Model Based Or Data Based Approaches For The Identification Of Structural Nonlinearity With Limited Output Measurements

Due to some natural and man-made factors, nonlinearity widely exists in the actual structure, including that the nonlinear behavior of rubber-bearing setting to resist seismic action in base-isolated building, and the nonlinear behavior of the structure because of the damage development in the long-term. Thus, the research on the identification of structural nonlinearity plays a very important role in the structural safety assessment and damage diagnosis. In this thesis, a new algorithm is proposed for the identification of structural nonlinearity under limited output measurements on the basis of summarizing the nonlinear structural identification research at home and abroad.This thesis first studies the identification method of nonlinear properties of the rubber-bearings in base-isolated building. For the case that proper mathematical models can be established for the base isolators, it is based on the extended Kalman filter for the parametric identification of nonlinear rubber-bearing isolators and the structure. For the general case that it is difficult to establish a proper mathematical model to describe the nonlinear behavior of a rubber-bearing isolator, a data based algorithm is proposed to identify the nonlinear property of rubber-bearing isolated system. First, structural parameters including the linear stiffness and damping of rubber-bearing under minor earthquake are identified based on the extended Kalman estimator approach. Then, nonlinear effect of rubber-bearing is treated as’ additional unknown fictitious loading’ on the building under severe earthquake. By sequential application of Kalman estimator for the structural responses and the least-squares estimation of the ’additional fictitious loading’, the nonlinear property of rubber-bearing can be identified. Compared with other algorithms based on the conventional extended Kalman filter, the proposed approach is more straight and concise. Then, based on substructure approach, the algorithm is extended to identify the nonlinear properties of the rubber-bearings in large size base-isolated buildings. Several numerical examples of small and large size base-isolated buildings under seismic excitation are carried out with limiter output measurements based on the proposed method to demonstrate its effectiveness.Second, for the model based identification of the structural nonlinearity, based on prior researches, a two-stage method is proposed. First, an equivalent linear system is used to make the conclusion about the location of the nonlinearity by the difference between structural parameters and equivalent linear parameters. Then by the unscented Kalman filter, the nonlinear parameters of the structure can be identified, and then the structural nonlinearity is identified. Then, based on substructure approach, the algorithm is extended to identify structural nonlinearity in large size model based structures under limited output measurements. By using the method of decentralized identification, the linear substructure is identified by the extended Kalman filter and the nonlinear substructure is identified by the unscented Kalman filter. The advantage of this method is that it can not only reflect the advantage of high calculation efficiency of extended Kalman filter, but also implement accurate recognition of the structural nonlinearity by the unscented Kalman filter. Several numerical examples of small and large size structures under different excitations with different nonlinear models are carried out with limiter output measurements based on the proposed method to demonstrate its effectiveness.Generally, for model free data based identification of the structural nonlinearity, a two-stage method proposed is also adopted. First, an equivalent linear system is used to make the conclusion about the location of the nonlinearity by the difference between structural parameters and equivalent linear parameters. Then the nonlinear restoring force is expanded by power series on the location of nonlinearity, and the coefficients of the series are identified by the unscented Kalman filter, and then the structural nonlinearity is identified. Several numerical examples of small size structures under white noise excitation with different nonlinear models and an experimental of structural nonlinearity identification are carried out with limiter output measurements based on the proposed method to demonstrate its effectiveness.Then, based on substructure approach, the algorithm is extended to identify structural nonlinearity in large size model free structures under limited output measurements. By using the method of decentralized identification, the linear substructure is identified by the extended Kalman filter and the nonlinear substructure is identified by the unscented Kalman filter. The advantage of this method is that it can not only reflect the advantage of high calculation efficiency of extended Kalman filter, but also implement accurate recognition of the structural nonlinearity by the unscented Kalman filter. Several numerical examples of large size structures under seismic excitation with different nonlinear models and an experimental study of structural nonlinearity identification are carried out with limiter output measurements based on the proposed method to demonstrate its effectiveness.