Polyester Resin–Quartz Composites in the Age of Artificial Intelligence and Digital Twins: Current Advances, Future Perspectives and an Application Example
Abstract
1. Introduction
2. Materials and Applications of UPR Composites
- One of the primary issues is dispersion. Quartz is much denser and more abrasive than UPRs and tends to agglomerate during mixing. If not properly stabilized, it can also quickly sediment over time. Inadequate dispersion can result in heterogeneities, local stress concentrations and reduced mechanical performance in the final product [23,26,27].
- Another key challenge is the increased viscosity of the resin–filler mixture. High viscosity complicates resin handling, mixing, and mold filling, especially in complex geometries. The use of reactive diluents or thixotropic additives can reduce viscosity and improve flow. However, these additives must be carefully selected to avoid adverse interactions with the curing process or degradation of mechanical properties [28].
- Air entrapment and degassing also become more difficult as viscosity rises. Bubbles introduced during mixing or filling may become trapped within the matrix or mold, leading to porosity, aesthetic defects, and weakened mechanical zones. Vacuum degassing, optimized mold design and proper treatment of molds with release agents are essential to mitigate this issue [29].
- Moreover, cure inhibition or delay may occur due to the adsorption of initiators onto the quartz surface or due to residual impurities on the filler surface interfering with radical propagation, or even a high filler content. To address these issues, precise control of initiator concentration, temperature, filler content and surface treatment (e.g., silane coupling agents) is necessary to ensure full conversion and a uniform cross-linked network [16,26,30]. The curing of quartz-filled UPR composites represents a highly complex, multivariate process governed by intricate interdependencies between chemical kinetics, filler characteristics, and processing conditions.
3. Polymerization of Unsaturated Polyester Resins
ROOH + Co3+ → ROO⋅ + H+ + Co2+
- During propagation, the macroradicals incorporate additional unsaturated units to progressively form a cross-linked network (Equation (3)), e.g., by styrene (Ar=C6H5).
→ [–CO–CH(CH2ĊHAr)–CH(OR)–CO-O(CH2)2O–]n
- Termination occurs via radical recombination (Equation (4)) or disproportionation (Equation (5)).
4. Kinetics and Chemical Analysis
5. Quartz Composite Manufacturing
6. Research Landscape in Thermoset Composites and Digital Manufacturing Technologies
6.1. UPRs and Their Composites
6.2. Digital Twins and Artificial Intelligence
7. Application Example: Conceptual Framework
- The physical plant layer encompasses the manufacturing hardware—continuous blending of ingredients and casting equipment, molds, and curing ovens. Comprehensive instrumentation is required to capture the system’s dynamic behavior, including flow meters, thermocouples or infrared sensors, in-line viscosimeters and vision systems for capturing recipes and visual appearance of the final product.
- The data acquisition layer is responsible for real-time data collection, preprocessing, and control. Programmable logic controllers (PLCs) and edge gateways acquire high-frequency sensor signals, perform filtering and synchronization, and host localized DT proxies for low-latency control tasks like recipe feedback and feed rate stabilization.
- The data and model layer, typically implemented on cloud or private computing infrastructure, manages the persistence storage and computational aspects of DT. It contains time series databases for real-time and historical data, model repositories encompassing both physics-based and machine learning models, and simulation engines for curing kinetics and rheology. This layer could also integrate surrogate models that enable near-real-time predictions based on high-fidelity offline simulations.
- At the top, the analytics and decision layer hosts the real-time state estimator and optimization engines. The state estimator fuses incoming sensor data with physics-based model outputs through advanced data assimilation techniques to reconstruct latent variables such as local viscosity, temperature fields, and degree of cure. The optimization engine subsequently adjusts process parameters to balance competing objectives such as product quality, cycle time, and energy efficiency. DT’s supervisory control interface issues updated setpoints-e.g., recipe changes, mold temperature, or mixing speed to the physical plant, closing the control loop.
7.1. Use Case: Curing Kinetics and Peak Time Prediction
7.2. Use Case: Laboratory-Scale Evaluation
7.2.1. Experimental Dataset
7.2.2. Numerical Evaluation
7.2.3. Results of Random Forest and Gradient Boosting
7.2.4. Augmentation
7.2.5. PCA–Principal Component Analysis
7.2.6. Algorithm Comparison
7.2.7. Key Findings
- Gradient Boosting (GBR) consistently outperforms Random Forest (RF) across all scenarios and data conditions. On the augmented dataset (×8), GBR achieves RMSE prediction errors of about two minutes, which are within an industrially acceptable range for process monitoring.
- Gel time is the most important predictor in Scenario A; excluding it in Scenario B reduces regression depending on the model and data conditions. For example, LOO R2 drops from 0.551 to 0.340 for GBR using the original data and from 0.938 to 0.922 using the augmented data.
