Instantaneous Identification of Degrading Hysteretic Oscillators Under Earthquake Excitation

Abstract

This article presents a technique for the structural identification of hysteretic oscillators that are characterized by degradation in stiffness. The main assumption of the proposed procedure is that it is possible to replace the expression of the time derivative of the restoring force with a polynomial approximation, characterized by time-varying coefficients. The work aims at generalizing a method that the authors have proposed for hysteretic nondegrading systems: system parameters are evaluated from instantaneous estimates of the time-varying coefficients. The instantaneous estimation, based on optimization techniques, is made possible through the temporal localization of frequency components, i.e., the representation in the joint time—frequency domain. A numerical application consisting of the instantaneous identification of a Bouc-Wen model with stiffness degradation under earthquake excitation is presented and discussed. Although the sensitivity of the estimation to exogenous noise is greater than in the nondegrading case, the global accuracy of the identification is satisfactory.

Accounting for Soil-Structure Interaction in the Calibration of Monitored Buildings

“…Comparing (5) with (1) it is possible to find the unknown linear parameters, , supposing to know while solving the system of equations (2). can be found by using numerical algorithms that minimize the cost function, , for the d-th DoF: (12) where te is the length of the signals and T denotes the linear TFD operator.…”

“…Another important classification of the identification methods for nonlinear systems is based on the domain in which the identification is performed: frequency, time, or joint time-frequency domain, e.g. [11], [12]. Using a joint time-frequency domain can be also useful to perform instantaneous estimates of the parameters value, whose stability over time is symptom of consistency of a given model, [13].…”

Identification of the hysteretic behaviour of a partial‐strength steel–concrete moment‐resisting frame structure subject to pseudodynamic tests

“…The parametric identification described above was applied to the three‐dimensional structure depicted in Figure (b), subject to the four levels of PGA reported in Table . The identification algorithm described at length in minimised the objective function Q ( t , p ) expressed in (5). In greater detail, Q ( t , p ) was extended to a 2‐DOF system as follows: where p = { k 11 , k 12 , k 22 , β 1 , β 2 , γ 1 , γ 2 , n 1 , n 2 , s 1 , s 2 , μ s 1 , μ s 2 } defines the vector of linear, hysteretic and slip parameters, respectively, referred to the system (21).…”

“…In addition, the availability of hysteretic mathematical models easily allows for the development of control laws for nonlinear structural hysteretic systems . Within this framework, our research tries to combine the benefit of: (i) the classical pseudodynamic (PsD) testing technique, as applied to structures for which strain‐rate effects can be neglected , and (ii) nonlinear identification techniques of complex nonlinear systems, capable of capturing hereditary characteristics of inelastic restoring forces of structures .…”

“…In this work, we consider the instantaneous‐based identification technique applied to nonlinear systems, which relies on a time‐frequency approach . The entailing formulation determines model parameters that minimize an error function between time‐frequency representations of measured and simulated signals, respectively.…”