A Machine Learning-Based Design Framework for Predicting the Minimum Laminate Configuration of Type IV Composite Overwrapped Pressure Vessels

Abstract

Type IV composite hydrogen storage vessels must ensure structural safety under high internal pressure, and determining the optimal laminate configuration typically requires repetitive finite element analysis (FEA), leading to significant computational cost during the early design stage. To address this limitation, this study proposes a machine learning (ML)-based design-assistance framework for predicting the minimum laminate configuration required to satisfy structural safety based on the Tsai–Wu failure criterion. Three geometric design variables—liner radius, liner length, and polar hole radius—were used as inputs, and a dataset was generated using ANSYS Workbench-based FEA. Five ML models—SVR, GPR, RF, XGBoost, and MLP—were applied and evaluated using leave-one-out cross-validation (LOOCV) and an independent test set. All models achieved high predictive accuracy, with LOOCV R² values ranging from 0.9801 to 0.9907 and test-set R² values from 0.9866 to 0.9949, while maintaining MAPE below 6%. The consistent performance between LOOCV and the independent test set indicates stable predictive behavior. Learning curve analysis demonstrated stable convergence and a small performance gap between training and validation, suggesting stable predictive behavior within the considered design space. Feature importance analysis using the RF model identified the liner radius as the dominant parameter, while the influence of liner length was relatively minor. These results demonstrate that the proposed ML-based surrogate model can serve as an efficient tool for rapid design decision-making, reducing reliance on repetitive FEA in the early design stage.

1. Introduction

Hydrogen has attracted increasing global attention as an alternative energy source for achieving carbon neutrality and reducing dependence on fossil fuels [1,2,3]. Owing to its high energy density and zero greenhouse gas emissions during combustion, hydrogen is considered a promising clean energy source for various applications [4,5,6]. However, due to its low volumetric energy density, efficient storage technologies are essential, and high-pressure gaseous storage has emerged as the most widely adopted method [7,8].

Composite overwrapped pressure vessels play a critical role in high-pressure hydrogen storage systems [9,10]. In particular, Type IV vessels, which consist of a polymer liner reinforced with carbon fiber-reinforced polymer (CFRP) through filament winding, are widely used in hydrogen mobility applications due to their lightweight characteristics and superior mechanical performance [11,12,13,14]. These vessels must simultaneously satisfy both lightweight design requirements and structural safety, making advanced design methodologies essential.

A key challenge in the structural design of Type IV composite pressure vessels is determining an appropriate laminate configuration that prevents failure under high internal pressure conditions [15]. Finite element analysis (FEA)-based structural evaluation has been widely employed as a standard approach for this purpose. Park et al. [16] combined netting analysis with FEA to optimize composite layer configurations and boss geometry while ensuring structural safety. Reda et al. [17] investigated the effect of winding angles on mechanical performance using ANSYS 2025 R2 Workbench-based FEA and netting analysis for Type IV vessels composed of a nylon 6 liner and CFRP. Farhood et al. [18] evaluated the influence of stacking sequence and winding angles on burst pressure using Tsai–Wu and maximum stress criteria. Atul et al. [19] analyzed stress distribution and failure behavior under varying winding angles using ANSYS ACP and validated the results with classical lamination theory (CLT). Regassa et al. [20] employed Abaqus to evaluate burst pressure for various laminate configurations and identified optimal winding patterns.

Although FEA-based approaches enable detailed evaluation of the structural behavior of composite pressure vessels, they often require iterative simulations across multiple design configurations, leading to substantial computational cost and time consumption [4,16,17,18,19,20]. This limitation becomes particularly significant during the early design stage, where extensive exploration of geometric configurations is required, thereby reducing design efficiency.

