Modelling the flow properties of rubber blends makes it possible to predict their rheological behaviour during the processing and production of rubber-based products. As the nonlinear nature of such complex processes complicates the creation of exact analytical models, it is appropriate to use artificial intelligence tools in this modelling. The present study was implemented to develop a highly efficient artificial neural network model, optimised using a novel training algorithm with fast parallel computing to predict the results of rheological tests of rubber blends performed under different conditions. A series of 120 real dynamic viscosity-time curves, acquired by a rubber process analyser for styrene-butadiene rubber blends with varying carbon black contents vulcanised at different temperatures, were analysed using a Generalised Regression Neural Network. The model was optimised by limiting the fitting error of the training dataset to a pre-specified value of less than 1%. All repeated calculations were made via parallel computing with multiple computer cores, which significantly reduces the total computation time. An excellent agreement between the predicted and measured generalisation data was found, with an error of less than 4.7%, confirming the high generalisation performance of the newly developed model.

College of Engineering and Technology American University of the Middle East Egaila 54200 Kuwait

Department of Electrical Engineering Automation and Informatics Faculty of Engineering Slovak University of Agriculture in Nitra Tr A Hlinku 2 949 76 Nitra Slovakia

Department of Mechanical Engineering Faculty of Technology Institute of Technology and Business in České Budějovice Okružní 10 370 01 České Budějovice Czech Republic

Department of Numerical Methods and Computational Modeling Faculty of Industrial Technologies in Púchov Alexander Dubček University of Trenčín Ivana Krasku 491 30 020 01 Púchov Slovakia

Zobrazit více v PubMed

Mark J.E., Erman B., Roland C.M. The Science and Technology of Rubber. 4th ed. Elsevier; Alpharetta, GA, USA: 2013.

Dick J.S. Basic Rubber Testing: Selecting Methods for a Rubber Test Program. 1st ed. ASTM International; West Conshohocken, PA, USA: 2003.

Gupta B.R. Rheology Applied in Polymer Processing. 1st ed. CRC Press; Boca Raton, FL, USA: 2022.

Wilczynski K. Rheology in Polymer Processing: Modeling and Simulation. 1st ed. Hanser Publishers; Cincinnati, OH, USA: 2020.

Standard Test Method for Rubber—Measurement of Unvulcanized Rheological Properties Using Rotorless Shear Rheometers. ASTM International; West Conshohocken, PA, USA: 2019.

Forrest M.J. Rubber Analysis—Polymers, Compounds and Products. 1st ed. Smithers Rapra Technology; Shewsbury Shropshire, UK: 2001.

Kopal I., Labaj I., Vršková J., Harničárová M., Valíček J., Ondrušová D., Krmela J., Palková Z. A Generalized Regression Neural Network Model for Predicting the Curing Characteristics of Carbon Black-Filled Rubber Blends. Polymers. 2022;14:653. doi: 10.3390/polym14040653. PubMed DOI PMC

Strobl G. The Physics of Polymers: Concepts for Understanding Their Structures and Behavior. 3rd ed. Springer; Berlin/Heidelberg, Germany: 2007.

Liptáková T., Alexy P., Gondár E., Khunová V. Polymérne Konštrukčné Materiály. 1st ed. EDIS; Žilina, Slovakia: 2012.

Ghoreishy M.H.R. A State of the Art Review on the Mathematical Modeling and Computer Simulation of Rubber Vulcanization Process. Iran. Polym. J. 2016;25:89–109. doi: 10.1007/s13726-015-0405-5. DOI

Hossain M. Ph.D. Thesis. Universität Erlangen-Nürnberg; Erlangen-Nürnberg, Germany: Jul 7, 2009. Modelling and Computation of Polymer Curing.

