1. Introduction
Non-destructive testing (NDT) for defect detection is a critical area of research, as it enables the evaluation of material integrity without compromising the structural or functional properties of the inspected surfaces [
1,
2].
In [
3], debonding is defined as the process of separation or failure of the adhesive bonds between the layers of a two-layer plate. This phenomenon may arise due to external loads that surpass the strength of cohesive forces between adjacent surfaces. The phenomenon of debonding may be initiated in areas exhibiting imperfect adhesion, and it can propagate as external loads increase, resulting in the formation of a debonded zone.
Numerous works in the literature demonstrate a strong interest in non-destructive analysis of heterogeneous material surfaces using various methodologies. Among these, acoustic analysis has proven to be particularly relevant, as emphasized by several authors. A study by Lago et al. [
4] focused on developing an accurate method for measuring the propagation speed of elastic waves in both homogeneous and non-homogeneous solid materials to evaluate their mechanical properties and associated uncertainties. Wang et al. [
5] provided an overview on NDT of composite materials. They surveyed established NDT techniques—including acoustic emission, ultrasonic testing, infrared thermography, terahertz testing, digital image correlation, X-ray, and neutron imaging—detailing their principles, practices, equipment, benefits, and limitations. Their review emphasized the critical need for robust NDT in composites and concluded that future NDT development will focus on intelligent, automated systems for enhanced accuracy and data processing. Wang et al. [
6] proposed an acoustic technique based on air-coupled ultrasonics as an innovative method for assessing the interfacial integrity of bonded structures.
Acoustic techniques have historically provided valuable information on various systems. In recent years, integration with artificial intelligence (AI), particularly deep learning, has significantly improved the effectiveness and automation of these studies. A remarkable example is the study conducted by Melchiorre et al. [
7], who addressed a deep learning-based solution for the analysis of acoustic emission (AE), a non-destructive method for structural health monitoring. Their work tackled the challenge of accurately identifying the onset time of elastic waves, a critical parameter for the early detection and localization of structural damage. Traditionally, this task has been approached using threshold-based methods, which often lack robustness in noisy or complex signal environments.
Despite the transformative capacity of artificial intelligence in data interpretation, the sensor’s integrity at the point of origin is paramount, defining the ultimate quality of the data underpinning all subsequent analytical endeavors. Consequently, parallel advancements in sensor research remain of significant importance. Hassani et al. [
8] directly addressed this by reviewing recent advances in sensor technologies for NDT and structural health monitoring (SHM) of civil structures. Their comprehensive review systematically evaluated a range of conventional and advanced sensor technologies, considering their suitability for providing optimal input for NDT/SHM systems and accurately assessing structural health. They focused on technologies based on their capabilities, reliability, maturity, affordability, popularity, ease of use, resilience, and innovation. Hassani et al. specifically presented and evaluated sensing techniques including fibre optics, laser vibrometry, acoustic emission, ultrasonics, thermography, drones, microelectromechanical systems (MEMSs), magnetostrictive sensors, and other next-generation technologies.
Consequently, numerous studies have explored how acoustic NDE techniques, synergistically empowered by AI and evolving sensor technology, can revolutionize material analysis through more efficient and accurate data processing.
While valuable progress has been made, many studies in the literature are constrained by their dependence on fixed experimental setups or the need for highly specific characterization of machine learning models for particular applications. This inherent specificity often requires considerable recalibration and effort when transitioning to novel material domains. Consequently, these approaches face significant hurdles in practical, real-world applications where variability in materials, bonding processes, production methods, and surface characteristics is the norm rather than the exception.
To address these limitations, we explore the use of transfer learning as a promising strategy to enhance the robustness of acoustic-based defect detection across different material domains. Transfer learning enables pre-trained models to adapt to new surfaces with significantly reduced training effort and data requirements [
9]. In recent years, transfer learning has demonstrated its effectiveness in various domains, including medical imaging [
10,
11], fault diagnosis [
12,
13], and structural health monitoring [
14,
15].
In this study, we investigate its application in conjunction with PICUS [
16,
17], a cost-effective acoustic analysis device developed for non-destructive surface inspection. PICUS digitizes and automates the traditional tap-test technique [
18] and interprets the resulting acoustic responses to identify subsurface defects, enabling the detection of subsurface defects in a scalable and portable manner. By digitizing and automating this process, PICUS enhances diagnostic precision while minimizing the risk of damage of the material under test.
