Single-Variable Multi-Criteria Optimization of Solid-Phase Volume Fraction in Solid–Liquid Mixing System of High-Viscosity Polyurethane Adhesive Based on CFD Coupled with Machine Learning

The solid-phase volume fraction is a core process parameter that determines the mixing quality of high-viscosity polyurethane adhesives. It exhibits complex nonlinear couplings with mixing homogeneity, rheological properties, and energy consumption. Traditional trial-and-error experiments and standalone CFD simulations are hindered by high costs, long computational cycles, and inefficient parameter optimization processes. Consequently, these limitations prevent them from satisfying industrial-scale process optimization demands. To address these challenges, this study proposes a single-variable, multi-criteria intelligent optimization method integrating CFD with machine learning. This study uses a 5000 L industrial stirred reactor as the research object. Twelve typical operating conditions were designed within the 8–32% solid-phase volume fraction range. Numerical simulations were conducted based on the laminar Mixture multiphase flow model. These simulations established a small-sample, high-fidelity operating condition database. To mitigate underfitting caused by limited CFD data, an adaptive cubic spline interpolation algorithm was employed for dataset augmentation. Subsequently, a comparative analysis was conducted between Gaussian process regression (GPR) and support vector regression (SVR) as small-sample surrogate models. Test results demonstrate that the GPR model achieves a coefficient of determination (R2) of 0.968, with significantly superior prediction accuracy and generalization performance compared to the SVR model. This study uses the solid-phase volume fraction as the sole decision variable. A five-criteria optimization model was constructed based on the optimal GPR surrogate, combined with the NSGA-II algorithm and ideal point decision criterion. Three optimal operating modes were identified—balanced, low-energy, and high-dispersion—tailored for different production scenarios. The proposed integrated collaborative optimization approach effectively reduces process development costs. It also provides comprehensive theoretical foundations and technical references for intelligent control and energy-efficient production of high-viscosity non-Newtonian solid–liquid mixing systems.