Identification Of Nonlinear Structural Systems Research Articles

Displacement measurement and nonlinear structural system identification: A vision‐based approach with camera motion correction using planar structures

Displacement measurement and nonlinear structural system identification: A vision‐based approach with camera motion correction using planar structures

Parameter identification of nonlinear structural systems through frequency response sensitivity analysis

Nonlinearity is ubiquitously encountered in structural systems, and it may have a great and complicated influence on the dynamic behaviours, including bifurcation, internal resonance, load history dependence, etc. Identifying the nonlinear system parameters is essential for analysis and design of the structure. To this end, a new approach is developed in this paper for nonlinear system parameter identification from frequency response sensitivity analysis. At first, the harmonic balance equation is established to govern the frequency response of the nonlinear system, upon which the frequency response and sensitivity analysis can be conducted. A remarkable feature is that the harmonic balance equation is algebraic so that the sensitivity analysis, pertaining to a linearized equation, is rather simple and straightforward. Then, parameter identification is modelled as a nonlinear least-squares problem, and the sensitivity approach is adopted in conjunction with the trust-region constraint for convergent solution. Numerical examples are conducted to demonstrate the feasibility and performance of the proposed approach.

A novel unscented Kalman filter for recursive state-input-system identification of nonlinear systems

Abstract The unscented Kalman filter (UKF) has proven to be an effective approach for the identification of nonlinear systems from limited output measurements. However, the conventional UKF requires that measurements of the input excitations are available to successfully perform nonlinear system identification, which limits its application in cases where it is difficult or impractical to measure the inputs. In this paper a novel unscented Kalman filter with unknown input (UKF-UI) is proposed for the simultaneous identification of nonlinear structural systems and external excitations. Based on the estimation-based procedures of the conventional UKF, the analytical recursive solutions of the proposed UKF-UI are derived in an analogous fashion resulting in a recursive nonlinear least-squares problem for the unknown input. Moreover, data fusion of partially measured acceleration and displacement responses is used to alleviate the drifts typically observed in the estimated inputs and displacements. Numerical and experimental validation examples are used to demonstrate the effectiveness of the proposed UKF-UI algorithm for the simultaneous identification of nonlinear parameters and unknown external excitations using data fusion of partially measured system responses.

Adaptive constrained unscented Kalman filtering for real-time nonlinear structural system identification

The unscented Kalman filter (UKF) is often used for nonlinear system identification in civil engineering; nevertheless, the application of the UKF to highly nonlinear structures could not provide accurate results. In this paper, an improvement of the UKF algorithm has been adopted. This methodology can consider state constraints, and it can estimate the measurement noise covariance matrix. The results obtained adopting a modified UKF have been compared to the ones obtained using the UKF for parameter estimation of a single degree of freedom nonlinear hysteretic system. The second part of this work shows results of an experimental activity on a base-isolated prototype structure. Both numerical and experimental results underline that the adopted algorithm produces better state estimation and parameter identification than the UKF, being capable of taking into account parameter boundaries. The adopted algorithm is more robust than the standard UKF in the case of measuring noise variation.

Identification of model-free structural nonlinear restoring forces using partial measurements of structural responses

Identification of nonlinear structural system is an important but challenging task for structural health monitoring. Due to the complexities of structural nonlinearities, it is hard to establish proper mathematical models for some structural nonlinear behaviors. Moreover, only partial structural responses can be measured in practice; it is essential to conduct identification of nonlinear structural systems using only partial measurements of structural responses. To cope with these issues, an algorithm is proposed in this article for the identification of some model-free structural nonlinear restoring forces using only partial measurements of structural responses. First, an equivalent linear structural system is introduced for the identification of the locations of structural nonlinearities. Then, a model-free structural nonlinear restoring force is approximated by a power series polynomial. The unknown coefficients of the power series polynomials together with other structural parameters are identified by the extended Kalman filter so that the characteristics of the behaviors of the model-free of nonlinear restoring forces can be identified. Some numerical examples including the identification of two nonlinear multi-story shear frames and a planar nonlinear truss with different structural nonlinear restoring forces are used to validate the proposed algorithm.

Locating and identifying model-free structural nonlinearities and systems using incomplete measured structural responses

Structural nonlinearity is a common phenomenon encountered in engineering structures under severe dynamic loading. It is necessary to localize and identify structural nonlinearities using structural dynamic measurements for damage detection and performance evaluation of structures. However, identification of nonlinear structural systems is a difficult task, especially when proper mathematical models for structural nonlinear behaviors are not available. In prior studies on nonparametric identification of nonlinear structures, the locations of structural nonlinearities are usually assumed known and all structural responses are measured. In this paper, an identification algorithm is proposed for locating and identifying model-free structural nonlinearities and systems using incomplete measurements of structural responses. First, equivalent linear structural systems are established and identified by the extended Kalman filter (EKF). The locations of structural nonlinearities are identified. Then, the model-free structural nonlinear restoring forces are approximated by power series polynomial models. The unscented Kalman filter (UKF) is utilized to identify structural nonlinear restoring forces and structural systems. Both numerical simulation examples and experimental test of a multi-story shear building with a MR damper are used to validate the proposed algorithm.

