Abstract
Nonlinearity exists widely in civil engineering structures; for example, the initiation and growth of damage under dynamic loadings is a typical nonlinear process. To date, for the purpose of structural evaluation and a better understanding nonlinear characteristics of complicated structures, a number of parametric and nonparametric methods have been developed for the identification of nonlinear restoring force (NRF). However, due to the highly individualistic nature of nonlinear systems, it would be inefficient to attempt to express the structural NRF in a general parametric form. For many nonparametric techniques, their nonparametric models or approximations may result in undesirable results or oscillations around unsmooth points. In this paper, on the basis of extended Kalman filter (EKF), a model-free NRF identification approach is proposed to circumvent the limitations mentioned above. The NRF to be identified was treated as ‘unknown fictitious input’, and thus, no prior assumptions or approximations for the NRF model were required. With the aid of a projection matrix, a modified version of observation equation was obtained. Based on the principle of EKF, the recursive solution of the proposed approach was analytically derived. The NRFs provided by the nonlinear components were identified by means of least squares estimation (LSE) at each time step. Numerical examples, including building structures equipped with magnetorheological (MR) damper and shape memory alloy (SMA) damper, demonstrated that the proposed approach is capable of satisfactorily identifying NRF without knowledge or intuitive assumptions of any nonlinear model class in advance.
Highlights
A model-free nonlinear restoring force (NRF) identification approach was proposed basing on the principle of extended Kalman filter (EKF)
The NRFs provided by the nonlinear components such as the MR damper and shape memory alloy (SMA) damper were treated as ‘unknown fictitious input’, and no prior assumptions or approximations for the NRF model were required
The NRFs were identified by means of least squares estimation (LSE) at the same time
Summary
Civil engineering structures are prone to deterioration or damage due to certain factors, such as strong dynamic loadings, material fatigue accumulation and environmental corrosion. Nonlinearity is generic in nature, and linear behavior is an exception [3]. The occurrence of a fault in an initially linear structure will, in many cases, result in nonlinear behavior. It is highly desirable to develop nonlinear identification algorithms to facilitate the evaluation of the structural performance and condition for the purpose of prevention of potentially catastrophic events. Nonlinear modeling is a challenging step, because nonlinearity may be caused by many different mechanisms and may result in plethora of dynamic phenomena. Without a precise understanding of the nonlinear mechanisms involved, the identification process is bound to fail. If little is known about the form of the model before starting the identification process, one may resort to nonparametric approximations or expressions
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