Prediction of tensile strength for carbon fiber reinforced composites through transfer learning

Abstract

With the emergence of Industry 4.0 and the widespread use of smart computing, there is an increasing demand for lightweight, corrosion-resistant, high-performance materials in intelligent manufacturing, attracting extensive attention to researching new composite materials. Intelligent-driven composite material performance analysis and prediction based on big data and machine learning have become important means for research on new composites. However, previous studies on composite performance analysis often focused on material characteristics, neglecting the combined influence of processing parameters, structure, and application environments. On the other hand, in actual factories, the process of obtaining the above auxiliary data is very difficult and time-consuming. Therefore, this article focuses on carbon fiber reinforced composites (CFRP), takes advantage of transfer learning to achieve high accuracy in smaller datasets, and proposes a data-driven framework which can not only use the characteristics of the material itself but also increase the material structure and processing parameters to improve the prediction accuracy of the tensile strength of new composites. After comparing four commonly used base learning models, the coefficient of determination (R ² ) of the ElasticNet model is improved by 7.67% and the mean absolute error (MAE) is reduced by 55.53%. For other models, please refer to results and discussion.

Introduction

The emergence of Industry 4.0 and the widespread use of smart computing have attracted widespread attention to developing new composites. The demand for lightweight, corrosion-resistant, environmentally friendly, low-cost, and safe materials is increasing in intelligent manufacturing, as represented by aerospace and new energy vehicles. ¹ According to relevant analysis, ² the global aerospace composites market is expected to grow by 33%. Due to the long time and high cost of traditional material development methods, intelligent-driven composite material performance analysis and prediction based on big data and machine learning have become important means for research on new composites.^3,4

Currently, research on predicting the mechanical properties of composites can be classified into two main categories: finite element analysis (FEA) and machine learning. In studies on predicting mechanical properties using the FEA, Zhang et al. ⁵ have successfully predicted the static mechanical strength of fabric fiber-reinforced composite laminates with varying porosity. Wang et al. ⁶ developed a predictive model to evaluate the performance variation with temperature of carbon fiber reinforced composites (CFRP). Although many researchers have used the FEA to predict the mechanical properties of composites,^7,8 most of them only consider a limited number of parameters for prediction. The mechanical properties of composites are influenced by various factors, including materials and processing parameters, making finite element modeling challenging. Using the Monte Carlo method, Gao et al. ⁹ established a fiber network model based on a three-dimensional microstructure to represent the statistical and random properties of the material. They proposed a tensile performance prediction method based on the microstructural properties in the model. However, the model error obtained by this simulation method is relatively large.

On the other hand, machine learning methods have been employed to predict the mechanical properties of composites. ¹⁰ For instance, Pathan et al. ¹¹ proposed a supervised machine learning approach to accurately predict unidirectional composites’ macroscopic stiffness and yield strength under lateral loading. Similarly, Qi et al. ¹² used a decision tree regression model to establish the relationship between the performance variables of carbon fiber monofilament and the macroscopic mechanical property parameters of composites. Divakarraju et al. ¹³ considered different fiber and matrix properties, volume fractions, and fiber distributions and obtained a prediction model for carbon fiber’s transverse and shear modulus. Zhao et al. ¹⁴ proposed a machine learning assisted multi-scale modeling strategy, which used a low computation cost model in conjunction with molecular dynamics simulation to predict the mechanical properties of CFRP based on the resin molecules. However, most of these studies relied on data generated by FEA, which introduces errors due to its limitations. These errors, when combined with those of the machine learning models, can lead to reduced prediction accuracy.

Compared to the above methods, fitting real data using machine learning methods can help address the limitations of theoretical modeling. For instance, Vineela et al. ¹⁵ used an artificial neural network model to predict the tensile strength of composites for different composition ratios. Sharan et al. ¹⁶ employed an artificial neural network model to predict the tensile strength of unidirectional carbon fiber reinforced composites, considering parameters including fiber strength and matrix strength. However, incorporating microstructure parameters like porosity into predicting process outcomes often results in poor practical applicability.

