for biomedical image segmentation and surpassed contemporary sliding-window convolutional neural networks (CNNs) on the ISBI EM Segmentation Challenge by processing entire images and fusing multi-scale features, thereby improving both accuracy and efficiency.²¹ Since then, U-Net and its 2D variants have become the de facto baseline for medical image segmentation in areas such as computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, retinal imaging, histopathology, and confocal microscopy, where they improve the objectivity and reproducibility of lesion and anatomy delineation.²³

U-Net architectures are widely adopted for segmentation and image analysis in fields beyond biomedicine. In materials science, the study of the microstructure of metals, ceramics, composites, and related systems is crucial for understanding the relationship between microstructure and properties. U-Net enables the automated segmentation of microstructures by delineating phases and features such as grains, precipitates, and pores. It has been used to segment metallography images and accurately identify steel phases in alloy micrographs,²⁴ as well as in electron microscopy of complex microstructures.²⁵ Related applications include defect segmentation in additively manufactured parts, grain identification in polycrystalline microstructures, and analysis of composite cross sections.

In the field of composites, U-Net segmentation has been employed in infrared thermography for the detection of subsurface damage, including impact damage,²⁶ micropores,²⁷ and deep flaws in thick sections.²⁸ In X-ray NDT, U-Nets have been used to segment porosity and delaminations in micro-CT slices of CFRP coupons²⁹ and to delineate pores and cracks in radiographic weld inspection,³⁰ demonstrating high accuracy and good generalization with small datasets.

In the ultrasonic NDT of composites, recent research has employed 2D U-Nets for pixel-wise segmentation of delaminations. The impact-induced delamination in sparse and noisy C-scan data from CFRP laminates was detected using data augmentation and validation on physical scans. This method outperformed threshold-based baselines and produced accurate delamination maps.³¹ Guided wavefield imaging has been employed to achieve delamination segmentation from full wavefield data. This has been achieved by converting Lamb wave measurements into two-dimensional (2D) frequency domain spectra and training a U-Net model to output defect maps. The model has been trained exclusively on simulations.³² To enhance ultrasonic image quality, an image reconstruction pipeline was developed that coupled a VGG encoder with a U-Net decoder for C-scan imaging of curved CFRP components using full matrix capture data. This approach yielded reliable segmentation of small defects.³³

Despite the growing use of U-Net architectures in ultrasonic NDT, most existing approaches rely on supervised learning using manually or synthetically labeled defect maps. These approaches often require task-specific preprocessing, such as frequency-domain transformations or mode selection. These constraints limit generalizability and hinder deployment in real-world SHM scenarios, where defect annotations are scarce, baseline data may be variable, and automation is essential. Furthermore, existing 2D approaches usually operate on single projections (e.g., XY plane of the reference frame or frequency spectra), which can result in the overlooking of spatiotemporal cues that are critical for guided wave interpretation.

To overcome these limitations, this paper proposes a self-supervised, attention-assisted tri-planar U-Net architecture designed for the detection of blind-spot anomalies in ultrasonic wavefields. The model learns directly from spatiotemporal acquisitions using masked pixel restoration and requires no defect labels or handcrafted features. Three orthogonal U-Nets, corresponding to XY, XT, and YT planes of the spatiotemporal reference frame (X, Y, T), are trained to reconstruct corrupted inputs using surrounding context. This enables the system to learn phase-consistent wave propagation patterns across space and time. Attention gates enhance localization and robustness by focusing the estimator on subtle scattering signatures and suppressing redundant wave energy. Residual denoising blocks within each U-Net preserve identity mappings and stabilize training under blind-spot masking, reducing over-smoothing and improving defect contrast. A probabilistic fusion scheme based on the product-of-experts (PoE) combines the three views using their predicted means and log-variances to yield a unified discrepancy map with calibrated uncertainty. Operating entirely in the space–time domain, the pipeline can handle large datasets via tiled inference. It avoids mode filtering or frequency conversion and supports uncertainty-aware thresholding for autonomous decisions. This framework enables fully unsupervised, near-real-time defect detection in high-resolution wavefield scans and offers a viable path towards deployable SHM solutions for composite structures.

Materials, manufacturing, and experimental setup

Materials and samples

Two eight-ply CFRP laminates were fabricated from Toray T700SC/2500 unidirectional prepreg.³⁴ The homogenized lamina properties are listed in Table 1.

Table 1.

Density (ρ), elastic moduli, and poisson ratios of the homogenized CFRP unidirectional ply with a fiber volume fraction of 60% (T700SC/2500 Toray).³⁴

ρ	E₁	E₂ = E₃	G₁₂ = G₁₃	G₂₃	ν₁₂ = ν₁₃	ν₂₃
1530 kg/m³	130 GPa	7.97 GPa	4.80 GPa	2.70 GPa	0.310	0.491

The laminates were manufactured via manual lay-up in a quasi-isotropic [0°/45°/90°/−45°]_S stacking sequence with the 0° fiber direction aligned to the global X-axis. To emulate subsurface delamination, controlled defects were introduced by inserting 0.10 mm-thick square polytetrafluoroethylene (PTFE) films at specified interlaminar interfaces during the manufacturing process. The two quasi-isotropic laminates are identified as QI-1 and QI-2 (QI denotes quasi-isotropic). QI-1 contains a 10 × 10 mm² PTFE insert and QI-2 contains a 5 × 5 mm² PTFE insert, both located at the mid-plane (Z = 0.56 mm).

The laminates were cured via vacuum-assisted hot pressing (see Figure 1(a)). An initial vacuum of −0.08 MPa was applied to evacuate entrapped air and volatiles, followed by consolidation at 8.6 MPa under the press platens. The cure cycle followed the manufacturer’s specifications and comprised isothermal curing at 130°C for 120 min. Each laminate measured approximately 200 × 200 mm² in the plane and 1.12 mm in thickness, comprising eight unidirectional plies, each 0.14 mm thick. Layups and embedded defects are summarized in Table 2. All dimensions and locations are reported in a global (X, Y, Z) reference frame with the origin at the geometric center of the bottom surface.

