Classifying Tensile Loading History of Continuous Carbon Fiber Composites Using X‐Ray Scattering and Machine Learning

The tensile loading history of continuous carbon fiber composites is classified using machine learning (ML) and crystallographic data from the polymer matrix. Composites with polyamide‐4,10 matrix and unidirectional 10° and 45°, and 0°/90° cross‐ply layups are subjected to single‐cycle uniaxial tensile loads corresponding to 25–90% of their nominal maximum strain, and mapped by X‐ray diffraction with approximately 1000 data points from each layup. The unit cell alterations are used as a feature set for optimizing three ML algorithms; linear discriminant analysis, support vector machines (SVM), and gradient‐boosted decision trees (GBDT), with the objective of predicting five discrete loading magnitudes of the respective layups. It is demonstrated that SVMs and GBDTs can be trained to achieve a classification accuracy of >90% on unseen test data, both in cases where the feature set consists of data points from individual layups only, but also when data from the three layups are aggregated. The performance of the models is also shown to be similar to a binary problem, in which the composites are categorized according to a threshold load.

Wide-angle X-ray scattering (WAXS) has been used extensively to probe crystalline order in carbon fiber composites and matrix polymers, including crystalline phases of nylon sheets, [21] the interphase between carbon and polyamide, [22] phase transitions of polyimide-confined nylon fibers, [23] and the local tensile deformations in polyamides, [24] for example.The studies conclude that early-state defects lead only to minor effects on crystalline information, and any assessment requires considerable statistical evidence.Furthermore, there are few rigorous physical models that connect microscale crystallographic information to the macroscale defects, and eventually to the composites' lifetime, and thus a more phenomenological or databased approach must be taken.
Machine learning (ML) methods have an advantage in that they can find correlations in large amounts of data, in principle connecting any input-output pair, given that the information is there. [25]In the context of health monitoring of composites and polymers, Pawar et al. [26] proposed a system for damage detection in helicopter rotor blades.By using simulated loads of the helicopter vibratory hub as input features for a support vector machine (SVM) classifier, [27] the rotor blades could be categorized into three classes relating to their structural integrity.Qiao et al. [28] used acoustic emission measurements and ML to monitor damage modes in carbon/epoxy composites.Specifically, they used a combination of SVMs and k-means clustering method, [29] together with real-time readings of specimens under the three-point bending test, and were able to distinguish between various damage events in the composites.Kurita et al. [30] used electron microscopy together with k-means method to predict Young's modulus in composites with varying fiber porosity and orientation.
When X-rays are concerned, Obdrup et al. [31] used WAXS and linear discriminant analysis (LDA) [32] to classify two structural conditions of polyethylene ropes.In their study, they demonstrated that a 100% classification accuracy could be obtained both with preprocessed 1D WAXS data and derived physical parameters as input features for the classifier.Elsewhere, Liu et al. [33] proposed a method for characterizing the extent of delamination in carbon fiber composites using lamb wave propagation and ML.The authors used X-ray absorption images to quantify the delamination area, which they correlated with the acoustic emissions through a comparative ensemble of ML methods.
In this study, we demonstrate how WAXS and ML can be combined to monitor the health of continuous carbon fiber composites.Particularly, the focus is on minute changes in the crystal structure of the bulk polymer matrix, at the onset of damage to the composites.To generate samples with variations in damage magnitude, material samples were subjected to single-cycle uniaxial tensile loads, at magnitudes progressively outside of the linear regime.Three layup configurations were investigated, 10°a nd 45°unidirectional (UD) and 0°/90°x-ply.We find that subtle alterations in matrix unit cell and crystallinity can be used as a feature set for training ML algorithms for predicting the relative magnitude of exposed loads to different material samples with a high accuracy.Three commonly used classification algorithms are considered and the performance of models trained on data from the separate composite layup configurations are compared, but also when trained using data from the three layups altogether.Additionally, we construct a scenario in which the specimens are successfully classified based on a threshold of loading history.