The contribution of this work is twofold:
Experimental Contribution: We design and implement a dedicated acquisition protocol using the PICUS device to collect acoustic data from two distinct polymeric test objects with controlled sub-surface defects. The specimens differ in thickness and material composition, mimicking realistic variations in composite structures.
Methodological Contribution: We develop a convolutional neural network (CNN) architecture trained on one surface type and evaluate the performance of transfer learning techniques when applied to the second surface. Performance metrics are compared with baseline models trained from scratch.
The remainder of the paper is structured as follows:
Section 2 details the materials, experimental setup, and data acquisition process. In particular,
Section 2.3 describes the neural network architecture and
Section 2.4 the transfer learning strategies employed.
Section 3 and
Section 4 present and discuss the results, including performance comparisons and generalization capability. Finally,
Section 5 summarizes the findings and outlines potential directions for future research.
2. Material and Methods
This study’s methodology follows the processing pipeline in
Figure 1, outlining the main signal processing steps. We initially acquired data from Test Object 1 using the PICUS device to train a convolutional neural network (CNN). This pre-trained model was then adapted via transfer learning with data from Test Object 2, allowing it to generalize effectively to the new domain.
In detail, the two test objects were prepared and fixed on an aluminium cube measuring 200 mm on each side, which served as a rigid backing to prevent the movement of the specimens, as shown in
Figure 2a. The test objects were designed to include intentional air cavities between the bonded polymeric layers to simulate debonding defects. The materials was chosen for their well-known mechanical characteristics [
19]. Test Object 1 is made of poly-methyl-methacrylate (PMMA). Two cavities A and B are modelled by a cylindrical geometry of 50 mm and 25 mm radius and 40 mm height. The plate is 3 mm thick. Test Object 2 shares the same cavity geometry but it is made of poly-vinyl-chloride (PVC) and the plate is 1 mm thick, as shown in the close-up in
Figure 2b.
Table 1 shows the properties of both materials.
The adhesion between the polymeric layers was achieved using a bisphenol A epoxy resin. The initial acoustic data were acquired using the PICUS system from a reference specimen (Test Object 1). These signals were recorded following controlled mechanical excitation of its surface and stored in audio files that formed the basis of Dataset 1. This dataset was used to train a CNN to classify two predefined defect types embedded in the test object structure.
Once the model was trained on Dataset 1, a transfer learning procedure was applied. Specifically, the pre-trained network was fine-tuned using a limited subset of samples from Dataset 2, which was collected from the second specimen with different material characteristics—primarily in terms of thickness and acoustic response. This step enabled the model to efficiently adapt its internal weights to the new domain with minimal data and computational effort.
Following fine-tuning, the adapted model was evaluated on the full Dataset 2, and the results were used for defect classification across the entire surface. The application of transfer learning led to a notable improvement in classification accuracy, confirming the method’s ability to generalize effectively to new materials.
2.3. Proposed Neural Network
Given that the dataset comprises one-dimensional time-series data acquired from the PICUS microphone, which captures localized surface excitations, a one-dimensional CNN was adopted. The 1D CNN architecture is particularly well-suited for this application as it can effectively learn and extract temporal patterns and local dependencies within the signal. By applying convolutional filters along the time axis, the network can capture salient features such as transient events and frequency-related characteristics without the need for manual feature engineering. This enables robust characterization of the underlying physical phenomena directly in the time domain, improving the model’s ability to generalize and accurately interpret the measured signals. The proposed CNN is developed using the Keras deep learning library with a TensorFlow backend. The model is implemented using a sequential architecture. The input layer processes a one-dimensional signal of length 1024 with a single channel. The first convolutional block comprises a 1D convolutional layer with 64 filters, a kernel size of 3, and ’same’ padding, and the ReLU (Rectified Linear Unit) activation function is used to introduce non-linearity followed by batch normalization to enhance training stability and convergence. A max pooling operation with a pool size of 2 is then applied to reduce the temporal resolution and computational cost.
The second block increases the model capacity through a convolutional layer with 128 filters, maintaining the same kernel configuration. This is again followed by batch normalization, max pooling with a pool size of 2, and a dropout layer with a dropout rate of 0.3 to prevent overfitting.
