Operational Modal Parameter Identification Methods In The Frequency Domain:Review And Comparative Studies With Engineering Structures

Modal parameters,including frequency,mode shape and damping ratio,are the primary parameters to characterize the dynamic characteristics of the engineering structures.Operational modal analysis has many advantages,such as requiring no excitation equipment and no interruption of structural service conditions,which is now widely used in civil engineering.What’s more,compared with the time domain method,the frequency domain approaches are simpler,more efficient and easier to implement.Under the support of the National Science Foundation of China,in this thesis,the theory and algorithm of frequency domain modal parameter identification methods under natural excitation are analyzed in depth,and the performance of various methods in practical application are compared using SHM data of two Benchmark structures.Therefore,the characteristics and the scope of application of various approaches are summarized.When conducting dynamic testing for large engineering structures,the degrees of freedom of interest are usually divided into multiple setups due to the limitation of sensors.a two-stage fast Bayesian approach for mode shape assembly were proposed to process the dynamic testing data,which can glue the local mode shapes identified in a single test group together to form the global mode shape and quantify its uncertainty.Finally,a cable-stayed bridge is used to verify the effectiveness of the method.The main work and conclusions of this paper are as follows:(1)The theory and algorithm of frequency domain method for operational modal analysis are systematically discussed,and it is classified into three categories:deterministic nonparametric method,deterministic parametric method and uncertainty analysis method.Nonparametric methods include traditional power spectrum method,power spectral density transmissibility(PSDT)method and coherence function method,and each method is divided into two categories according to whether singular value decomposition(SVD)is used or not.Parametric method include Poly MAX method.Uncertainty analysis methods include maximum likelihood estimation method and Bayesian method.Nonparametric method identify modal parameters by using spectrum characteristics or SVD technology.Poly MAX method identify modal parameters by means of modal model,and distinguish the physically true modes from the spurious modes by using stability diagram;The maximum likelihood method transmits the noise information in the signal to the modal parameters by means of the variance of the spectrum,while the Bayesian method embeds the error model into the probability model,which can accommodate the influence of multiple uncertainties,and the theoretical derivation is religious.(2)Through SHM data of two Benchmark structures including Canton Tower and Ting Kau Bridge,the performance of various frequency domain methods were compared with each other.The results show that the ability of traditional power spectrum method to identify close modes is inferior to frequency domain decomposition method,PSDT method and coherence function method;The PSDT method and the coherence function method can effectively eliminate the spurious modes near the first true mode of the Canton Tower and produce more sharp peaks compared with the power spectrum method;It is found that the uncertainty identified by Bayesian method is obviously more scientific than maximum likelihood estimation method,especially for the uncertainty of damping ratio;The damping ratio identified by Bayesian FFT method is smaller than that identified by Poly MAX method.(3)The influence of the key parameters on the modal analysis is studied,such as window function,the number of extraction point for fast Fourier transform(NFFT)and the length of data used in the identification process.Besides,the number of modes that can be identified and the variation of identified parameters are discussed with the measuring point in different location.The influence of the wind speed is also studied.The results show that signals windowed by Kaiser window can produce more sharp peak curve;If NFFT length is too short,it is easy to lose modes,while if it is too long,the peak curve would have too many burrs and interfere with the selection of peak values;The longer the analysis signal length,the smoother the peak curve,which can reduce the risk of identifying false modes,but when it continues to increase,the influence on the peak curve tends to be stable;For Canton Tower,the amplitude near the top of the tower is relatively large and the nodes of mode shape are less,so that the modal number identified by the response of the measuring point is more.While for Ting Kau Bridge the modal number identified by the response of the measuring point is relatively small because the nodes of mode shape are mostly near the midspan.(4)In the ambient vibration test for large-scale structures,the degrees of freedom of interest are usually divided into multiple setups due to the limitation of sensors.A two-stage fast Bayesian approach for mode shape assembly were proposed to process the dynamic testing data of the structures.In the first stage,the most probable values and uncertainties of the natural frequency,damping ratio and local mode shapes were identified for different setups using fast Bayesian FFT approach.In the second stage,the optimal value of the global mode shape is quickly obtained by analytic iterative optimization algorithm,and the analytical solution of the Hessian matrix of the negative logarithmic likelihood function with respect to the global mode shape is derived to quantify the uncertainty of the global mode shape.Theoretical analysis shows that the uncertainties of local mode shapes can characterize the quality of data of each group,so this method has the ability to automatically assign weights according to the information of each group.(5)In order to verify the effectiveness of two-stage fast Bayesian approach for mode shape assembly,this method is applied to the dynamic testing data of a cable-stayed footbridge,and the global mode shape is identified and its uncertainty is quantified.The results show that this method has high computational efficiency,which can effectively restrain the influence of the group with poor data quality in the process of mode shape assembly.The "suppression effect" is more obvious for the group with relatively poor data quality.