An Intelligent Signal Classification Framework for Crack Detection in Polymeric Materials Using Ensemble Learning

1  Introduction

Nondestructive testing (NDT) plays a fundamental role in ensuring the structural integrity, safety, and operational reliability of engineering materials and components across a wide range of industrial sectors, including aerospace, civil infrastructure, manufacturing, and energy systems. Among the various damage mechanisms affecting structural performance, crack initiation and propagation are particularly critical, as they may lead to stiffness degradation, loss of functionality, and catastrophic failure if not detected at an early stage. Consequently, the development of reliable, efficient, and automated crack detection methodologies remains a central research topic within structural health monitoring (SHM) and condition-based maintenance.

Traditional NDT techniques, such as magnetic particle inspection, visual inspection, ultrasonic testing, X-ray imaging, acoustic emission, and vibration-based analysis, have been widely employed due to their well-established physical principles and practical applicability [1,2]. However, these approaches often suffer from limitations related to operator dependency, sensitivity to environmental noise, limited repeatability, and increasing difficulty in dealing with complex materials, loading conditions, and heterogeneous structures. In response to these challenges, recent research has increasingly focused on the integration of data-driven techniques into conventional NDT frameworks, leading to the emergence of intelligent nondestructive testing systems capable of enhanced automation, adaptability, and diagnostic accuracy [3].

Machine learning (ML) and deep learning (DL) techniques have demonstrated significant potential in extracting meaningful information from complex and noisy NDT data. Recent studies report a rapid growth in ML-assisted crack detection and fault diagnosis methods applied to different materials, structures, and sensing modalities, including vibration signals, acoustic responses, ultrasonic measurements, and image-based inspection data [4–8]. These works indicate that learning-based approaches are particularly effective in handling nonlinear signal behavior and uncertain operating conditions commonly encountered in real-world NDT applications.

Although image-based crack detection has received considerable attention in recent years, especially with the adoption of convolutional neural networks and vision-based inspection systems [3,6,9], signal-based approaches remain highly attractive for industrial applications due to their lower cost, reduced data storage requirements, and ease of integration into continuous monitoring systems. Studies focusing on vibration, acoustic, and resonant signal analysis combined with ML classifiers have demonstrated promising performance for crack detection and damage identification, even when using limited sensor configurations [10–14]. These characteristics support the development of scalable and cost-effective intelligent NDT solutions suitable for online monitoring.

Despite these advances, several challenges remain open. The selection of appropriate learning algorithms, feature extraction strategies, and validation procedures continues to be an active area of research. Ensemble-based methods, particularly Random Forest, have attracted increasing attention due to their robustness to noise, strong generalization capability, and intrinsic interpretability through feature importance analysis [15–19]. Applications of Random Forest models in structural damage detection, deformation monitoring, and crack identification have reported encouraging results, highlighting their suitability for engineering diagnostic problems [17–20].

In addition, recent literature emphasizes the importance of adopting reliable validation protocols and statistical testing when comparing ML models for NDT applications. The use of cross-validation schemes combined with nonparametric statistical tests has been increasingly recommended to ensure fair model comparison and to avoid biased or over-optimistic performance assessments [8,21]. Such methodological rigor is essential for the development of trustworthy intelligent NDT systems intended for real-world deployment.

In this context, the present study proposes an intelligent signal classification framework for crack detection in polymeric materials based on machine learning techniques. A comprehensive comparative analysis is conducted using Random Forest, Support Vector Machines, k-Nearest Neighbours, AdaBoost, and Boosted Trees under a consistent five-fold cross-validation protocol supported by nonparametric statistical testing. By focusing on signal-based crack detection and emphasizing robustness, interpretability, and methodological consistency, this work contributes to the advancement of intelligent nondestructive testing systems and provides relevant insights for SHM and predictive maintenance applications.