Table 2.

Quasi-isotropic (QI) plate identifiers and delamination characteristics for each laminate.

ID	Delamination size (X–Y)	Delamination position (Z)
QI-1	10 × 10 mm²	0.56 mm
QI-2	5 × 5 mm²	0.56 mm

Experimental setup

The laminates were inspected using a Laser Ultrasonic Visualizing Inspector (LUVI-CP1, Tsukuba Technology Co., Ltd), which was selected for its high-resolution, non-contact laser ultrasonic guided wave (LUGW) imaging capability.³⁵ The LUVI-CP1 uses a pulsed Nd:YAG source to generate broadband UGWs via thermoelastic transduction. The short, impulsive surface heating generates a wide spectral content that simultaneously excites multiple plate modes.^36,37 This broadband response arises from the rapid heating of the surface, followed by thermal relaxation, which produces mode-rich wavefields suitable for defect detection and characterization.³⁸ To ensure strictly non-destructive operation, the laser fluence was kept below the ablation threshold so that generation remained in the thermoelastic regime. The fixed laser pulse parameters are summarized in Table 3.

Table 3.

LUVI-CP1 (Tsukuba Technology Co., Ltd) default laser pulse characteristics.

Duration	Beam radius	Absorbed energy	Power density
1 × 10⁻⁸ s	0.25 mm	4.4 × 10⁻⁴ J	5.89 × 10¹⁰ W/m²

The LUVI-CP1 operates by sequentially exciting discrete points on an $N_{x} \times N_{y}$ raster and recording the corresponding responses with a fixed receiver, as illustrated in Figure 1(b). By reciprocity, these point-source measurements are equivalent to a scanned-receiver acquisition and are reconstructed as a 2D UGW field on the surface.³⁹ In this study, a 50 × 50 mm² region on the top surface (Z = 1.12 mm) was scanned using a 250 × 250 grid with a spatial resolution of $Δ_{x} = Δ_{y} \approx 0.2$ mm (see Figure 1(b)). This spacing provides ∼10 samples per wavelength for the fundamental antisymmetric $A_{0}$ mode over 0–1.0 MHz, thereby satisfying the spatial sampling requirements necessary for the accurate reconstruction of dispersive fields. The laser incidence angle varied slightly across the scan ( $\approx 4 ° - 5 °$ ). Previous studies have shown that angles <30° have a negligible influence on excitation amplitude, thus preserving spatial uniformity.¹¹

Wavefield reception used a broadband piezoelectric sensor (AE-900S WB, NF Co., Ltd.) with a nominal sensitivity range from 0.1 to 1.0 MHz. The sensor was bonded to the top surface (Z = 1.12 mm), outside the scan area to avoid direct laser interaction while retaining high sensitivity to out-of-plane UGW motion (see Figure 1(c)). The laser operated at a pulse repetition rate of 500 Hz; signals were sampled at a frequency of $f_{s} = 10$ MHz with $N_{t} = 1000$ samples per point. This produced a time window of $T = 100$ µs that captured the direct arrivals while limiting boundary reflections and temporal aliasing.

As UGW propagation in CFRP is directionally dependent, the receiver was repositioned between measurements to vary the propagation–fiber orientation while keeping the excitation grid fixed. Two configurations were acquired per laminate: PA (0°, parallel to X-axis) and PC (90°, parallel to the Y-axis), as illustrated in Figure 1(d). Specimens were supported on soft polyurethane foam to passively isolate ambient vibrations. To improve the signal-to-noise ratio (SNR), four consecutive waveforms were averaged at each grid point. The procedure was repeated for all laminate types and propagation configurations, yielding two cubes per laminate and four spatiotemporal datasets in total. All measurements were performed at a controlled room temperature of 20°C. The relative humidity was not actively controlled during the acquisitions. Each acquisition was organized as a three-dimensional array $W \in R^{X \times Y \times T}$ with spatial axes (X, Y) and time T.

Methodology

A self-supervised, attention-assisted tri-planar, blind-spot defect detection pipeline is proposed for processing ultrasonic wavefield data. The method transforms raw ultrasonic measurements into a structured spatiotemporal tensor, W , which is then processed through a sequence of filtering, learning, and detection stages, as illustrated in Figure 2.

Following the reconstruction of W (Figure 2(a)), preprocessing involves narrowband temporal filtering centered on the excitation carrier frequency, along with spatial detrending to suppress background bias (Figure 2(b)). The resulting wavefield is decomposed into three orthogonal planes, XY (plan view), XT, and YT (space–time cross-sections), to capture both spatial and temporal features (Figure 2(c)). Each of these planes is analyzed independently using a dedicated 2D U-Net model trained in a blind-spot regime (Figure 2(d)). These networks output both denoised wavefield estimates and pixel-wise uncertainty quantification. The plane-wise outputs are then integrated using a robust PoE fusion mechanism to produce a joint posterior characterized by a fused mean and log-variance (Figure 2(e)). This fusion yields a volumetric anomaly score, from which spatial and space–time defect maps are derived.

Post-processing (Figure 2(f)) involves denoising, morphological filtering, and adaptive thresholding to generate the final binary defect mask. The following sections provide detailed descriptions of each pipeline component, including the preprocessing strategy, the U-Net architecture, the PoE fusion approach, and the generation of defect maps.

Preprocessing

The raw ultrasonic acquisition was decoded and reshaped into a volumetric wavefield, $W \in R^{X \times Y \times T}$ , where X, Y, and T denote the spatial and temporal dimensions of the scanning grid and the acquisition duration, respectively. A series of preprocessing steps were applied to enhance the signal quality, reduce artifacts, and prepare the data for learning.