Furthermore, many existing prediction models neglect the effects of practical application environments and processing parameters, leading to predictions that deviate significantly from real-world outcomes. On the other hand, different machine learning models are often trained and evaluated to select the model with the highest accuracy due to the lack of dataset analysis and model analysis. ¹⁷ For example, Shirolkar et al. ¹⁸ selected a suitable prediction model for the mechanical properties of carbon fibers by comparing different machine learning models. However, the characteristics of the composite material itself vary with the composition content and the processing environment, making it difficult for this method to select the optimal learning model. In the process of material development, apart from the characteristics of the composite material itself, the additional environmental factors generated during the processing and the composition ratio structure of the composites will also bring significant changes to the strength of the material. As a typical material in composite research, CFRP has shown wide application value in strengthening various and optimizing structures. ¹⁹ Among the many indicators of material performance, tensile strength plays a critical role in determining the ability to withstand tensile forces and resist damage. At present, several application cases have emerged in the field of material performance research using machine learning algorithms to predict tensile strength, such as fused deposition modeling. ²⁰ Therefore, we chose the tensile strength of CFRP as our prediction object.

This paper first aims to determine the various factors that affect the mechanical properties of CFRP through correlation analysis between data. Secondly, more effective transfer learning for smaller data sets can provide accurate prediction of the mechanical properties of CFRP. Finally, through the data-driven framework we proposed, an optimized prediction method is provided to select the most appropriate relearning model in accordance with user requirements. This makes the prediction method of composites not only more suitable for the characteristics of small data sets, but also maintains its accuracy or improves its prediction accuracy and reduces processing time without reducing the prediction accuracy of traditional machine learning methods, thereby improving the overall development efficiency of the system. After comparing 4 commonly used base learning models, the coefficient of determination (R ² ) of the ElasticNet model is improved by 7.67% and the mean absolute error (MAE) is reduced by 55.53%. For other models, please refer to results and discussion.

The major contributions of this study can be summarized as follows:

1) To solve the problem of limited datasets. We used the generative adversarial networks (GAN) method, which is commonly used in data augmentation technology, to improve the dataset.

2) We proposed a data-driven framework based on specialized machine learning models to predict the tensile strength of CFRP.

2-1 First, our framework can provide users with a variety of requirements, such as sample prediction accuracy, execution location, and available computing resources minimization, to adapt to different composite usage scenarios and provide customized solutions.

2-2 Second, our framework can use data correlation analysis to determine the establishment of multiple factors such as processing parameters, structure, and application environment, which is convenient for accurate parameter adjustment of learning models.

2-3 Finally, our framework is based on transfer learning, which can achieve high accuracy even with a small amount of data. By selecting a base learning model and adding highly relevant data, the framework can re-learn from the existing model to optimize the accuracy and processing time.

Framework design and implementation

Methodology

Scenario and problem statement

In our study, we considered the scenario shown in Figure 1. We can collect multiple influencing factors and target mechanical properties of composites from factory A and define them according to user requirements, so as to select the optimized base learning model of factory A as the target, and use a small amount of learning data obtained from factory B or the learning data fitted by the GAN method to generate a re-learned model for factory B to predict the mechanical property. The issues considered in this research paper are as follows:

1) Data collection: Due to the small scale of the factory or specific production methods, the number of samples collected is often limited, making it challenging to train a high-accuracy prediction model.

2) Multiple influencing variables: In actual production, a large number of influencing factors are typically collected. However, not all of these factors contribute meaningfully to the prediction and may even introduce noise, thereby reducing the prediction accuracy of the model.

3) Model comparison: Due to limited data set and lack of comprehensive data analysis, researchers often rely on experience and survey results to select and compare different machine learning algorithms. There is no guarantee that the trained model will meet the requirements.

4) Model evaluation: Model evaluation typically focuses on prediction accuracy but often overlooks other important factors, such as computational efficiency, robustness, and adaptability to real-world applications.

Figure 1.

Scenario for the prediction of mechanical properties of composites. Case A is when there is sufficient data, and case B is when there is not enough data.

Requirements

Based on the scenario outlined above, we can summarize several key requirements for predicting mechanical properties of composites as follows:

1) Data analysis: The collected data sets often contain various influencing factors. Efficient analysis is required to identify the factors most relevant to the target mechanical properties, reducing the impact of less relevant variables and enhancing the prediction accuracy.

