1. Introduction
Damage diagnosis and analysis play a pivotal role within the broader field of structural engineering. This process is instrumental in averting catastrophic failures. Damage diagnosis mainly consists of three steps: detection, isolation, and identification. While an anomaly can be investigated during the detection stage, efforts are focused on pinpointing the types of the fault (locations and severity included) along with the damaged component in the isolation and identification phases, respectively [
1]. Following these steps, the remaining useful life of a structure can be estimated. Damage diagnosis is particularly valuable when applied to large, complex and costly engineering structures, especially those made of fiber-reinforced (FRP) composites as they exhibit heightened sensitivity to Low-Velocity Impacts (LVIs) [
2,
3]. LVIs could induce Barely Visible Damages (BVD) such as delamination, as well as fiber failures, and matrix cracking that can significantly diminish the residual strength of the structure [
4,
5,
6]. Notably, LVI damage typically found its maximum extension at the surface opposite to the impacted one; this aspect complicates the malfunction identification process with various challenges. Furthermore, structural changes could also result from the environmental and operational conditions (EOCs), naturally affecting the components during their life cycle: factors such as temperature [
7] and load variations [
8] can lead to fatigue crack onset and propagation [
9,
10].
The pressing need to enhance safety and reliability while simultaneously reducing design and maintenance costs is driving advancements in data collection, processing methods, and computing power.
One of the promising remedies to the issue is structural health monitoring (SHM). SHM facilitates the establishment of a detection and tracking strategy for damage progression to estimate the structural residual life span. This, in turn, enables the implementation of condition-based maintenance policies by collecting, interpreting, and analyzing data gathered by opportunely distributed sensors embedded or attached to the structures [
11,
12].
Within the domain of SHM, a range of methods can be employed to enhance the continuous monitoring of structural health. These methods encompass eddy current, vibration analysis, acoustic emission analysis, electrical resistance measurements, impedance analysis, infrared thermography, and damping assessment [
10]. Moreover, the choice of the appropriate sensor type is a contentious issue. Various sensors, including the acoustic emission (AE) sensors, Eddy-current transducers, accelerometers, laser interferometers, fiber-optic sensors, and piezoelectric lead zirconate titanate (PZT) elements, have demonstrated their utility in structural health monitoring. Notably, many of these sensors operate in a passive manner. However, PZT sensors can be used as active actuators as well, in terms of dual piezoelectric effect. Compact size, low weight, minimal power consumption, and the ability to generate the wave signal with the desired amplitude, frequency, and waveform are the main advantages offered by PZT elements, making them a preferred choice for SHM.
Beyond all these merits, SHM based on ultrasonic guided waves (UGW) stands out as one of the most accurate techniques that can be used in a variety of plate-like structures, spanning from airplanes to medical composites, for malfunction diagnosis [
13], because of their powerful capability of long-distance propagation with high speed and little loss of energy. UGWs are dependent on the properties and thickness of the medium they propagate through. Cost-effectiveness, ability to monitor large areas (guided waves can propagate with little attenuation in thin-walled structures), and high sensitivity to detect small damages are all benefits of SHM based on UGW and PZT elements [
14]. UGWs signals are generated and received by the PZTs across the monitored area, so variations in the signals are then analyzed to diagnose damage in the structure [
15]. The anomaly detection is mostly carried out according to the supervised paradigm, based on observation of relative changes in the inspected part: signals recorded in a current state are compared to a dataset gathered in the pristine state of the structure (i.e., reference or benchmark), serving as the baseline. Deviations, resulting from baseline measurements, may be treated as an indication of damage [
13]. Health indicators, damage-imaging approaches, as well as machine learning tools can be used for the damage-related features extraction.
In recent decades, significant efforts have been dedicated to the development of UGW-based damage detection algorithms by combining several techniques, including damage index (DI), time of flight, time reversal (TR) technique, and probability-based diagnostic imaging, in order to extract features from the captured signal that can be connected to damage at various states. For instance, the time of flight algorithm relies on the time lag between the incident wave that the sensor first captures and the wave scattered by damage that the same sensor subsequently captures [
4,
5,
7,
16]. The time reversal technique consists of identifying the presence of damage in the vicinity of a path between two sensors by verifying the similarity between the reconstructed signal and the original incident signal [
17]. Probability-based diagnostic imaging describes a damage event using a color-scale image to represent the likelihood of a damage occurrence at a specific location of the structure [
8]. Damage index-based techniques entail calculating the ratio between a structure’s initial and diminished impedance capability, which can then be used to determine the severity and location of the damage [
18].