2  Random Forest-Based Intelligent Classification

Random Forest is an ensemble machine learning algorithm that constructs multiple decision trees and aggregates their outputs to perform classification, regression, or anomaly detection tasks. Originally proposed by Breiman [15], the method has become one of the most widely adopted supervised learning techniques due to its high predictive accuracy, robustness to noise, and suitability for high-dimensional data [15]. These characteristics make Random Forest particularly attractive for expert systems aimed at automated decision-making in complex and uncertain environments.

2.1 Principle of Operation

The Random Forest algorithm operates by generating a collection of independent decision trees, each trained using a bootstrap sample drawn with replacement from the original dataset. During tree construction, node splitting is performed using a randomly selected subset of input features. This dual randomization—both in data sampling and feature selection—promotes diversity among the trees and enhances generalization capability [16].

For classification problems, the final decision is obtained through majority voting across all trees, whereas regression outputs are computed as the average of individual predictions. An important advantage of Random Forest is the use of out-of-bag (OOB) samples for internal validation. These samples, which are not used in the training of individual trees, provide an unbiased estimate of classification performance without requiring a separate validation dataset. From an expert systems perspective, this internal validation mechanism enhances decision reliability while reducing model complexity.

2.2 Advantages of Intelligent Decision Systems

Random Forest offers several properties that are particularly relevant for intelligent fault diagnosis and decision-support applications:

•   High classification accuracy in the presence of noisy and partially overlapping data.

•   Reduced risk of overfitting due to ensemble averaging and variance control.

•   Capability to handle large feature spaces without requiring extensive feature selection.

•   Availability of feature importance measures, supporting interpretability and knowledge extraction.

•   Computational efficiency and scalability, enabling integration into real-time or embedded inspection systems.

These characteristics align well with the requirements of expert systems, where robustness, transparency, and reliability of decisions are essential.

2.3 Applications for Nondestructive Testing and Condition Monitoring

In nondestructive testing and structural condition monitoring, Random Forest has been successfully employed as a decision engine for automated fault diagnosis. Typical applications include:

•   Classification of structural or material states (e.g., intact, cracked, degraded) using vibration, acoustic, or strain signals acquired from embedded sensors [17].

•   Intelligent fault detection in rotating machinery and mechanical components operating under variable load and environmental conditions [18].

•   Regression-based estimation of degradation indicators and remaining useful life in engineering systems [19].

•   Integration with signal processing and feature extraction techniques for automated crack detection in heterogeneous materials [9].

These studies demonstrate that Random Forest is well suited to handling nonlinear signal characteristics, measurement uncertainty, and imbalanced class distributions, conditions commonly encountered in real-world NDT scenarios.

2.4 Comparison with Alternative Machine Learning Approaches

Compared to other widely used classifiers such as Support Vector Machines (SVMs) and Artificial Neural Networks (ANNs), Random Forest offers several practical advantages, including improved interpretability through feature importance analysis, reduced sensitivity to hyperparameter tuning, and competitive performance with relatively low computational cost. While deep learning approaches may outperform ensemble methods in highly unstructured data domains, such as raw image analysis, Random Forest remains a robust and interpretable solution for signal-based expert systems, particularly when data availability is limited or explainability is required.

In this study, Random Forest is employed as the core intelligent classifier within a broader decision-support framework for fault diagnosis, and its performance is systematically compared with alternative machine learning models to assess robustness and reliability.

3  Materials and Methods

3.1 Signal Acquisition and Dataset Construction

The experimental dataset used in this study was constructed from signals acquired from engineering material specimens subjected to controlled operating conditions. Three distinct structural states were considered: intact metallic material, intact polymeric material, and polymeric material containing induced cracks. These classes were selected to represent both material heterogeneity and damage-related structural degradation, which are common challenges in nondestructive testing (NDT) applications.

The acquired signals were organized into a structured dataset, where each sample corresponds to a feature vector extracted from the raw measurements and labeled according to its structural condition. This formulation enables the problem to be addressed as a supervised multi-class classification task, suitable for intelligent fault diagnosis systems.

