MACHINE MODELING AND SIMULATIONS, Machine Modelling and Simulations 2025

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Modeling the Influence of Carbon Black Type and Loading on the Mixing Dynamics of Rubber Blends Using a Generalized Regression Neural Network
Ivan Kopal, Juliána Vršková, Ivan Labaj, Marta Harničárová, Jan Valíček

Last modified: 18. 06. 2025

Abstract


This study presents the first systematic application of a Generalized Regression Neural Network (GRNN) to quantify how the type and concentration of carbon black affect the mixing dynamics of natural‑rubber blends. The model was designed to approximate the time evolution of torque and temperature during mixing, using carbon black loadings of 45–60 phr for four grades (N121, N339, N550, N660) together with mixing time as inputs. The outputs were the instantaneous torque and temperature recorded throughout each mixing run. Training and validation were performed on 32 experimental curves obtained from 16 laboratory mixing trials, with model performance assessed by 10‑fold cross‑validation. The calibrated GRNN accurately reconstructed the nonlinear relationships between formulation, mixing time and rheological response, achieving an average RMSE of 0.0005 (0.05 % of the normalized data range) and a coefficient of determination R² = 1, which indicates an excellent agreement between predictions and measurements. The proposed model constitutes a robust and flexible tool for intelligent monitoring and control of mixing operations in the rubber industry and allied sectors, and it can be readily adapted to other processes that require real‑time prediction of complex dynamic behavior.

Acknowledgement: This research was supported by the Operational Programme Integrated Infrastructure – project CEDITEK II (ITMS2014+ code 313011W442).