A representative Power Spectral Density (PSD) was estimated to identify the dominant frequency content of W . This was computed within a centered region of interest (ROI) measuring 124 × 124 pixels, corresponding to 24.8 × 24.8 mm in physical space. A real-valued Fast Fourier Transform (FFT) was applied to each pixel in the ROI along the temporal axis, and the resulting periodograms were averaged spatially to produce a single PSD estimate. The peak frequency $f_{peak}$ was identified as the maximum of the PSD. A narrow passband centered at $f_{peak}$ was then defined with a bandwidth of $w = 0.2 f_{peak}$ , padded by an 8% guard region on both sides, and clipped to the Nyquist interval.

Temporal bandpass filtering was performed independently on each trace in W using a real-valued FFT-based approach. The FFT was computed for each temporal signal, and the spectrum was multiplied elementwise by a raised-cosine mask that transitions smoothly between the passband and stopband. The inverse real FFT was then applied to reconstruct the filtered trace. As the mask was real and symmetric, the resulting filter exhibited zero phase distortion and no group delay.

After bandpass filtering, each temporal frame was spatially detrended to eliminate low-frequency spatial bias. This was achieved by subtracting a Gaussian-blurred version of each frame, where the spatial smoothing kernel had a standard deviation of $σ = 2$ pixels in both the X and Y directions. No smoothing was applied along the temporal dimension to preserve the fine-scale structure of the wavefield.

Tri-planar modeling

To leverage the structural anisotropy of ultrasonic wavefields, the preprocessed wavefield W is transformed into a set of three orthogonal 2D slices: a spatial (XY) and two space–time planes (XT and YT). These views capture complementary aspects of the wavefield. The XY slices preserve spatial localization at fixed times, while the XT slices and YT slices reveal temporal propagation patterns along horizontal and vertical cross-sections, respectively. Each plane is processed independently using a dedicated model, enabling plane-specific feature learning and localized denoising.

The XY network ingests full spatial frames of shape $(X, Y, 1)$ , which correspond to a single time index. In contrast, the XT and YT networks operate on space–time slices of shape $(X, T^{'}, 1)$ and $(Y, T^{'}, 1)$ , respectively, where $T^{'}$ denotes the temporal window length.

For XT/YT, $T^{'}$ (and the inference window length $L$ ) was chosen to satisfy two requirements: (i) compatibility with the architecture’s temporal downsampling schedule and (ii) sufficient temporal context to include both the direct arrival and the early wave–defect interaction interval. The XT/YT encoders perform asymmetric pooling with a temporal stride of 4 across three downsampling stages (consistent with a depth-4 U-Net), yielding an overall temporal downsampling factor of $4^{3} = 64$ . Accordingly, $T^{'}$ was selected as a multiple of 64 to avoid fractional feature-map sizes. In this study, $T^{'} (= L)$ was set to 512 frames, and inference employed overlapping windows with stride $S = 384$ frames (i.e., 128-frame overlap) to mitigate window-boundary artifacts. When necessary, the final window was zero-padded to satisfy architectural constraints and subsequently cropped to restore the original dimensions after prediction.

During training, slices are randomly sampled along their indexing dimensions. To facilitate inference on long sequences, XT and YT predictions are computed in temporally overlapping chunks, which are then cropped and reassembled to preserve continuity and avoid edge artifacts.

Network architecture

Blind-spot U-Net backbone per plane

Each orthogonal view of the ultrasonic wavefield (XY, XT, and YT) is processed by an independent 2D U-Net architecture adapted for blind-spot learning. The backbones use an encoder–decoder topology with symmetric skip connections augmented by lightweight residual denoising blocks and are trained to reconstruct masked regions from surrounding spatial or spatiotemporal context. The tri-planar decomposition enables specialization: the XY model learns from instantaneous spatial patterns (e.g., wavefront morphology), while the XT and YT models capture directional propagation dynamics along the temporal axis.

The encoder comprises two downsampling stages that use plane-specific max pooling factors. The XY model, illustrated in Figure 3, employs isotropic strides of 2 × 2, reflecting the balanced resolution of the spatial plane. In contrast, the XT and YT models use asymmetric pooling strides of 2 × 4 to increase temporal compression and to extend the receptive field along time. Each encoder block comprises depthwise-separable convolutions with batch normalization and Swish activations. Deeper layers incorporate dilated convolutions to further expand the receptive field without increasing the number of parameters. Dilation rates are symmetric (2, 2) and (4, 4) in the XY model, and asymmetric (1, 2) and (1, 4) in the XT and YT models, favoring temporally elongated contexts. The decoder mirrors the encoder in depth and layout, using bilinear upsampling to restore spatial or temporal resolution. Skip connections preserve fine-grained information by linking encoder and decoder features at corresponding scales. In cases of resolution mismatch due to asymmetric pooling, encoder features are resized via bilinear interpolation prior to concatenation, ensuring proper alignment and preventing reconstruction artifacts.

Notably, the network does not enforce blind-spot constraints through architectural modifications such as masked or asymmetric convolutions. Instead, the blind-spot behavior is imposed entirely at the data level through structured masking during training. This enables the architecture to remain fully convolutional and context-aware, while the optimization process ensures that predictions are based solely on unmasked context.

Attention gates and residual blocks

To enhance feature selectivity, the U-Net backbone incorporates two complementary mechanisms in all planes: attention-gated skip connections and residual blocks.^40,41 These components suppress irrelevant features and allow information to be modulated adaptively across layers.