A third convolutional block is added to further enhance the feature extraction capability. It consists of a 1D convolutional layer with 256 filters, followed by batch normalization, max pooling, and a dropout layer with an increased dropout rate of 0.5, introducing stronger regularization at deeper layers.
To transition from convolutional to dense layers, a global average pooling (GAP) layer is employed, which reduces the temporal dimension by computing the average over each feature map. The resulting feature vector is fed into two fully connected layers with 128 and 32 units, respectively, each using the ReLU activation function. A dropout layer (rate = 0.5) is applied after the penultimate dense layer to further reduce the risk of overfitting.
The final output layer consists of a fully connected softmax layer, with 2 neurons (equal to the number of output classes), enabling multi-class classification. The network is trained using the Adam optimizer, and categorical cross-entropy is adopted as the loss function. The learning rate
, the decay rate of the first-moment
, and the decay rate of the second-moment
were systematically varied. The optimal performance was achieved with a learning rate of
, a first moment decay rate of
, and a second moment decay rate of
, consistent with the practical recommendations reported in [
20,
21]. Model performance is evaluated using the classification accuracy metric. The architecture of the proposed neural network is illustrated in
Figure 4, which provides a graphical representation of the structure described above.
To evaluate the inter-class performance of the proposed model, we employed the classification report provided by the
sklearn.metrics.classification_report function [
22]. This report summarizes key performance metrics for each individual class, enabling a detailed analysis of the classifier’s ability to distinguish between different target categories. For each class, the classification report computes the following metrics:
Precision: Defined as the ratio between true positives (TP) and the sum of true positives and false negatives (TP + FN), precision measures the accuracy of the positive predictions for each class. High precision indicates a low false positive rate.
Recall (Sensitivity or True Positive Rate): Calculated as the ratio between true positives (TP) and the sum of true positives and false negatives (TP + FN). Recall quantifies the model’s ability to correctly identify all relevant instances of a given class.
F1-Score: The harmonic mean of precision and recall, providing a balanced measure that accounts for both false positives and false negatives. This metric is particularly useful when dealing with class imbalance.
Support: The number of true instances for each class in the test dataset, indicating the distribution of samples across classes.
In addition to per-class metrics, the report also includes macro, micro, and weighted averages of precision, recall, and F1-score, offering a global view of the classifier’s performance that takes into account either all classes equally (macro), the individual decisions (micro), or the class frequency (weighted).
2.4. Transfer Learning
Transfer learning is a machine learning technique in which knowledge gained while solving one problem (the source task) is leveraged to improve learning performance in a different but related problem (the target task). This can be formally defined through the concepts of domain and task.
A domain
is defined as
where
denotes the feature space, and
is the marginal probability distribution of data
.
Given a domain
, a task
is defined as
where
is the label space, and
is the predictive function to be learned.
In the context of transfer learning, we define
A source domain with an associated source task.
A target domain with a corresponding target task.
Transfer learning aims to improve the performance of the predictive function
in the target domain
, by leveraging knowledge from
and
[
23], even when
In deep learning applications, transfer learning typically involves reusing the parameters
learned from a source model and adapting them to a target model:
where
represents the parameter updates obtained through fine-tuning on the target dataset.
In this study, we adopted a fine-tuning strategy within a transfer learning framework to adapt a pre-trained model to a second, distinct dataset. This approach enables the transfer of knowledge extracted from one or more source tasks to a new learning scenario, thereby enhancing generalization capabilities and reducing the amount of labelled data required for training in the target domain [
23].
Transfer learning, therefore, allows for differences in domains, tasks, and data distributions between training and testing stages, providing a flexible and efficient solution in scenarios where labelled data in the target domain is scarce or expensive to obtain.
Based on the relationship between source and target domains and tasks, transfer learning can be categorized into
Inductive transfer learning: the target task is supervised (i.e., labelled data is available).
Transductive transfer learning (domain adaptation): the source and target tasks are the same, but the domains differ.
Unsupervised transfer learning: neither source nor target tasks have labelled data, focusing primarily on representation learning.
