Dynamic Predicted Mean Vote/Predicted Percentage of Dissatisfied Prediction Using Lagrangian-Driven Deep Clustering and Reinforcement Learning for HVAC Energy Optimization

Abstract Forecasting indoor thermal comfort is crucial for optimizing HVAC energy, with Fanger's predicted mean vote (PMV) formula serving as the gold standard for evaluating thermal sensation, despite its nonlinear complexity. Traditional Lagrange interpolation fails to accurately fit PMV across its broad input range, thereby limiting the potential of white box models. The proposed DCLIMURLDTC model—Deep Clustering Lagrangian Interpolation Model using Reinforcement Learning for Dynamic Thermal Comfort—overcomes these constraints by grouping PMV-dependent variables into five clusters, reducing nonlinearity and enabling accurate piecewise interpolation. Reinforcement learning calibrates cluster boundary weights for adaptive thermal modeling. Validated against seasonal data, DCLIMURLDTC delivers accurate comfort predictions while reducing HVAC energy usage. Results show a 22.17% decrease in energy consumption compared to nominal operation, confirming the model's efficiency. Optimal comfort is achieved at ∼25 °C, though elevated relative humidity lowers satisfaction. Statistical metrics corroborate the model's reliability and robustness in diverse conditions. The integration of deep clustering and Lagrangian interpolation, reinforced by machine learning, addresses limitations in empirical PMV modeling, presenting a versatile solution for dynamic HVAC environments. Ultimately, DCLIMURLDTC advances adaptive modeling for indoor thermal comfort, offering significant energy-saving potential and enhanced predictive accuracy across varying climate applications.