Materials
Figure 1a,b illustrates the employed samples and sample layups (DSM Engineering Materials).All samples were continuous carbon fiber-reinforced thermoplastic composites with a polyamide-4,10, and 60% fiber content by weight.Panels were hot pressed from eight layers of tapes in two configurations, UD and 0°/90°, providing panels with a thickness of approx. 2 mm.From these panels, samples of 200 Â 10 mm (see Figure 1b) were cut using waterjet cutting to obtain UD samples with fibers oriented under 10°, 45°, and orthotropic (0°/90°) orientation with respect to the loading direction.To allow proper gripping and avoid failure in the grips, tabs were cut from the same material and subsequently glued on the ends prior to testing.
The selected three fiber orientations were chosen to introduce a variety of damage mechanisms.As an example where multiple layers with varying orientations interact under mechanical loading, the 0°/90°x-ply was chosen.Since the deformation behavior of a 0°UD will be dictated by the fibers, and that of a 90°UD by very local deformation in between fibers and at fiber interfaces, 10°and 45°UD were chosen instead since they show a more pronounced contribution of the matrix to the total deformation, expressed by the distinct nonlinearity in the stress/strain curve (see, e.g., Figure 2a, vide infra) before triggering failure.

Mechanical Loading
Figure 1b shows the loading direction.Uniaxial tensile tests were performed using a Zwick Z1484 equipped with a 200 kN load cell using a gripping length of 100 mm.The test protocol was according to ISO527, providing a nominal strain rate of 1% min À1 for strains up to 0.25% to determine the modulus and a strain rate of 5% min À1 for the remainder of the test.Strains were measured using an optical extensometer (VideoXtens) providing a resolution of 0.5, which with a gauge length of approx.70 μm results in a resolution in strain below 0.0001%.To obtain an indication of the strength of the samples, a single sample was loaded up to failure.Next, to vary the mechanical histories to the test samples, pristine samples were loaded for one cycle to a maximum of 25, 50, 75, and 90% of their strength.Subsequently, the samples were unloaded and reloaded to a maximum of 10% to evaluate their stiffness after the preloading, and samples were unloaded and removed for the scattering experiments.0.5 Â 0.5 mm 2 .The samples were mounted horizontally on a motorized stage, with the thickness of the sample normal to the incident beam.Three parallel scan lines across the sample lengths were performed (see Figure 1c) with a step size of 0.6 mm and an exposure time of 1 s per scan, totaling approx.200 point-like X-ray illuminations per sample (see Table 1).
The scattered X-rays were recorded by a Pilatus 2M detector with a pixel size of 172 Â 172 μm 2 , placed 0.64 m downstream of the sample, accommodating a q-range of approx.3-30 nm À1 .The isotropic regions of the diffraction signal were reduced to the intensity I as a function of the scattering vector q.First, this required identifying the isotropic regions, which might vary due to the out-of-plane waviness of the fibers. [34]The scattering images were thus integrated radially, and a Gaussian was fitted to the resulting radial profile, giving an azimuthal maximum intensity χ 0 for each of the scattering images.Subsequently, the images were masked and integrated azimuthally, excluding angles χ 0 AE 35 ∘ .This was done to exclude as much of the anisotropic signal as possible (i.e., matrix-fiber interphase), not directly relating to the bulk matrix.Furthermore, the resulting 1d WAXS profiles were deconvoluted into their respective components by performing a curve fit to the experimental data from all the scans of the samples.The Bragg reflections and the amorphous halo of the polymer were each represented by a Pseudo-Voigt function, and the background was fitted with a Kohlrausch-Williams-Watts exponential [35] and a linear function.Prior to the fitting procedure, the scattering intensity was normalized to sum to one, to account for differences in beam intensity.The curve fitting was done using the lmfit library [36] in Python.
From the fits to the WAXS profile, in total 21 parameters were extracted.Of these, 20 were associated with the polyamide-4,10 unit cell, and one represented the degree of crystallinity in the material.These parameters were subsequently employed in the supervised learning (vide infra).First, the relative intensities of the peaks were calculated as: with i, j representing the [001], [002], [100], and [010/110] reflections (see e.g., Figure 3c), and [q min , q max ] = [3,30] nm À1 , the q-range of the experiment.Similarly, the crystallinity was estimated by the sum of the intensity components from all crystalline peaks I k , divided by the intensity of the amorphous phase I a : The index k iterates over the seven crystalline peaks that are present in the 1d scattering profile (Figure 3c).In addition, we also considered the full width at half-maximum and the relative (inverse space) distances of the reflections from the polyamide.These were taken directly from the results of the curve-fitting procedure.