To overcome these limitations, machine learning (ML)-based approaches have been increasingly applied to composite structure design for predicting structural responses and enabling optimal design. Shaik et al. [21] utilized FEA-generated data to predict burst pressure in thin-walled pressure vessels using XGBoost and Random Forest models, demonstrating that ML can significantly accelerate structural evaluation compared to conventional FEA. Santos et al. [22] applied various ML models, including GPR, kPCA-Lasso, and ensemble methods, to predict burst strength based on filament winding process data, achieving high prediction accuracy, particularly with ensemble approaches. Kadri et al. [23] employed a Bi-LSTM deep learning model to predict ductile damage in Type IV hydrogen tank composites, demonstrating the effectiveness of hybrid FEM–ML frameworks. Li et al. [24] combined Kriging surrogate models with response surface methods to perform reliability analysis and particle swarm optimization (PSO)-based design optimization of composite hydrogen storage vessels. Koutsawa and Bouhala [25] used polynomial chaos expansion (PCE) surrogate models to quantify uncertainty in Type IV vessel design and identify key design variables. Li et al. [26] proposed a hybrid framework integrating FEA and artificial neural networks (ANNs) to optimize laminate design by simultaneously considering filament winding parameters and dome geometry. Alcántar et al. [27] applied genetic algorithms (GA) and simulated annealing (SA) to achieve lightweight optimization of Type IV composite pressure vessels, resulting in up to 11.2% weight reduction. Wang et al. [28] combined FEM-generated data with multi-layer deep neural networks (DNNs) to predict failure indices and performed efficient layup optimization using transfer learning and GA.

However, existing ML-based studies primarily focus on predicting structural responses—such as burst pressure, strength, and damage states—for vessels with fixed geometries, or on optimization under limited design conditions [21,22,23,26,28]. In contrast, ML frameworks that directly support design decision-making by predicting the minimum required laminate configuration for arbitrarily given geometric parameters, remain underexplored. Furthermore, despite the high cost of FEA-based data generation, which limits the availability of large datasets, systematic evaluation and comparison of ML model generalization performance under small-data conditions remain relatively limited.

Therefore, this study proposes an ML-based early design-assistance framework based on the selected geometric design parameters for directly predicting the minimum laminate configuration required to ensure structural safety in Type IV hydrogen storage vessels. Identifying this minimum laminate sequence is critical for achieving lightweight design while maintaining structural integrity, yet it typically requires iterative FEA-based evaluation. To address this challenge, three key geometric design variables—liner radius, liner length, and polar hole radius—are used as inputs. Based on FEA-generated data, five ML models—Support Vector Regression (SVR), Gaussian Process Regression (GPR), Random Forest (RF), eXtreme Gradient Boosting (XGBoost), and Multi-Layer Perceptron (MLP)—are applied. The generalization performance of these models is systematically evaluated using leave-one-out cross-validation (LOOCV) and an independent test set, providing a direct and efficient alternative to conventional iterative FEA-based design approaches. Unlike previous studies that primarily focused on predicting structural responses, the proposed framework directly supports preliminary design by estimating the minimum laminate configuration from geometric design parameters.

2. Methodology

2.1. Type IV Vessel Design and Input Variables

The pressure vessel consists of a cylindrical section and dome regions. In this study, an isotensoid dome profile was adopted, as it is known to provide favorable stress distribution and reduce stress concentration under internal pressure conditions [29,30]. The geometry and key design parameters of the Type IV composite pressure vessel are illustrated in Figure 1. Three key geometric design variables were selected as inputs: liner radius (r), liner length (L), and polar hole radius (r_p). These variables were chosen as primary geometric parameters governing the structural behavior and load distribution of the pressure vessel. The selected parameter ranges are summarized in

Table 1. Pressure vessel design parameters.

Variable	Symbol	Values (mm)
Liner radius	r	30, 40, 50, 60
Liner length	L	220, 260, 300
Polar hole radius	rp	8, 10, 12, 14, 16 1, 18 1

¹ Applied only to liner radii of 50 and 60 mm, as larger radii require proportionally larger polar hole sizes for physically realistic configurations.

