Nonparametric Identification Of Frequency Response Function

The frequency response function(FRF)is a powerful tool which can describe the dynamic characteristics of the system quickly and intuitively.It possesses important research and application value and can be applied to dynamic modal analysis and optimization of mechanical structures and detection of structural damage.The nonparametric identification method is the basis of identifying complex dynamic systems,which does not require too much user intervention and can be used to define the model structure or order.In the present work,the nonparametric identification methods of FRF based on two different models are studied in depth,which are the Local Rational Method and Gaussian process respectively.To improve the identification accuracy,the influencing factors of the identification accuracy of FRF are analyzed,and the improvement and optimization methods are developed.The main findings of the present work are as follows:(1)The identification of FRF is thoroughly studied based on Local Rational Model.To eliminate the bias of least-squares estimate in the literature,a weight strategy is introduced to construct a new objective function,which guarantees the consistency of parameter estimates,and the variance of estimated FRF is provided.Further,the improved method are extended to multivariable system and the case of dynamic errors-in-variables system.(2)The identification of the FRF is developed using Gaussian process.To sufficiently take into account the stability and smoothness of the FRF,the FRF is modeled by an applied covariance function in the frequency domain,and the Gaussian process regression method of FRF is established.For the numerical problem of estimating hyperparameters,which describe the covariance function,a strategy using QR decomposition is adopted,which can circumvent the directly inverse and determinant operations of the covariance matrix with high condition number,and the robustness of the hyperparameter estimation results are enhanced as a result.(3)Verification and application of nonparametric identification algorithm forFRF modeling.The effectiveness and accuracy of the proposed method are verified by simulation examples and designed dynamic experiment.The results show that the improved method based on the Local Rational Model can accurately reveal the low-damping characteristics of the system even under the condition of severe signal-noise ratio.Gaussian process regression can identify FRF with high accuracy,but there is still room for improvement for modeling the resonance peak.The results of this thesis contribute to further improve the nonparametric identification accuracy of FRF and lay a sound foundation for the application of FRF.