Krmela J., Artyukhov A., Krmelová V., Pozovnyi O. Determination of Material Parameters of Rubber and Composites for Computational Modeling Based on Experiment Data. J. Phys. Conf. Ser. 2021;1741:012047. doi: 10.1088/1742-6596/1741/1/012047. DOI

Hagan M.T., Demuth H.B., Beale M.H., De Jesús O. Neural Network Design. 2nd ed. Martin Hagan; Stillwater, OK, USA: 2014.

Lubura J., Kojić P., Pavličević J., Ikonić B., Omorjan R., Bera O. Prediction of rubber vulcanisation using an artificial neural network. Hem. Ind. 2021;75:277–283. doi: 10.2298/HEMIND210511026L. DOI

Schwartz G.A. Prediction of Rheometric Properties of Compounds by Using Artificial Neural Networks. Rubber Chem. Technol. 2001;74:116–123. doi: 10.5254/1.3547632. DOI

Karaağaç B., İnal M., Deniz V. Artificial neural network approach for predicting optimum cure time of rubber compounds. Mater. Des. 2009;30:1685–1690. doi: 10.1016/j.matdes.2008.07.010. DOI

Uruk Z., Kiraz A., Deniz V. A comparison of machine learning methods to predict rheometric properties of rubber compounds. J. Rubber Res. 2022;25:265–277. doi: 10.1007/s42464-022-00170-7. DOI

Uruk Z., Kiraz A. Artificial intelligence based prediction models for rubber compounds. J. Polym. Eng. 2023;43:113–124. doi: 10.1515/polyeng-2022-0166. DOI

Mehlig B. Machine Learning with Neural Networks: An Introduction for Scientists and Engineers. CUP; Cambridge, UK: 2021.

Deepa A., Thasliya F.P.A. Back propagation. Int. J. Res. Appl. Sci. Eng. Technol. 2023;11:334–339.

Seidl D., Ružiak I., Koštialová Jančíková Z., Koštial P. Sensitivity Analysis: A Tool for Tailoring Environmentally Friendly Materials. Expert Syst. Appl. 2022;208:118039. doi: 10.1016/j.eswa.2022.118039. DOI

Specht D.F. A general regression neural network. IEEE Trans. Neural Netw. 1991;2:568–576. doi: 10.1109/72.97934. PubMed DOI

Al-Mahasneh A.J., Anavatti S., Garratt M., Pratama M. Applications of General Regression Neural Networks in Dynamic Systems. In: Asadpour V., editor. Digital Systems. 1st ed. Volume 1. IntechOpen; Rijeka, Croatia: 2018. pp. 133–154.

Bontempi G., Birattari M., Bersini H. Lazy Learning: A Logical Method for Supervised Learning. In: Kacprzyk J., editor. New Learning Paradigms in Soft Computing. Springer; Berlin/Heidelberg, Germany: 2002. pp. 97–149.

Ghosh S. Kernel Smoothing: Principles, Methods and Applications. 2nd ed. Wiley; Hoboken, NJ, USA: 2018.

Mohebali B., Tahmassebi A., Meyer-Baese A., Gandomi A.H. Probabilistic Neural Networks: A Brief Overview of Theory, Implementation, and Application. In: Samui P., Bui D.T., Chakraborty S., Deo R.C., editors. Handbook of Probabilistic Models. 1st ed. Butterworth-Heinemann Elsevier Ltd.; Oxford, UK: 2020. pp. 347–367.

Bates D.M., Watts D.G. Nonlinear Regression Analysis and Its Applications. 1st ed. Wiley; Hoboken, NJ, USA: 2007.

Shwechuk J.R. Ph.D. Thesis. University of California; Berkeley, CA, USA: May 6, 2023. Concise Machine Learning.

Martínez F., Charte F., Frías M.P., Martínez-Rodríguez A.M. Strategies for time series forecasting with generalized regression neural networks. Neurocomputing. 2022;491:509–521. doi: 10.1016/j.neucom.2021.12.028. DOI

López C.P. Deep Learning Techniques: Cluster Analysis and Pattern Recognition with Neural Networks. Examples with MATLAB. 1st ed. Lulu Press Inc.; Morrisville, NC, USA: 2021.