. It should be noted that polar hole radii of 16 mm and 18 mm were applied only to liner radius cases of 50 mm and 60 mm. This constraint was introduced to ensure physically realistic design configurations, as larger liner radii require proportionally larger polar openings. Accordingly, the range of polar hole sizes was extended for larger vessel geometries to avoid impractical design combinations. In total, 60 design configurations were generated for subsequent FEA-based analysis.

2.2. FEA-Based Dataset Generation

The finite element mesh for both the CFRP overwrap and the liner was first generated separately in ANSYS Workbench. The generated mesh was then imported into ANSYS ACP-Pre, where the composite layup, including the stacking sequence, ply orientations, and layer thicknesses, was defined. The liner material was modeled as polyamide 6 (PA6), while the composite layers were modeled using carbon fiber/epoxy. The material properties of PA6 and carbon fiber/epoxy were obtained from the ANSYS Engineering Data library and are summarized in

Table 2. Material properties of PA6.

Property	Values
Young’s Modulus (MPa)	1111
Poisson’s Ratio	0.3499
Tensile Yield Strength (MPa)	36.74
Tensile Ultimate Strength (MPa)	71.89

and

Table 3. Material properties of carbon fiber/epoxy.

Property		Values
Young’s Modulus X direction (MPa)	$E_1$	209,000
Young’s Modulus Y, Z direction (MPa)	$E_2=E_3$	9450
Poisson’s Ratio XY, XZ	$v_{12}=v_{13}$	0.27
Poisson’s Ratio YZ	$v_{23}$	0.4
Shear Modulus XY, XZ (MPa)	$G_{12}=G_{13}$	5500
Shear Modulus YZ (MPa)	$G_{23}$	3900

, respectively.

The composite structure consisted of hoop and helical layers. The hoop layers were designed to primarily sustain circumferential loads, while the helical layers contributed to both axial and dome-region load transfer. The thickness and winding angle of the hoop layers were set to 0.03 mm and 90°, respectively. The helical layers had a thickness of 0.06 mm and were assigned a winding angle corresponding to the minimum winding angle (α). The minimum winding angle (α) was determined to ensure stable fiber placement without slippage in the dome region during the filament winding process, and was calculated using Equation (1) [16], given by:

$$\mathit{sin}\alpha ={\displaystyle \frac{r_p}{r}}$$

(1)

where α is the minimum winding angle, r is the liner radius, and $r_p$ is the polar hole radius. The stacking sequence was defined as repeated sets of [90°/90°/±α°], representing the combination of hoop and helical layers. The corresponding fiber orientations implemented in ANSYS ACP-Pre are illustrated in Figure 2.

An internal pressure of 78.75 MPa was applied, corresponding to the operating pressure of 35 MPa with a safety factor of 2.25. This loading condition reflects standard design requirements for high-pressure hydrogen storage vessels [16]. For the finite element modeling, SOLID185 (an 8-node hexahedral element) was utilized for the CFRP composite layers, while SOLID187 (a 10-node tetrahedral element) was employed for the liner. To ensure the accuracy of the FEA results for each design configuration, a mesh independence study was conducted by testing various mesh sizes ranging from 1 mm to 6 mm. Structural failure was evaluated using the Tsai–Wu failure criterion. The Tsai–Wu failure criterion can be expressed as:

$$IRF=F_i{\sigma }_i+F_{ij}{\sigma }_i{\sigma }_j$$

where i, j = 1,…,6, $F_i$ and $F_{ij}$ are the material strength coefficients determined from the composite strength properties, and ${\sigma }_i$ is the stress components expressed in Voigt notation. In this study, the inverse reserve factor (IRF) was used as the failure index, where IRF < 1 indicates a safe condition, IRF = 1 represents the onset of failure, and IRF > 1 indicates failure [31]. A representative distribution of the Tsai–Wu failure index (IRF) obtained from FEA is presented in Figure 3.