2) User requirements: Practical constraints such as execution time, model size, and available computational resources must be considered in actual production.

3) Adaptability: The framework should facilitate the selection of machine learning models that meet specific requirements, reducing development time. It should also be flexible enough to switch models based on different production scenarios or user demands for model performance.

4) Reusability: Once a base model is selected, the framework should enable the reuse of previously trained models or store new models for future use, enhancing the prediction system’s overall efficiency and reusability.

Approach

Our approach is illustrated in Figure 2. First, we proposed a model selection policy. We establish a knowledge-sharing database to store trained models and performance metrics of Factory A, such as model accuracy, execution time and size. Our framework can define corresponding user’s policy according to the user requirements, and our framework can use our model selection algorithm to select the base model that meets the user’s conditions from the database. Second, users only need to import the data obtained from Factory B or the synthetic data into our framework. Thirdly, through data correlation analysis, we can determine the factors affecting the target variables, screen reasonable data, and pre-process and optimize the dataset of Factory B. Fourthly, combined with the optimized data of Factory B, our framework can use the base model of Factory A to quickly create a re-learning data model belonging to Factory B. Fifthly, according to the user’s requirements, we select reasonable computing nodes to quickly deploy the computing environment of the re-learning model of Factory B and implement performance prediction and model evaluation.

Figure 2.

Overview of approach for mechanical property prediction of composites.

In addition, to address the issue of insufficient data samples and generate high-precision learning models, we use the GAN method to create synthetic data to compensate for the lack of sufficient actual data. When sufficient relevant data samples are available, we can directly use transfer learning to retrain the learning model selected as the base model of our framework. Moreover we use Bayesian optimization to fine-tune and retrain the model. The evaluation results, including performance metrics, are stored in the database for future reference, further improving the adaptability and reusability of the framework.

Design of data-driven framework

This section discusses the design of our data-driven framework. The proposed framework is shown in Figure 3

Figure 3.

Overview of data-driven framework proposed in this study.

Data collection and processing

Regarding material selection, factors such as fiber strength, matrix density, fiber content, are considered to ensure the appropriate materials and configuration ratios are chosen during the prediction process. For structural design, parameters like the number of plies can affect composite materials' strength, stiffness, and stability. Regarding processing parameters, defects can be minimized, and the performance of composite materials can be improved by optimizing process parameters such as temperature, pressure, and processing time. In terms of environmental factors, the performance of composites may vary under different environments, such as ambient temperature, necessitating the selection of appropriate materials and design solutions for specific application scenarios.

First, to address the challenge of selecting influential factors for prediction, we employ the maximal information coefficient (MIC) to measure the correlation between two variables. MIC allows us to assess the degree of association between variables without assuming a linear relationship. We define the correlation based on the MIC coefficient: less than 0.3 corresponds to a weak correlation, values between 0.3 and 0.7 are defined as moderate correlation, and greater than 0.7 is considered a strong correlation. By applying MIC, we screen out factors strongly related to the target variables. Secondly, in the case of insufficient data, we use GAN method to generate synthetic data to improve the model’s prediction accuracy. For cases where there are relevant and sufficient datasets, our framework can utilize transfer learning to select the base model from the source database. It can be transferred to the processing nodes in the target domain according to user needs, waiting for the optimized dataset established after correlation analysis to predict the target model for further learning. Finally, we use Bayesian optimization to fine-tune the retrieved model to maintain better performance and improve the accuracy and processing time of the underlying model.

Model selection

We select the appropriate base model based on users’ different needs in different scenarios based on their pre-defined policies. Algorithm 1, the core part of our framework, outlines the model selection process. Our input covers policy definition such as accuracy, time, and size, and is equipped with three corresponding priority criteria. After the algorithm is started, each model in the database will be iteratively checked to determine whether it meets the given standards and ranges. If there is a model that meets the requirements, the most suitable model will be output according to the priority. If there is no model that meets the conditions, the framework asks the user to redefine the requirements and continue screening. This model selection algorithm provides a step-by-step approach to identifying the best-suited model from the library based on given conditions. It offers a flexible and scalable method for selecting the most appropriate model to meet specific needs.

