Wavelet Entropy and Machine Learning Analysis of Nonlinear Dynamics in Tubular Light Pipes

This study presents a hybrid framework primarily designed to predict electrical energy consumption in tubular light pipe systems while also providing interpretability through wavelet-based analysis. Indoor and outdoor illuminance were continuously monitored at one-minute intervals between January and May in Istanbul, Turkey. Using the continuous wavelet transform (CWT) with predefined scale ranges, multi-scale features such as scale-wise energy, relative wavelet energy, and wavelet entropy were extracted to quantify illumination variability and stability. These features were combined with contextual parameters (e.g., month and weather) to predict electrical energy consumption and the energy-saving ratio under a threshold-based lighting control strategy. Among the evaluated models, Random Forest was selected as the primary model due to its balance between prediction accuracy and interpretability, achieving lower prediction errors compared to baseline models (RMSE = 7.84 for RF, 9.39 for Linear Regression, and 8.28 for ARIMA), although the observed improvements are influenced by the inherent variability in the dataset. Feature-importance and SHapley Additive exPlanations (SHAP) analyses revealed that low-frequency wavelet components and low Wavelet Entropy values were found to strongly influence the predictive behavior, indicating that stable illumination leads to reduced artificial lighting demand and higher energy savings. A Lyapunov-inspired stability interpretation suggests that the system exhibits stable behavior consistent with asymptotic convergence. Unlike existing studies, the proposed framework integrates wavelet entropy with interpretable machine learning to jointly model illumination dynamics and energy demand. This enables more reliable prediction of lighting energy demand under highly variable daylight conditions.