Curing process monitoring of polymeric composites with Gramian angular field and transfer learning-boosted convolutional neural networks

Continuous and accurate monitoring of the degree of curing (DoC) is essential for ensuring the structural integrity of fabricated composites during service. Although machine learning (ML) has shown effectiveness in DoC monitoring, its generalization and extendibility are limited when applied to other curing-related scenarios not included in the previous learning process. To break through this bottleneck, we propose a novel DoC monitoring approach that utilizes transfer learning (TL)-boosted convolutional neural networks alongside Gramian angular field-based imaging processing. The effectiveness of the proposed approach is validated through experiments on metal/polymeric composite co-bonded structures and carbon fiber reinforced polymers using raw sensor data separately collected through the electromechanical impedance and fiber Bragg grating (FBG) measurements. Four indicators, accuracy, precision, recall, and F1-score are introduced to evaluate the performance of generalization and extendibility of the proposed approach. The indicator scores of the proposed approach exceed 0.9900 and outperform other conventional ML algorithms on the FBG dataset of the target domain, demonstrating the effectiveness of the proposed approach in reusing the pre-trained base model on the composite curing monitoring issues.

Continuous and accurate monitoring of the degree of curing (DoC) is essential for ensuring the structural integrity of fabricated composites during service.Although machine learning (ML) has shown effectiveness in DoC monitoring, its generalization and extendibility are limited when applied to other curing-related scenarios not included in the previous learning process.To break through this bottleneck, we propose a novel DoC monitoring approach that utilizes transfer learning (TL)-boosted convolutional neural networks alongside Gramian angular field-based imaging processing.The effectiveness of the proposed approach is validated through experiments on metal/polymeric composite co-bonded structures and carbon fiber reinforced polymers using raw sensor data separately collected through the electromechanical impedance and fiber Bragg grating (FBG) measurements.Four indicators, accuracy, precision, recall, and F1-score are introduced to evaluate the performance of generalization and extendibility of the proposed approach.The indicator scores of the proposed approach exceed 0.9900 and outperform other conventional ML algorithms on the FBG dataset of the target domain, demonstrating the effectiveness of the proposed approach in reusing the pre-trained base model on the composite curing monitoring issues.

Introduction
The 'cradle-to-grave'-inspired life cycle assessment and health management of composite structures have been the subject of intensive research over the years.It articulates the continuous monitoring of structural integrity and health status of the composites using onboard sensors in a timely or, preferably, a near real-time manner from curing through service to the end-of-life of the composites, so as to enhance the structural durability, lower the maintenance cost, and extend the residual service life as progressive aging.Particularly, the degree of curing (DoC) is an essential quality-assurance indicator in the 'cradle' stage of polymer-matrix composites and is vital to warrant the structural integrity and performance of the fabricated composites in service.
Due to the features of cost-effectiveness, simplicity of post-signal processing, and high sensitivity to DoC variation, electromechanical impedance (EMI) has proven its advantage over diverse techniques available for DoC monitoring, such as infrared thermal imaging and optoelectronic measurement [1][2][3][4].The EMI method has further been advanced with the increased introduction of machine learning (ML) algorithms [5][6][7][8][9].Demonstrated application paradigms include the prediction of DoC using simulation data-based ML [10], which concentrates on optimizing the autoclave co-curing process for sandwich composite structures using a decision tree (DT) and random forest [11].The DoC prediction of the thermosetting prepreg in the compression molding process using an integrated method embracing genetic algorithm and back propagation is explored, and the feasibility is discussed [12].Though showing effectiveness and promising prospect, conventional ML-driven DoC monitoring is often restricted by the intrinsic bottleneck of ML algorithms, including particularly the poor generalization and inferior extendibility, when ML algorithms are attempted to new scenarios that are not included in the training processing (e.g., different kinds of polymers, different layouts of composites, different types of sensors, etc.) [13][14][15][16][17][18][19][20].Motivated by this, we develop a new DoC monitoring approach, which comprises the transfer learning (TL)-boosted convolutional neural networks (CNNs), in conjunction with a Gramian angular field (GAF)-based imaging processing.
The proposed approach aims to tackle the bottleneck of applying a pre-trained base model (PBM) to the curing monitoring of composite structures with different layouts.To validate the feasibility and effectiveness of the proposed approach on enhancing generalization capacity and extendibility without the need to increase the training dataset scale, experiments are carried out on polymetric composites with embedded fiber Bragg gratings (FBG) sensors, essentially different from the previous experiments for PBM.Four indicators, accuracy, precision, recall, and F1-score are adopted to assess the performance of the proposed approach.The final results of the proposed approach are discussed and compared with conventional ML algorithms, demonstrating the effectiveness of the proposed approach.