- Stratified bootstrap augmentation effectively addresses the limited sample sizes. The largest performance gains occur between ×1 and ×3, albeit diminishing improvements up to ×8 to ×10. A multiplier of ×8 provided Gradient Boosting with sufficient data to reach R2 > 0.90 in both scenarios while maintaining a conservative noise level (σ = 5% of standard deviation). This approach preserves the original feature distributions while simulating realistic measurement uncertainty.
- Principal component analysis (PCA) reveals that the curing process is governed by three independent physical dimensions: curing reactivity (gel time, catalyst concentration), the thermal environment (mold and ambient temperature), and the resin’s thermal state. Low-variance principal components (PC5) carry the strongest correlations with peak time, indicating that standard-based dimensionality reduction would discard critical predictive information.
- Among the four benchmarked algorithms, Gradient Boosting (GBR) offers the highest accuracy. On augmented data, it also exhibits the lowest cross-validation variance for Scenario A. A Random Forest (RF) exhibits the most stable performance on original data relative to its mean R2. SVR performs comparably to GBR on augmented data. MLP requires more data to achieve acceptable predictions.
- The complete data pipeline—from RANSAC-based outlier detection to stratified bootstrap augmentation, and further, to ensemble model comparison—provides a reproducible, statistically transparent framework for predicting peak times in highly filled thermoset composite systems. This framework supports developing digital twin strategies for quartz–UPR manufacturing processes.
8. Discussion and Further Perspectives
- A laboratory-scale evaluation of peak time prediction in highly filled quartz–UPR composites provides preliminary evidence that supports the feasibility of DT–AI integration. Gradient Boosting Regression (GBR) outperformed Random Forest consistently across scenarios, achieving promising prediction accuracies for industrial relevance. Nevertheless, due to the limited size of the laboratory dataset, there are significant concerns regarding the applicability of these models to full-scale production. A limited sample size increases the risk of overfitting, and performance metrics may not be applicable under different environmental conditions, batch variations, or equipment configurations.
- Gel time was found to be the most influential predictor. While this highlights the importance of kinetic parameters for accurate prediction, it also reveals the model’s strong dependency on a variable that is usually unavailable in industrial processing. In practical manufacturing environments, determining gel time in real time is rarely performed, so predictive models must operate without direct access to this parameter.
- Although stratified bootstrap augmentation improved model robustness and reduced variance, synthetic augmentation cannot fully substitute for diverse experimental data. To improve model robustness, a broader experimental design is necessary that incorporates variations in MEKP concentration, filler loading, and process parameters. Additionally, the current laboratory dataset does not represent industrial effects such as equipment drift and strong thermal gradients, which could limit the model’s predictive reliability when transferred to full-scale production.
- Principal component analysis (PCA) identified three independent physical dimensions —curing reactivity, thermal environment, and resin thermal state—underscoring the importance of retaining low-variance components for accurate prediction. However, dimensionality reduction based on small datasets risks discarding subtle yet critical effects, and PCA insights may not be applicable to larger, more heterogeneous production datasets.
- Neural network approaches, including MLPs, required substantially more data to achieve acceptable performance. This emphasizes that AI-assisted models are strongly constrained by the availability of experimental data. Thus, despite promising lab-scale results, the robustness and scalability of AI-enhanced DT frameworks in real-world, large-scale thermoset production remain unverified.
9. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
| AI | Artificial Intelligence |
| ANNs | Artificial Neural Networks |
| BPO | Benzoyl peroxide (Bz-O-O-Bz) |
| CaCO3 | Calcium Carbonate |
| Coct | Cobalt Octoate |
| CV | Cross Validation |
| DT | Digital Twin |
| DSC | Differential Scanning Calorimetry |
| FTIR | Fourier Transform Infrared Spectroscopy |
| FRPs | Fiber-Reinforced Plastics |
| GBR | Gradient Boosting Regression |
| IoT | Internet of Things |
| LCA | Life Cycle Assessment |
| LOO | Leave-One-Out Cross Validation |
| MEA | Mean Absolute Error |
| MEKP | Methyl Ethyl Ketone Peroxide |
| MES | Manufacturing Execution System |
| MLP | Multilayer Perceptron |
| MSE | Mean Squared Error |
| NMR | Nuclear Magnetic Resonance |
| PC | Principal Component |
| PCA | Principal Component Analysis |
| PET | Polyethylene Terephthalate |
| PVAc | Polyvinyl Acetate |
| QPCs | Quartz-Reinforced Polyester Resin Composites |
| R2 | Coefficient of Determination |
| RANSAC | Random Sample Consensus |
| RF | Random Forest |
| RMSE | Root Mean Squared Error |
| RTM | Resin Transfer Molding |
| SVR | Support Vector Regression |
| OOB | Out-of-Bag (estimate) |
| UPR | Unsaturated Polyester Resin |
| VE | Vinyl Ester |
| ZDMP | Zero-Defect Manufacturing Platform |
References
- Wang, R.M.; Zheng, S.R.; Zheng, Y.P. Polymer Matrix Composites and Technology; Woodhead Publishing: Oxford, UK, 2011; pp. 1–45. [Google Scholar] [CrossRef]
- Ashby, M.F.; Jones, D.R.H. Engineering Materials 2: An Introduction to Microstructures and Processing, 4th ed.; Butterworth-Heinemann: Oxford, UK, 2013; pp. 477–492. [Google Scholar]
- Penczek, P.; Czub, P.; Pielichowski, J. Unsaturated polyester resins: Chemistry and technology. Adv. Polym. Sci. 2005, 184, 62–76. [Google Scholar] [CrossRef]
- Yang, L. Properties of Quartz-Reinforced Polyester Resin Composites (QPCs). J. Membr. Sci. Technol. 2022, 12, 1000315. [Google Scholar]
- Bledzki, A.K.; Gassan, J. Composites reinforced with cellulose-based fibers. Prog. Polym. Sci. 1999, 24, 221–274. [Google Scholar] [CrossRef]
- Monostori, L.; Kádár, B.; Bauernhansl, T.; Kondoh, S.; Kumara, S.; Reinhart, G.; Sauer, O.; Schuh, G.; Sihn, W.; Ueda, K. Cyber physical systems in manufacturing. CIRP Ann. Manuf. Technol. 2016, 65, 621–641. [Google Scholar] [CrossRef]
- Boschert, B.; Rosen, R. Digital Twin-The Simulation Aspect. In Mechatronic Futures; Hehenberger, P., Bradley, D., Eds.; Springer: Cham, Switzerland, 2016; pp. 59–74. [Google Scholar] [CrossRef]
- Lu, Y.; Xu, X.; Wang, H.; Zheng, X. Industry 4.0: A survey on technologies, applications and open research issues. J. Ind. Inf. Integr. 2017, 6, 1–10. [Google Scholar] [CrossRef]
- Nguyen, P.; Kim, M.; Nichols, E.; Yoon, H.-S. AI-Driven Digital Twins for Manufacturing: A Review Across Hierarchical Manufacturing System Levels. Sensors 2026, 26, 124. [Google Scholar] [CrossRef]
- Amini Niaki, S.; Haghighat, E.; Campbell, T.; Poursartip, A.; Vaziri, R. Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture. Comput. Methods Appl. Mech. Eng. 2021, 384, 113959. [Google Scholar] [CrossRef]
- Wu, Z.; Yang, Y.; Hao, J.; Soutis, C. Optimization and integration of polymer composites manufacturing powered by artificial intelligence. Front. Chem. Sci. Eng. 2025, 19, 121. [Google Scholar] [CrossRef]
- Ramezankhani, M.; Crawford, B.; Narayan, A.; Voggenreiter, H.; Seethaler, R.; Milani, A.S. Making Costly Manufacturing Smart with Transfer Learning under Limited Data: A Case Study on Composites Autoclave Processing. J. Manuf. Syst. 2021, 59, 345–354. [Google Scholar] [CrossRef]
- Ramezankhani, M.; Nazemi, A.; Narayan, A.; Voggenreiter, H.; Harandi, M.; Seethaler, R.; Milani, A.S. A Data-Driven Multi-Fidelity Physics-Informed Learning Framework for Smart Manufacturing: A Composites Processing Case Study. In Proceedings of the IEEE 5th International Conference on Industrial Cyber-Physical Systems (ICPS), Coventry, UK, 24–26 May 2022; pp. 430–436. [Google Scholar] [CrossRef]
- Xu, C.; Lu, S.; Zhang, Y.; Song, Z.; Liu, H. Digital Twins for Defect Detection in FDM 3D Printing Process. Machines 2025, 13, 448. [Google Scholar] [CrossRef]
- Laurenzano, G. Entwicklung Ungesättigter Polyesterharze aus Nachwachsenden Rohstoffen. Ph.D. Thesis, TU Braunschweig, Braunschweig, Germany, 2016; pp. 4–10. [Google Scholar]
- Waigaonkar, S.; Babu, B.J.C.; Rajput, A. Curing studies of unsaturated polyester resin used in FRP products. Indian J. Eng. Mater. Sci. 2011, 18, 31–39. [Google Scholar]
- Akhmetova, S. Development of Mineral Fillers for Acid-Resistant Filling Composites. J. Compos. Sci. 2024, 8, 284. [Google Scholar] [CrossRef]
- Hsu, C.P.; Kinkelaar, M.; Hu, P.; Lee, J. Effects of thermoplastic additives on the cure of unsaturated polyester resins. Polym. Eng. Sci. 1991, 31, 1450–1460. [Google Scholar] [CrossRef]
- DIN EN 13310; Kitchen Sinks—Functional Requirements and Test Methods. DIN: Berlin, Germany, 2019.