The dynamic test was conducted on a test bench with a base consisting of a steel plate measuring 800 × 300 × 6.35 mm3, supported by four vibration-damping feet, each with a load capacity of up to 400 kg and equipped with locknuts for fine leveling adjustment. This base ensures structural rigidity and isolation from external vibrations, thereby maintaining the repeatability of the tests.

A Hercules induction electric motor (½ CV, 220 V/380 V, 1685 RPM) was mounted at the left end of the base using four headless “½ × 6” bolts. The rigid mounting and use of leveling feet ensure proper angular and horizontal alignment of the output shaft, minimizing clearances and undesired displacements.

Torque transmission between the motor and the test shaft is achieved through a GS50 flexible coupling (designed for shafts up to 22 mm in diameter). This element compensates for angular and axial misalignments, reducing localized stresses and acting as a protective mechanism in the event of shock or overload, thus preserving the integrity of the motor and bearing system.

The test shaft, made of AISI 1020 steel (20 mm Ø × 500 mm L), is supported by two central processing unit 204 self-aligning pillow block bearings, positioned 80 mm and 320 mm from the left end. These bearings ensure smooth rotation and minimize radial play, keeping the shaft centered and allowing for accurate vibration measurements.

At the center section of the shaft, 200 mm from the coupling, a 1045 steel flywheel disc (150 mm Ø × 16 mm thickness) is mounted. The disc contains five 8 mm holes spaced at 60° intervals. It functions as a rotational inertia stabilizer, enhancing system consistency and facilitating repositioning at specific angular positions marked at 0°, 90°, 180°, and 270°. Fig. 1 illustrates the experimental setup.

Figure 1: Experimental setup.

The signal acquisition system was configured to interface with an Arduino Uno R3, mounted on a Deutsches Institut für Normung rail inside a PVC enclosure measuring 280 × 180 × 140 mm3, along with an I2C TCA9548A multiplexer, which is responsible for addressing the four MPU6050 accelerometers. The wiring is organized in plastic conduits fixed laterally to the base, maintaining a minimum distance of 50 mm from the steel plate to avoid mechanical and electrical interference.

The system’s actuation is managed by a Metaltex IF10 frequency inverter (1 CV, 220 V), whose control interface includes:

•   A 22 mm illuminated on/off push button (Lukma), for motor power switching;

•   A 22 mm two-position rotary switch, for quick selection of rotation direction;

•   A 22 mm 10 kΩ linear potentiometer, for gradual adjustment of output frequency;

•   A 22 mm mushroom-style emergency stop button with latching mechanism;

•   A 10 A type C single-phase circuit breaker and RAC-2 coupling relay, providing electrical protection and isolation during maintenance operations.

Fig. 2 illustrates the electrical control system housed in the enclosure.

Figure 2: Electrical control box.

The data acquisition was based on vibration measurements taken at four specific points on the test bench, corresponding to the bolts numbered 1 through 4 that secure the motor to the base. The sensors were mounted on the nut and bolt at the upper end, with one MPU6050 sensor installed at each point 1, 2, 3, and 4, respectively. The Arduino Uno R3’s I2C bus was extended via a TCA9548A multiplexer, enabling sequential reading of the four sensors without address conflicts.

The data acquisition was performed at a sampling frequency of 100 Hz. For each excitation level, which ranged from 2 to 22 Hz in increments of 2 Hz, five data vectors of 4004 samples per sensor were recorded. This corresponds to 20 vectors per frequency (5 vectors × 4 sensors) and a total of 220 acceleration vectors (11 frequencies × 20 vectors). The firmware developed in the Arduino Integrated Development Environment managed the selection of the multiplexer channel, acquisition of acceleration values along the three axes, and serial transmission of the data. The three axes (x, y, and z) were combined into a single value using the Euclidean norm, defined as:

sinal=x2+y2+z2(1)

The vibration samples were organized into three groups according to the material of the base-fixing bolts: (1) metal, (2) intact Polylactic Acid, and (3) Polylactic Acid with induced cracks. Each vector contains 4004 temporal samples, sufficient to characterize the system’s mechanical and spectral responses.

