Performance enhancement of hybrid shake table via passive load balancing and nonlinear system identification using coupled ODE modelling

Abstract This study aims to identify a suitable passive load-balancing mechanism for a hybrid shake table, which decouples spatial and planar motion for enhanced control. By minimizing reliance on extensive experimental data, the research seeks to improve system stiffness, compensate for heavy payloads, and enhance the overall performance of shake tables. A regression-based nonlinear least-squares (NLS) technique enhanced by the trust-region-reflective (TRR) algorithm is proposed for system identification. A fusion-based approach is adopted, in which experimental data is used to develop a reduced-fidelity state-space model (SSM) of the shake table, while simulation data is used to evaluate passive load-balancing mechanisms. The study solves higher-order coupled ordinary differential equations (ODEs) to estimate stiffness and damping parameters for various configurations. Among the four vertical motion actuator (VMA) assembly configurations, the configuration equipped with a passive hydraulic damper exhibited superior performance. It attained the highest fit percentages (98.01% and 87.66%), the highest coefficient of determination R 2 values (0.9996 and 0.9847), the lowest normalized root mean square error (NRMSE) values (0.0022 and 0.0083), minimal amplitude errors (0.0338 and 0.1350), and the most negligible phase errors (0 and 0.08) for displacement and velocity responses, respectively. Among the passive mechanisms analyzed, a hydraulic damper proved to be the most effective load-balancing mechanism, demonstrating high stiffness, superior damping, and optimal force compensation. This enhancement is attributed to its nonlinear spring and damping characteristics, which enhance stability under heavy loads. This research presents a standardized approach for solving coupled ODEs in dynamic systems. The findings provide a novel framework for improving shake table performance, with potential applications in earthquake simulation, robotics, and industrial motion platforms.