Computational Section
Three supervised learning algorithms were chosen for predicting the mechanical testing history of the materials; LDA, SVMs, and gradient-boosted decision trees (GBDTs).
LDA [32] is a classification and dimensionality reduction technique which uses decision boundaries in the N-dimensional feature space to separate features of data belonging to different classes.The class densities are modeled as a multivariate Gaussian (where the training data is used to estimate the distribution), and by assuming that they have a common covariance matrix, the decision boundaries can be drawn where their posterior probabilities are equal.Having closed-form solutions and no hyperparameters to tune, LDA is both fast to compute and simple to use.
SVMs [27] is a method which also uses hyperplanes to separate classes of data.The strength of this algorithm lies in its ability to achieve this in an optimal way when the classes cannot be separated by a linear boundary, or when they overlap.The objective of SVMs is to maximize the margin between the decision boundary and two neighboring classes, while under the constraint that some points are allowed to be on the wrong side of the margin.As opposed to LDA, this method has a higher versatility in that more complicated kernels (decision boundary shapes) can be applied, but the training complexity increases rapidly with large datasets. [37]BDTs [38] is an ensemble learning method which uses decision trees as the base estimator.As opposed to averaging ensemble methods, gradient-boosted trees are trained sequentially, where subsequent estimators "learn from the mistakes" of their predecessors.This is achieved by more heavily weighing training examples that have been misclassified by earlier estimators, and thus the training instances that are difficult to predict have a higher influence on estimators later in the chain.Predictions are then made by combining a weighted majority vote from all of them.
Table 1 lists the dataset specifications.Five datasets were constructed from parameters of the reduced WAXS curve and their associated mechanical testing histories.Three datasets consisted of X-ray scans (illuminations) stemming from samples of the respective fiber orientations.The remaining two were a combination of data collected from all three layups, and the two UD, respectively.The fiber orientation was not included as a feature in the mixed datasets.The five datasets were separately used for optimizing, training, and testing instances of the three classification algorithms.In total, there were 21 input features per sample scan, as described in Section 2.3, and five possible outputs, corresponding to the relative amounts of mechanical loading associated with the samples, described in Section 2.2.The chosen pipeline for training and independent testing of the classifiers was as follows.The data were first split into 70% for training and validation and 30% for testing.Subsequently, mean value μ and standard deviation σ were calculated for each feature (in the training set).These were used for standardizing the features to have a zero mean and a unit variance.An observation x j belonging to feature i was thus transformed according to z j = (x j Àμ i )/σ i .Following this, the classification algorithms were optimized by performing an exhaustive grid search of a combination of hyperparameters, using stratified fivefold cross-validation on the training data.The optimal set of parameters was chosen based on the algorithms' performances in terms of the classification accuracy.
Here I is the indicator function, N is the number of test instances, ŷ is the predicted label, and y is the true label.Bootstrap validation of the algorithms with optimal parameters was performed for 10 000 rounds (resampling of the training data), before retraining the models on the full training dataset, and ultimately evaluated on the external test data.We used the scikit-learn [39] implementations of LDA and SVM, and the XGBoost library [40] for GBDT.The radial basis function [41] was chosen as the kernel in the SVM.In addition, two other hyperparameters were important for the SVM's performance, which related to the complexity of the decision surface and the influence of individual training samples, respectively.These were optimized by the grid search routine.The GBDTs were used with a Softmax objective function.During optimization, we also tune the depth of each decision tree, the learning rate, and the number of training rounds.The values of hyperparameters used are listed in Table S2, Supporting Information.LDA was used with a singular value decomposition solver, having no hyperparameters to tune.

