Parameter Estimation Theory Based On AR Model With Additive Noises And Its Application In Structural Damage Identification

Civil structures are subjected to many adverse factors such as occasionally experience natural disasters,and extreme events induced by humans,thus leading to different types of structural damages.The identification of structural damages has been extensively studied nowadays,and various damage detection methods have been proposed.Among which the vibration-based method is effective in the detection of structural damages.Usually small,inner structural damages can lead to changes in the vibration responses.Hence,the responses of the structures are deterministic of the structural states.This types of method aims at extracting subtle changes in the vibration signals to detect or locate the damages.In all the vibration-based methods,auto-regressive(AR)model based methods used for damage detection offer a number of potential advantages compared to alternatives.The AR model represents the correlations between the observations at the current time with the prior observations.In effect,the model assumes that there are errors in the current observations but no errors in the past.However,all the observations in the real cases in civil engineering usually contains unneglectable noises,using the classical AR model may lead to errors since it ignore the errors in the previous observations.This study introduces a new solution for the AR model with additive noise based on the total least squares thoery.The new method can not only detect the structurakl damage degree and location,but also can be used in real cases in structural engineering.The achievements of this paper are shown in follows,(1)Systematically study the damage identification thoery of the AR model based method,detailly including inspection and preprocessing of data,the order determination and so on.Then some model solution method are introduced.After a sensitive damage indicator is chosen,the least-squares(LS)solution for the AR model is used for damage identification of simulated systems and structures in mathematical simulation and finite element simulations.Results prove that the LS solution for the AR model can be used for identify both the damage degree and damage location of structures.(2)The errors in the previos observations are ingored in the classical AR model,which leading to bias in the results of the estimated parameters.In this section,an statistical model which considers all the possible errors in the observations is established.Then the bias of the AR parameter estimation results obtained by the LS solution are calculated quantitatively as well as their effection on the damage identification results are also studied for the first time.After different levels of errors are added to the obsevations in the mathematical and numerical simulations,damage identification results are analyzed compared with the results of nosie-free obsevations to study the influence of the errors on damage identification results.(3)A new damage identification method based on AR model with additive model and its extended total least-squares method(TLS_E)is presented in this section.Fisrtly,the statistical model above is extended to a more normal one named AR model with additive noises.Secondly,without considering the correletions between the errors of obseved vector with designed matrix,AR parameters are estimated by a existed total leat squares method(TLS_p),finding out instability in the results.Then an improved algorithm TLS_E considering the possible correletions between errors of the observed vectors with the designed matrix are proposed,and indicating its effectiveness in structural identification even in high amount of noises in the mathematical simulations.Finally,the proposed methhod is used for identifying damages in a finite element model,showing that this method can not only identify the damage degree and location,but also can behave better than the traditional AR model and LS solution.(4)A shaking table test with a 1/30 scale model was carried out to study its seismic performance.Not only the dynamic characteristics and the responses of the model subject to different seismic intensities are investigated via the analyzing of shaking table test data and the observed cracking pattern of the scaled model,but also the corresponding finite element analysis of shaking table model is established and the results are coincident well with the test.The most important is that the proposed method is applied to the experimental data to identify the damage of the structure after suffering from different waves.The damage identification results coincide well with the test and numerical simulation,not only indicating that this building is well designed and can be safely put into use,but also proving that the proposed method can be put into real use.In conclusion,this study may make a significant contribution to the literature because the proposed method can reduce the identification errors,which can behave good even in high amount of noises and may be more practical than classical identification methods based on the AR models.Furthermore,the paper proved that errors in the observations of the AR model can lead to bias to the damage identification results,these bias are also calculated.A shaking table test is also conducted to study the behavior of a high-rise building after suffering from different seismic intensities.Finally,the proposed damage identification method is used to identify damages in the building,indicating the practical uses of this new method.