Time-Varying/Nonlinear System Identification Method Based On The Integration Of Wavelet Multi-resolution Decomposition And Kalman Filter With Partial Measurements

In recent years,vibration-based system identification has become an important research topic in structural health monitoring,including the identification of linear and nonlinear systems.At present,most research work on the identification of structural parameters is focused on the linear time-invariant system.However,the structural parmaters of many practical civil engineering structures may exhibit time-varying behavior under the environmental erosion,structural damage,material aging and load effect etc.Therefore,identifying the time-varying structural parameters plays an important role in safety assessment and damage detect.In addition,it is well-known that most structures could exhibit intrinsically nonlinear behavior,especially when they are subjected to strong excitation or when they are damaged,serious damage will occur when the earthquake excitation is very intense—meaning that steel may yield,concrete may crack or be crushed.For the purpose of damage identification or health monitoring,it is necessary to develop techniques that can quantify nonlinear behavior in the structure.Based on the research background mentioned above,this paper mainly focuses on the identification of "time-varying system" and "non-linear system".However,the problems encountered in identifying the nonlinear characteristics of civil infrastructures and time-varying behaviors are complex.The main challenges can be summarized as fol ows:(1)The structural responses at all dynamic degrees of freedom(DOFs)must be measured,which is obviously impractical for real applications;(2)The nonlinear model of a system is assumed to be known,and only the model parameters are to be identified,meaning that the nonlinear characteristics of the underlying structures may not be captured accurately;(3)Assuming that the possible damage location of the building can be identified a priori.It is necessary to locate the damage in advance,and to determine the "target area" where damage may occur.To overcome the above limitations in previous research,a new algorithm based on the integration of wavelet multiresolution analysis and Kalman filter with partial measurements of structural acceleration responses is proposed.Due to the merits of these two methods,this integrated algorithm can be used to identify time-varying parameters and forces with limited observations.and do not require prior knowledge of structural nonlinearity and/or location.Chapter 1 of this thesis summarizes the research progress of "time-varying system"and "nonlinear system identification".And the main research contents and innovation points are briefly introduced.In Chapter 2,an identification method for identifying time-varying physical parameters of linear structures was proposed.The main idea is as follows:First,the time-varying structural stiffness and damping parameters are expanded at multi-scale profile by wavelet multiresolution decomposition,so a time-varying parametric identification problem can be converted into a time-invariant one.Then,structural responses are estimated recursively by an integrated Kalman filter using partial measurements of structural acceleration responses.The scale coefficients of the expansion can be obtained via the solution of a nonlinear optimization problem(Lsqnonlin)by minimizing the error between estimated and observed accelerations.Then,the original time-varying parameters are re-constructed.In Chapter 3,the proposed algorithm can be extended to the identification of time-varying physical parameters of nonlinear structural systems based on the integration of wavelet multi-resolution decomposition of the time-varying structural parameters and the extended Kalman Filter for the estimation of structural responses using partial structural acceleration responses.The main idea is as follows:First,the time-varying parameters of hysterestic models are expanded at multi-scale profile by wavelet multiresolution decomposition.Then,structural responses are estimated recursively by Extended Kalman filter using partial measurements of structural acceleration responses.The scale coefficients of the expansion can be obtained via the solution of a nonlinear optimization problem(Lsqnonlin)by minimizing the error between estimated and observed accelerations.Then,the original time-varying parameters of nonlinear systems are re-constructed.It is worth noting that the method we proposed in this chapter is based on the knowledge of hysterestic model.In Chapter 4,a method for identifying structural model-free nonlinear characterestics is proposed.The main idea is as follows:First,the nonlinear forces generated by the damaged or yielding components are regarded as the unknown 'additional virtual force' imposed on a linear structure,and expanding 'additional virtual force' at multi-scale profile by wavelet multiresolution decomposition.Then,structural responses are estimated recursively by Kalman filter with partial measurements of structural acceleration responses.The scale coefficients of the expansion can be obtained by minimizing the error between estimated and observed accelerations.Then,the unknown force are re-constructed.The proposed method do not require prior knowledge of structural nonlinearity and/or measurements at all DOFs.In Chapter 5,an offline substructural identification method based on WMRA and KF-UI is proposed for the identification of nonlinear behavior in a building.The idea of "divide and rule" is adopted here for large-scale structures,the substructuring method can divide the global structure into seperate substructures.Since the substructures are independent,the nonlinear analysis can be computed seperately to release the computation load,avoiding the nonlinear analysis of the global structure.The nonlinear forces generated by the damaged or yielding components,the of each substructure are regarded as unknown inputs imposed on the substructure.The main idea is as follows:First,expanding 'unknown nonlinear forces' at multi-scale profile by wavelet multiresolution decomposition.Then,structural responses and the boundary forces are estimated recursively by KF-UI method with partial measurements of structural acceleration responses.The scale coefficients of the expansion can be obtained by minimizing the error between estimated and observed accelerations.Then,the unknown nonlinear forces are re-constructed.The proposed method does not require prior knowledge of structural nonlinearity and/or measurements at all DOFs.The Chapter 6 summarizes the main work and the innovation point of the thesis,a prospect for future work is also proposed at the end.