Deterministic-stochastic subspace identification method for identification of nonlinear structures as time-varying linear systems

This paper proposes the use of the deterministic-stochastic subspace identification (DSI) method, an input-output parametric linear system identification method, for characterization of nonlinear dynamic structural systems based on their time-varying amplitude-dependent instantaneous (i.e., based on short time-windows) modal parameters. Performance of the DSI method for estimation of instantaneous modal parameters of nonlinear systems is investigated using numerical as well as experimental data. In this study, DSI is used for extracting instantaneous modal parameters of single degree-of-freedom (SDOF) as well as 7-DOF systems with different hysteretic material behavior. Nonlinear responses of the SDOF and 7-DOF systems are simulated due to different seismic excitations using the OpenSees structural analysis software. Modal identification results are compared with those obtained using wavelet transform and the exact values. Effects of four input factors are studied on the variability of identified instantaneous modal parameters: (1) type of material nonlinearity, (2) level of nonlinearity, (3) input excitation, and (4) length of data windows used in the identification. The accuracy of the identified instantaneous modal parameters is evaluated along the response time history while varying the above mentioned input factors. Overall, DSI outperforms the wavelet transform for short-time/instantaneous modal identification of nonlinear structural systems and provides reasonably accurate results especially when the material hysteretic behavior is smooth such as the considered Giuffré-Menegotto-Pinto hysteretic model. Finally, DSI has been applied for short-time modal identification of a full-scale seven-story reinforced concrete shear wall structure based on its measured response to different seismic base excitations on a shake table. The identified instantaneous natural frequencies of the first vibration mode can accurately track the variation in the structure's effective stiffness along its response.

Real-time nonlinear structural system identification via iterated unscented Kalman filter

Structural system identification has attracted much attention in the structural dynamics field over the past decades. The unscented Kalman filter (UKF) is often used to deal with nonlinear system identification in civil engineering field. In practices, applying a UKF to highly nonlinear structural systems is not a trivial task, particularly those subject to severe loading. Recently, a new technique, the iterated unscented Kalman filter (IUKF) is applicable to highly nonlinear systems. In this paper, the IUKF is applied for nonlinear structural system identification (NSSI). Experimental results show that the IUKF produces better state estimation and parameter identification than the UKF, and the IUKF is also more robust to measurement noise levels.

The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing

The use of heterogeneous, non-collocated measurements for nonlinear structural system identification is explored herein. In particular, this paper considers the example of sensor heterogeneity arising from the fact that both acceleration and displacement are measured at various locations of the structural system. The availability of non-collocated data might often arise in the identification of systems where the displacement data may be provided through global positioning systems (GPS). The well-known extended Kalman filter (EKF) is often used to deal with nonlinear system identification. However, as suggested in (J. Eng. Mech. 1999; 125(2):133–142), the EKF is not effective in the case of highly nonlinear problems. Instead, two techniques are examined herein, the unscented Kalman filter method (UKF), proposed by Julier and Uhlman, and the particle filter method, also known as sequential Monte Carlo method (SMC). The two methods are compared and their efficiency is evaluated through the example of a three degree-of-freedom system, involving a Bouc–Wen hysteretic component, where the availability of displacement and acceleration measurements for different DOFs is assumed. Copyright © 2008 John Wiley & Sons, Ltd.

Application of the unscented Kalman filter for real-time nonlinear structural system identification

Over the past few decades, structural system identification based on vibration measurements has attracted much attention in the structural dynamics field. The well-known extended Kalman filter (EKF) is often used to deal with nonlinear system identification in many civil engineering applications. In spite of that, applying an EKF to highly nonlinear structural systems is not a trivial task, particularly those subject to severe loading. Unlike the EKF, a new technique, the unscented Kalman filter (UKF) is applicable to highly nonlinear systems. In this paper, the EKF and UKF are compared and applied for nonlinear structural system identification. Simulation results show that the UKF produces better state estimation and parameter identification than the EKF and is also more robust to measurement noise levels. Copyright © 2006 John Wiley & Sons, Ltd.

Damage identification of nonlinear structural systems

Damage identification of nonlinear structural systems

Spectral Identification of Nonlinear Structural Systems

The paper discusses a spectral method for identification of nonlinear systems encountered in structural applications. The nonlinearity is accounted for by a combination of linear subsystems and known zero-memory nonlinear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a “Gram-Schmidt” type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of a Duffing oscillator with nonlinear damping elucidates the applicability of the proposed method.