This formalism provides a theoretical foundation for the development and assessment of transfer learning techniques across various application domains. This study leverages a CNN in combination with transfer learning to improve performance on a target task characterized by limited annotated data. Transfer learning in a CNN refers to the reuse of a neural network model trained on a source task to facilitate learning in a different but related target task. This is particularly effective when the source task has access to large-scale labelled data, while the target task suffers from limited annotated samples.
A CNN model trained on the source task learns a set of parameters:
where
represents the weights of the
ℓ-th layer of the CNN with
L total layers.
In transfer learning, the target model reuses the parameters of the first
layers of the source model:
The remaining layers, , are either
The final target model parameters are
with the following:
where
denotes the parameter updates derived from fine-tuning on the target dataset.
This formulation allows the CNN to retain general low-level features (e.g., edges, textures) learned from the source task while adapting high-level semantic representations to the target task. The optimization objective in the target domain becomes
where
is the loss function for the target task (e.g., cross-entropy), and
are the target data and labels.
Transfer learning via CNN is particularly beneficial when but the feature spaces are sufficiently similar to allow knowledge reuse.
This is typically achieved by transferring learned features, model parameters, or data representations from the source to the target. Therefore, this can be considered a paradigm within machine learning where a model, meticulously pre-trained on an extensive dataset for a generalized source task, is subsequently adapted or “transferred” to a distinct yet inherently related target task. This methodology fundamentally deviates from training a model ab initio, which necessitates prodigious volumes of labelled data and computational expenditure. The underlying principle is the leveraging of knowledge encapsulation within the pre-trained model, specifically its learned hierarchical feature representations and optimized parametric values (weights and biases), to expedite and enhance learning on the target task, particularly when target-specific labelled data is scarce. The technical mechanisms of knowledge transfer unfold in a gradient-driven fashion. A pre-trained deep neural network, often a CNN for computer vision or a Transformer-based architecture for Natural Language Processing (NLP), serves as the foundational architecture. These models, having been exposed to vast and diverse datasets, develop robust internal representations. Early layers of such networks tend to learn universal, low-level features—such as edge detectors, gradient orientations, or basic n-gram patterns—which are largely invariant to the specific downstream task. Deeper layers progressively synthesize these low-level features into more abstract and semantically rich representations, ultimately becoming more task-specific. In feature extraction, the base or convolutional embedding layers of the pre-trained model, which are responsible for extracting salient features, are treated as fixed and untrainable components. Their learned weights are “frozen,” meaning they are not updated during backpropagation to the new target dataset. The output of these frozen layers, essentially a high-dimensional feature vector, then serves as input to a newly added, task-specific “head” (e.g., a fully connected classifier) that is randomly initialized and trained from scratch on the target data. This method is computationally efficient, as only newly added layers require gradient computation and weight updates, effectively using the pre-trained model as a powerful general-purpose feature extractor [
24].
Fine-tuning, a more sophisticated form of transfer learning, involves not only adding new task-specific layers but also selectively unfreezing and continuing to train some or all of the pre-trained layers on the target dataset. A specialized variant of transfer learning, domain adaptation, addresses scenarios where the source and target tasks may be identical, but there is a significant statistical disparity, or “domain shift,” between their respective data distributions. The effectiveness of transfer learning stems from the empirically observed phenomenon that deep neural networks learn hierarchical representations, where lower layers capture generalizable patterns and higher layers capture more abstract, task-specific features. By transferring these robust initial layers, the model benefits from a strong inductive bias, requiring less data and fewer training iterations to achieve high performance on new, related tasks. This makes transfer learning an indispensable technique for tasks with limited labelled data or when computational resources are limited.
This approach is particularly advantageous in our case as the domain adaptation is applicable in the two datasets and is shown schematically in
Figure 5, which shows how the model exploits the features and patterns learned during the initial training.
Specifically, for this adaptation, we employed a feature extraction strategy by freezing the weights of all layers except for the final two in the pre-existing model. This allows the network to retain previously learned representations while adapting to the new domain through the fine-tuning of its final layers. The line
for layer in model.layers[:−3]: layer.trainable = False achieves this by setting the trainable attribute to False for every layer except for the last three (two dense layers and dropout in our case). By freezing these earlier layers, we essentially preserve the low-level and high-level feature detectors that the model has already learned. Only the weights of the final dense layers are allowed to be updated during training on the new dataset. This targeted fine-tuning allows the model to learn the specific mappings from the pre-extracted features to the new target classes, without risking the degradation of the robust feature representations learned from the original, larger dataset. This method typically leads to faster convergence and improved performance on the new task compared to training a model from scratch. The procedure is graphically illustrated in
Figure 6, where the frozen weights and the fine-tuned part of the network are highlighted using different colours.
