Research On Structural Response Reconstruction Method Based On VME And Improved KF

Structural health monitoring has been widely used in the fields of aerospace,civil engineering,and mechanical engineering by simulating human self-awareness and self-diagnosis capabilities to real-time perceive,identify,and evaluate the safety and performance evolution of structures.Complete dynamic responses are the foundation and guarantee of structural health monitoring,and the measurement of responses depends on sensor systems.However,due to the limitations of economic conditions,structural complexity,and diversity of operating conditions,the number of sensors installed on the structure is limited,and some key locations may not be able to install sensors.Therefore,it has important research significance to use the response of limited measurement points to estimate the response of unmeasured points.Based on the structural response reconstruction method,it is possible to reconstruct displacement and velocity responses that are difficult to measure through easily measured acceleration responses,providing effective and comprehensive information for structural health monitoring.Based on previous research,this dissertation carries out the following research:(1)A structural response reconstruction method combining variational modal extraction and the mode superposition method is proposed.Firstly,the measured dynamic response is decomposed into modal responses using variational mode extraction.Then,modal responses at the unmeasured position are calculated through the modal transformation matrix.Finally,the mode superposition method is used to reconstruct the unknown dynamic response.The robustness of the proposed method is tested through numerical examples,and the practicability of the proposed method is verified through the experiment of a simply supported beam.(2)A new method of response reconstruction based on Kalman filter algorithm under colored measurement noise is proposed.Firstly,the colored noise is described as a first-order AR model,and the observation equation is reconstructed with the measurement state amplification method to whiten the colored noise.However,there is a certain correlation between the system noise and the newly constructed measurement noise.Therefore,based on the undetermined coefficient method,further reconstructing the state transition equation can eliminate the cross-correlation of noises within the same filtering period,and obtain a more accurate Kalman filter model under colored measurement noise.Finally,numerical simulation of the rail model verifies the feasibility of the proposed method and its advantages over traditional Kalman filtering algorithms.(3)An improved Sage-Husa adaptive Kalman filter algorithm under colored measurement noise is proposed and applied to structural response reconstruction.Firstly,the estimating formula of the measurement noise covariance matrix is equivalently converted into the form of the sum of the positive semidefinite matrix and the positive-definite matrix by being rewritten with the covariance matrix of the residual vector,thereby preventing the possibility of filtering divergence;then an adaptive forgetting factor model based on the exponential function is constructed,which not only ensures stable estimation when the variance of measurement noise fluctuates slightly,but also significantly improves the convergence speed of the algorithm when the measurement noise suddenly increases.Finally,the results of a numerical simulation and an experimental test show that the proposed algorithm has good adaptability and significantly improves the effect of the response reconstruction.