Predictive Modeling of Nonlinear Breakdown Voltage in Silicone Rubber Polymer Insulators with Fly Ash Filler Using the GLME and BPNN Methods

Abstract

The expansion of Indonesia's transmission and distribution network increases the demand for high-voltage insulator materials with reliable dielectric performance and sustainable manufacturing. Silicone rubber (SiR) filled with coal fly ash is a promising alternative; however, its breakdown voltage varies nonlinearly with filler composition, temperature, and fly ash source. This study proposes a complementary statistical machine learning framework using Generalized Linear Mixed Effects (GLME) for interpretable statistical analysis and a Backpropagation Neural Network (BPNN) for flexible nonlinear prediction. The analysis used 512 secondary observations from four Indonesian fly ash sources, with filler compositions of 10–80% and temperatures of 35–50°C. Breakdown voltage increased with fly ash content up to an optimum of approximately 60–65% before declining at higher loadings, while increasing temperature consistently reduced dielectric strength. GLME achieved R² = 0.7457, RMSE = 0.0354, and MAPE = 1.57%, whereas the five-fold cross-validated BPNN showed slightly better average predictive performance, with R² = 0.7617, RMSE = 0.0343, and MAPE = 1.56%. GLME provides interpretable and statistically testable coefficients, whereas BPNN captures additional complex nonlinear patterns without requiring a predefined functional form. SEM and XRF characterization supported the observed nonlinear trends through particle dispersion and fly ash oxide composition, predominantly SiO₂ and Al₂O₃. The proposed complementary framework combines statistical interpretability with nonlinear predictive capability, supporting fly ash composition selection, efficient material screening, and breakdown voltage prediction for high voltage silicone rubber insulator applications.