To determine the target output—the minimum number of laminate sets (N)—a systematic iterative FEA procedure was conducted for each design configuration. After calculating the corresponding minimum winding angle (α), a monotonic search was performed by increasing N in increments of one set. At each step, the maximum Tsai–Wu inverse reserve factor (IRF) across the vessel was evaluated. The convergence criterion was defined as the first instance where the maximum IRF fell below 1.0 (max IRF < 1). To strictly verify that the identified N was the absolute minimum, the preceding configuration (N-1) was also evaluated to confirm that it exhibited structural failure (max IRF ≥ 1). This complete iterative procedure was repeated for all generated design cases to build the final dataset. The resulting minimum laminate sets ranged from 5 to 20, with a mean of 12.27 and a standard deviation of 4.26.

2.3. Data Splitting Strategy

To ensure an objective evaluation of model generalization performance and to prevent overfitting, the dataset was divided into a training–validation set (50 samples) and an independent test set (10 samples). The test set was strictly excluded from all training and hyperparameter optimization processes and was used solely for final model evaluation. Stratified random sampling based on liner radius was employed to maintain a balanced distribution of geometric configurations across both datasets. Specifically, four liner radius categories (30, 40, 50, and 60 mm) were proportionally represented in both the training–validation and test sets. This approach was adopted to minimize potential data imbalance and evaluation bias that may arise from simple random sampling. The resulting test set consisted of 2, 2, 3, and 3 samples for liner radii of 30, 40, 50, and 60 mm, respectively. To further assess model generalization under limited data conditions, leave-one-out cross-validation (LOOCV) was applied to the training–validation set. LOOCV was selected due to the limited dataset size, as it allows the model to be trained on nearly the entire training dataset in each iteration while providing an estimate of predictive error within the considered design space.

2.4. Machine Learning Models

Five machine learning models with different learning mechanisms were employed to predict the minimum laminate configuration of the Type IV hydrogen storage vessels: Support Vector Regression (SVR), Gaussian Process Regression (GPR), Random Forest (RF), eXtreme Gradient Boosting (XGBoost), and Multi-Layer Perceptron (MLP). These models represent kernel-based methods (SVR, GPR), ensemble-based methods (RF, XGBoost), and neural network-based methods (MLP). SVR is a regression model based on structural risk minimization, which aims to find an optimal function within a specified error margin while maintaining generalization capability [32,33]. GPR is a Bayesian nonparametric model that provides probabilistic predictions and uncertainty estimation, making it suitable for small datasets [34,35]. RF and XGBoost are ensemble-based models that improve prediction accuracy by aggregating multiple decision trees and minimizing residual errors, respectively [36,37]. MLP is a feedforward neural network capable of capturing nonlinear relationships between inputs and outputs [38]. These models were selected to systematically compare their generalization performance across diverse learning paradigms, particularly under limited data conditions.

2.5. Model Evaluation Metrics

The performance of the machine learning models was evaluated using four standard regression metrics: the coefficient of determination (R²), root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).

R² measures the proportion of variance in the target variable that is explained by the model, and is defined as:

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

(2)

where $y_i$ is the actual value, $\widehat{y_i}$ is the predicted value, $\overline{y}$ is the mean of actual values and $n$ is the number of samples.

RMSE represents the square root of the mean squared error and penalizes larger deviations more heavily:

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

(3)

MAE measures the average absolute difference between predicted and actual values:

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

(4)

MAPE expresses the prediction error as a percentage, allowing relative comparison of model performance:

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

(5)

In general, a higher R² value and lower RMSE, MAE, and MAPE values indicate better model performance.

2.6. Hyperparameter Optimization

Hyperparameter optimization was performed using grid search on the training–validation dataset (50 samples). The search ranges and optimal hyperparameters for each model are summarized in

Table 4. Hyperparameter search space and optimal values for each model.