TL strategy
According to [21,22], the TL is a multi-task learning framework that tries to learn various tasks simultaneously, even in different scenarios.Therefore, the TL can be utilized to bridge the gap of applying the pre-trained deep learning (DL) models in the source domain to the target domain, as shown in figure 1.The conventional DL methods are traditionally leveraged for isolated learning tasks, requiring customization every time for a new dataset in other application scenarios, which lack the flexibility to adapt to changes in time-dependent applications.Nevertheless, those limitations can be primarily surmounted by TL, which could implement the knowledge transferring from the source domain to a new target domain.
The TL strategy adopted in this study is taking the PBM as a feature extractor in the reconstructed model.The weight values inside PBM are objective to be reused in a new scenario.The mathematical definition of TL goes as follows: supposing that there is a domain D, which could be described with a two-element tuple, including feature space χ and marginal probability P (X), where X is a set of sample data, defined as X = {x 1 , x 2 , . . ., x n } with vectorized element x i (i = 1, 2, . . ., n).Then equation ( 1) can be yielded as: (1) Moreover, suppose there is a task T, which can also be defined as a two-element tuple of the label space γ and an objective function f.The f is described as P (γ|X) from the probabilistic perspective.Then the mathematical definition of a task is rendered by equation (2): T = {γ, f} = {γ, P (γ|X)} . ( The above-mentioned domain can be further separated into the source domain D S and the target domain D T in detail.Accordingly, the tasks can be categorized into the source task T S and the target task T T .Considering the framework introduced by equation ( 1), the TL can be described as applying the knowledge learned from the T S to solving the T T .Hence, the defined purpose of this study can be expressed by equation ( 3): According to [23][24][25], the CNN model is readily available for image-relevant tasks based on various processing layers, such as the convolutional layers, pooling layers, dense layers, etc.The TL strategy boosted by the feature extraction can then be diagrammatically presented in figure 2.
Figure 2 indicates that the reconstructed model contains weight values learned from GAF images of the source domain, which plays the role of 'brain' in a rebuilt model.Three convolution-pooling blocks are frozen to prevent the current weight values from being updated when reused in a new case.The output of Block#3 is bottleneck features that are then vectorized into a column as an input of the classifier followed.The final results of DoC monitoring are exported from the output layer.

Series data to GAF images
To meet the requirement of TL-boosted CNN, it is necessary to convert sensor data into images.Thus, the method of GAF is introduced to convert all the sensor data obtained at the cradle stage to images.The GAF is an approach that converts series data into visual representations.It involves constructing a matrix from the data, normalizing its rows, computing the Gram matrix through dot products, and converting it into an image using color mapping.The resulting image visually elucidates cyclic patterns and relationships within the original time-series data.
In detail, GAF includes two kinds of image-transformation methods, which are Gramian summation angular field (GASF) and Gramian angular difference field (GADF) [26], given by equations ( 4) and ( 5): where the I denotes the unit row vector; T is the set of rescaled series data; θ is the value of arc cosine based on the data.Specifically, for the data obtained by the EMI and FBG measurement, θ i can be calculated using the equations ( 6) and (7).
For measured EMI signals, the θ i can be explained using the equation ( 6): where where ε = {ε 1 , ε 2 , . . ., ε i , . . ., ε n }. ε i is micro-strain values that are measured by optical sensors.By referring to the well-known Gramian matrix, equations ( 4) and ( 5) can be further deduced as equations ( 8) and ( 9), which are the core equations implementing the process of sensor data to images

