Machine learning evaluation of PI control effects on neutral equilibrium in bridge virtual pier 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 s. 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.