Recently, a procedure introduced by Falcetelli et al. [
19] utilized the TR method and a Frequencies Compensation Transfer Function (FCTF) approach to reconstruct both Narrow-Band and actual Broad-Band AE signals. A variety of sensor layouts and materials were used in the study’s experimental testing; two different AE sources were also employed: (1) a Numerically Built Broadband (NBB) signal, and (2) a Pencil Lead Break (PLB). Abaqus
®/CAETM was applied to numerically verify the findings while implementing absorbing boundaries to reduce edge reflections. After that, the suggested method was employed to detect damage in an aluminum flat plate.
Furthermore, investigation concerning damage diagnosis methods of components manufactured by FRP composite materials is witnessing increasing attention [
11,
20]. Perfetto et al. [
8] used experimental and numerical techniques to inquire about guided wave propagation in the composite winglet structure at various actuation frequencies. They developed a damage detection technique based on their investigation of the guided wave propagation’s dispersion property. In the same work, the authors used a composing procedure consisting of Probability Ellipse (PE) and the guided ultrasonic wave propagation technique to investigate the location of a malfunction throughout a composite winglet when subjected to a LVI damage; the sensitivity analysis regarding the location of the actuating PZT was performed, jointly to an analysis on the effects of the load on the PE field value. The presence of a spar stiffener on the dispersion and scattering/reflection phenomena of guided waves were evaluated as well by means of the finite element method.
Parallel with a sharp increase in the computational power, modern techniques such as artificial intelligence (AI) have proved their potential. This technology offers several critical benefits that make it an excellent tool for solving a vast majority of complex human problems, making faster decisions, being constantly available, and reducing human error. AI encompasses various methods, including artificial neural networks (ANN), machine learning (ML), and deep learning (DL) algorithms, which are all well suited for SHM and monitoring tasks. These techniques, thanks to their robust information fusion and pattern analysis abilities, enable the classification or regression-based diagnosis of damages [
21,
22]. ML techniques for SHM are entirely data driven; and for this reason, a large set of data must be provided to describe the structural state comprehensively [
23].
Rai and Mitra [
24] presented a hybrid physics-aided multi-layer feed-forward neural network to improve damage detection under Lamb wave responses in a numerically modelled aluminum thin panel. To localize damage positions around an aluminum flat plate, Perfetto et al. [
25] combined the finite element method and ANN. In this study, the damage index calculated on the 0-order symmetric UGW propagating mode demonstrated its usefulness in differentiating between different damage regions.
Zhang et al. [
26] used ML to recognize the size and shape of damages in a simulated aluminum beam with 17 different damage configurations by the classification of selected features. Kumar and Mitra [
27] tested an Orthogonal Matching Pursuit process combined with a ML algorithm to automate the damage detection process, offering an efficient technique tested on a numerically modelled aluminum panel.
Melville et al. [
28] used a DL Lamb waves-based algorithm for rapid, accurate, and automated damage position detection by comparing the full wavefield images of a pristine and a damaged state of two identical aluminum plates. Sampath et al. [
29] proposed a hybrid method that incorporated a DL model with higher order spectral analysis in order to detect fatigue cracks in an aluminum specimen. Gao and Hua [
30] explored a broadband Lamb wave DL algorithm for damage localization and quantification on a corroded aluminum plate.
Lee et al. [
31] presented an automated technique through ultrasonic wave pattern using a deep autoencoder (DAE) for the damage detection and classification through automatic feature extraction with unsupervised clustering.
Chiachío et al. [
32] proposed a multilevel Bayesian procedure for the damage assessment in layered composites using through-transmission ultrasonic data; the method was first validated on synthetically generated data (damage hypothesis was, however, based on the uniform reduction in the Young’s modulus of several layers at specific area), and then evaluated on real signals from post-impact damage experiments.