Attention gates are used for all skip connections between the encoder and decoder stages. Each gate computes a soft, spatially varying relevance mask to modulate the encoder features before merging. The gating mechanism projects both the encoder and decoder features into a shared intermediate space via 1 × 1 convolutions, sums them, applies an ReLU activation, and passes the result through another 1 × 1 convolution followed by a sigmoid function. The resulting attention map $ψ \in {[0, 1]}^{W \times H \times 1}$ is applied elementwise to the encoder feature map before concatenation. This mechanism enables the model to suppress irrelevant activations and focus on semantically salient regions, particularly in later stages when the decoder has access to higher-level context.

To avoid premature suppression of relevant features, the attention logits are neutrally initialized (bias = 0), resulting in initial attention weights close to 0.5. This ensures that most encoder features are transmitted unfiltered during the initial stages of training, enabling the gating mechanism to refine its selectivity as the learning progresses.

In addition, each encoder and decoder stage uses lightweight residual blocks that implement identity-preserving mappings and improve gradient flow. Each block consists of two depthwise-separable convolutions with Batch Normalization and Swish activations, followed by a skip connection that adds the input to the block output. No activation is applied after the residual sum. This design encourages the network to learn corrections rather than full reconstructions, which reduces over-smoothing in undisturbed wave regions and stabilizes training under blind-spot masking, in line with the residual learning principle.

Output parameterization and uncertainty maps

Each network produces two outputs for each input slice: a denoised estimate of the wavefield and a calibrated measure of predictive uncertainty. This dual-output formulation is implemented via parallel 1 × 1 convolutional heads that are appended to the final decoder layer. The first head predicts the posterior mean μ at each pixel, representing the network’s best estimate of the true wavefield under the blind-spot constraint. The second head predicts a raw latent field $β \in R$ , which is transformed into a strictly positive standard deviation via the softplus activation $σ = softplus (β)$ , ensuring $σ > 0$ in a smooth and numerically stable manner. The corresponding log-variance is then computed as $s = \log v = \log (σ^{2}) = 2 \log σ$ . To avoid degenerate uncertainties, particularly during early training or near high-error regions of the input domain, s is clipped to a bounded interval:

s \in [2 \log σ_{\min}, 2 \log σ_{\max}]

(1)

where

σ_{\min} = 10^{- 3}

and

σ_{\max} = 10

. This regularization helps stabilize training dynamics and avoids numerical instabilities in both the loss function and downstream fusion operations.

The predicted log-variance, s, provides a probabilistic measure of reconstruction confidence and is incorporated directly into the masked negative log-likelihood (NLL) loss. It also plays a critical role in the fusion stage, where uncertainty estimates across planes are used to perform a weighted combination of predictions. This output parameterization allows the model to express both aleatoric uncertainty, which arises from inherent signal ambiguity (e.g., due to noise or material complexity), and epistemic uncertainty, stemming from incomplete contextual information induced by the blind-spot masking strategy. The resulting uncertainty-aware formulation supports robust and interpretable predictions in both the denoising and defect detection stages.

Training

Each tri-planar model was trained independently using a self-supervised blind-spot learning framework, wherein the network learns to reconstruct masked regions of an input slice using only the surrounding spatial or spatiotemporal context. This approach eliminates the need for ground-truth labels, as the supervisory signal is derived directly from the corrupted input.

During each training step, a 2D slice is sampled from the XY, XT, or YT plane. A composite masking scheme is then applied to enforce the blind-spot constraint and prevent identity mapping. This includes two to five spatial block masks (7–15 pixels wide), which are randomly placed across the slice, and additional temporal gaps spanning 16 to 48 frames for XT and YT. The resulting masked input is set to zero at the occluded pixels and can be perturbed with additive Gaussian noise. This masking strategy promotes learning across both local and extended contexts. Crucially, only the masked pixels contribute to the training loss. The model minimizes a masked NLL loss under a heteroscedastic Gaussian assumption.⁴² Let $μ_{i}$ and $s_{i}$ denote the predicted mean and log-variance at pixel i, and let $η_{i}$ be the unmasked ground-truth value, the loss is defined as:

L_{N L L} = \frac{1}{\sum_{i} (m_{i} + ε)} \sum_{i} m_{i} \frac{1}{2} [{(η_{i} - μ_{i})}^{2} e^{- s_{i}} + s_{i}]

(2)

where

m_{i} \in {0, 1}

indicates whether pixel i is masked and

ε > 0

is a small constant added for numerical stability to avoid division by zero. This formulation promotes calibrated uncertainty by penalizing both over- and under-confidence.

In addition to the intensity-domain masked NLL, an optional gradient-domain regularizer is introduced to promote spatial edge fidelity by penalizing discrepancies in finite-difference spatial gradients. This term is only applied to XY slices, where the accurate preservation of spatial sharpness (e.g., scattering boundaries and localized discontinuities) is important for subsequent anomaly localization. The term is omitted for XT and YT views for two reasons. First, along the temporal axis, UGW signals are naturally smooth, band-limited oscillatory wave packets; enforcing a spatial-gradient penalty across the time dimension can overemphasize high-frequency components and introduce ringing or seam artifacts. Second, the space–time planes combine axes with different physical units (millimeters vs microseconds), so summing gradient penalties directly across heterogeneous axes is not physically commensurate and can bias optimization toward one axis. Let $\nabla_{x}$ and $\nabla_{y}$ denote the forward finite differences along the two spatial axes of an XY slice. The auxiliary gradient loss is defined as a masked mean squared error (MSE) on gradients:

L_{\nabla} = \frac{1}{\sum m_{i}} \sum_{i} m_{i} ({(\nabla_{x} η_{i} - \nabla_{x} μ_{i})}^{2} + {(\nabla_{y} η_{i} - \nabla_{y} μ_{i})}^{2})

(3)

unlike the intensity-domain NLL term,

L_{\nabla}

acts purely on geometric sharpness and is therefore formulated independently of the uncertainty parameter

s

. The total training objective is

L = L_{N L L} + α L_{\nabla},

with

α = 0.005

controlling the strength of gradient regularization.