Mechanical Loading
Figure 2 shows the mechanical characterization of employed materials.Figure 2a shows the tensile stress as a function of strain for the three fiber orientations, where each test represents an individual sample.The curves of the samples with 10°and 0°/90°orientation display discontinuities, which are indications of damage events such as fiber failure.All curves overlap to a good approximation, demonstrating reasonably good reproducibility.However, when comparing the initial modulus of each experiment (see Figure 2b), the modulus of the pristine samples displays large deviations for all layups, even up to 20% variation between the minimum and maximum.This is not uncommon for thermoplastic composites and finds its origin in its intrinsic scatter, i.e., its sensitivity to fiber waviness, (local) fiber orientation, and (local) fiber volume fraction. [34]he statistical relevance of the magnitude of stiffness can be improved by adding more measurements.However, it will be difficult to use classical approaches linking secant modulus to mechanical loading, [7,8] since the variability of the local stiffness would exceed the anticipated decrease in stiffness caused by damage.This is also reflected in the stiffness measured during the secondary loading, displaying no clear trend of stiffness reduction after preloading.
Although one might argue that the lack of stiffness reduction implies no damage is induced by the preload, it is important to realize that the stiffness of the composite is dictated by the carbon fibers.However, since the matrix material is viscoelasticviscoplastic, there are various stress-induced deformation and relaxation mechanisms on the molecular level which can introduce (local) changes that do not affect the macroscopic stiffness.As a result, a decrease in stiffness is actually not always present [9] and it is often difficult to distinguish between compliance changes caused by creep and actual damage. [6]2.WAXS Figure 3 summarizes the results of the X-ray experiments.Figure 3a shows a chosen example of the diffraction pattern from one sample with 10°fiber orientation.The labeled isotropic reflections are contributions from the polyamide-4,10 matrix reported in ref. [21].There is also an anisotropic reflection apparent at χ % 80 ∘ , perpendicular to the fiber axis.At the higher scattering angles, this is attributed to the more oriented crystalline domain in the matrix-fiber interphase, [22] and the tail of the signal stemming from elongated pore structures within the fibers at lower angles.[42] The radially averaged profile of the latter is shown in Figure 3b, for scattering angles up to q = 4, used for determining the local fiber orientation of the samples.
Figure 3c shows a representative example of the fit to the reduced scattering profile.The α-phase dominates the curve with the distinct [100] and [010/110] reflections. [21]Apart from the reflections associated with the α-phase, the profile shows three additional reflections from which the middle peak gives an evidence for the pseudo-hexagonal phase. [21]We assume that the effect of mechanical load is easiest to be discerned from the majority phase and focus on the α peaks alongside the amorphous scattering.Particular attention is placed on the relative peak positions with increasing tensile loading.
Figure 3d shows a box plot of the normalized (inverse space) distance between the [100] and [010/110] reflections as a function of the mechanical loading, q ¼ ðq 010=110 À q 100 Þ=½q 010=110 À q 100 0%σ max .The median value is represented by the orange line, and the top and bottom represent the 25th and 75th percentiles, respectively.Here, the whiskers are determined by multiplying the interquartile range by 1.5, outliers represented by the circles.The variability of the measured values along the scanlines within samples is relatively low, indicating that the effects from the mechanical loading manifest homogeneously across the sample length.
Jones et al. [21] showed that in a well-crystallized polyamide-4,10 the Bragg peak positions are such that q 010/110 À q 100 = 2.8 nm À1 , a value substantially higher than in our experimental data (approx.2.55 nm À1 ).Lower inverse space distances between these peaks are commonly associated with lattice defects in polyamides. [43]Therefore, we infer that, due to the relatively fast cooling rate during processing, in combination with topological constraints (entanglements), the polymer chains end up forming crystals where lattice defects are more frequent than expected.
Figure 3d also shows that the value of q 010/110 À q 100 tends to increase.This indicates that molecules use mechanical energy to rearrange themselves and let lattice defects migrate out of the crystalline structures.This crystal perfectioning mechanism is pronounced for the samples with 10°fiber orientation and much less/not present for samples with 45°and 0°/90°fiber orientations.This is consistent with the observation that samples with 10°fiber orientation exhibit the largest macroscopic strain-at-break (see Figure 2a) and, therefore experience a larger molecular mobility gain.

