Data-Based Model-Free Hysteretic Restoring Force and Mass Identification for Dynamic Systems

Most of the currently available vibration-based damage detection approaches identify structural damage in the form of decrease in structural stiffness based on extracted eigenparameters and/or their derivates, and the basic hypothesis behind them is the system should be linear and the mass distribution of the system is usually known. Different from the stiffness degradation, the hysteretic restoring force of a dynamic system provides a more informative and direct description on the initiation and development of damage in structures under dynamic loadings and can be employed to quantitatively evaluate the energy dissipation during vibration. In this study, a data-based model-free hysteretic behavior identification approach with incomplete external excitations was proposed for the identification of structural hysteretic restoring force without the prior knowledge of structural mass distribution and the numerical model of the nonlinearity of the structure. The accuracy and feasibility of the approach for both structural mass and hysteretic behavior identification was illustrated: first, via numerical simulation with a lumped-mass multi-degree-of-freedom structure incorporating nonlinear magnetorheological (MR) dampers and a consistent mass plane truss structure incorporating a pseudo-elastic shape memory alloy model to mimic the nonlinearity in dynamic systems. Second, a dynamic test on a four-story frame structure equipped with MR dampers was carried out and the corresponding dynamic response was employed to validate the reliability of the proposed approach for both structural mass and hysteretic behavior identification. The results show that the proposed approach is capable of identifying different types of structural nonlinearity, which numerical model is unknown, with incomplete inputs and unknown mass distribution. The approach provides a promising way for damage detection and monitoring in the form of hysteretic behavior and energy dissipation for engineering structures under dynamic loadings, which should be dealt with as nonlinear systems.