Algorithm 1 model selection
1	Input: Policy P, priority order O
2	Output: Base model B
3	Function MODEL_SELECTION(P, O)
4	B ← an empty list           ▷ store models that satisfy the policy
5	for each model in database do
6	is_base_model ← true
7	for each metric in metrics of P do         ▷ select the model that satisfies all the metrics
8	if model[metric] > policy[metric] then
9	is_base_model ← false
10	Break
11	end if
12	end for
13	if is_base_model is true then
14	Add model to B
15	end if
16	end for
17	if B is not empty then
18	Sort B by GET_PRIORITY_ORDER(·, O)       ▷ Sort by priority metric
19	B ← B[0]
20	return B
21	else
22	return ∅        ▷ No match conditions
23	end if
24	end function
25
26	function GET_PRIORITY_ORDER(model, O)
27	keys ← metrics name list        ▷ metrics consist of accuracy, time, and size
28	priority ← keys[O]      ▷ the metric used to sort by priority
29	return model[priority]      ▷ return the value required for sorting
30	end function

Model generation and deployment

After selecting a base model, the next crucial step is to generate a predictive model through training and fine-tuning to obtain a fully trained and optimized model. At the same time, the model and its complete evaluation results are stored in the shared database for future reference. To reduce the risk of overfitting and improve the model’s generalization ability, we use sequential Bayesian optimization to optimize the model’s hyperparameters. This method combines sequence models with Bayesian optimization, gradually optimizing the model by selecting the optimal hyperparameters at each step. Once the prediction model has been thoroughly evaluated and optimized, it can be deployed to the user-specified computing node, for example, on the cloud or edge nodes near the user’s device specified by the user. After deployment, users can borrow their computing power on designated computing nodes to accurately predict the mechanical properties of fiber-reinforced composites (FRP), thereby promoting practical applications and engineering decisions.

Implementation

Data augmentation

During the manufacturing process of FRP, data collection is always a time-consuming and labor-intensive task. To handle this problem, we employ deep generative models to generate synthetic data. ²¹ These models are designed to learn the underlying distribution of real data and generate new data points with similar characteristics. We use conditional tabular generate adversarial networks (CTGAN), ²² a variant of deep generative models designed to create synthetic tabular data. CTGAN is based on the framework of GAN. It consists of a generator network that creates synthetic data and a discriminator network that evaluates the similarity between synthetic and real data. Through iterative training, CTGAN generates synthetic data that closely mirrors the statistical properties of real data. The primary advantage of using CTGAN to create synthetic data is that it can greatly reduce the workload and cost of data collection. Researchers can quickly obtain large data samples for model training, optimization, and evaluation by generating synthetic data. This approach provides a more efficient and economical way to obtain data for research in FRP.

Transfer learning

In the context of FRP, where rich relevant data sets exist, employing domain adaptation techniques can be very effective. One such method, transfer component analysis (TCA), ²³ aims to bridge the gap by modeling the distribution differences between the source and target domains. TCA can be leveraged to map the source and target domain data into a shared feature space which aligns the data distributions, enabling the model to adapt to the target domain. The application of TCA in FRP is of great significance. First, it allows the transfer of knowledge learned from the source domain to the target domain even if the data distribution is different, overcoming the common issue of limited labeled data in the target domain. Second, TCA helps to effectively utilize the rich and relevant data sets in the field of FRP. We perform feature alignment on the tabular data of the source domain and the target domain, and then incorporate the aligned feature data into the model for joint training to improve the training accuracy of the model. By using TCA, our approach can maximize the use of relevant data sets, improving the performance and applicability of the model in the field of FRP.

Policy definition

In our framework, users have the flexibility to define their specific policies by setting conditions and corresponding actions. These conditions may encompass the desired accuracy rate for sample predictions, the time requirements for actual predictions, and any constraints related to computing terminal resources. The user needs to input a requirement dictionary and a priority number as shown in the example, and the framework will output a base model. When there are few samples collected and there is a lack of relevant data sets, users can use CTGAN to augment the data, thereby increasing both the diversity and number of samples. If relevant data sets are available, transfer learning can be used to improve model performance by calling data sets from the database. Our framework selects, trains, and optimizes models based on user conditions.