To detect dynamic changes caused by cracks in the PLA bolts, a Random Forest classifier was employed. The forest consists of 100 decision trees, each trained on a distinct bootstrap sample from the training set. At each decision node within a tree, a random subset of mmm features extracted from the signals is considered. The final classification is determined by majority voting across all trees. The classification margin for a sample (X, Y) is defined as:

mg(X,Y)=1T∑t=1TI(ht(X)=Y)−maxj≠Y1T∑t=1TI(ht(X)=Y)(2)

where T is the number of trees in the forest; ht(X) is the label assigned to sample X by tree t; I (⋅) is the indicator function; and Y is the true label of X. The classification margin quantifies the forest’s confidence in its prediction.

The generalization error of the forest is:

PE=Pr (mg(X,Y)<0(3)

which satisfies

PE≤ρ(1−s2)s2(4)

where s=E[mg(X,Y)] is the average strength of the forest, and ρ=E(hi(X),hj(X))for i≠j is the average correlation between trees [16].

Fig. 3 shows the experimental setup with the sensor placement locations.

Figure 3: Accelerometer mounting point.

Please note that point 4 is located at the rear of the figure and therefore cannot be shown. Fig. 4 provides a detailed view of the positioning of the MPU6050 sensors at one of the measurement points.

Figure 4: Accelerometer point.

Although the experimental test rig is equipped with multiple accelerometers to capture vibration at different coordinates, data acquisition for this study was restricted to the sensor at position P1. This choice was made to evaluate the efficacy of the proposed ensemble learning framework under a minimalist single-sensor monitoring scenario, simulating a low-cost industrial application.

In the cracked polymeric condition, the damage was introduced by a controlled mechanical incision performed on the PLA bolts using a precision cutting tool, ensuring repeatability in crack location and severity across all tested samples.

3.2 Data Pre-processing and Dimensionality Reduction

Prior to model training, all feature vectors, derived exclusively from the single sensor node (P1), were standardized using Z-score normalization to ensure zero mean and unit variance. This step is essential to avoid scale-related bias, particularly for distance-based classifiers and kernel-based methods.

To reduce feature redundancy and mitigate the curse of dimensionality, Principal Component Analysis (PCA) was applied to the normalized dataset from P1. The number of retained principal components was selected such that at least 95% of the cumulative variance was preserved. This strategy balances information retention and computational efficiency while improving model generalization. The transformed feature space was subsequently used as input for all machine learning models to guarantee a fair comparison.

3.3 Machine Learning Models

To ensure a fair and comprehensive assessment of the proposed Random Forest-based fault diagnosis framework, its performance was systematically compared with several widely used machine learning classifiers commonly applied in nondestructive testing and condition monitoring applications [6–8,20]. All stages of signal processing, feature extraction, dimensionality reduction, and machine learning implementation were carried out using MATLAB R2023b (MathWorks Inc., Natick, MA, USA) [22].

Random Forest was adopted as the primary classifier due to its robustness, resistance to overfitting, and strong performance in noisy environments. The model was implemented as an ensemble of decision trees trained using bootstrap aggregation, with random feature selection at each split [15,16]. The number of trees was set to 300 to ensure model stability. Internal validation was performed using out-of-bag (OOB) samples, and OOB-based variable importance measures were computed to evaluate the relevance of the extracted features. The effectiveness of Random Forest in structural damage detection and structural health monitoring applications has been demonstrated in several previous studies [17–20].

Support Vector Machines (SVM) were employed as a nonlinear baseline classifier. An SVM with a radial basis function (RBF) kernel was selected due to its ability to model complex decision boundaries, which are typical in signal-based crack detection and fault diagnosis problems [6,8]. This classifier was included to provide a well-established benchmark for comparison with ensemble-based methods.

The k-Nearest Neighbors (kNN) algorithm was incorporated as a distance-based reference method. Despite its simplicity, kNN has been successfully applied in pattern recognition and fault classification tasks, making it a useful baseline for evaluating the performance gains offered by more advanced machine learning and ensemble approaches [6].