Fundamental of EMI and FBG measurements
The piezoelectric wafer and host structure are usually connected by adhesive.The principle of EMI based on a piezoelectric wafer is that when an electrical signal is applied to the piezoelectric material, it produces mechanical deformation, which in turn causes a voltage change in the transducer.This voltage can then be converted into impedance or admittance signals to measure the mechanical performance deterioration indirectly.Moreover, the piezoelectric wafer simultaneously serves as the actuator and receiver in the EMI measurement.The equation for EMI measurement can be theoretically described by equation (10) in terms of [27]: (10) where C = , and φ = ω•a cp .The parameters in equation (10) have been presented in the nomenclatures table.
Due to the variation of the resin matrix properties, the DoC of the composite fluctuates in the curing process.Apart from Zstr , other parameters in equation ( 10) stay unchanged through the curing process since the ambient temperature is constantly kept at 120 • C. The Zstr is only affected by the variation of structural properties through the curing process due to the chemical and physical reactions.Hence, the obtained EMI signals can be used for characterizing the curing progress in terms of equation (10).
FBG is a representative and widely used type of optical fiber grating, with a period typically in the sub-micron range.When light waves pass through the Bragg grating, a strong reflection is formed for light that satisfies the phase-matching condition.The phase-matching condition can be described in equation (11): where n 0 represents the effective refractive index of the grating region; Λ represents the grating period.
As can be seen from equation (11), FBG is sensitive to temperature and strain by inducing changes in n 0 and Λ, making them commonly used as temperature and strain sensors.The formulas for wavelength shift independently under the temperature and strain can be given by equations ( 12) and ( 13): where ∆λ T represents the wavelength shift induced by temperature, while ∆λ ε denotes the wavelength shift induced by strain; ∆T and ∆ε are the variations of temperature and strain, respectively.

Design of experiments
A series of experiments have been designed and carried out to validate the proposed approach in this study.As mentioned above, the experimental data are collected from EMI and FBG measurements based on the piezoelectric wafer and the optical fiber.The discrepancies leading to different curing regularity of composites consist in overall sizes, ply sequence, and materials, as shown in table 1.Specifically, table 1 presents specifications for an experimental setup involving composite materials and sensor instrumentation.The source domain consists of ten plies with a complex [(0,90)] 10 stacking sequence, while the target domain employs eight plies with a simpler [0] 8 sequence.The composite patch measures 100 mm × 100 mm × 2 mm, accompanied by a 300 mm × 300 mm × 3 mm aluminum plate used in both domains.The target domain features a larger 400 mm × 400 mm × 1.6 mm composite patch.The source domain employs 6 mm diameter piezoelectric wafers (0.5 mm thick), while the target domain uses 8.2 µm diameter optical fibers, including a 125 µm cladding.These variations highlight material composition, size, and sensor types, which are crucial in this study.

EMI measurement configuration.
The experiments in the source domain are designed to evaluate the curing process of composite structures using EMI.This specimen is a cocured structure comprising composite and metal.The system of EMI measurement and fabricated samples are illustrated in figure 3.
Figure 3 shows that the testing platform comprises a WK6500B impedance analyzer (Wayne Kerr Electronics Ltd, London), a PC controller, and a heating facility.The impedance analyzer is connected to the piezoelectric transducer with heat-resistance wires.The analyzer obtains the data through the entire curing process.The PC controller is to manipulate the frequency from 100 kHz to 600 kHz with a step of 1 kHz.The heating time of the curing process is about 240 min, with a data sampling interval of 2 min, and 121 groups of raw data are obtained.
The specimen to be co-cured is made of aluminum plate 6061-T6 and T300 woven prepreg.The piezoelectric sensor is actuated with a voltage magnitude of 1 V in the experiment.It should be noted that only the real part of EMI data is adopted for curing process evaluation due to its high sensitivity to structural variation.

FBG measurement configuration.
Another experiment is designed for the curing process measured by FBG sensors.The FBG data is the micro-strain, which varies with the curing process progressing.In this study, the DoC monitoring based on FBG data is a target task to test the extendibility of the proposed approach.The FBG measurement system is shown in figure 4(a).It contains a heating cabinet, a portable FBG demodulator (AeroGator, Technobis Fibre Technologies B.V.) with a maximum sampling frequency of 19.2 kHz in the length scope from 1515 nm to 1585 nm, and a controller.Figures 4(b) and (c) are separate bottom and top views of the cured specimen with an embedded optical fiber.
This experiment lasts 180 min with heating, alongside a data sampling interval of 3 min, and 63 groups of curing data are obtained at last.Considering the complexity of analyzing the initial FBG data, these are preprocessed with normalization before serving as a dataset in the target domain.

Dataset construction using raw sensor data
Although substantial efforts have been made in ML-related research for composites, insufficient data quantity still dramatically limits the development of competitive models.Thus, a simple but effective method, mean interpolation (MI), is applied to increase the quantity of the samples based on the originally obtained EMI and FBG data.MI is a simple method to estimate missing data points in a dataset.The operating principle involves calculating the average of neighboring data points on either side of the missing value.This average is then used to fill in the missing value, assuming that the missing point is likely to be close in value to its neighbors.MI method is quick and easy to operate but may not capture more complex patterns or variations in the data as effectively as more sophisticated interpolation methods.