Policy: {‘mae': 10, ‘time': 2.0, ‘size': 700}

priority_order: 0

Action: MODEL_SELECTION(policy, priority_order)

Experiment

Experiment dataset

The dataset used in this experiment comes from the open-source Composite Materials Handbook (CMH) compiled by the US Department of Defense, ²⁴ including one 100 samples, with representative shown in Table 1. The influencing factors of these data are listed from left to right as fiber strength (σ _f ), matrix density (ρ _m ), matrix content (V _m ), composite material density (ρ _c ), fiber content (V _f ), void percentage (V _d ), thickness of ply (t _p ), loading axis (LA, where 0 indicates the tensile direction is consistent with the fiber axis and one indicates it is perpendicular), number of plies (N), ambient temperature (T _a ), processing temperature (T _p ), processing pressure (P), and processing time (T).

Table 1.

Examples of representative data.

NO	Fiber	Matrix	σ f (ksi)	ρ m (g/cm3)	V m (wt%)	ρ c (g/cm3)	V f (%)	V d (%)	t p (in)	LA	N	T a (°F)	T p (°F)	P (ksi)	T (min)	σ c (ksi)
1	T-50012k	976	575	1.28	31	1.59	61.5	1	0.0053	0	8	75	240	85	60	298
2	HITEX336k	E7K8	560	1.27	34	1.58	58	0.39	0.0058	1	20	75	300	55	120	6.9
3	Celion12k	938	515	1.3	34.5	1.565	57.5	0.65	0.0058	1	20	75	355	90	120	9.6
4	AS412k	3502	550	1.26	32	1.575	59.5	0.5	0.0055	1	24	180	350	85	120	4.39
5	AS412k	3501-6	550	1.27	37.5	1.56	54	0	0.0057	0	8	75	240	85	60	262
6	T-30015k	976	530	1.28	25	1.64	69	0	0.0049	1	15	260	250	100	45	3.81
7	T-65012k	976	650	1.28	42	1.59	60.7	0	0.0053	0	9	250	350	95	90	260
8	AS412k	5250	550	1.25	27	1.62	65	0.45	0.0051	0	8	450	250	85	60	292
9	IM612k	APC-2	635	1.28	32	1.55	61.5	0.1	0.0053	0	8	180	720	60	45	344
10	M55J6k	954-3	583	1.19	23.2	1.665	59.2	0.4	0.0024	0	16	72	350	100	120	320

In this experiment, the ultimate tensile strength of CFRP is selected as the prediction target, which is an important indicator of the unidirectional tape mechanical performance. The types of CFRP include carbon-epoxy, carbon-bismaleimide, carbon-peek, and carbon-cyanate ester, and these type differences have a significant impact on the performance of CFRP. The distribution histogram of each variable is shown in Figure 4. Our data includes nine types of fibers and 11 types of matrices (indicated by numbers in Figure 4). In addition, it is worth noting that when the tensile direction is consistent with the fiber direction (LA = 0), the tensile strength is above 150 ksi, and when the tensile direction is perpendicular to the fiber direction (LA = 1), the tensile strength is within 50 ksi.

Figure 4.

Distribution histogram of each variable.

Representative model

Due to the complex nonlinear relationship between multiple variables and the objective function, to prove the validity of the framework, we selected three machine learning models capable of handling nonlinear data and a linear regression model as representative models to predict the ultimate tensile strength of CFRP. The decision tree regression (DTR) model can fit nonlinear relationships and automatically handle feature selection and feature interactions. As a representative ensemble learning model, the random forest regression (RFR) model can improve prediction accuracy and stability by combining multiple decision tree models. The multi-layer perceptron (MLP) regression model based on neural networks can handle nonlinear problems and has powerful expressive and generalization capabilities. The ElasticNet model, which combines L1 regularization and L2 regularization, is a classic linear regression model. To minimize the accuracy differences caused by fine-tuning the models, we mostly used the default hyperparameters provided by the sklearn library, as shown in Table 2.

Table 2.

The model used in the experiment.