Model	Hyperparameter	Search Space	Optimal Value
SVR	C	[0.1, 1, 10, 100]	10
	epsilon	[0.001, 0.01, 0.1]	0.001
	gamma	[scale, auto]	auto
GPR	-
RF	n_estimators	[50, 100, 200, 300]	200
	max_depth	[3, 4, 5, 6, 7]	6
	min_samples_split	[2, 3, 4, 5]	2
XGBoost	learning_rate	[0.01, 0.05, 0.1, 0.2]	0.2
	max_depth	[3, 4, 5, 6, 7]	5
	n_estimators	[50, 100, 200, 300]	100
	subsample	[0.7, 0.8, 0.9, 1.0]	0.8
MLP	hidden_layer_sizes	[(16, 8), (24, 12), (32, 16), (64, 32), (128, 64), (24, 24, 12), (32, 32, 16), (64, 64, 32)]	(24, 12)
	activation	[relu, tanh, logistic]	relu
	learning_rate_init	[0.001, 0.01, 0.1]	0.01

. For GPR, hyperparameters were automatically optimized during model training by maximizing the log-marginal likelihood (LML) and were, therefore, excluded from the grid search process.

3. Results and Discussion

3.1. Cross-Validation Performance Evaluation

To quantitatively evaluate model performance and assess generalization capability under limited data conditions, leave-one-out cross-validation (LOOCV) was applied to the training–validation dataset. Given the relatively small dataset size (50 samples), LOOCV enables efficient utilization of available data by training the model on all but one sample in each iteration, thereby providing a robust estimate of model performance. The LOOCV results are summarized in

Table 5. LOOCV performance evaluation on training dataset.

Model	LOOCV (Training Set) Evaluation
	R2	RMSE	MAE	MAPE
SVR	0.9907	0.3909	0.2978	2.54%
GPR	0.981	0.5577	0.4384	3.46%
RF	0.9801	0.5703	0.4781	4.28%
XGBoost	0.9894	0.4163	0.3263	2.71%
MLP	0.9871	0.4604	0.3784	3.05%

, and the relationship between predicted and actual laminate counts is illustrated in Figure 4. Among the evaluated models, SVR achieved the best performance, with an R² of 0.9907, RMSE of 0.3909, MAE of 0.2978, and MAPE of 2.54%. XGBoost also demonstrated strong performance, with an R² of 0.9894 and MAPE of 2.71%. MLP, GPR, and RF followed with slightly lower but still competitive performance. Overall, all models exhibited high predictive accuracy, with R² values exceeding 0.98 and MAPE below 5%. These results indicate that the proposed approach provides reliable predictions across different model architectures. In particular, the consistently low prediction errors observed in SVR and XGBoost suggest their strong suitability for this problem.

To further assess the robustness of the proposed models, additional 5-fold cross-validation was performed. The results are summarized in

Table 6. 5-fold performance evaluation on training dataset.

Model	5-Fold (Training Set) Evaluation
	R2	RMSE	MAE	MAPE
SVR	0.9794	0.5809	0.4635	3.86%
GPR	0.9827	0.5319	0.4138	3.32%
RF	0.9706	0.6938	0.5833	5.43%
XGBoost	0.9862	0.4747	0.3602	3.08%
MLP	0.9841	0.5106	0.3798	3.04%

. The results showed consistently high predictive performance across all models, confirming the robustness of the proposed framework.

3.2. Independent Test Set Evaluation

To further evaluate the generalization performance of the models, an independent test set consisting of 10 samples was used. This dataset was completely excluded from the training and validation processes, ensuring an unbiased assessment of model performance. The test set results are summarized in

Table 7. Performance evaluation on independent test dataset.