AdaBoost was implemented as a representative boosting algorithm that sequentially combines weak learners by assigning higher weights to previously misclassified samples. Boosting-based methods have demonstrated promising capabilities in detecting subtle damage signatures in noisy structural signals and were therefore included for comparative purposes [6,20].

Finally, Gradient Boosted Trees were considered to evaluate a more advanced boosting-based ensemble technique. Unlike Random Forest, boosted trees are trained sequentially with the objective of minimizing classification error. This class of methods has shown strong performance in structured signal classification and damage detection problems, particularly in scenarios involving nonlinear relationships and complex feature interactions [18,20].

3.4 Cross-Validation Strategy

A stratified five-fold cross-validation scheme was adopted to ensure reliable and unbiased performance evaluation. This approach is widely used in machine learning-based fault diagnosis to reduce the influence of data partitioning and improve generalization assessment [6,8].

3.5 Performance Metrics

Model performance was evaluated using accuracy, precision, recall, and F1-score, which are standard metrics in multi-class fault diagnosis and condition monitoring studies [6–8]. Aggregated confusion matrices were also analyzed to identify misclassification patterns between structural states.

3.6 Statistical Analysis

To assess the statistical significance of performance differences among classifiers, nonparametric statistical tests were employed. The Friedman test was used to rank the classifiers across cross-validation folds, followed by pairwise Wilcoxon signed-rank tests comparing the proposed Random Forest model with the remaining classifiers. The use of nonparametric statistical testing is recommended in comparative machine learning studies due to the non-Gaussian nature of performance distributions [6,17]. A significance level of α = 0.05 was adopted. The statistical analyses and performance evaluations were carried out using MATLAB R2023b (MathWorks Inc., Natick, MA, USA) [22].

4  Results and Discussion

This section presents a comprehensive comparative evaluation of machine learning classifiers applied to nondestructive testing (NDT) signal classification. The assessed models include Random Forest (RF), Support Vector Machine with radial basis function kernel (SVM-RBF), k-Nearest Neighbors (kNN), AdaBoost, and Boosted Trees. All classifiers were evaluated under an identical experimental protocol using a stratified five-fold cross-validation scheme, ensuring methodological fairness, reproducibility, and statistical consistency.

4.1 Classification Performance

Table 1 summarises the classification performance of all evaluated models in terms of mean accuracy, standard deviation, median accuracy, precision, recall, F1-score, and average Friedman ranking. Among the analysed classifiers, Random Forest achieved the best overall performance, with a mean accuracy of 73.18% and the lowest variability across cross-validation folds (standard deviation of 2.05%). Furthermore, RF exhibited a well-balanced trade-off between precision (0.727) and recall (0.732), resulting in the highest F1-score (0.727) among all models.

Boosting-based approaches (AdaBoost and Boosted Trees) ranked second, both achieving a mean accuracy of 62.12% with comparable precision, recall, and F1-score values. These results indicate that ensemble learning strategies based on boosting are effective for NDT signal classification, particularly due to their ability to model nonlinear decision boundaries and cope with noisy measurements. Nevertheless, their performance remained consistently below that of Random Forest across all evaluated metrics.

The kNN classifier presented intermediate performance, with a mean accuracy of 48.64% and relatively higher variability across folds. This behaviour suggests sensitivity to local data distribution and distance metrics in the reduced PCA feature space. In contrast, the SVM-RBF classifier yielded the lowest mean accuracy (44.09%). Despite exhibiting relatively high precision, SVM-RBF suffered from reduced recall, indicating a conservative decision strategy that led to a higher number of false negatives and, consequently, a lower F1-score.

Fig. 5 illustrates the distribution of classification accuracy across the five cross-validation folds using boxplots. Random Forest exhibits the highest median accuracy and the lowest dispersion, indicating superior robustness compared to the remaining classifiers. This behaviour is further illustrated in Fig. 6, which shows the accuracy distributions using violin plots and highlights the consistency of Random Forest across folds.

