Application of Machine Learning to Evaluate the Influence of PI Control Parameters on the Stability of Neutral Equilibrium Mechanism as a Virtual Pier in Bridge Systems

This study investigates the application of Neutral Equilibrium Mechanism (NEM) in active control systems for bridge structures, with a focus on analyzing the effects of proportional gain (GP) and integral gain (GI) parameters on vertical displacement stability. A scaled bridge model equipped with dual NEMs, displacement sensors, and servo motors was used to simulate dynamic loading responses in a closed-loop control system. Machine learning techniques, including Random Forest Regression and Neural Networks, were employed to develop nonlinear predictive models. These were supplemented by K-means clustering and feature sensitivity analysis to evaluate control strategies and identify optimal parameter settings. The experiment collected over 21.3 million high-resolution time-series data points across four PI control parameter combinations. Results demonstrated that the optimal parameter configuration (GP = 1.0, GI = 0.010) significantly reduced maximum vertical displacement from 5.02 mm and 5.23 mm (at points A and B) to 0.39 mm and 0.38 mm, respectively, while cutting stabilization time to 9.8 seconds. The Neural Network model achieved excellent predictive performance with an R² of 0.934 and RMSE of 0.038. Clustering and sensitivity analyses revealed that medium-gain settings (GP = 1.0, GI = 0.010) optimally balanced system stability and structural symmetry. This research confirms the feasibility of machine learning-based analytical models for bridge displacement control and provides data-driven guidance for parameter optimization, offering valuable insights for future intelligent bridge control system design.