History Classification
Figure 4 presents various aspects of the classification algorithms' performance.In Figure 4a, the classification accuracies on unseen test data are shown for the three classifiers, respectively, for each of the five datasets introduced in Section 3 (Table 1).When trained on the datasets consisting of the UD 10°layup (represented by the first set of columns in Figure 4a), LDA, SVM, and GBDT all achieve accuracy scores above 96%, showing good generalization from the training data to unseen data samples.The accuracies of the predictions are slightly worse on the individual UD 45°and 0°/90°datasets (column sets 2 and 3 in Figure 4a), with the lowest score at 87.5% test accuracy using LDA, and the highest using SVMs with 91.3%.
The datasets consisting of samples from different fiber orientations, have features belonging to the same class which are more scattered, i.e., do not necessarily follow similar trends (conversely to those of the individual layups), and thus the learning task is conceivably more complex (see e.g., Figure 3d).Here, the SVMs and GBDTs are able to describe the variance in the data to a reasonably high degree, whilst the LDA model struggles in comparison, as shown in Figure 4a (column sets 4 and 5).This is not all that surprising, since one of the assumptions of LDA is that the covariance of the features across classes is identical, [32] which they in this case clearly are not.Figure 4c further demonstrates the performances using this dataset, by showing the amount of correctly predicted data samples within each of the three fiber orientations.For comparison, the change in accuracy compared to the algorithms trained on data from the respective layups only is also shown.The SVMs and GBDTs show only slight performance decrease compared to their counterparts trained on single fiber orientation data only, while that of LDA drops more drastically, more than À30% on the 10°data.
Figure 4d shows the confusion matrix of the GBDTs predictions on unseen samples of the multilayup dataset.Most of the instances follow the diagonal as correct predictions.The superand subdiagonals represent the slight miss-classifications, where samples are predicted to have only a slightly better or worse condition, in terms of the loading history.Only a few instances fall into this category.More severely, there are 17 miss-classifications in the cell corresponding to the samples loaded to 75% of the maximum load, which are here classified as having only a 25% σ max loading history.This corresponds to approx.7% of the total number of samples with 75% σ max as the true label.The cells of "extreme" miss-classifications (0-90 pairs) have no entries.The figure also highlights that the 0% σ max class is underrepresented, with only 19 (68%) samples correctly classified.
Table 2 shows the training scores of the algorithms, together with the mean and standard deviations from the bootstrap resampling routine.Although the GBDTs show the best performance  on the test data in most cases, they have training scores close to 100%, and test scores that are considerably lower.This indicates overfitting, and that more regularization could be used to further improve the generalization to unseen data samples.This is also the case for the SVMs, most notably on the dataset of all layups, where the accuracy score drops from 97.1% on the training data to 88.2% on the external test data.When comparing the test scores of the classifiers from all experiments to the mean values from the bootstrap resampling, we note that they are mostly within the estimated standard deviations.This indicates that the test scores are quite representative for the general performance of the algorithms.The distributions of the test scores from the Bootstrap resampling are shown in Figure S1, Supporting Information.

Binary Classification
The results in Section 4.3 demonstrate that the samples with five different loading histories can be distinguished with high accuracy, using features from the X-ray experiments as data for training classification algorithms.In engineering applications, it may be sufficient to have a more granular view of whether a certain part needs replacement or is a candidate for further inspection, i.e., above or below some threshold of exposed load.
Here, this scenario was simulated by redefining the class labels of the X-ray features of the different samples.One class consisted of the unloaded materials together with those loaded to 25% of the maximum while the second class consisted of those loaded to 50% of the maximum and above.This threshold could in principle have been arbitrary, but here it was chosen based on the failure events of the materials loaded to 50% and above, visible in the stress-strain curves in Figure 2.
Optimizing the algorithms followed the same procedure as described in Section 3.
Figure 4b shows the classification accuracies on the unseen test data.The overall performance of the GBDTs and SVMs is similar when compared to the multiclass case (see Figure 4a), though LDA displays varying results in comparison.On the combined datasets (all layups þ UD layups), the performance of LDA increases drastically but worsens when predicting the 45°and 0°/90°samples.Intuitively, the learning task becomes less complex when going from five to two classes, so one would expect an increase in performance given that the features of one class (in this case 0% and 25% σ max ) are more similar to each other than to the second class (50, 75, and 90% σ max ).In contrast, the dataset in the binary case consists of data points from more than just one material sample, meaning that the algorithms also need to account for variability of the features across samples, which again makes the learning objective more complex.Considering the performance across the five discussed datasets, the results in Figure 4a,b suggest that these "mechanisms" are (for better or worse) affecting the performance of the simpler LDA model, while the GBDTs and SVMs seem versatile enough to adapt and perform well regardless.
Since this binary classification problem is unbalanced with respect to the number of instances belonging to each class (see Table 1), we also report the F1-scores (Equation S(2), Supporting Information) of the algorithms. [44]These are qualitatively similar to those presented in Figure 4b, and are shown in Figure S2, Supporting Information.