Model	Hyperparameters
ElasticNet	alpha = 0.5, l1_ratio = 0.95
DTR	min_samples_split = 2, min_samples_leaf = 1
RFR	n_estimators = 100, min_samples_split = 2 min_samples_leaf = 1
MLP	hidden_layer_sizes=(3,), activation = ‘relu’ max_iter = 1000000, solver = ‘adam’

Evaluation metrics

Four commonly used statistical analysis metrics were employed to evaluate the accuracy of our mechanical property prediction model, including root mean squared error (RMSE), mean absolute percentage error (MAPE), Mean Absolute Error (MAE), and R ² . The expressions for these metrics are given in Equations (1)–(4), where $\widehat{{\mathrm{y}}_{\mathrm{i}}}$ is the predicted value, y _i is the measured value, and n is the number of samples. Other evaluation metrics include model execution time and size.

$RMSE=\sqrt{{\displaystyle \sum }_{i=1}^n\frac{{\left(\widehat{y_i}-y_i\right)}^2}{n}}$

(1)

$MAPE=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\left|\frac{\widehat{y_i}-y_i}{y_i}\right|\times 100\%$

(2)

$MAE=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\left|\widehat{y_i}-y_i\right|$

(3)

$R^2=1-\frac{{\displaystyle \sum }_{i=1}^n{\left(\widehat{y_i}-y_i\right)}^2}{{\displaystyle \sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2}$

(4)

Results and discussion

Data analysis results

The results of data analysis, as illustrated in the MIC heat map in Figure 5, highlight the correlation between influencing factors and the target variables, as well as the interrelationships among different influencing factors. Based on these results, we selected influencing factors with MIC value greater than 0.3 relative to the target variable and used them as feature variables for model training. The comparison results in Figure 6 demonstrate that the R² of each model has improved. The overall increase of the DTR model is 3.8%, the overall increase of the RFR model is 1.77%, and the increase of the MLP model is 4.43%. In addition, feature selection reduced the complexity of the models, enhancing their practicality and applicability in real-world forecasting scenarios. This has important implications for the actual forecasting process. Meanwhile, the error of the four models was reduced by 18.3%, further validating the effectiveness of this approach in improving model accuracy and efficiency.

Figure 5.

Heatmap of MIC matrix.

Figure 6.

The results of removing variables with little correlation.

CTGAN and transfer learning

When using CTGAN for data augmentation, we divide the data set into 80% training set and 20% test set to simulate the situation of small data sets. Each model was evaluated 10 times, and the average results were recorded. By using CTGAN to generate synthetic data, it can be observed from Figure 7(a) that the MAE is reduced in all models. Among them, the MAE of the DTR model is reduced by 25.72%, the MAE of the RFR model is reduced by 24.56%, and the MAE of the MLP model is reduced by 30.88%. These results show that the synthetic data generated by CTGAN effectively enhances the models’ ability to fit the real data, providing more meaningful information and improving prediction accuracy.

Figure 7.

Comparison of MAE of four models with (a) data augmentation using CTGAN, and (b) transfer learning using TCA.

When using TCA for transfer learning, the real data set was used as the target domain and 1040 synthetic samples generated by CTGAN were used as the source domain. As shown in Figure 7(b), the ElasticNet and DTR models exhibit a more significant reduction in MAE, while the reduction in the RFR and MLP models is relatively smaller. This can be attributed to the high quality of synthetic data generated by CTGAN, which allows the models to learn more effective information. In addition, the MLP and RFR models inherently have better learning capabilities. The MLP model has powerful feature extraction capabilities and performs better when processing complex data; while the RFR model reduces the noise interference of a single tree through the averaging of multiple trees, improving the accuracy and generalization ability of the model and robustness. Overall, the TCA method effectively improves model accuracy for small data sets, demonstrating its value in leveraging synthetic and real data for enhanced performance.

Through the above analysis, it can be concluded that both the CTGAN method and the TCA transfer learning method can improve the accuracy of the model on small data sets. The synthetic data generated by CTGAN provides more effective information, while TCA method improves the generalization ability of the model by transferring model knowledge. According to different actual scenarios, we can choose one of the methods to optimize the small data set model.