Figure 5: Boxplot representation of classification accuracy obtained across five-fold cross-validation for all evaluated machine learning classifiers.

Figure 6: Violin plot showing the distribution of classification accuracy across five-fold cross-validation for the evaluated classifiers. Black markers indicate mean accuracy values.

Fig. 5 presents the boxplot representation of classification accuracy obtained across the five cross-validation folds. The Random Forest model exhibits the highest median accuracy and the smallest interquartile range, confirming its superior stability and robustness. In contrast, kNN and SVM show wider dispersion, indicating higher sensitivity to data partitioning and reduced generalization capability. Boosting-based models (AdaBoost and Boosted Trees) demonstrate intermediate behaviour, with accuracy values consistently below those of Random Forest but with moderate variability.

Complementing this analysis, Fig. 6 illustrates the distribution density of accuracy values using violin plots. This representation highlights not only central tendency but also the probability distribution of performance outcomes. Random Forest shows a concentrated distribution around higher accuracy levels, reinforcing its consistency across folds. Conversely, SVM presents a skewed distribution toward lower accuracy values, while kNN exhibits broader density spread, confirming its instability in the PCA-reduced feature space.

Together, these visual analyses corroborate the statistical findings reported in Table 1, demonstrating that Random Forest achieves not only higher average performance but also greater reliability, a critical requirement for intelligent decision-support systems in nondestructive testing applications.

Table 1 presents a quantitative summary of the performance of the evaluated models, detailing mean accuracy, standard deviation, median, precision, recall, F1-score, and the Friedman mean ranking. The analysis of these data, supported by the graphical representation in Fig. 7, reveals a clear performance hierarchy among the classifiers for the fault detection task.

Figure 7: Average performance of the models: mean accuracy and standard deviation across the 5-fold cross-validation.

The Random Forest (RF) algorithm established itself as the most effective classifier, achieving the highest mean accuracy (73.18%) and the lowest variability across cross-validations. As illustrated in Fig. 7, which displays the mean accuracy with respective error bars (standard deviation), the RF exhibits the highest bar combined with the smallest error interval (2.05%), visually confirming its superiority in terms of precision and stability. Furthermore, the RF demonstrated a remarkable balance between precision (0.727) and recall (0.732), resulting in the highest F1-score (0.727). This balance is critical in nondestructive testing (NDT), as it simultaneously minimizes the occurrence of false positives and the failure to detect actual cracks.

In contrast, the boosting-based models (AdaBoost and Boosted Trees) showed intermediate performance, tying with a mean accuracy of 62.12%. Fig. 8 evidences that, although their standard deviations (3.97%) are moderate, there is no overlap between their error bars and those of the RF, reinforcing the distinction in performance. The SVM with RBF kernel presented the lowest performance, with an accuracy of 44.09%. Visual analysis of Fig. 8 highlights the significant performance gap between the SVM and the ensemble methods, suggesting that the decision boundary generated by the RBF kernel was insufficient to properly separate the classes within the projected feature space.

Figure 8: Comparison of classifier rankings across the cross-validation folds.

Beyond the mean and standard deviation, the distributional stability is detailed in Figs. 5 and 6:

•   Dispersion Analysis (Fig. 5): The RF displays the most compact box (smallest interquartile range), indicating high resilience to variations in data partitioning. Conversely, kNN and SVM present more elongated boxes, denoting greater instability.

•   Density Analysis (Fig. 6): The probability mass of the Random Forest distribution is concentrated at the top of the chart (high accuracy), whereas that of the SVM shifts to lower ranges, corroborating this model’s difficulty in generalizing adequately.

The results presented in this subsection indicate that the Random Forest classifier consistently achieved superior performance compared to the remaining methods. This behavior is not limited to mean accuracy values but is also reflected in the stability of the results across validation folds, suggesting a higher robustness of ensemble-based approaches for vibration-based crack detection in nondestructive testing.