Source domain dataset construction.
The number of initial samples measured by EMI is 121, but the sample quantity increases to 961 when enhanced with the MI.By trial and error, ten classes are determined with a DoC interval of 10%, which means DoC_i∈ The EMI data, serving as the source domain dataset, is partitioned into training and testing sets with an 8:2 ratio.To improve the convergence performance and trainability of the CNN model, the data for training and testing are randomly shuffled.Herein, the task in the source domain is to implement a PBM model with high accuracy of DoC monitoring.

Target domain dataset construction.
The initial experimental data in the target domain are obtained via FBG measurement with the optical fiber, including six gratings.It is effortless to find out that there are discrepancies between the composite structures and collected raw data in the source and target domains.
Similarly, 497 samples are obtained in the enhanced dataset after being augmented with MI based on the initial FBG data in the target domain.Then, the FBG data in the enhanced dataset are also transformed into the GAF images.This image dataset is further split into training and testing sets to study the performance of the reconstructed model with the TL strategy.Based on the weight values of the PBM trained by the dataset in the source domain, the rebuilt CNN model driven by the TL strategy is adopted to quantify the DoC for the curing data from a new case comprising other composite structures, which is the target domain.

Curing data collected by EMI and FBG measurements
The curve plots of the initial sensor data in the source and target domains are independently illustrated in figures 5(a) and (b).It should be noted that, in figure 5(a), the curves are manually selected with the step of 10 min to show the overall evolution regularity more intuitively.
As heating time increases, the peak frequency of the system shifts towards the right of the initial state curve (0 min), as shown in the plots in figure 5(a).In addition, the resistance magnitude decreases as the heating duration becomes longer.Figure 5(b) shows the normalized FBG data, which initially displays an increasing pattern before decreasing to zero.The peaks in figure 5(b) refer to the gel point, indicating the moment of phase transition.According to the results shown in figures 5(a) and (b), it demonstrates that EMI and FBG measurements can effectively characterize the curing process.

Transforming sensor data to GAF images
Transforming series data into images with GAF can capture relationships between data points.In the context of EMI and FBG signals mentioned in this study, the GAF conversion turns signal dynamics into structured images, aiding pattern recognition, feature extraction, and visualization.It is suitable for EMI and FBG signals because it can reveal complex patterns, invariant to time shifts, and simplify the communication of findings.Therefore, the GAF algorithm is suitable for converting the data of FBG and EMI into corresponding images.
To maximize the generalization capability of the TL method, the sensor data from experiments are herein converted into GAF images, which serve as the input of the proposed approach.However, owing to the great difficulties of showing all the transformed GAF images in one paper, only images at the initial and final stages through the curing process are presented, as shown in figures 6(a) and (b).It can be observed directly from these figures that the transformed GAF images present different features by comparison.
The transformed image using the EMI signature with 700 frequency points yields 700 pixels in horizontal and vertical directions, as shown in figure 6(a).Similarly, six pixels are distributed along the horizontal and vertical directions in figure 6(b), whose conversion is achieved based on the FBG signatures.It should be pointed out that the cross area in figure 6(a) is a counterpart to the peak frequency in figure 5(a).As the heating duration, the placement of the cross area gradually shifts from bottom-left to top-right.

DoC monitoring with TL strategy among different composites
As mentioned above, this study aims to implement the DoC monitoring between different composite structures by transferring the knowledge learned from the source domain to the target domain.Then, the training cost in the new scenario can be significantly lowered, accompanied by an improved ultimate performance.Figure 7 displays four curves with double vertical axes.It is evident that two of the curves exhibit increasing and stable trends for accuracy, while the loss curves display decreasing and stable patterns.All four curves converge towards a constant value, indicating that the PBM exhibits superior convergent performance.Moreover, the minimal discrepancy between the training and testing curves signifies a well-trained CNN model.
Four broadly used metrics in the ML community, accuracy, precision, recall, and F1-score, are introduced herein to evaluate the PBM performance quantitatively.The evaluated PBM scores using the four indicators are enumerated in table 2. All indicator scores in the source domain are above 0.9500, confirming the superior performance of the PBM in accurately quantifying the DoC as defined in this study.

