Research On The Strain Modal Identification Based On Power Spectral Density Transmissibility

The operational condition of engineering structures is becoming increasingly complicated,which leads to damage and catastrophic failure of structures.Therefore,the research of catastrophic mechanism and safety monitoring have been critical issues ought to be resolved.When studying the structural catastrophic mechanism and implementing safety assessment for engineering structures,an issue of fundamental importance is to properly identify structural dynamic properties.Recently,strain modes have attracted widespread attention due to its much higher sensitivity to structural damage than those of displacement modes.Therefore,strain modal analysis has become a hot research topic in the field of structural health monitoring.However,how to accurately identify the strain modal parameters from the measured strain measurement is still a problem not well addressed.In this regard,this thesis is devoted to studying the strain modal analysis based on Power Spectral Density Transmissibility(PSDT)of strain measurements under the support of the National Science Foundation of China entitled “Research on the Strain Modal Identification of Bridge Engineering based on PSDT”(Award No: 51778204).The thesis extends the concept of PSDT to strain measurements,and proves that the PSDT of strain measurements is equivalent to the amplitude ratio at the system poles by using the limit theorem of complex functions.Based on the unique properties of strain PSDT,the natural frequencies can be identified using the PSDT subtraction function while strain mode shapes can be identified by taking SVD for the PSDT matrix.Finally,the accuracy and efficiency of the proposed method are verified by numerical examples and dynamic testing of two laboratory models.The main contribution and conclusion of this thesis are outlined as follows:1.Strain PSDT defined as the ratio of the power spectra of strain at arbitrary two points with respect to the same reference output is formulated by changing the reference outputs.Based on the strain frequency response function which reflects the input-output relationship,the strain PSDT in the modal domain is derived,and its properties approaching the resonant frequencies are investigated in detail.According to the limit theorem of complex ratio function,the unique properties of the PSDT of strain measurements at the system poles are revealed,which indicates that it is independent of the selection of reference output,the natural excitation and the displacement modes.Meanwhile,this thesis proves that at the system pole,the PSDT of two different measurements is equivalent to the amplitude ratio of the strain modes.The properties of strain PSDT lays a theoretical foundation for the identification of strain modes.2.Based on the unique properties of strain PSDT,it can be proved that the system's poles are zeros of the PSDT subtraction function.This indicates that it is possible,by using the reciprocal value of the PSDT subtraction function,to obtain a function with poles equal to the system's poles.Only a subset of the poles of the functions will correspond to the real poles of the system.To reduce the risk of finding additional fault peaks,in this thesis,a strain PSDT matrix is constructed by incorporating a number of strain PSDT functions obtained under different transferring outputs.With the aid of successful locating of stable system poles,strain mode shapes can be identified by taking SVD for the PSDT matrix.3.The strain responses of a three-span continuous box girder bridge subject to ambient vibration was generated to verify the proposed method.The PSDT was utilized to identify the strain modes,which were also compared with calculated from finite element model.Results indicate the performance of the proposed method is satisfactory.This thesis also investigates the effects of different parameters such as sampling frequency,noise level and time duration on the identification results.4.Dynamic testing of a two-span continuous beam laboratory model and a simply-supported steel bridge was conducted.By analyzing the strain measurements,the strain modes were identified using the strain PSDT approach proposed in this thesis.The accuracy of the proposed method was verified by comparing with the results of finite element model and the results identified by using classic stochastic subspace identification(SSI)method.In addition,the effects of the excitation location,time duration and resampling rate on the modal analysis results are also investigated in detail.Results indicate the robustness of the strain PSDT in real applications.