Calibrating Vaiana–Rosati phenomenological model for generic symmetric/asymmetric hysteretic behaviors by enhanced response sensitivity analysis

The Vaiana–Rosati phenomenological model (VRM) provides a closed-form expression to describe generic generalized force–displacement hysteretic behaviors. It utilizes two sets of physically interpretable parameters to explicitly formulate symmetric/asymmetric hysteretic loops without solving differential equations. To calibrate the VRM, this paper proposes an enhanced response sensitivity analysis method to identify parameters that minimize a least-squares objective function defined by the residual between the measured and theoretical hysteresis forces. The objective function is linearized by the response sensitivity and minimized using the Tikhonov regularization. Furthermore, the trust-region constraint is combined with the Tikhonov regularization process to enhance parameter convergence. Numerical simulations about symmetric/asymmetric hysteresis and experimental investigations on a wire rope isolator and a magnetorheological damper verify the proposed method’s accuracy and effectiveness, offering a unified framework for calibrating the VRM to simulate symmetric/asymmetric and rate-independent/rate-dependent hysteretic curves.