Stockbridge dampers are widely used in overhead transmission lines to mitigate aeolian vibrations and protect conductors from fatigue failure. This research addresses the limitations of linear damping models in accurately representing the dynamic behavior of Stockbridge dampers, utilizing Bouc-Wen nonlinear damping, and captures experimentally observed vibrations. A novel approach is proposed to develop a nonlinear model of Stockbridge dampers using neural networks to learn complex nonlinear relationships and genetic algorithms for parameter optimization. The objectives of this research are to improve the accuracy of damper performance prediction, enhance design optimization strategies, and gain deeper insights into the damper's complex dynamics. The methodology involves analyzing similar SDOF and MDOF systems and exercising nonlinear properties, and applying optimization to validate the approach, developing a neural network model that accounts for nonlinearities and 3D motion, validated against experimental data and finite element analysis results.