To improve robustness and reduce overfitting to acquisition-specific statistics, mild physically plausible augmentations are applied to the target slice prior to masking. These include amplitude scaling, small temporal shifts, limited frequency-domain phase perturbations, and additive noise. Each augmentation is applied with a specified probability and bounded magnitude to preserve signal realism.

Training uses the Adam optimizer with a base learning rate of $3 \times 10^{- 4}$ . A cosine annealing schedule with a linear warm-up adjusts the learning rate from zero to its maximum value and then gradually decreases towards a minimum threshold. Learning rate updates are applied explicitly at each step. Early stopping was applied to the masked NLL objective with a patience value of $p = [150]$ training steps and $δ_{\min}$ value of $[10^{- 5}]$ , that is, training was terminated if the moving-best masked NLL did not improve by at least $δ$ over $P$ consecutive steps. The model weights corresponding to the lowest masked NLL were restored at termination.

Inference and fusion

During inference, the three plane-specific networks are applied independently to the input wavefield volume. Each model operates on 2D slices extracted along its respective plane, with execution taking place in a tiled manner. Inference for the XY model proceeds frame by frame over all time indices $t \in {1, \dots, T}$ , while the XT and YT models are evaluated along the temporal axis using streamed overlapping windows of length $L$ and stride $S < L$ . Overlapping windows are recombined by center-cropping each prediction and stitching only the central region, which suppresses boundary artifacts introduced by padding and receptive-field truncation. The final window is zero-padded as required to satisfy architectural constraints, such as pooling or dilation, and is then cropped back to the original dimensions after prediction. Each network produces two outputs per pixel: the predicted mean $μ$ and the corresponding uncertainty parameter, reported as the log-variance s. These outputs represent a per-pixel Gaussian posterior distribution over the wavefield amplitude, providing a quantification of both the reconstruction and its confidence.

To integrate the three plane-wise predictions into a unified volumetric estimate, a PoE fusion scheme is employed. This approach assumes conditional independence between views and treats each network as a distinct Gaussian expert.⁴³ For each plane $k \in {X Y, X T, Y T}$ , the model provides a mean $μ_{k}$ and a log-variance $s_{k}$ , which together define a Gaussian likelihood. The corresponding precision, which is the inverse variance, is computed as $λ_{k} = e^{- s_{k}}$ . To allow for confidence modulation, a temperature parameter $γ > 0$ is introduced, resulting in tempered precisions: ${\tilde{λ}}_{k} = λ_{k}^{γ} = e^{- γ s_{k}}$ . When $γ = 1$ , the fusion preserves the probabilistic interpretation of the experts’ variances. Values of $γ < 1$ soften confidence differences (more conservative fusion when uncertainty calibration may be imperfect), while values of $γ > 1$ increase selectivity and allows the most confident plane to dominate locally. In this study, $γ = 1.5$ was fixed to balance robustness and selectivity. Assuming a joint Gaussian posterior, the fused prediction is obtained through a precision-weighted combination of the individual estimates. Exploiting the additive property of Gaussian precisions, the fused parameters are computed as:

λ^{*} = \sum_{k} {\tilde{λ}}_{k}, v^{*} = {(λ^{*})}^{- 1}, {μ^{*} = v}^{*} \sum_{k} {\tilde{λ}}_{k} μ_{k}, s^{*} = - \log λ^{*}

(4)

here,

μ^{*}

and

s^{*}

denote the fused mean and log-variance, respectively, and

v^{*}

is the corresponding variance. Numerical safeguards are applied during fusion, including clipping extreme log-variance values and adding a small stabilizing constant

ε

to prevent division by zero.

From the fused prediction, a standardized discrepancy volume $D (X, Y, T)$ is computed to quantify local deviations between the observed signal W and the model expectation:

D (X, Y, T) = \frac{| W - μ^{*} |}{\sqrt{e^{s^{*}} + ε}}

(5)

where

s^{*}

is the fused log-variance and

ε > 0

is a small constant added for numerical stability. This normalized measure expresses deviations in units of fused uncertainty, providing a statistically interpretable anomaly score. High values of D indicate localized departures from the model’s prediction and correspond to regions of potential defect or scattering.

The fusion and discrepancy computations are performed in a streaming manner and are synchronized with the per-plane inference. Overlapping tile boundaries are blended smoothly to minimize edge artifacts, and intermediate maps can be stored in a memory-mapped format to support the processing of large-scale acquisitions. This design ensures that the entire fusion pipeline remains deterministic, memory-efficient and scalable to arbitrarily large spatiotemporal volumes.

Although the experimental inserts were centered to standardize the defect-to-boundary distance and to reduce early boundary reflections within the selected acquisition window, the proposed detector does not require damage to be centered within the scanned ROI. This follows from two design properties: (i) each tri-planar network (XY/XT/YT) is fully convolutional and trained with a masked-pixel restoration objective and (ii) inference is performed locally using tiled (and, for XT/YT, streamed) windows. The anomaly statistic is computed pointwise from the standardized residual between the measured wavefield and the fused PoE prediction. Accordingly, for defects located in the interior of the ROI, the method is approximately shift-consistent; translating the defect primarily translates the residual pattern, rather than changing the underlying decision rule, provided that comparable incident wave energy and SNR are available at that location.

This tiled/streamed inference formulation also supports scalability to large acquisitions and complex components. Peak GPU memory is governed by the per-tile (or per-window) tensor dimensions and network depth, rather than by the full spatiotemporal wavefield volume. Consequently, memory does not grow with the global acquisition size. The computational cost grows approximately linearly with the number of processed tiles and, for XT/YT inference, with the number of overlapping temporal windows required to cover the target extent.