- Das, S.K.; Nath, M.R.; Das, R.C.; Mondal, M.; Bhowmik, S. Quartz Reinforced Unsaturated Polyester Resin Composites: Preparation and Characterization. Asian J. Appl. Chem. Res. 2021, 10, 14–25. [Google Scholar] [CrossRef]
- Yuan, J.; Zhou, S.; Gu, G.; Wu, L. Effect of the particle size of nanosilica on the performance of epoxy/silica composite coatings. J. Mater. Sci. 2005, 40, 3927–3932. [Google Scholar] [CrossRef]
- Sreenivasan, V.S.; Rajini, N.; Alavudeen, A.; Arumugaprabu, V. Dynamic mechanical and thermogravimetric analysis of Sansevieria cylindrica/polyester composite. Compos. Part B Eng. 2015, 69, 76–86. [Google Scholar] [CrossRef]
- Pączkowski, P.; Głogowska, K. Preparation and characterization of quartz-reinforced hybrid composites based on unsaturated polyester resin from post-consumer PET recyclate. Materials 2024, 17, 1116. [Google Scholar] [CrossRef]
- Shahid, A.T.; Hofmann, M.A.; Silvestre, J.D.; Garrido, M.; Correia, J.R. Life cycle assessment of an innovative bio-based unsaturated polyester resin and its use in glass fibre reinforced bio-composites produced by vacuum infusion. J. Clean. Prod. 2024, 441, 140906. [Google Scholar] [CrossRef]
- Bogner, B. Composites for chemical resistance and infrastructure applications. Reinf. Plast. 2005, 49, 30–34. [Google Scholar] [CrossRef]
- Kominar, J.; Hunston, D.L.; Manson, J.A. Failure of highly filled quartz/polyester particulate composites as a function of coupling agent content. Polym. Compos. 1994, 3, 61–66. [Google Scholar] [CrossRef]
- Hock, K.; Paternoster, R.; Reichenberger, R. Kunststoffformkörper und Verfahren zu Dessen Herstellung. DE102004055365A1; DPMA, 4 November 2004. [Google Scholar]
- Malkin, A.Y.; Kulichikhin, V.G.; Khashirova, S.Y.; Simonov-Emelyanov, I.D.; Mityukov, A.V. Rheology of Highly Filled Polymer Compositions-Limits of Filling, Structure, and Transport Phenomena. Polymers 2024, 16, 442. [Google Scholar] [CrossRef] [PubMed]
- Afendi, M.; Banks, W.M.; Kirkwood, D. Bubble free resin for infusion process. Compos. Part A Appl. Sci. Manuf. 2005, 36, 739–746. [Google Scholar] [CrossRef]
- Simitzis, J.; Stamboulis, A.; Tsoros, D.; Martakis, N. Kinetics of Curing of Unsaturated Polyesters in the Presence of Organic and Inorganic Fillers. Polym. Int. 1997, 43, 380–384. [Google Scholar] [CrossRef]
- Worzakowska, M. Kinetics of the curing reaction of unsaturated polyester resins catalyzed with new initiators and a promoter. J. Appl. Polym. Sci. 2006, 102, 1870–1876. [Google Scholar] [CrossRef]
- Nava, H. Polyesters, Unsaturated. In Kirk-Othmer Encyclopedia of Chemical Technology; Wiley: New York, NY, USA, 2015. [Google Scholar] [CrossRef]
- Cioffi, M.; Hoffmann, A.C.; Janssen, L.P.B.M. Rheokinetics and the influence of shear rate on the Trommsdorff (gel) effect during free radical polymerization. Polym. Eng. Sci. 2001, 41, 595–602. [Google Scholar] [CrossRef]
- Vafayan, M.; Beheshty, M.H.; Nasiri, H. A Kinetic Model for Low Temperature Curing of an Unsaturated Polyester Resin with Single and Dual Initiators. Polym. Polym. Compos. 2007, 15, 183–190. [Google Scholar] [CrossRef]
- Ramis, X.; Salla, J.M. Effect of the inhibitor on the curing of an unsaturated polyester resin. Polymer 1995, 36, 3511–3521. [Google Scholar] [CrossRef]
- Kamal, M.R.; Sourour, S. Kinetics and thermal characterization of thermoset cure. Polym. Eng. Sci. 1973, 13, 59–64. [Google Scholar] [CrossRef]