Performance on Smaller Datasets
Collecting X-ray data from material samples can often be both expensive and time-consuming.ML algorithms may also require large amounts of data to converge and be viable as a modeling technique.It is therefore interesting, from a practical standpoint, to have an idea of how much data, i.e., X-ray scans, is required to successfully train a classifier with a sufficient performance.We therefore investigate how the classification algorithms perform when the relatively large amount of data available here is diminished.This numerical experiment is performed using subsets of data from the dataset of all sample layups for training the classifiers, with classifying the five loading histories as the objective.
Figure 5 shows the performance of the three algorithms as a function of the number of data points used for training and validation.Data points were drawn randomly from the full dataset, and training the models followed the same procedure as in Section 3, with the exception that the full amount of prescribed data was used for training and validation (no data was set aside for external testing).Each point along the curve in Figure 5 is the mean value of the validation score from 10 000 bootstrapping rounds, and the shaded areas are the standard deviation.(In the resampling procedure, we allow drawing data samples from the full dataset in a stratified manner, but the number of samples is restricted to the prescribed amount, indicated by the x-axis of Figure 5).There is a rapid increase in the accuracy of all three algorithms up to approximately 75% classification accuracy, or 10% of the full dataset size.Following this, the SVMs and GBDTs behave similarly and have slight increase in performance with increasing amounts of training data.The curves of these two, do not stabilize, and their trends are still positive when granted the full dataset, at which point their performance is comparable to what was found in Figure 4.The LDA classifier's performance looks to stabilize at 75% accuracy and does not improve when using larger amounts of data for the training.

Conclusion
WAXS and ML can be applied for discriminating between the mechanical loading history of carbon fiber composite materials.This was demonstrated for three layup configurations (i.e., 10°UD, 45°UD, and 0°/90°x-ply) uniaxially stretched to various loads.This procedure was based on employing characterizations of the polyamide matrix unit cell as a feature set for optimizing three supervised classification algorithms, LDA, SVMs, and GBDTs, with the learning objective of classifying the material samples into five distinct classes, corresponding to the amount of exposed mechanical loading.X-ray measurements indicate that the samples with 10°fiber orientation undergo distinct crystal enhancement when exposed to the mechanical loading.The loading history of these samples was thus easier to predict by the models, compared to those with 45°and 0°/90°fiber orientation.
The classifiers were subsequently generalized by expanding the dataset to include features stemming from the three layups altogether.The GBDTs and SVMs performed well also in this case, having accuracy scores of approx.90%.A binary classification task was also investigated by segregating materials into two classes of mechanical loading, based on whether there were visible failure events in the stress-strain curves from the mechanical testing.The results showed that the accuracy of SVMs and GBDTs was similar to that of the multiclass case, while LDA displayed a varying performance depending on the layup.
Considering the demonstrated versatility of GBDTs and SVMs, the results suggest that these two algorithms seem the best candidates out of the three for correlating WAXS data to exposed loads in discussed composites.This takes into account that composites with different fiber orientations might display dissimilar trends in the evolution of the unit cell morphology, with respect to the magnitude of mechanical loading.ML algorithms with nonlinear decision boundaries might be required to explain the variance in the data.
This study shows that correlations between the mechanical loading history and nanoscopic information from composites without visible macroscopic cracking or delamination can be found.The study does not consider the importance of the individual features used for building the models.For instance, it may be sufficient to use information from a subset of the Bragg reflections for making these predictions.This may be an important aspect from an application stand-point, where peak intensities or reachable scattering angles can be limited.Additionally, the basis for these results was limited to using characterizations of the polyamide unit cell in the bulk matrix only-There are other features present in the wide angles of the scattering pattern that might augment the feature space, i.e., the fiber-matrix interphase, as known in the prior art. [22]Scattering fingerprints from the lower scattering angles might also augment the feature space for making these predictions, for example, larger microscopic defects and pores in the carbon fibers, as discussed elsewhere. [42]