Dipietrangelo et al. [
33] proposed a ML application for impact localization on an isotropic plate. The authors compared polynomial regression and shallow neural network results, confirming the effectiveness of the ML procedure in detecting and localizing damages under different combinations of training/test sets.
A state-of-the-art review of the different data-driven solutions for SHM and damage detection is provided in [
34]. Several works dealing with ML can be found in literature also for composites.
He et al. [
35] discussed the use of vibration-based monitoring and machine learning algorithms (MLAs) for anticipating delamination damage in FRP composites. To create a database for the MLAs’ training, the authors used a theoretical model of a FRP beam with delamination under vibration. Support Vector Machines (SVM) demonstrated the best prediction performance for both discrete and continuous parameters of delamination location and size among theMLAs tested: Back Propagation Neural Network (BPNN), Extreme Learning Machine (ELM), and SVM. The study demonstrated the potential to enhance the prediction capability of MLAs in assessing delamination damage and provided evidence for the applicability of SVM for structural health monitoring of delamination damage in FRP composites.
Viotti and Gomes [
36] presented an innovative technique for identifying delamination in sandwich composite structures utilizing ML. The method employed sensor data to train an ML network to categorize the damage location and estimate its size. The technique exhibited promising results, achieving an average accuracy of 85% in pinpointing damage location. However, accurately estimating the extent of the damage solely from modal datasets remains challenging.
Given the extensive range of structures operating under variable environmental conditions, such as fluctuating temperature and humidity, the adoption of resilient learning models, domain-adaptation algorithms, and transfer learning models holds potential advantages. In the realm of non-destructive tests, where boundaries between classes are not distinctly defined, fuzzy classifiers have demonstrated remarkable capabilities [
37,
38].
To date, the damage classification using UGW procedure reported in literature mainly deals with isotropic components and simulated (numerical) dataset. The next logical step, in line with current research trends, involves working with more complex specimens made of anisotropic composite materials, and employing more advanced techniques, such as ML. Therefore, this study proposes a combined approach that integrates guided wave propagation with ML for the detection and classification of damage in flat FRP composite plates.
The remainder of this paper is structured as follows.
Section 2 provides details on the case study, the testing process, the noise reduction methodology, the signal pre-processing, as well as both features extraction and selection phases. After that, the considered ML algorithms and the classification stage along with the provided results are discussed in
Section 3. Finally, the
Section 5 summarizes the entire procedure.
4. Classification and Results
In the realm of machine learning, three fundamental classification techniques exist: supervised, unsupervised, and reinforcement learning. While the output labels are not introduced in an unsupervised classification procedure such as clustering, they are pre-distinguished in supervised ML algorithms such as Support Vector Machine (SVM). On the other side, a reinforcement learning algorithm works in such a manner to maximize the cumulative rewards; in this process, the data type is not predefined [
50,
51].
The objective of the current study is to conduct a comparative evaluation of the accuracy of diverse supervised machine classifiers. For this purpose, labels (classes) are introduced along with the dataset.
4.1. R-Classification
In the present study, supervised machine learning algorithms were employed for detecting the damage location, i.e., the R-Classification. Two different feature vectors were evaluated, derived from selected features obtained from sensors 2 and 3, and features belonging to sensors 4 and 5 (refer to
Table 4 and
Table 5, respectively). The Classification Learner application available in MATLAB
® was used for this sake. The dataset was partitioned such that 85% was allocated to the training phase and the remaining 15% to the testing phase. Importantly, these two sets were randomly selected from the specified feature vectors before entering the application environment.
As a starting point, all available classification algorithms in the eight families, i.e., decision trees, discriminant analysis, Support Vector Machines, nearest neighbor, kernel approximation, ensemble, neural network, and Naive Bayes classifiers, were trained on the feature vector belonging to sensors 2 and 3. Upon comparing the validation accuracies, it was found that the “Bagged Trees” belonging to the ensemble family exhibited the highest performance, e.g., 92.9%.