Model evaluation

By using our framework, based on the previous experiment, we fine-tune the model hyperparameters. Table 3 shows the overall evaluation results, and Figure 8(b) shows the distribution of predicted results for each model. Given that models possess diverse characteristics, their performance differs across various evaluation criteria. The ElasticNet model has the smallest size but the largest error. The DTR model achieves a satisfactory balance in terms of accuracy, execution time and size, while also demonstrating a good prediction effect. The RFR model has the smallest error, but the longest prediction time and largest model size. The MLP model has the smallest execution time, but the error and size are relatively large. By using our framework, the MAE of the four models is reduced by 55.53%, 38.58%, 45.30%, and 42.46%, respectively, and the R2 is improved by 7.67%, 5.19%, 3.47%, and 6.28%, respectively.

Table 3.

The evaluation results of the models.

Model	RMSE (ksi)	MAPE (%)	MAE (ksi)	R 2	Time (ms)	Size (KB)
ElasticNet	21.55	33.04	14.69	0.9752	0.592	0.687
DTR	15.28	18.73	10.62	0.9875	0.375	10.39
RFR	12.19	12.19	7.56	0.9921	2.723	633.16
MLP	18.07	18.34	12.63	0.9825	0.099	334.11

Figure 8.

Scatter distribution of prediction results for each model on (a) train set and (b) test set.

By comparing Figure 8(a) and (b), we can observe the MAE differences between the various models on both training and test sets. Since tensile properties are affected by many factors and there may be complex non-linear relationships, the ElasticNet model, using a simple linear combination, may not be able to capture the detailed changes in the data well. Its large MAE could result from regularization, which helps prevent overfitting but also limits the ability of the model to learn complex data relationships, resulting in a large average absolute deviation between the predicted and true values. The DTR model suffers from overfitting because the noise and details in the training set may be over-learned during the training process, thus performing poorly on the generalization ability and resulting in high MAE. On the other hand, the RFR model mitigates overfitting by employing an ensemble of multiple decision tree models, each built using random features and samples. This ensemble approach helps to reduce the impact of overfitting from any single decision tree, leading to better performance on the test set. The MLP model has only three neurons in the hidden layer, which may be relatively small for capturing the complex relationships in the data, especially for tensile strength, that may have complex non-linear relationships. The activation function, ReLU, although helps alleviate the gradient vanishing problem, the structure of the model may limit its ability to fit the data. Different models have different characteristics. We can define different policies to select base model based on actual user requirements and user scenarios.

Discussion

We used some material parameters and processing parameters, combined with data augmentation and transfer learning methods, to obtain four machine learning models with different characteristics. Through our data-driven framework, we can train machine learning models that meet the needs of different scenarios based on historical data. For example, in the creation of high-performance composites for critical aircraft components like wings and engines, the framework facilitates the selection of optimal fiber-matrix ratios and processing parameters, ensuring mechanical properties are met economically. Similarly, in the automotive industry, where lightweight materials are essential, our prediction model can identify material parameter combinations with minimal fiber content while meeting design requirements. However, challenges remain. Data quality and quantity are crucial as inaccurate or insufficient data can lead to unreliable predictions. Model interpretability is another concern, especially in safety-critical applications. Continuous model validation and updating are necessary to account for evolving materials and manufacturing processes. Future research should focus on refining data collection and management, enhancing model interpretability, and establishing robust validation frameworks.

Conclusion

Accurate predictive models are paramount in the field of composite materials, where understanding and predicting mechanical properties are crucial for applications ranging from aerospace to automotive industries. This paper presents a comprehensive data-driven framework designed for rapid deployment and prediction in a machine learning environment tailored for composite materials. The framework seamlessly integrates data processing, model selection, and model generation, enabling the selection of influential factors that enhance prediction accuracy while reducing model complexity. By addressing the challenge of generating high-precision models from small datasets, we have incorporated the CTGAN method to synthesize effective data and utilized the TCA method in transfer learning to leverage knowledge from large datasets. Our framework was successfully applied to predict the tensile strength of carbon fiber-reinforced composite materials, significantly reducing MAE and improving R ² , thereby demonstrating its effectiveness and practicality. This work significantly contributes to the field by providing a robust and efficient approach to predictive modeling in composite materials.

In the future, our research will delve into the intricate relationship between fiber state parameters—such as residual fiber length, dispersion, and orientation—and the mechanical properties of FRP. By building a machine learning model to explore this influence, we aim to further enhance the predictive capabilities and understanding of composite materials, paving the way for more sophisticated and accurate models in future studies.