Responses Reconstruction Based On Moving-window Kalman Filter Using Limited Measurements

One of the key problems in structural health monitoring is how to correctly monitor the dynamic response of the structures,which depends on the sensory system,frequently.Considering the restrictions of economic conditions,and equipment,it is impossible to install sensors in all parts of the structure.Many parts or even some key parts are not equipped with sensors,which cannot provide complete and effective information for structural health monitoring and safety assessment.In recent decades,with the help of response reconstruction technology,the dynamic response reconstruction at the unmeasured locations with a limited number of sensors has attracted many researchers’ interests.The Kalman filter algorithm,as a powerful iterative algorithm that uses the measured response to estimate the state vector of the system optimally with the minimum mean square error as the best criterion,has been applied by many researchers to reconstruct the unmeasured responses of the structure.These existing response reconstruction methods based on Kalman filter algorithm assumed that the measurement noise variance R and the process noise variance Q were known and they were constant.In fact,however,they are unknown and time-varying.Therefore,this thesis is devoted to the unmeasured response reconstruction using limited measurements based on moving-window Kalman filter with the unknown measurement and process noise variance.The main contributions are as follows:Firstly,the structural response reconstruction based on moving-window Kalman filter with unknown measurement noise variance was studied.Based on Kalman filter algorithm and moving window technology,the estimation equation of measurement noise variance and the reconstruction equation of structural response were derived.Numerical examples using the two-dimensional simply supported overhanging beam and the three-storey frame structure were conducted to verify the proposed method.The results demonstrated that without pre-set the measurement noise variance,the unmeasured responses can be reconstructed accurately.Secondly,the structural response reconstruction based on moving-window Kalman filter algorithm with the unknown measurement and process noise variances was investigated.After the estimation of unknown measurement noise variance,the moving-window technique was used further to estimate the process noise variance.The response reconstruction equation and the reconstruction error equation of structural response were established when both measurement noise and process noise variance were unknown.Two-dimensional simply supported overhanging beam structure and three-storey frame structure were still taken as numerical examples to verify the proposed method.The estimated measurement and process noise variance were time-varying.Whether in time domain or frequency domain,the error between reconstructed response and measured response was very small,which verified the feasibility and validity of the method.Finally,experimental investigations using the simply supported overhanging beam and three-story frame at the laboratory were conducted.Two different excitation modes,including random load and hammering load,and two different sampling frequencies,including 200 Hz and 500 Hz,were considered to verify the methods proposed in Chapters 2 and 3.The experimental results showed that the reconstructed structural responses at unmeasured locations with unknown R and Q were in good agreement with the measured ones,which further verified the effectiveness and practicability of the proposed methods.