Identification of hysteretic oscillators under earthquace loading by nonparametric models

Nonparametric identification techniques are used to process recorded data of nonlinear structural responses and to represent the constitutive relationship of the structure. When hysteretic systems are dealt with, attention must be given to the appropriate subspace of the state variables in which the restoring force can be approximated by a single-valued surface. Nonparametric models are investigated, defined by two different descriptions: the first, in which the restoring force is a function of displacement and velocity, is commonly used; and the second, in which the incremental force is a function of force and velocity is less adopted. The ability of the second variable space to better reproduce the behavior of hysteretic oscillators is shown by analyzing different cases. Meanwhile, approximation of the real restoring function in terms of orthogonal (Chebyshev) polynomials and nonorthogonal polynomials is investigated. Finally, a mixed parametric and nonparametric model that exhibits a very satisfactory behavior in the case of important hardening and viscous damping is presented.