Hou J., Lu X., Zhang K., Jing Y., Zhang Z., You J., Li Q. Parameters Identification of Rubber-like Hyperelastic Material Based on General Regression Neural Network. Materials. 2022;15:3776. doi: 10.3390/ma15113776. PubMed DOI PMC

Kowalski P.A., Kusy M. Algorithms for Triggering General Regression Neural Network. In: Harmati I.Á., Kóczy L.T., Medina J., Ramírez-Poussa E., editors. Computational Intelligence and Mathematics for Tackling Complex Problems 3. 3rd ed. Springer; Cham, Switzerland: 2022. pp. 177–182.

Chiroma H., Noor A.S.M., Abdulkareem S., Abubakar A.I., Hermawan A., Qin H., Hamza M.F., Herawan T. Neural Networks Optimization through Genetic Algorithm Searches: A Review. Appl. Math. Inf. Sci. 2017;11:1543–1564. doi: 10.18576/amis/110602. DOI

Matlab . Parallel Computing Toolbox™ User’s Guide R2013b. Matlab; Natick, MA, USA: 2013.

Xu S. An Introduction to Scientific Computing with Matlab® and Python Tutorials. 1st ed. Chapman & Hall/CRC; London, OH, USA: 2022.

Rubber Test Mixes—Preparation, Mixing and Vulcanisation—Equipment and Procedures. International Organization for Standardization; Geneva, Switzerland: 2011.

Labban A., Mousseau P., Bailleul J.L., Deterre R. Optimization of Thick Rubber Part Curing Cycles. Inverse Probl. Sci. Eng. 2010;18:313–340. doi: 10.1080/17415971003589517. DOI

Nakajima N. The Science and Practice of Rubber Mixing. 1st ed. Technomic Publishing Company, Rapra Technology; Shropshire, UK: 2000.

Lipińska M., Soszka K. Viscoelastic Behavior, Curing and Reinforcement Mechanism of Various Silica and POSS Filled Methyl-Vinyl Polysiloxane MVQ Rubber. Silicon. 2019;11:2293–2305. doi: 10.1007/s12633-019-0081-8. DOI

Noordermeer J.W.M. Encyclopedia of Polymeric Nanomaterial. 2015th ed. Volume 3. Springer; Berlin/Heidelberg, Germany: 2014. Vulcanization; pp. 1–16.

Zhang H., Li Y., Shou J.Q., Zhang Z.Y. Effect of Curing Temperature on Properties of Semi-Efficient Vulcanized Natural Rubber. J. Elastomers Plast. 2015;48:331–339. doi: 10.1177/0095244315576243. DOI

Saito T., Yamano M., Nakayama K., Kawahara S. Quantitative Analysis of Crosslinking Junctions of Vulcanized Natural Rubber through Rubber-State NMR Spectroscopy. Polym. Test. 2019;96:107130. doi: 10.1016/j.polymertesting.2021.107130. DOI

Han I.S., Chung C.B., Lee J.W. Optimal Curing of Rubber Compounds with Reversion Type Cure Behavior. Rubber Chem. Technol. 2000;73:101–113. doi: 10.5254/1.3547572. DOI

Liu X., Tian S., Tao F., Yu W. A Review of Artificial Neural Networks in the Constitutive Modeling of Composite Materials. Compos. Part B Eng. 2021;224:109152. doi: 10.1016/j.compositesb.2021.109152. DOI

Kanwar H. Mathematical Statistics. 1st ed. Mohindra Capital Publishers; Chandigarh, India: 2022.

Kopal I., Labaj I., Vršková J., Harničárová M., Valíček J., Tozan H. Research Data for the Study Titled Intelligent Modelling of the Real Dynamic Viscosity of Rubber Blends Using Parallel Computing. Mendeley Data; London, UK: 2023. PubMed DOI PMC

Intelligent Modelling of the Real Dynamic Viscosity of Rubber Blends Using Parallel Computing