Performance variation with defect location is therefore governed primarily by position-dependent wavefield physics and measurement conditions rather than by the network architecture. In particular: (i) proximity to plate boundaries introduces reflected wave packets that can temporally overlap with defect-scattered components and reduce contrast in the standardized residual; (ii) spatial non-uniformity in excitation/measurement (e.g., energy roll-off across the scan or local SNR gradients) affects both reconstruction fidelity and the predicted uncertainty used in PoE fusion; and (iii) direction-dependent propagation, attenuation, and interference in CFRP can modify the saliency of XT/YT signatures depending on location and propagation direction. The pipeline mitigates these effects via narrowband filtering, frame-wise detrending, uncertainty-aware PoE fusion (down-weighting low-confidence regions), and overlap blending at tile boundaries. However, defects very near ROI edges or in regions dominated by strong reflections may benefit from an extended scan extent and/or time-gating to emphasize first-arrival wavefields.

Post-processing

A lightweight post-processing stage is applied to improve the stability and spatial coherence of the discrepancy map, while preserving physically meaningful wavefield structures.

To suppress impulsive artifacts in the fused discrepancy volume, median filtering is employed as a non-linear denoising step. A small spatial kernel is applied frame-wise, ensuring that edge geometry and structural boundaries are retained.

Defect map construction

Let $D (X, Y, T)$ denote the standardized discrepancy volume obtained after fusion and post-processing refinement. Scalar defect maps are derived via dimensional aggregation:

\begin{array}{l} M (X, Y) = A_{t} [D (X, Y, T)] \\ M (X, T) = A_{y} [D (X, Y, T)] \\ M (Y, T) = A_{x} [D (X, Y, T)] \end{array}

(6)

where

A_{t}

denotes an upper temporal percentile operator, typically

p \in [0.90, 0.99]

, that emphasizes persistent or extreme deviations while attenuating transient anomalies. The operators

A_{y}

and

A_{x}

apply robust percentile aggregation over the respective spatial dimensions. For visualization purposes, the resulting maps are normalized per panel to enhance perceptual contrast; this normalization does not affect subsequent thresholding procedures.

A preliminary binary mask $B_{0}$ is obtained by thresholding the scalar defect map $M (i, j)$ at its $p$ -th percentile, where $p \in (0, 100)$ is the percentile level (default $p = 99.8$ ). Let $c_{p} (\cdot)$ denote the operator that returns the $p$ -th percentile of its input, and $1 {\cdot}$ is the indicator function. The threshold $τ_{p}$ and the initial binary mask are defined as:

τ_{p} = c_{p} (M), B_{0} (i, j) = 1 {M (i, j) \geq τ_{p}}

(7)

To improve the spatial coherence and reduce false positives, the candidate mask $B_{0}$ is refined using the following morphological operations: (i) opening removes isolated speckle, (ii) closing bridges sub-pixel gaps, and (iii) connected-component filtering removes small regions below an area threshold. The result is a topologically coherent, size-controlled mask that improves robustness to noise and tiling seams while maintaining accurate localization for subsequent quantification.

To support autonomous decision-making, two scalar metrics are computed from the final mask B and its corresponding defect map: the defect area fraction $ϕ$ and the mean defect score $δ$ :

\begin{array}{l} ϕ = \frac{a r e a B}{a r e a (s c a n)} \\ δ = \frac{1}{| B |} \sum_{(i, j) \in B} M (i, j) \end{array}

(8)

where

| B |

denotes the number of nonzero pixels in the mask. A detection is declared when both

ϕ \geq ϕ_{\min}

and

δ \geq δ_{\min}

, with default thresholds

ϕ_{\min} = 0.05 %

and

δ_{\min} = 1

. These criteria jointly ensure that detections are spatially significant and exhibit a sufficient discrepancy signal, thereby improving robustness to spurious activations due to noise, small artifacts, or weak outliers.

Results

The results for the two tested specimens are reported using the binary anomaly masks $B$ computed for each of the three orthogonal planes: spatial (XY), spatiotemporal along the X-axis (XT), and spatiotemporal along the Y-axis (YT). These representations provide complementary views of the defect signature in both space and time.

Results for plate QI-1

As detailed in Table 2, plate QI-1 contains a centrally located delamination with in-plane dimensions of 10 × 10 mm², situated at a through-thickness position of $Z = 0.56$ mm.

The results presented correspond to two wave propagation directions PA and PC, parallel and perpendicular to the fiber orientation of the top ply, respectively, as defined in Figure 1(d).

PA direction

Figure 4 shows the training loss curves for the three U-Net architectures for plate QI-1 (PA). The blue curves indicate instantaneous loss and the green curves represent a 50-step moving average. The dashed red lines mark the lowest loss achieved and the orange dotted lines indicate when this minimum first occurs. All models demonstrate rapid initial convergence (within ∼50–150 steps), followed by a plateau with minimal improvements. Among them, the XY U-Net (Figure 4(a)) achieves the lowest loss the fastest, while the XT U-Net (Figure 4(b)) converges more slowly. Furthermore, the plots demonstrate that the early stopping mechanism was successfully triggered in all three experiments, thereby preventing overfitting once convergence was reached.

Figure 5(a) presents the binary anomaly mask $B (M (X, Y))$ , which highlights the regions in the XY plane with the greatest wavefield perturbations. The mask primarily captures the outer boundaries of the delamination, the regions inducing the strongest scattering and wavefront distortion. The anomaly is spatially confined to $X \in [20, 30]$ mm and $Y \in [20, 30]$ mm, which is consistent with the known geometric extent of the defect. The XT plane representation, in Figure 5(b), shown as $B (M (X, T))$ , reveals two nearly horizontal features at $X \approx 20$ mm and $X \approx 30$ mm. These correspond to the vertical edges of the delamination and emerge shortly after wave excitation. Their prompt appearance confirms that the defect is detectable immediately upon interaction with the incident wavefront, suggesting that shorter acquisition durations may suffice for reliable detection.