The next step was to implement an optimization scheme for this family using “Bayesian optimization” as the optimizer, “expected improvement per second plus” as the acquisition function with 200 iterations, and “decision tree” as the learner type to find the tuned hyperparameters.
Figure 14 shows the performance of the optimization procedure in terms of minimum classification error versus the number of optimizer iterations. The Best point hyperparameter (the red square in the figure) was reached after 33 iterations when the ensemble method was set to “Bag”. The observed minimum classification error, the number of learners, the maximum number of splits, and the number of predictors to sample were, in that order, 0.0368, 366, 134, and 3.
Figure 15a,b show the confusion matrices for the training and testing phases, respectively, using the optimized network on the assumption of the sensors pair S2–S3. In the confusion matrices, R-Class 1, R-Class 2, R-Class 3, and R-Class 4 are represented by numbers 0, 1, 2, and 3, respectively. The validation accuracy increased in this instance to 96.32%. Only 5 out of 136 samples were mistakenly classified. Furthermore, the observed accuracy in the testing stage was 95.83%. Additionally, the average F1-score and sensitivity of the testing phase are both 0.958.
As depicted in the graphs of
Figure 15, out of the 136 samples randomly assigned to the training phase, only 5 were misclassified. Specifically, 1 sample from R-Class 2 was classified as R-Class 1, 1 sample from R-Class 2 was classified as R-Class 3, 2 samples from R-Class 3 were classified as R-Class 4, and just 1 sample from R-Class 3 was classified as R-Class 4. During the testing phase, only 1 sample from R-Class 4 was incorrectly classified as R-Class 3.
The process previously outlined was then applied to the feature vector selected from sensors 4 and 5, as specified in
Table 5. In the training phase, the initial accuracy was 92.71%, with the “Bag” ensemble method exhibiting superior performance. Using the same optimization settings as the previous case, the AdaBoost ensemble method with 488 learners, a learning rate of 0.86794, a maximum of 6 splits, and a minimum classification error of 0.028429 was determined through the tuning procedure. The optimization procedure based on the minimum classification error per number of iterations is illustrated in
Figure 16. It is worth mentioning that after 144 iterations, the Best point hyperparameters were explored. The training and testing confusion matrices with accuracy values of 96.32% and 91.67%, respectively, are shown in
Figure 17a,b. In the confusion matrices, R-Class 1, R-Class 2, R-Class 3, and R-Class 4 are represented by numbers 0, 1, 2, and 3, respectively. Furthermore, during the testing phase, the average F1-score and sensitivity stand at 0.935 and 0.958, respectively.
Comparatively, the accuracy during the training phase remained consistent at 96.32% for both feature vectors. However, the testing accuracy in the cases of sensors 4 and 5 was slightly lower than in the first case, i.e., 91.67% and 95.83%, respectively, despite a higher number of selected features (12 compared to 9 for sensors 2 and 3).
As depicted in the previous graphs of
Figure 17, out of the 136 samples randomly assigned to the training phase, again only 5 were misclassified. Specifically, 2 samples from R-Class 3 were classified as R-Class 1, 1 sample from R-Class 3 was classified as R-Class 2, 1 sample from R-Class 3 was classified as R-Class 4, 1 sample from R-Class 4 was classified as R-Class 3. During the testing phase, only 1 sample from R-Class 1 was incorrectly classified as R-Class 4, and only 1 sample from R-Class 2 was incorrectly classified as R-Class 3.
While the four receiving sensors were initially installed on the plate structure under consideration, the results of the training and testing phases on the two distinct conditions, i.e., sensors pair S2–S3 and S4–S5, suggest that analyzing the signals of only two sensors, either in the lower or upper part of the structure, can be sufficient to identify the occurrence of the damage and its location within the faulted region.
4.2. S-Classification
The feature matrix, consisting of 540 samples and 13 features, is utilized for size detection, specifically for the S-Classification. During the testing phase, 10% of the dataset was allocated for evaluation and the 5-folds cross-validation method was selected as the validation scheme. The best performing machine learning classifier models were determined by running various algorithms, and the results are summarized in
Table 6.