4.2 Statistical Analysis

To determine whether the observed performance differences were statistically significant, nonparametric statistical tests were conducted in conjunction with the visual performance analysis presented in Figs. 5 and 6. While the graphical distributions provide qualitative insight into model stability and central tendency, statistical testing quantitatively verifies whether these differences are systematic rather than random.

First, the Friedman test was applied to the classification accuracy values obtained across the five cross-validation folds. As reported in Table 2, the test yielded a p-value of 0.0007, indicating statistically significant global differences among the evaluated classifiers at the 5% significance level. This result confirms that the performance separation visually observed in Figs. 5 and 6, particularly the higher concentration of accuracy values for Random Forest, reflects genuine methodological differences rather than sampling variability.

Following this result, pairwise Wilcoxon signed-rank tests were performed to compare the proposed Random Forest classifier with the remaining models. The corresponding p-values are also summarised in Table 2, with all pairwise comparisons resulting in a p-value of 0.0625. Although this value does not reach statistical significance at the conventional 5% level, this outcome is expected given the limited number of folds adopted in the cross-validation procedure, which constrains the minimum attainable p-value in the Wilcoxon test.

Importantly, even in the absence of strong pairwise statistical significance, the graphical evidence reinforces the dominance of Random Forest. In Fig. 5, RF exhibits the highest median accuracy and the smallest dispersion across folds, indicating superior stability. Similarly, Fig. 6 shows a concentrated distribution of performance values in the upper accuracy region, while the competing classifiers display broader or skewed distributions toward lower performance. These patterns are consistent with the Friedman ranking reported in Table 1, where Random Forest achieved the best average rank.

Therefore, the combined interpretation of statistical tests and visual distributions provides a coherent conclusion: Random Forest delivers not only higher average performance but also greater consistency and reliability, characteristics that are particularly critical for intelligent nondestructive testing and decision-support systems operating under uncertainty.

To validate whether the observed differences are systematic, non-parametric statistical tests were applied. The Friedman test, used to check for global differences, returned a p-value of 0.0007 (α = 0.05), confirming statistical heterogeneity among the models (Table 2).

The statistical hierarchy of the models is visualized in Fig. 7, which presents the Friedman Mean Ranking. In this chart, the axis represents the average position occupied by each classifier across the folds (where a value of 1 indicates the best possible performance).

•   The Random Forest stands alone in the first position (Rank 1.0), confirming that it outperformed competitors in 100% of the cross-validation runs.

•   The boosting methods share the second position (Rank 2.5), followed by kNN (Rank 4.0) and SVM (Rank 5.0).

This visual ordering in Fig. 7 is crucial, as it synthesizes not only the magnitude of accuracy but the consistency of the RF’s superiority over other methods, regardless of data partitioning.

Complementarily, the Wilcoxon signed-rank post-hoc test (Table 2) indicated a p-value of 0.0625 for all pairwise comparisons with the RF. As previously discussed, this value represents the lower mathematical limit for a 5-fold cross-validation (1/24) and should be interpreted as strong evidence of practical dominance, limited only by the sample size of the experimental protocol, rather than an absence of efficacy of the proposed model.

The statistical analysis reinforces the observed performance trends. Although the pairwise Wilcoxon tests did not reveal statistically significant differences at the 5% significance level, the Friedman ranking consistently favored the Random Forest model, indicating systematic dominance rather than isolated performance gains. This result highlights the importance of combined statistical evaluation when assessing machine learning models for intelligent fault diagnosis.

4.3 Discussion and Practical Implications

The superior performance of Random Forest can be attributed to its ensemble-based architecture, which combines multiple decision trees trained on different subsets of data and features. This structure enhances generalisation capability while reducing sensitivity to noise, an essential characteristic in nondestructive testing applications, where measurement uncertainty and operational variability are inherent.