Similarly, Figure 5(c) depicts the YT view via $B (M (Y, T))$ . Here, the anomaly manifests as an inclined band, reflecting the interaction of the wavefront with the defect along the Y-axis. The spatial separation of approximately 10 mm between the two dominant features corroborates the lateral extent of the delamination. The most pronounced interaction occurs within the first 10–20 µs after the wavefront arrives, during which constructive interference between the incident and scattered waves is most evident.

PC direction

Figure 6(a) presents the binary anomaly mask $B (M (X, Y))$ in the XY plane. The response localizes into two narrow, vertically oriented clusters centered at approximately $X \approx 20$ mm and $X \approx 30$ mm, with support along Y ranging from $\sim$ 19 to 29 mm. As expected for a delamination, the mask highlights the defect’s perimeter, where the discontinuity in interlaminar stiffness leads to strong wave scattering and mode conversion. The lateral separation in X and the shared extent in Y correspond to an in-plane defect size of approximately 10 × 10 mm², centered near $(X, Y) \approx (25, 25)$ mm.

In the XT view (Figure 6(b)), the mask $B (M (X, T))$ exhibits quasi-horizontal features at $X \approx 20$ mm and $X \approx 30$ mm throughout the 0–100 µs window. These features correspond to the vertical edges of the delamination and become visible immediately after the incident wavefront reaches the defect.

The complementary YT representation (Figure 6(c)), $B (M (Y, T))$ , reveals a band concentrated around $Y \approx 20$ − 30 mm. This is consistent with the expected temporal sweep of the wavefront across the delamination in the Y-direction. The $\sim 10$ mm spacing between the dominant features again matches the nominal size of the defect. The most significant wave–defect interaction occurs within the first $\sim 10 - 15$ µs after the wave arrives, when the incident and scattered wavefields overlap. Additional patches observed at later times likely correspond to reverberations or multiple scattering effects.

Results for plate QI-2

Plate QI-2 contains a centrally located delamination with in-plane dimensions of 5 × 5 mm², positioned at a through-thickness depth of $Z = 0.56$ mm. Results are reported for both wave propagation directions PA and PC.

PA direction

Figure 7(a) shows the binary anomaly mask $B (M (X, Y))$ in the spatial XY plane. The detected anomaly forms a compact cluster centered around $(X, Y) \approx (25, 25)$ mm, with a lateral extent of only a few millimeters in both directions. This localization is consistent with the expected signature of a small delamination, as the anomaly highlights the defect’s perimeter where stiffness discontinuities cause the strongest wave scattering.

In the XT plane (Figure 7(b)), the anomaly mask $B (M (X, T))$ reveals two closely spaced horizontal features at $X \approx$ 25 mm, which correspond to the lateral edges of the delamination. The YT view (Figure 7(c)) displays two narrow horizontal anomaly bands centered at $Y \approx 25 mm$ , with a spacing of roughly 5 mm between the primary features, reflecting the actual defect dimensions. The most significant wave–defect interaction occurs within the first 5–10 μs after wave arrival, when the interference between the incident and scattered fields is at its strongest. This early and sustained visibility suggests that the defect can be detected within the initial portion of the wavefield response without loss of diagnostic information. Additionally, the less pronounced features that appear later in the time window are likely due to scattering phenomena within the plate.

PC direction

A similar trend is observed for the wave propagation PC (see Figure 8), where the position and shape of the delamination are clearly localized across all three orthogonal planes.

Summary of the results

Table 4 reports the sample identifiers, training durations, and inference times for each wave propagation direction and U-Net architecture (XY, XT, and YT). Models were trained on a commercial laptop equipped with an Intel® Core™ i7-11800H CPU and an NVIDIA RTX 3060 GPU (6 GB VRAM). The code was developed in Python using the TensorFlow and Keras libraries.

Table 4.

Training and inference statistics for the three U-Net architectures (XY - XT - YT).

Sample	Direction	Training time	Inference time	Total time	$ϕ$ (%)	$δ$
QI-1	PA	55–359–198 s	85–211–217 s	1201 s	0.702	1.351
QI-1	PC	42–276–253 s	82–201–211 s	1101 s	0.824	1.171
QI-2	PA	55–224–160 s	82–208–205 s	983 s	0.832	1.467
QI-2	PC	70–264–162 s	79–199–206 s	1049 s	0.750	1.550

Training used per-slice mini-batches with automatic mixed precision enabled. Peak GPU memory usage during both training and inference was approximately 6 GB (monitored using nvidia-smi). Since inference is executed in a tiled/streamed manner for XT/YT and frame-wise for XY, the peak VRAM is primarily governed by the dimensions of the tile/window tensor $(H \times W$ for XY and $H \times T^{'}$ for XT/YT), rather than by the size of the full spatiotemporal acquisition volume.

Discussion

Tri-planar signatures and their physical interpretation

The tri-planar decomposition provides complementary evidence about delamination-induced scattering because each view emphasizes a different invariant of the spatiotemporal wavefield. The XY view captures instantaneous spatial morphology, including wavefront curvature, localized phase perturbations, and compact scattering features. In contrast, XT and YT preserve propagation dynamics and therefore encode arrival-time structure, apparent group velocity along the slicing direction and the temporal history of wavefront–defect interaction. In the present results, the XY anomaly maps tend to emphasize the delamination perimeter rather than filling the insert footprint uniformly, which is physically consistent with guided-wave interaction with a stiffness discontinuity. The strongest mismatch relative to a smooth, context-predictable wavefield occurs at defect edges, where abrupt changes in local stiffness promote scattering and mode conversion. Conversely, the defect boundaries manifest as banded structures in XT/YT (often quasi-horizontal and sometimes weakly inclined), representing the intersection of laterally bounded discontinuities with a space–time plane. The onset of these bands indicates the time at which the incident wavefront reaches the defect, while their separation reflects the in-plane defect extent along the corresponding spatial axis. These observations clarify why combining views is beneficial: when one view becomes ambiguous due to interference or reduced contrast, the remaining views can still carry a coherent signature of the same discontinuity.