4. Discussion
This research investigated how transfer learning, integrated with a 1D-CNN classifier, can enhance non-destructive material testing. We particularly focused on overcoming the pervasive and challenging issue of surface variability. The study’s results affirm that our developed model exhibits strong generalization capabilities across varying acquisition surfaces. This crucial characteristic ensures its practical viability in applications where surface uniformity is frequently unpredictable.
Therefore, this research specifically addressed the pervasive and challenging issue of variability in surface properties. The findings unequivocally prove the proposed model’s ability to generalize robustly across diverse acquisition conditions. This represents a pivotal advance, as such adaptability is paramount for reliable deployment in real-world scenarios where consistent surface conditions are often unattainable. Our experimental setup involved training the network on a first specimen (Test Object 1) and then rigorously evaluating its performance on a second (Test Object 2), with highly encouraging outcomes. Notably, the classification performance, particularly precision, achieved improvements, which is crucial for a field demanding highly accurate defect identification.
This study represents a first step toward the deployment of a field-capable device that can locally fine-tune a neural network through transfer learning, enabling widespread monitoring of potential defects in various types of materials, including in the restoration sector or in the structural and materials health sector.
The proposed approach highlights the potential of integrating the PICUS device as a core component in a highly adaptable, easy-to-use tool. This system can leverage experimental lab data to adapt neural network parameters in response to new environmental or material conditions.
One of the central challenges for NDT analysis is the identification of different defect-prone zones, such as detachments or hollow areas, often based on limited prior knowledge. Here, AI offers a viable and scalable solution. The proposed workflow allows training to begin in the lab using test objects with known defects, facilitating a supervised learning setup. By registering coordinates during acquisition, labels can be accurately assigned, which supports effective and precise training.
While this approach requires an initial data acquisition effort, it brings significant advantages during the fine-tuning phase, where the network is adapted to specific surfaces encountered in the various areas of employment. Importantly, through transfer learning, the network can be retrained using only a small subset of annotated data, reducing the burden on the expert, who would otherwise need to manually label large datasets to train a model from scratch.
This methodology presents clear benefits in terms of efficiency and scalability and significantly accelerates the deployment of trained models during diagnosis projects. In our view, this approach represents a promising and novel application of transfer learning in the SHM (Structural Health Monitoring) application, especially considering that most of the existing literature focuses on domains such as medicine or acoustic diagnostics.
As shown in our results, the model’s performance is in line with expectations and confirms the suitability of this type of neural architecture for identifying defects in complex, variable surfaces.
Author Contributions
Conceptualization, M.L.G., F.M., G.C. and A.S.; methodology, M.L.G., F.M. and G.C.; software, M.L.G. and F.M.; validation, M.L.G., F.M. and G.C.; formal analysis, M.L.G., F.M., G.C. and A.S.; investigation, M.L.G., F.M. and G.C.; resources, M.L.G., F.M., G.C. and A.S.; data curation, M.L.G., F.M. and G.C.; writing—original draft preparation, M.L.G. and F.M.; writing—review and editing, M.L.G., F.M. and G.C.; visualization, M.L.G. and F.M.; supervision, G.C. and A.S.; project administration, G.C. and A.S. All authors have read and agreed to the published version of the manuscript.
Funding
This research received no external funding.
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
The data presented in this study are available on request from the corresponding author.
Conflicts of Interest
The authors declare no conflicts of interest.
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Figure 1.
Flowchart of the transfer learning methodology for acoustic defect classification. Acoustic data from a reference specimen (Test Object 1) trained an initial CNN. This pre-trained model was then fine-tuned via transfer learning using limited data from a second specimen (Test Object 2) with different material characteristics. The adapted model was subsequently evaluated for defect classification on the full Dataset 2, demonstrating improved accuracy and generalization.
Figure 2.