- Mazumder, M.R.H.; Govindaraj, P.; Salim, N.; Antiohos, D.; Fuss, F.K.; Hameed, N. Digitalization of composite manufacturing using nanomaterials-based piezoresistive sensors. Compos. Part A Appl. Sci. Manuf. 2025, 188, 108578. [Google Scholar] [CrossRef]
- Abdullah, I. DSC Cure Kinetics of an Unsaturated Polyester Resin Using Empirical Kinetic Model. Pak. J. Sci. Ind. Res. Ser. A 2015, 58, 99–105. [Google Scholar] [CrossRef]
- Malik, M.; Choudhary, V.; Varma, I.K. Current Status of Unsaturated Polyester Resins. J. Macromol. Sci. Part C Polym. Rev. 2000, 40, 139–165. [Google Scholar] [CrossRef]
- Urban, M.W.; Gaboury, S.R.; McDonald, W.F.; Tiefenthaler, A.M. Probing Polymer Structures by Photoacoustic Fourier Transform Infrared Spectroscopy. Adv. Chem. 1990, 227, 287–313. [Google Scholar]
- Dell Erba, R.; Martuscelli, E.; Musto, P.; Ragosta, G.; Leonardi, M. Unsaturated polyester resins: A study on mechanism and kinetics of the curing process by FTIR spectroscopy. Polym. Netw. Blends 1997, 7, 1–11. [Google Scholar]
- Huang, Y.-J.; Chen, C.-J. Curing of unsaturated polyester resins: Effects of comonomer composition. II. High-temperature reactions. J. Appl. Polym. Sci. 1993, 47, 1533–1549. [Google Scholar] [CrossRef]
- Molina, J.; Laroche, A.; Richard, J.-V.; Schuller, A.-S.; Rolando, C. Neural Networks Are Promising Tools for the Prediction of the Viscosity of Unsaturated Polyester Resins. Polymers 2019, 7, 375. [Google Scholar] [CrossRef]
- Mo, Q.; Huang, Y.; Ma, L.; Lai, W.; Zheng, Y.; Li, Y.; Xu, M.; Huang, Z. Study on Microwave Curing of Unsaturated Polyester Resin and Its Composites Containing Calcium Carbonate. Polymers 2022, 14, 2598. [Google Scholar] [CrossRef]
- Orak, S. Investigation of vibration damping on polymer concrete with polyester resin. Cem. Concr. Res. 2000, 30, 171–174. [Google Scholar] [CrossRef]
- Rojas, A.J. The curing of unsaturated polyester resins in adiabatic reactors and heated molds. Polym. Eng. Sci. 1981, 21, 1122–1127. [Google Scholar] [CrossRef]
- Bergmann, K.; Demmler, K. Untersuchung des Härtungsablaufs ungesättigter Polyesterharze mittels NMR. Colloid Polym. Sci. 1974, 252, 193–206. [Google Scholar] [CrossRef]
- Rai, N.; Pitchumani, R. Optimal cure cycles for the fabrication of thermosetting-matrix composites. Polym. Compos. 1997, 18, 566–581. [Google Scholar] [CrossRef]
- Li, M.; Zhu, Q.; Geubelle, P.H.; Tucker, C.L. Optimal curing for thermoset matrix composites: Thermochemical considerations. Polym. Compos. 2001, 22, 118–131. [Google Scholar] [CrossRef]
- Barakat, A.; Al Ghazal, M.; Tamo, R.S.F.; Phadatare, A.; Unser, J.; Hagan, J.; Vaidya, U. Development of a Cure Model for Unsaturated Polyester Resin Systems Based on Processing Conditions. Polymers 2024, 16, 2391. [Google Scholar] [CrossRef] [PubMed]
- Silva, M.P.; Santos, P.; Parente, J.M.; Valvez, S.; Reis, P.N.B.; Piedade, A.P. Effect of Post-Cure on the Static and Viscoelastic Properties of a Polyester Resin. Polymers 2020, 12, 1927. [Google Scholar] [CrossRef] [PubMed]
- Matůšková, E.; Vinklárek, J.; Honzíček, J. Effect of Accelerators on the Curing of Unsaturated Polyester Resins: Kinetic Model for Room Temperature Curing. Ind. Eng. Chem. Res. 2021, 60, 14143–14153. Available online: https://pubs.acs.org/doi/10.1021/acs.iecr.1c02963 (accessed on 5 July 2025). [CrossRef]
- Li, W.; Lee, L.J. Low temperature cure of unsaturated polyester resins with thermoplastic additives: I. Dilatometry and morphology study. Polym. Eng. Sci. 2000, 41, 685–696. [Google Scholar] [CrossRef]
- Breiman, L. Random Forests. Mach. Learn. 2001, 45, 5–32. [Google Scholar] [CrossRef]
