Predictive modelling of graphene-enhanced greases using classical feedback control and quantum kernel regression

This paper investigates two predictive modeling approaches for estimating the thermal and tribological performance of graphene-enhanced greases, aiming to reduce reliance on protracted endurance tests. Seven grease formulations with varying graphene concentrations (0–4 wt%) were prepared and tested under a uniform load to capture temperature evolution, wear scar area and coefficient of friction. A classical piecewise regression model, augmented by a Linear Quadratic Regulator (LQR), leverages feedback control to correct temperature predictions and subsequently estimate wear using a polynomial fit. This framework demonstrated high accuracy in tracking transient thermal behaviour, maintaining temperature deviations within ±1 °C of measured data. In parallel, a quantum-classical hybrid model employs a fidelity-based quantum kernel with support vector regression. By encoding partial early-cycle temperature measurements (e.g., from 30 to 120s) into a higher-dimensional Hilbert space, the quantum approach captures subtle nonlinearities and yields strong correlations for both final temperature and wear scar area. Moreover, consistent performance on IBM Quantum models with realistically simulated noise underscores the model’s potential for practical industrial implementation. Collectively, these results confirm the viability of advanced computational tools, both classical and quantum, for rapid, data-driven lubricant assessments. They highlight opportunities to optimize graphene content while minimizing costly trial and error testing.