A Regularization-Based Motion Reconstruction Method for Rank-Deficient Shaking Tables

Large-scale rank-deficient shaking table systems in vibration testing applications often suffer from observability singularity due to inherent structural and actuation constraints, making accurate motion reconstruction challenging. Addressing this issue without increasing hardware complexity remains an important requirement for reliable state monitoring and control.

A regularized sensor fusion framework is proposed to achieve high-precision six-degree-of-freedom (6-DOF) pose estimation using only intrinsic actuator displacement and force measurements. By incorporating a dynamic regularization term derived from the system model, the ill-posed kinematic reconstruction problem is transformed into a strictly convex and numerically stable formulation. In addition, an adaptive credibility weighting mechanism based on residual evaluation is developed to enhance robustness against uncertainties and measurement disturbances.

The proposed method is validated through simulations and experiments on a kiloton-scale shaking table. The results demonstrate that the proposed approach effectively improves estimation accuracy and robustness under coupled vibration conditions, enabling reliable monitoring of dynamic behavior in rank-deficient systems.

The proposed regularized sensor fusion framework provides a practical solution for state reconstruction and intelligent monitoring of large-scale vibration test platforms. By integrating dynamic regularization and adaptive credibility weighting, the method achieves accurate and robust motion reconstruction for rank-deficient shaking table systems.