- Fernández-León, J.; Keramati, K.; Baumela, L.; González, C. A digital twin for smart manufacturing of structural composites by liquid moulding. Int. J. Adv. Manuf. Technol. 2024, 130, 4679–4697. [Google Scholar] [CrossRef]
- Sobhani, O.; Toliati, H.; Elmaz, F.; Gerdposhteh, S.P.; Carius, B.; Mets, K.; Mercelis, S. A hybrid predictive modeling approach for catalyzed polymerization reactors. Chem. Eng. J. Adv. 2024, 20, 100662. [Google Scholar] [CrossRef]
- Allam, A.; Moussa, M.; Nashed, G.; Iqbal, M. A Deep-Reinforcement-Learning-Based Digital Twin for Manufacturing Process Optimization. Systems 2024, 12, 38. [Google Scholar] [CrossRef]
- Nasiri, S.; Khosravani, M.R.; Reinicke, T.; Ovtcharova, J. Digital Twin Modeling for Smart Injection Molding. J. Manuf. Mater. Process. 2024, 8, 102. [Google Scholar] [CrossRef]
- Liu, Y.; Huo, M.; Li, M.; He, L.; Qi, N. Establishing a Digital Twin Diagnostic Model Based on Cross-Device Transfer Learning. IEEE Trans. Instrum. Meas. 2025, 74, 3533610. [Google Scholar] [CrossRef]
- Silva, B.; Marques, R.; Faustino, D.; Ilheu, P.; Santos, T.; Sousa, J.; Rocha, A.D. Enhance the Injection Molding Quality Prediction with Artificial Intelligence to Zero-Defect Manufacturing. Processes 2023, 11, 62. [Google Scholar] [CrossRef]
- Rothenhäusler, X.; Ruckdäschel, H. Strategies for the fast optimization of the glass transition temperature of sustainable epoxy resin systems via machine learning. J. Appl. Polym. Sci 2024, 141, e55422. [Google Scholar] [CrossRef]
- Pai, S.M.; Shah, K.A.; Sunder, S.; Albuquerque, R.Q.; Brütting, C.; Ruckdäschel, H. Machine learning applied to the design and optimization of polymeric materials: A review. Next Mater. 2025, 7, 100449. [Google Scholar] [CrossRef]
- Ke, K.-C.; Huang, M.-S. Quality Prediction for Injection Molding by Using a Multilayer Perceptron Neural Network. Polymers 2020, 12, 1812. [Google Scholar] [CrossRef]
- Nayak, S.K.; Satapathy, A.; Mantry, S. Response surface method and neural computation for the analysis and prediction of erosion response of glass-polyester composites filled with waste marble dust. Mater. Today 2021, 44, 4425–4432. [Google Scholar] [CrossRef]
- Zheng, K.K.; Le, Q.; Pan, L.; Huang, J. Friction and Wear Prediction of Copper-Free Resin-Based Brake Materials: A Hybrid PSO-FPA-BP Neural Network Approach. Wear 2026, 589, 206536. [Google Scholar] [CrossRef]
- Zhang, F.; Miyao, T.; Izumiya, Y.; Chen, C.H.; Funatsu, K. Designing Heat-Resistant and Moldable Polyester Resin by the Integration of Machine Learning Models with Expert Knowledge. Appl. Polym. Mater. 2024, 6, 4579–4586. [Google Scholar] [CrossRef]
- Kaspi, O.; Yosipof, A.; Senderowitz, H. RANdom Sample Consensus (RANSAC) Algorithm for Material-Informatics: Application to Photovoltaic Solar Cells. J. Cheminform. 2017, 9, 34. [Google Scholar] [CrossRef]
- Fischler, M.A.; Bolles, R.C. Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography. In Readings in Computer Vision: Issues, Problems, Principles, and Paradigms; Sternberg, S.A., Ed.; Morgan Kaufmann: San Francisco, CA, USA, 1987; pp. 726–740. [Google Scholar]
- Friedman, J.H. Greedy Function Approximation: A Gradient Boosting Machine. Ann. Stat. 2001, 29, 1189–1232. [Google Scholar] [CrossRef]
- Breiman, L. Bagging Predictors. Mach. Learn. 1996, 24, 123–140. [Google Scholar] [CrossRef]
- Efron, B.; Tibshirani, R.J. An Introduction to the Bootstrap; Chapman & Hall: New York, NY, USA, 1993. [Google Scholar]