Table 6 showcases that the Ensemble-Subspace KNN algorithm boasts the highest validation accuracy of 94.65%. It is important to note that this algorithm uses the Subspace method for the ensemble and the nearest neighbors learning type, with a total of 30 learners. The Ensemble-Subspace KNN algorithm, alongside the Ensemble-Bagged Trees, Ensemble-Boosted Trees, and Kernel-SVM Kernel, achieved the highest accuracy in the testing phase, which was 98.15%. During the testing phase, the mean F1-score and sensitivity were recorded as 0.990 and 1, therefore. A higher accuracy in the testing phase compared to the validation accuracy suggests that the algorithm has not been overfitted during the training phase. Furthermore, since the accuracy in the testing phase is high enough, no optimization process was carried out to tune the hyperparameters.
The confusion matrices for the training and testing phases of the Ensemble-Subspace KNN algorithm are shown in the following graphs,
Figure 18a,b. It should be emphasized that S-Class 1, S-Class 2, and S-Class 3 are represented by indices 0, 1, and 2, respectively.
As depicted in the previous graph, out of the 486 samples randomly assigned to the training phase, 26 samples were misclassified. Specifically, 6 samples from S-Class 1 were classified as S-Class 2, 13 samples from S-Class 2 were classified as S-Class 1, 1 sample from S-Class 2 was classified as S-Class 3, 4 samples from S-Class 3 were classified as S-Class 2, and 2 samples from S-Class 3 were classified as S-Class 1. During the testing phase, only 1 sample from S-Class 2 was incorrectly classified as S-Class 1.
5. Conclusions
This research explored the application of machine learning (ML) classification techniques to classify damaged plates based on their failure location and size, e.g., R-Classification and S-Classification tasks.
In the initial phase of the experiment, a composite plate measuring 300 mm × 300 mm was used, with a cuboid of 20 mm × 25 mm placed on its surface to simulate various reversible damage configurations. Guided waves were propagated over the plate through a central piezoelectric sensor, and the resulting diagnostic waves were captured by four sensors placed in diametrically opposed directions. The plate was divided into four equal regions, and the experiment was repeated 40 times for each region, moving the damage position in each of the plate’s four zones. After collecting 160 signals, high-frequency noises were filtered out using the Butterworth filter, and 30 features were extracted in the time, frequency, and time-frequency domains. The 120 extracted features were designated as the primary feature vector for each experiment. To examine the ability to localize damage using only two sensors, 9 features were selected for the combination of sensors 2 and 3, and 12 features were selected for the combination of sensors 4 and 5 using the sequential forward selection procedure. Several ML classifiers were then used to classify the labeled signals using MATLAB® Classification Learner App. As the primary accuracy was not satisfactory, an optimization process was employed to find optimized hyperparameters. The final accuracy in the training and testing phases was 96.32% and 95.83%, respectively, for the selected features from sensors 2 and 3. Meanwhile, the training accuracy remained consistent at 96.32%, but the testing accuracy decreased to 91.6% for the combination of sensors 4 and 5.
In the second section and to intelligently detect the damage size, three cuboids of 20 mm × 25 mm, 20 mm × 35 mm, and 20 mm × 45 mm were used to experimentally simulate various damage scenarios on the same plate as the previous part. For each damage size, the test was repeated 180 times, changing their positions across the plate. Once the 540 signals were collected by the four sensors, the same procedure involving noise reduction, feature extraction, and feature selection was employed with the difference that the data from all four receiving sensors is used in the feature extraction. In the classification stage the 13 selected features were fed into the existing classifiers models, the Ensemble-Subspace KNN emerges as the best performer, scoring 94.7% and 98.1% accuracy in the validation and testing phases, respectively.
The findings demonstrated the potential of this technique for the damage diagnosis in composite plate-like structures, whereas only two receivers can be employed for the automatic sake of localization and severity without losing accuracy.
Implementing the proposed methodology may present certain challenges, particularly due to potential uncertainties arising from varying environmental conditions. This is because piezoelectric sensors, which are integral to the methodology, are highly sensitive to temperature changes. This sensitivity could lead to shifts in the distribution of classes between the training (source) and testing (target) domains. A possible solution to mitigate these effects could involve the use of a domain-adaptation algorithm, which could be explored in future research.