An KF-based Study On The Identification Of System States And Unknown Inputs

It is well-known that damage detection is an important part of structural health monitoring.On the basis of input and\or output data,the variations of structural parameters(e.g.stiffness,damping and mode shape)can be identified and used for structural evaluation.However,due to practical limitations,the observations including the structural responses and external excitations are often limited.Moreover,due to the highly individualistic nature of nonlinear behavior caused by structural damage,it would be ineffcient to attempt to express the structural nonlinear restoring force(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 order to circumvent the aforementioned limitations,relavant research has been conducted in this dissertation on the basis of the Kalman filter(KF).(1)Based on KF and recursive least squares estimation,a time-domain approach is proposed for estmating system state and identifying structural parameters.Two cases,saying full observations and limited observations,are considered.The feasibility of the proposed approach is verified by several numerical examples.(2)The classic KF is not applicable when the external excitation is unknown.Also,it can not be employed to handle nonlinear problems.To circumvent the aforementioned limitations,an improved KF with unknown input(KF-UI)approach is proposed for the estimation of structural states with limited measurements.By introducing a projection matrix,a revised version of observation equation is obtained.The umeasured responses are estimated in a recursive manner,and the unknown inputs are identified by means of least squares estimations at the same time.The accuracy of the proposed approach is numerically verified via several linear and nonlinear examples.(3)The global responses are not sensitive to local damages.For the purpose of evaluating structural condition more efficiently,utilization of multitype measurements including local and global information for structural health monitoring is required.Based on the improved KF-UI approach introduced before,a multi-scale response reconstruction approach is proposed for simultanesly estimating the unmeasured global and local structural responses as well as the unknown loading.The global responses(i.e.acceleration and displacement)and local response(i.e.strain)are fused together for the response reconstruction and loading identification.The reliability of the proposed approach is also numerically validated.(4)The classic extended Kalman filter(EKF)can be used for parameter identification with known input.The proposed KF-UI approach in this dissertation can be performed without the knowledge of input.However,the structural parameters can not be identified by this method.Thus,by introducing the unknown structural parameters to the vector of system state,an EKF-UI approach is proposed for the simultaneous identification of structural parameters and external forces.Several numerical examples including linear and nonlinear structures are employed for the validation of the proposed approach.(5)Based on the aforementioned EKF-UI approach,a model-free nonlinear restoring force(NRF)identification approach is proposed.The NRF to be identified is treated as ‘unknown fictitious input',and thus,no prior assumptions or approximations for the NRF model are required.The accuracy of approach is validated via several sorts of nonlinear systems and compared with the power series polynomial method.