2. 3 .
Figure 1c,d illustrates the conducted WAXS experiment and polyamide-4,10 unit cell.The experiments were conducted at the Swiss-Norwegian beamline BM01 at the European Synchrotron Radiation Facility (ESRF), Grenoble, France.The energy of the beam was E = 17.8 keV and the beam size

Figure 1 .
Figure 1.a) Layups of the composites investigated.The 10°and 45°are UD and the 0°/90°is of a 4S stacking sequence.b) Dimensions of the samples with tabs.The samples are loaded uniaxially, in the direction indicated by the red arrow.c) Geometry of the WAXS experiments.The samples are mounted on a motorized stage, with the X-ray beam s in transmission mode perpendicular to the sample surface (x-, z-plane).Between each scan, the sample is translated along r to probe the full length of the sample.Three parallel scan lines along r are performed for varying z. d) Illustration of the crystalline polymer sheets within the matrix.The polymer chains are oriented along the c direction, and the intersheet and interchain directions correspond to the a and b axes, respectively.

Figure 2 .
Figure 2. a) Uniaxial strain as a function of stress for all samples of the three layups.The loading of the different samples to various strains is represented by colored curves, where the sample loaded until failure is shown in black.Following the initial loading, each sample is stretched to 10% of the maximum load (not shown) to assess differences in stiffness.b) Measured stiffness of the samples before (circles) and after (triangles) loading.

Figure 3 .
Figure 3. a) Example of a diffraction pattern from the composites (10°layup).The Bragg reflections of the bulk polymer are annotated in red and represented by the isotropic rings in the image.b) Intensity as a function of azimuthal angle from radially integrating the intensity in (a).The measured anisotropy is perpendicular to the fiber axis and is due to the preferred orientation of the polymer crystals in the fiber-matrix.The maximum of the streak χ 0 is found by fitting a Gaussian to the profile, and angles χ 0 AE 35 ∘ are not included in the azimuthal integration.The inset depicts the azimuthal angle in the (q r, q z )-plane.c) Chosen example of the azimuthally integrated diffraction pattern, with a representative curve-fit to the profile.The Bragg reflections of the polymer unit cell are labeled corresponding to that of (a).The background signal is represented by an exponential and a linear function, and the Bragg peaks of the crystalline and amorphous polymer phases are represented by the Pseudo-Voigt function.d) Box plots of the measured difference in position of the 100 and 010/110 reflections in all samples.

Figure 4 .
Figure 4. Performance of the classification algorithms trained on the different datasets in terms of classification accuracy on the external test data.Subfigure a) shows the performance in the multiclass case, and b) shows the corresponding scores of the binary classification setting.c) Accuracy scores per layup of the classification algorithms trained on the full dataset (all layups), with multiclass classification as the objective.The percentage change in accuracy compared to the algorithms trained only on data from the respective layups is also shown.d) Confusion matrix of the GBDT predictions on unseen samples when trained on the full dataset (all layups).The rows and columns represent the number of instances of actual and predicted loading, respectively.

Figure 5 .
Figure 5. Median validation accuracy as a function of dataset size for the three classification algorithms.At each point, bootstrap validation is performed for 10 000 rounds.The standard deviations are indicated by the shaded areas.

Table 1 .
Number of data points collected by X-rays of each class for the different datasets.

Table 2 .
Performance of the classification algorithms in terms of classification accuracy on the training dataset and external test dataset (multiclass).The corresponding mean scores and standard deviations from the Bootstrap resampling routine are also listed.