- Moreno-Barea, F.J.; Jerez, J.M.; Franco, L. Improving Classification Accuracy Using Data Augmentation on Small Data Sets. Expert Syst. Appl. 2020, 161, 113696. [Google Scholar] [CrossRef]
- Jolliffe, I.T. Principal Component Analysis, 2nd ed.; Springer: New York, NY, USA, 2002. [Google Scholar] [CrossRef]
- Vapnik, V.N. The Nature of Statistical Learning Theory, 2nd ed.; Springer: New York, NY, USA, 2000. [Google Scholar]
- Rumelhart, D.E.; Hinton, G.E.; Williams, R.J. Learning Representations by Back-Propagating Errors. Nature 1986, 323, 533–536. [Google Scholar] [CrossRef]















| C=C in: | Wavenumber (cm−1) | Wavenumber (cm−1) |
|---|---|---|
| Styrene | 912 | 992 |
| Polyester | – | 982 |
| Component/Parameter | Range | Unit |
|---|---|---|
| Filler Granucol® 10/2022 | 68–75 | % = 10 g/kg |
| Resin Polipol® 3506-X-A | 25–32 | % = 10 g/kg |
| MEKP Peroxan ME 50 LX | 0.8/1.5/2.2 | % (relative to resin) |
| Temperature of resin | 14.3–35.0 | °C |
| Temperature of mold | 13.0–47.0 | °C |
| Temperature of filler | 18.3–26.5 | °C |
| Time to gelation (tgel) | 1.0–16.0 | min |
| Ambient Temperature | 15.3–27.0 | °C |
| Thickness of material | 8.4–14.4 | mm |
| Scenario | Features | n |
|---|---|---|
| A (with tgel) | tgel, MEKP, Tresin, Tmold, Tambient, thickness | 6 |
| B (without tgel) | MEKP, Tresin, Tmold, Tambient, thickness | 5 |
| Library | Description |
|---|---|
| pandas | Data manipulation |
| NumPy | Numerical Operations |
| scikit-learn | Machine learning models |
| matplotlib | Visualization |
| seaborn | Visualization |
| Parameter and Data Type | Random Forest | Gradient Boosting |
|---|---|---|
| X numpy.array (n_samples × n_features) | tgel, MEKP, Tresin, Tmold, Tambient, thickness | tgel, MEKP, Tresin, Tmold, Tambient, thickness |
| Y numpy.array (n_samples) | Target variable: PeakTime | Target variable: PeakTime |
| n_estimators | 300 | 200 |
| max_depth | 4 | 3 |
| min_samples_leaf | 5 | 5 |
| max_features | 0.7 | – |
| random_state | 42 | 42 |
| Output Parameters | Type | Description |
|---|---|---|
| y_pred | numpy.array | Predicted peak time for test data [min] |
| y_train_pred | numpy.array | Predicted peak time for training data (overfitting assessment) |
| R2 | float | Coefficient of determination (cross-validated) |
| R2_train | float | Training R2 (used to calculate overfitting gap) |
| RMSE | float | Root mean squared error (min) |
| MAE | float | Mean absolute error (min) |
| feature_importances_ | numpy.array | Gini-based relative importance of each input feature |
| oob_score_ | float | Out-of-bag R2 estimate (RF only) |
| staged_predict() | generator | Prediction after each boosting stage, 1→200 (GBR only) |
| train_score_ | numpy.array | Training loss per boosting iteration (GBR only) |
| LOO predictions | numpy.array | Leave-One-Out predicted values for all n samples |
| CV R2 (mean ± std) | float | Mean and error from repeated 5 × 5 cross-validation |
| Residuals | numpy.array | Actual versus predicted values (min) |
| Multiplier | Random Forest | Gradient Boosting | |||
|---|---|---|---|---|---|
| n | A | B | A | B | |
| ×1 | 76 | 0.328 ± 0.139 | 0.065 ± 0.137 | 0.445 ± 0.146 | 0.092 ± 0.192 |
| ×2 | 152 | 0.549 ± 0.102 | 0.421 ± 0.115 | 0.730 ± 0.097 | 0.687 ± 0.095 |
| ×3 | 228 | 0.628 ± 0.059 | 0.570 ± 0.064 | 0.823 ± 0.045 | 0.789 ± 0.047 |
| ×4 | 304 | 0.673 ± 0.055 | 0.598 ± 0.065 | 0.873 ± 0.032 | 0.843 ± 0.034 |
| ×5 | 380 | 0.699 ± 0.036 | 0.628 ± 0.038 | 0.901 ± 0.029 | 0.878 ± 0.034 |
