Online Operational Modal Parameters Identification For Linear Time-varying Structures Following Adaptive Principal Component Analysis

The operational modal parameters identification of linear time-varying(LTV) structures is of great both theoretical significance and engineering application value for vibration control, fault diagnosis and other fields. This paper proposed the online operational modal parameters identification methods following adaptive principal component analysis based on the description of “time-frozen” and “instaneous” for linear time-varying structures. Finally, these methods are analysed and validated through the theoretical derivation and numerical simulation. The main content is as follows:(1) The mapping between mathematical parameters of principal components and the modal coordinates of displacement response are established based on principal component analysis(PCA). Moreover, the physical meaning of parameters and applicable conditions of operational modal parameters identification for linear time invariant(LTI) structures based on PCA are elaborated and proved mathematically. Finally, numerical simulations are used to verify the method.(2) Based on the theory of “short term time invariant”, the operational modal parameters identification method for linear time-varying structures following moving window principal component analysis(MWPCA) is proposed with combining operational modal parameters identification for linear time invariant structures based on PCA and moving window technique. After choosing the appropriate size of moving window, the instantaneous modal frequency and modal shape could be identified effectively. On this basis, the moving window recursive principal component analysis method based on the autocorrelation matrix recursive or eigenvalue eigenvector recursive is proposed with combining MWPCA method and autocorrelation matrix online recursive or the MWPCA based on the eigenvalue eigenvector online recursive. Moreover, the moving window recursive principal component analysis(MWRPCA) based on the eigenvalue eigenvector recursive has the advantages of lower time complexity、space complexity and numerical stability through theoretical analysis and numerical simulation.(3) Based on the theory of “forgetting factor weighted”, the operational modal parameters identification method for linear time-varying structures following principal component analysis with forgetting factor is proposed with combining operational modal parameters identification for linear time invariant structures based on PCA and weighted forgetting factor technique. After choosing the appropriate forgetting factor, the instantaneous modal frequency and modal shape could be identified effectively. On this basis, the recursive principal component analysis with forgetting factor(RPCAWF)method based on the autocorrelation matrix recursive or eigenvalue eigenvector recursive is proposed with combining principal component analysis with forgetting factor method and autocorrelation matrix online recursive or the principal component analysis with forgetting factor based on the eigenvalue eigenvector online recursive. Moreover, the RPCAWF based on the eigenvalue eigenvector recursive has the advantages of lower time complexity、space complexity and numerical stability through theoretical analysis and numerical simulation.