Model	Test Set Evaluation
	R2	RMSE	MAE	MAPE
SVR	0.9866	0.5702	0.4618	5.90%
GPR	0.9893	0.5093	0.2862	2.29%
RF	0.9907	0.4753	0.379	3.93%
XGBoost	0.9913	0.4608	0.3088	2.90%
MLP	0.9949	0.3530	0.2586	1.86%

, and the relationship between predicted and actual laminate counts for the independent test set is illustrated in Figure 5. All models maintained high predictive accuracy on the independent test set, with R² values ranging from 0.9866 to 0.9949 and MAPE below 6%. Notably, the performance observed on the test set is consistent with the LOOCV results, indicating that the models generalize well to unseen data despite the limited dataset size. Among the models, SVR and XGBoost continued to exhibit strong performance, while the remaining models also demonstrated stable and reliable predictions. These results confirm that the proposed ML framework can effectively predict the minimum laminate configuration for new design conditions. Figure 5 presents a parity plot comparing the predicted and actual minimum laminate configurations for the independent test set. The close agreement between the predicted and actual values further demonstrates the predictive performance and practical applicability of the proposed framework.

3.3. Learning Curve Analysis

To further investigate model performance under limited data conditions, learning curve analysis was conducted. The learning curves for the five models are presented in Figure 6. As the number of training samples increased, all models exhibited stable convergence, with both training and validation errors decreasing. The performance gap between training and validation remained small across all models, indicating minimal overfitting. These results suggest stable predictive behavior within the considered design space. In particular, the consistent convergence behavior suggests that the proposed framework can effectively capture the relationship between geometric parameters and the required laminate configuration without requiring large-scale datasets. It should be noted that the learning curves are intended to illustrate the convergence behavior of the proposed models for the present dataset rather than to define a general minimum data requirement.

3.4. Feature Importance Analysis

To identify the relative influence of the input variables on the predicted laminate configuration, permutation feature importance analysis was conducted for all five machine learning models (SVR, GPR, RF, XGBoost, and MLP). The results are presented in Figure 7. Among the three geometric design variables, the liner radius exhibited the highest importance, indicating that it is the dominant factor governing the required laminate configuration. In contrast, the liner length showed relatively low importance, suggesting a minor influence on structural requirements. The polar hole radius demonstrated moderate importance. These results can be interpreted from a structural perspective. The liner radius directly affects the stress distribution under internal pressure, leading to significant changes in the required laminate thickness. On the other hand, the liner length has a relatively smaller impact on stress concentration and load distribution, resulting in a reduced influence on laminate configuration. These results are consistent with established pressure vessel mechanics, where the liner radius has the greatest influence on hoop stress under internal pressure. This agreement indicates that the proposed machine learning model successfully captures physically meaningful relationships governing the required laminate configuration.

4. Conclusions

This study proposed a machine learning (ML)-based design-assistance framework for predicting the minimum laminate configuration required to satisfy the Tsai–Wu failure criterion for Type IV composite overwrapped pressure vessels. Three key geometric design variables—liner radius, liner length, and polar hole radius—were used as inputs, and five ML models were applied based on FEA-generated data.

The results demonstrated that all models achieved high predictive accuracy, with R² values exceeding 0.98 and MAPE below 6% in both cross-validation and independent test evaluations. The consistent performance across LOOCV and the test set confirms the robustness and generalization capability of the proposed framework, even under limited data conditions.

In addition, learning curve analysis revealed stable convergence behavior with minimal overfitting, indicating that reliable performance can be achieved even with relatively limited training data. Furthermore, feature importance analysis identified the liner radius as the dominant design parameter. These findings provide meaningful design insights by clarifying the relative influence of geometric variables on laminate configuration.

Overall, the proposed framework offers a practical approach for predicting the minimum laminate configuration and has the potential to reduce the reliance on repetitive FEA simulations during the early design stage. Future work will extend the proposed framework by incorporating additional design and operational factors, including winding-angle optimization, material variability, laminate thickness variation, manufacturing defects, residual stresses, and environmental loading, to further improve its applicability to practical composite pressure vessel design.