| ×6 | 456 | 0.710 ± 0.040 | 0.626 ± 0.048 | 0.916 ± 0.021 | 0.894 ± 0.026 |
| ×8 | 608 | 0.752 ± 0.026 | 0.659 ± 0.031 | 0.932 ± 0.013 | 0.916 ± 0.016 |
| ×10 | 760 | 0.765 ± 0.034 | 0.655 ± 0.038 | 0.940 ± 0.010 | 0.926 ± 0.012 |
| Original Data | Augmented Data | |||
|---|---|---|---|---|
| Model | R2 | RMSE | R2 | RMSE |
| Random Forest Scenario A | 0.430 | 5.63 min | 0.761 | 3.61 min |
| Random Forest Scenario B | 0.145 | 6.90 min | 0.656 | 4.33 min |
| Gradient Boosting Scenario A | 0.551 | 5.00 min | 0.938 | 1.83 min |
| Gradient Boosting Scenario B | 0.340 | 6.06 min | 0.922 | 2.07 min |
| Original Data | Augmented Data | |||||||
|---|---|---|---|---|---|---|---|---|
| Feature | Radom Forest | Gradient Boosting | Random Forest | Gradient Boosting | ||||
| Scenario | A | B | A | B | A | B | A | B |
| tgel | 41.3 | – | 32.7 | – | 35.1 | – | 29.6 | – |
| Thickness | 23.5 | 36.8 | 24.8 | 26.4 | 21.1 | 28.1 | 26.4 | 28.1 |
| Tresin | 9.9 | 21.8 | 11.2 | 20.8 | 11.5 | 17.3 | 11.1 | 15.0 |
| Tambient | 8.8 | 21.8 | 9.4 | 14.0 | 4.9 | 12.8 | 8.9 | 16.8 |
| Tmold | 15.2 | 16.5 | 18.3 | 23.1 | 11.0 | 17.5 | 13.2 | 21.1 |
| MEKP | 1.3 | 3.1 | 3.6 | 14.0 | 16.2 | 24.4 | 10.8 | 19.1 |
| Scenario | PC | Eigenvalue | Variance % | Cumulative % | Dominant Feature | Correlation with Peak Time |
|---|---|---|---|---|---|---|
| A | PC1 | 1.806 | 29.7 | 29.7 | Gel time (+0.67) | +0.485 |
| PC2 | 1.162 | 19.1 | 48.8 | Ambient temperature (+0.63) | −0.222 | |
| PC3 | 1.026 | 16.9 | 65.7 | Resin temperature (+0.87) | +0.019 | |
| PC4 | 0.969 | 15.9 | 81.6 | Thickness (+0.65) | +0.322 | |
| PC5 | 0.801 | 13.2 | 94.8 | Mold temperature (+0.76) | −0.438 | |
| PC6 | 0.317 | 5.2 | 100.0 | Gel time (+0.71) | −0.005 | |
| B | PC1 | 1.247 | 24.6 | 24.6 | Mold time (+0.71) | +0.087 |
| PC2 | 1.098 | 21.7 | 46.3 | Thickness (+0.74) | −0.227 | |
| PC3 | 1.024 | 20.2 | 66.5 | Resin temperature (+0.91) | +0.014 | |
| PC4 | 0.953 | 18.8 | 85.3 | Ambient temperature (+0.77) | +0.331 | |
| PC5 | 0.745 | 14.7 | 100.0 | Mold temperature (+0.66) | −0.578 |
| Algorithm | Original A | Augmented ×8 A | Original B | Augmented ×8 B |
|---|---|---|---|---|
| Random Forest | 0.328 | 0.752 | 0.065 | 0.659 |
| Gradient Boosting | 0.445 | 0.932 | 0.092 | 0.916 |
| SVR (RBF) | 0.171 | 0.914 | 0.058 | 0.857 |
| MLP (ANN) | −0.927 | 0.692 | −0.534 | 0.652 |
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© 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
Share and Cite
Suess, M.; Kurzweil, P. Polyester Resin–Quartz Composites in the Age of Artificial Intelligence and Digital Twins: Current Advances, Future Perspectives and an Application Example. Polymers 2026, 18, 753. https://doi.org/10.3390/polym18060753
Suess M, Kurzweil P. Polyester Resin–Quartz Composites in the Age of Artificial Intelligence and Digital Twins: Current Advances, Future Perspectives and an Application Example. Polymers. 2026; 18(6):753. https://doi.org/10.3390/polym18060753
Chicago/Turabian StyleSuess, Marco, and Peter Kurzweil. 2026. "Polyester Resin–Quartz Composites in the Age of Artificial Intelligence and Digital Twins: Current Advances, Future Perspectives and an Application Example" Polymers 18, no. 6: 753. https://doi.org/10.3390/polym18060753
APA StyleSuess, M., & Kurzweil, P. (2026). Polyester Resin–Quartz Composites in the Age of Artificial Intelligence and Digital Twins: Current Advances, Future Perspectives and an Application Example. Polymers, 18(6), 753. https://doi.org/10.3390/polym18060753