Propagation-direction effects and anisotropy

Differences observed between PA and PC datasets are expected even for quasi-isotropic laminates because the measured UGW field can remain direction-dependent due to finite stacking, frequency-dependent dispersion, and directionally varying attenuation and interference. Changing propagation direction modifies the statistics of the incident field and the structure of mode superposition. This, in turn, affects the saliency of defect-scattered components relative to the background. In practice, this can manifest as changes in the sharpness and persistence of space–time signatures (XT/YT band contrast and temporal spread) and changes in the spatial localization patterns in XY, particularly once boundary-reflected packets begin to overlap with the primary wave packet. The tri-planar strategy is therefore not only redundant, but also stabilizing: it mitigates the direction-specific weakness of any single view by enabling the fused estimate to exploit whichever plane contains the most informative defect evidence under that propagation condition.

Why uncertainty-aware PoE fusion reduces artifacts and improves robustness

The PoE fusion is not a simple averaging operation, it produces a consensus posterior in which each plane contributes in proportion to its local confidence. Each network outputs a per-pixel mean and log-variance, enabling heteroscedastic uncertainty to increase in regions where reconstruction is intrinsically ambiguous (e.g., low-energy segments, complex interference, or tile-boundary/padding effects). In the PoE formulation, these uncertainties translate into local precisions, meaning that uncertain views are automatically down-weighted, while consistent high-confidence agreement across planes reduces the fused variance and yields a sharper, more stable prediction. This mechanism is particularly relevant for wavefields, where the amount of information can vary significantly over time and space. Late-time reverberations, spatially non-uniform SNR and view-specific tiling artifacts can each produce spurious residual structure if all views are treated equally. By coupling fusion to predicted uncertainty (and tempering it through numerical safeguards), the pipeline suppresses these view- and location-dependent failure modes without requiring plane-specific heuristics. This improves the interpretability and repeatability of the resulting discrepancy maps.

Early-time detectability and operational implications

In all cases, the most salient defect evidence emerges shortly after the incident wavefront reaches the delamination boundary. This is when the incident and scattered components overlap, and the discontinuity induces a high-contrast perturbation relative to the learned context. At later times, the wavefield increasingly exhibits dispersion, attenuation, and multi-path interference, including boundary reflections that can generate structured residuals unrelated to damage and reduce the signal-to-clutter ratio. This temporal evolution explains why the strongest anomaly signatures are concentrated near the first arrival interaction window and why later-time maps may contain weaker or more diffuse activations. The temporal aggregation strategy adopted (using an upper-percentile operator over time) further supports early-time decision-making by emphasizing persistent or extreme deviations while de-emphasizing transient clutter. This suggests that reliable detection may be achievable from temporally truncated acquisitions. From an inspection standpoint, this motivates future reporting of a “time-to-detection” criterion, defined as the earliest time at which the area fraction and mean-score decision metrics cross their thresholds. This would directly quantify the minimum acquisition window required for reliable automated decisions.

Environmental effects and field variability

It is worth mentioning that environmental and operational conditions can influence UGW wavefields through changes in wave speed, dispersion, attenuation, and measurement coupling, which may alter the statistics learned by a self-supervised predictor. While the proposed approach is baseline-free in the sense that it does not require a pristine reference measurement, substantial temperature- or coupling-induced shifts could modify the background wavefield sufficiently to affect the standardized residual distribution and, consequently, threshold-based decisions.

Conclusions

A baseline-free, self-supervised framework was developed to detect delaminations in CFRP laminates using LUGW wavefield measurements. Experiments were conducted on two quasi-isotropic eight-ply [0/45/90/−45] s plates containing centrally embedded mid-plane PTFE inserts (QI-1: 10 × 10 mm²; QI-2: 5 × 5 mm²; Z = 0.56 mm), and data were acquired for two propagation directions (PA and PC).

The proposed tri-planar blind-spot U-Net models, combined through an uncertainty-aware PoE fusion, consistently localized delamination-related scattering signatures without requiring pristine baseline measurements or labeled defect annotations. In all cases, elevated anomaly responses emerged shortly after wave arrival at the defect, indicating that reliable decisions can be derived from early-time segments of the wavefield.

Automated detection was implemented using a dual decision criterion based on defect area fraction and mean anomaly score. Across specimens and propagation directions, measured area fractions ranged from sub-percent values up to approximately 0.8%, with mean anomaly scores between approximately 1.17 and 1.55.

On a laptop-class GPU, end-to-end processing (training and inference across all three planes) required on the order of 10³ seconds per dataset, supporting practical deployment in automated inspection workflows.

While this study validates the framework on flat CFRP coupons with controlled PTFE inserts, extending the evaluation to service-induced defects (e.g., impact delamination, kissing bonds, and porosity) and to curved or stiffened geometries remains a key next step. Such anomalies modify local stiffness and impedance, producing scattering, mode conversion, and phase perturbations that the proposed baseline-free detector is designed to capture as departures from context-predictable propagation. Future work will broaden the scope of experimental validation to include off-center defects, multiple through-thickness locations and non-planar components under more complex boundary conditions. These tests will complement with calibrated numerical wave-propagation models (e.g., Finite Element and Spectral Element method) to generate controlled datasets for systematic sensitivity and robustness studies with respect to defect morphology, location/depth, boundary conditions, and noise.

Footnotes

ORCID iDs

Shain Azadi

Yoji Okabe

Valter Carvelli

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data will be made available on request.*

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