Moreover, the balanced precision and recall achieved by Random Forest highlight its suitability for practical fault detection scenarios, in which both false positives and false negatives can lead to significant operational and safety consequences. In contrast, classifiers such as SVM and kNN exhibited limitations either in recall or stability, which may reduce their effectiveness in real-world inspection and monitoring systems.

From a knowledge engineering and decision-support perspective, Random Forest offers an additional advantage through its intrinsic interpretability via feature importance analysis. This capability enables insights into the most relevant signal components contributing to crack detection, aligning closely with the scope of Expert Systems, which values not only predictive accuracy but also explainability and transparency in intelligent decision-making.

Overall, the obtained results demonstrate that Random Forest provides a robust, accurate, and interpretable solution for automated nondestructive inspection of polymeric materials. The proposed approach contributes to the advancement of intelligent NDT systems and supports the development of reliable condition monitoring and predictive maintenance strategies within the context of Industry 4.0.

Beyond predictive accuracy, the Random Forest model provides intrinsic interpretability through feature importance analysis, enabling the identification of signal components most relevant to crack detection. This characteristic is particularly relevant for intelligent nondestructive testing and expert systems, where transparent and explainable decision-making is essential to support engineering judgment and practical deployment.

The feature importance analysis provided by the Random Forest model offers valuable insights into the most informative signal components. This interpretability supports its integration into expert systems, where transparent and explainable decision-making is essential for engineering judgment.

These findings demonstrate that the proposed framework can support intelligent nondestructive testing applications using simplified sensing configurations, contributing to scalable, low-cost, and automated condition monitoring solutions suitable for industrial environments.

5  Conclusion

This section summarizes the main findings and contributions of the present study, emphasizing the scientific outcomes, practical implications, and relevance of the proposed approach for intelligent nondestructive testing and automated fault diagnosis.

•   An intelligent nondestructive testing framework for crack detection in engineering materials based on machine learning-driven signal classification was developed and validated.

•   A comprehensive comparative analysis involving Random Forest, Support Vector Machines, k-Nearest Neighbours, AdaBoost, and Boosted Trees demonstrated that ensemble-based approaches are well suited for vibration-based crack detection.

•   The Random Forest classifier achieved superior and more stable performance, presenting the highest mean and median accuracy, balanced precision and recall, and the best overall Friedman ranking.

•   Although pairwise Wilcoxon tests did not indicate statistically significant differences at the 5% level, the consistent dominance of Random Forest across multiple performance metrics highlights its robustness and reliability for nondestructive testing applications involving noisy and nonlinear signal data.

•   Beyond predictive accuracy, Random Forest provides intrinsic interpretability through feature importance analysis, which is particularly valuable for expert systems and transparent decision-support in engineering applications.

•   The proposed framework represents a low-cost, scalable, and automated solution for intelligent nondestructive testing, supporting its integration into sensor-based monitoring platforms and Industry 4.0 environments.

Despite the promising results, this study presents some limitations that should be acknowledged. The experimental evaluation was conducted under controlled laboratory conditions and focused on a limited set of material configurations and damage scenarios, which may restrict the direct generalization of the findings to complex real-world operating environments.

In addition, the analysis was based on vibration signals acquired from a single sensing modality and a specific experimental setup. Although this choice allowed a controlled and cost-effective assessment of the proposed framework, future investigations should consider multimodal sensing strategies and broader datasets to further assess robustness and applicability.

Acknowledgement: The authors would like to thank the institutional support of UNESP-Universidade Estadual Paulista and UniRV-Universidade de Rio Verde.

Funding Statement: The authors received no specific funding.

Author Contributions: Rafael de Oliveira Silva, Roberto Outa and Fábio Roberto Chavarette contributed equally to conceptualization and problem formulation, data analysis, and manuscript writing; Experiment implementation and critical manuscript review; Supervision and final review. All authors reviewed and approved the final version of the manuscript.

Availability of Data and Materials: The dataset generated and analyzed during the current study may be made available by contacting the corresponding author upon reasonable request. All experimental data were obtained under controlled laboratory conditions.

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no conflicts of interest.

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