(a) Photograph of the two test objects mounted on the same aluminium cube (200 mm per side), which serves as a rigid support to constrain vibrations during testing. Test Object 1, located on top, is made of PMMA with a plate thickness of 3 mm. Test Object 2, below, is made of PVC with a plate thickness of 1 mm. Both contain two cylindrical cavities—A (large, 50 mm radius) and B (small, 25 mm radius)—that simulate debonding defects. (b) Close-up view of Cavity A in the PVC specimen, showing the air interface beneath the bonded polymeric layer. The transparency of the material and the surface grid allow visual assessment of defect geometry and position.
Figure 3.
Schematic diagram of the PICUS system used for non-destructive surface inspection. The system includes a mechanical actuator for stimulus generation, a microphone for acoustic signal capture, and an Arduino-based microcontroller for synchronized control and data acquisition.
Figure 4.
Schematic representation of the proposed 1D CNN architecture. The model processes a univariate time series of length 1024 and consists of three convolutional layers with ReLU activation, interleaved with max pooling and dropout for feature extraction and regularization. The final classification is performed through fully connected dense layers with a softmax output.
Figure 5.
Schematic representation of knowledge transfer from Test Object 1 to Test Object 2 through the application of transfer learning.
Figure 6.
Visual representation of the transfer learning strategy: frozen layers are marked in blue, while the trainable layers adapted to the new task are highlighted in green.
Figure 7.
Defect localization map for Test Object 2, obtained by applying a CNN model trained on Test Object 1.
Table 1.
Properties of the PMMA and PVC used for the test objects.
Property | PMMA | PVC |
---|
Density (kg/m3) | 1200 | 1400 |
Young Modulus (GPa) | 3.2 | 2.1 |
Yield Strength (MPa) | 54–72 | 35–52 |
Tensile Strength (MPa) | 48–80 | 41–65 |
Fracture Toughness (MPa·m⌃1/2) | 0.7–1.6 | 1.5–5.1 |
Glass Transition Temp (°C) | 85–160 | 75–100 |
Specific Heat (J/kg·°C) | 1500–1600 | 1400 |
Thermal Conductivity (W/m·K) | 0.25 | 0.29 |
Dielectric Constant | 3.2 | 4.4 |
Table 2.
Model classification report performed on Test Object 1.
Class | Precision | Recall | F1-Score | Support |
---|
0 | 0.99 | 0.95 | 0.97 | 239 |
1 | 0.88 | 0.96 | 0.92 | 81 |
Accuracy | | | 0.96 | 320 |
Macro Avg | 0.93 | 0.96 | 0.94 | 320 |
Weighted Avg | 0.96 | 0.96 | 0.96 | 320 |
Table 3.
Classification report of the model trained on Test Object 1 and tested in Test Object 2.
Class | Precision | Recall | F1-Score | Support |
---|
0 | 0.99 | 0.96 | 0.97 | 1212 |
1 | 0.88 | 0.97 | 0.92 | 388 |
Accuracy | | | 0.96 | 1600 |
Macro Avg | 0.93 | 0.96 | 0.95 | 1600 |
Weighted Avg | 0.96 | 0.96 | 0.96 | 1600 |
Table 4.
Classification report showing precision, recall, F1-score, and support for each class. The model was initially trained on Test Object 1 using a transfer learning approach and subsequently fine-tuned for Test Object 2.
Class | Precision | Recall | F1-Score | Support |
---|
0 | 0.98 | 0.98 | 0.98 | 1086 |
1 | 0.95 | 0.95 | 0.95 | 354 |
Accuracy | | | 0.98 | 1440 |
Macro avg | 0.97 | 0.97 | 0.97 | 1440 |
Weighted avg | 0.98 | 0.98 | 0.98 | 1440 |
Table 5.
Classification report showing precision, recall, F1-score, and support for each class. The model was trained on Test Object 1 using a transfer learning approach and evaluated on Test Object 2 without additional fine-tuning.
Class | Precision | Recall | F1-Score | Support |
---|
0 | 0.75 | 1.00 | 0.86 | 1086 |
1 | 0.00 | 0.00 | 0.00 | 354 |
Accuracy | | | 0.75 | 1440 |
Macro avg | 0.38 | 0.50 | 0.43 | 1440 |
Weighted avg | 0.57 | 0.75 | 0.65 | 1440 |
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