Identification Of Structural Load And Stiffness Evolution Based On Bayesian Learning Of Dynamic Sparse System

In system identification,tracking and identifying structural physical parameters,such as structural stiffness parameters and external loads in real time is very important for assessing the safety state of structure timely and it has been a hot topic in the field of structural health monitoring at home and abroad.In model-based structural system identification methods,Kalman filter,which has been widely studied and applied in structural dynamic system identification,utilizes measured data of system to estimate system state and parameters to be identified online with Bayesian recursive algorithm.Due to structural model error,incompleteness of measured data,measurement noise and other reasons,the solving for inverse problem of structural system identification is often ill-posed and ill-conditioned.Moreover,the implementation of Kalman filter requires setting system process noise and measurement noise parameters and unreasonable setting for these parameters can lead to inaccurate or even divergent estimated results.As the core of artificial intelligence,machine learning has strong ability to mine and extract potential information of data.Bayesian machine learning method can not only implement posteriori analysis for all possible value but also automatically perform the razor principle to achieve balance between data fitting and model complexity.In this paper,the way to combine Bayesian machine learning and dual Kalman filter is studied and dynamic sparse constraint in system identification is embedded in dual Kalman filter.Then a dual Kalman filter method for dynamic sparse system is established.The proposed method has the advantages of automatically learning the Kalman filter noise parameters and greatly alleviating the influence of subjective setting for noise parameters.Moreover the robustness and accuracy of Kalman filter is improved and better identification results for structural dynamic load and evolution of stiffness are obtained.The main research contents of this paper are as follows:Based on the dynamic sparsity characteristics in dynamic identification of structural systems,which is as prior information to regularize the model,a dual Kalman filter algorithm for dynamic sparse system is established.By using Bayesian learning theory,the analytic expression of estimating noise parameters in real time for dual Kalman filter is deduced and it avoids artificial setting and adjustment of noise parameters.On the basis of previous theoretical work for dynamic sparse dual Kalman filter,the proposed dual Kalman filter algorithm for dynamic sparse system is applied to track and identify the external dynamic load,who has dynamic sparseness characteristics in some case.The method for synchronously identifying structural state vector and external load is established.Then numerical simulation,in which three different types of load is put on a structure finite element model separately,is performed to verify the proposed method.Based on the dynamic sparseness characteristics of structural stiffness dynamic evolution,a synchronous identification method for structural state vector and stiffness evolution is established.Then the method for synchronously identifying structural state vector,dynamic load and stiffness evolution is formed by combining load identification algorithm and numerical simulation is performed to verify the proposed method under known and unknown load separately.