DoC monitoring on the FBG dataset of the target domain.
As above mentioned, the TL strategy is employed on the target domain dataset.In this section, the PBM is utilized to extract features from the new dataset using the built-in frozen layers.The history curves on the target domain dataset changing with epochs are shown in figure 8.
Figure 8 shows that the two curves with a consistent upward trend represent accuracy plots, while the other two indicate    To investigate the performance of TL-boosted CNN on the testing dataset, a confusion matrix (CM) diagram is plotted, as shown in figure 9. Furthermore, to provide a more comprehensive and intuitive assessment of the model's performance, the CM is normalized to a scope of [0,1].It should be noted that there are ten classes, ranging from DoC_1 to DoC_10, with the horizontal axis indicating the actual classes and the vertical axis representing the predicted classes.The numbers displayed in the grids of figure 9 indicate the percentage of correctly classified samples within each class.Based on the values presented in figure 9, it can be concluded that the DoC quantitative identification exhibits significantly high precision in every class.Overall, the proposed TL-boosted CNN approach performs well on the target domain dataset for DoC quantitative identification.It only takes 6.58 s to be fully trained, compared to the 238.19 s required for PBM training on the same workstation.This reduction in training time consumption amounts to a remarkable 97.20% due to the avoidance of training a model from scratch using the FBG dataset of the target domain.Thus, the efficiency of the proposed approach in saving training time is clearly demonstrated.

Comparison between TL-boosted CNN and conventional ML algorithms.
In this section, indicator scores of the developed TL-boosted CNN approach are compared with those of the conventional ML methods, such as DT, knearest neighbors (KNN), support vector machine (SVM), and Gaussian naïve Bayes (GNB).The proposed approach and the above ML algorithms are all evaluated on the same FBG dataset of the target domain to determine their performance.
To visually compare the performance of TL-boosted CNN and the usual ML methods, a bar graph is created and illustrated in figure 10.The graph is color-coded, and the bar height represents the magnitude of the score, with greater height indicating better performance.A table displaying all indicators is attached to the bar graph to provide exact numeric values.According to figure 10, the rebuilt model driven by the TL approach significantly outperforms the classic ML methods of DT, KNN, SVM, and GNB.The scores of the TL-boosted CNN model are specifically highlighted in orange to emphasize their superiority over conventional methods.

Conclusions
This study presents a new way to monitor the curing process of polymeric composites at the cradle stage, which has important implications for improving their quality and service performance.Our main objective is to develop an effective approach for monitoring the curing process and quantifying the DoC of polymeric composite materials with the utilization of relevant data from other similar cases.Thus, we present an approach comprising GAF transformation, CNN model, and TL strategy, to improve the accuracy and efficiency of curing monitoring of composite structures.
The proposed approach is evaluated with the performance indicators, achieving scores above 0.9900 in quantifying the DoC on the FBG data of the target domain, with a reduction of training time up to 97.20% alongside enhancing the model generalization capacity.The proposed approach also indicates a significant improvement in the accuracy of DoC monitoring over conventional ML algorithms regarding indicator scores for performance evaluation.
Despite the inspiring results, there are still limitations to this study, such as the necessity for further validation on larger datasets and more extensive types of composites.In the follow-up research, we plan to modify this approach using multiple source domains with more complicated features and explore its potential applications in other industrial fields using various composite structures, such as aerospace, wind energy, transportation, etc.

Figure 2 .
Figure 2. Architecture of rebuilt CNN model boosted by TL strategy.

Figure 4 .
Figure 4. FBG measurement system for curing monitoring: (a) overall view, (b) bottom view of the specimen, (c) top view of the specimen.

4. 3 . 1 .
Training a PBM on the EMI dataset of the source domain.This section describes training a basic CNN model to function as a PBM, with batch size set at 32 and epochs at 200 on the training set.The performance of the PBM is then verified on the testing set.The model training history curves using the source domain dataset are illustrated in figure 7.

Figure 6 .
Figure 6.GAF at the initial and final stages: (a) using EMI dataset of the source domain, (b) using FBG dataset of the target domain.

Figure 7 .
Figure 7. History curves of PBM using the EMI dataset of the source domain.

Figure 8 .
Figure 8. History plots of the rebuilt model on the FBG dataset of the target domain.

Figure 9 .
Figure 9. Normalized CM of DoC quantitative identification with TL-boosted CNN on FBG dataset of the target domain.

Figure 10 .
Figure 10.Comparison of the proposed approach and four conventional ML methods on the FBG dataset in the target domain.
the real part of the EMI signals, which are actual resistance values, that are measured by piezoelectric sensors.Similarly, for measured FBG signals, the θ i can be explained using the equation (7):

Table 1 .
Specifications of samples used in experiments.

Table 2 .
Indicator scores of the PBM on the dataset in source domain.