Model-free nonlinear restoring force identification for SMA dampers with double Chebyshev polynomials: approach and validation

Xu, Bin; He, Jia; Dyke, Shirley J.

doi:10.1007/s11071-015-2257-0

Cited by 20 publications

(10 citation statements)

References 36 publications

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“…A two-stage general procedure was presented by Masri et al [28] for developing data-based, model-free representations of complex nonlinear systems under arbitrary dynamic loads. By using a power series polynomial to represent the NRF, a data-based approach was proposed for the identification of chain-like structure equipped with magneto-rheological (MR) damper [29,30] and shape memory alloy (SMA) damper [31]. The generalized two-variable Chebyshev polynomials and their relevant relations were further discussed by Cesarano and Fornaro [32,33].…”

Section: Literature Surveymentioning

confidence: 99%

Model-Free Identification of Nonlinear Restoring Force with Modified Observation Equation

Zhang

et al. 2019

Applied Sciences

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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.

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Section: Literature Surveymentioning

confidence: 99%

Model-Free Identification of Nonlinear Restoring Force with Modified Observation Equation

Zhang

et al. 2019

Applied Sciences

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“…Meanwhile, Nayeri et al [24] provided an algorithm combining natural excitation technology and eigenvalue realization technology to identify the modal parameters of structures with unknown mass. Xu et al [25] investigated a timedomain algorithm for simultaneous identification of mass and nonlinear restoring force based on the least square algorithm and verified the algorithm with a chain-like nonlinear structure of six degrees of freedom with a Magnetorheological (MR) damper mounted in the middle. Huang et al [26] employed the Kalman filter (KF) technique together with energy equilibrium equations to develop a method that can identify the damping, stiffness and mass of the structure simultaneously online.…”

Section: Introductionmentioning

confidence: 99%

A Joint State-Parameter Identification Algorithm of a Structure with Non-Diagonal Mass Matrix Based on UKF with Unknown Mass

Wang

Lei

2022

Buildings

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Inaccurate mass estimates have been recognized as an important source of uncertainty in structural identification, especially for large-scale structures with old ages. Over the past decades, some identification algorithms for structural states and unknown parameters, including unknown mass, have been proposed by researchers. However, most of these identification algorithms are based on the simplified mechanical model of chain-like structures. For a chain-like structure, the mass matrix and its inverse matrix are diagonal matrices, which simplify the difficulty of identifying the structure with unknown mass. However, a structure with a non-diagonal mass matrix is not of such a simple characteristic. In this paper, an online joint state-parameter identification algorithm based on an Unscented Kalman filter (UKF) is proposed for a structure with a non-diagonal mass matrix under unknown mass using only partial acceleration measurements. The effectiveness of the proposed algorithm is verified by numerical examples of a beam excited by wide-band white noise excitation and a two-story one-span plane frame structure excited by filtered white noise excitation generated according to the Kanai–Tajimi power spectrum. The identification results show that the proposed algorithm can effectively identify the structural state, unknown stiffness, damping and mass parameters of the structures.

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“…Alternatively, non‐parametric modeling can simulate the nonlinear hysteretic behavior without the need for parameters having physical significance 11–13 . Some nonparametric models of MR damper have been presented in the previous literature, for example, Masri et al 13,14 simulated the performance of MR dampers by Chebyshev polynomials, Xu et al 15 estimated nonlinear restoring force (NRF) using a power series polynomial including a double Chebyshev polynomial function 16 . Li et al 17 proposed an innovative approach based on hybrid extended Kalman filter and wavelet multiresolution analysis for the identification of hysteretic structural systems.…”

Section: Introductionmentioning

confidence: 99%

Identification of model‐free hysteretic forces of magnetorheological dampers embedded in buildings under unknown excitations using incomplete structural responses

Lei

Yang

Huang

et al. 2021

Struct Control Health Monit

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Summary Magnetorheological (MR) damper is efficient to mitigate vibration of the structure subject to severe excitations. The identification of nonlinear characteristics of MR damper has attracted increasing attention. However, it is still challenging to identify model‐free hysteresis of MR dampers embedded in structures using only incomplete measurements of structural responses under unknown excitations. In this paper, an identification technique is proposed for this tough task, namely, nonparametric identification of MR nonlinear restoring forces in building structures under unknown excitations. The proposed technique involves identifications in two stages. In the first stage, the identification of linear parameters of bare structure and MR dampers under low‐level unknown excitations is conducted based on the generalized extended Kalman filter with unknown input (GEKF‐UI) by the authors. In the second stage, the hysteretic forces of MR dampers are proposed to be treated as “unknown fictitious forces” to the corresponding linear bare structure identified in the first stage. The generalized Kalman filter with unknown inputs (GKF‐UI) by the authors is adopted to identify all unknown inputs including the “unknown fictitious forces” originated from MR dampers. To demonstrate the proposed technique, some numerical examples are used to identify model‐free hysteresis of single or multi MR dampers with different nonlinear restoring force models in shear frames under unknown external force excitations or unknown seismic excitations, respectively. Furthermore, experimental testing of the identification of model‐free MR damper in a multi‐story shear frame under unknown external excitation is conducted.

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Model-free nonlinear restoring force identification for SMA dampers with double Chebyshev polynomials: approach and validation

Cited by 20 publications

References 36 publications

Model-Free Identification of Nonlinear Restoring Force with Modified Observation Equation

Model-Free Identification of Nonlinear Restoring Force with Modified Observation Equation

A Joint State-Parameter Identification Algorithm of a Structure with Non-Diagonal Mass Matrix Based on UKF with Unknown Mass

Identification of model‐free hysteretic forces of magnetorheological dampers embedded in buildings under unknown excitations using incomplete structural responses

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