Adaptive Based Operational Modal Parameter Online And Real-time Identification For Slow Linear Time-varying Structures

Modal parameters(natural frequencies,modal shapes,and damping ratios)can reflect the dymanic characteristics of the structure,which can be applied to the dynamic design of the structure,fault diagnosis,etc.Operational modal analysis(OMA)can identify the modal parameters(natural frequencies,modal shapes,and damping ratios)of the structure only from the vibration response signals collected by the vibration sensor,but most studies are only suitable for linear time invariant structures and cannot be identified online and real-time.Based on the priciple component analysis(PCA),blind source separation and manifold learning OMA method,this paper combines moving window,online recursion technique,incremental learning and other methods to online and real-time identify the modal parameters of the slow linear time-varying(SLTV)structure.The main contents are as follows:(1)An adaptive window function based and an adaptive window length based moving window PCA online and real-time operational modal parameter identification method for SLTV structures are studied.This method takes the absolute value of the variance contribution rate difference between adjacent modes as the adaptive index(AI).Before PCA decomposition,the window function and window length are selected according to AI to avoid modal exchange and improve the identification results of modal shapes and natural frequencies of SLTV structures.The simulation results of a three-degree-of-freedom system with a slow time-varying mass and a time-varying cantilever with a low density show that these two methods have better recognition accuracy than the rectangular fix-size moving window PCA method.(2)A moving window variable step-size ESAI based online and real-time operational modal parameter identification method for SLTV structures is studied.According to the similarity between blind source separation and OMA problems,this method first applied variable step-size EASI algorithm to the identification of modal paremeters.Then,two variable step-size methods,exponential decay and time decreasing,are selected,and combined with the moving window technique,the moving window variable step-size EASI method is proposed to identify the online and real-time modal shapes and narutal frequencies of the SLTV structures.The simulation results of a three-degree-of-freedom system with a slow time-varying mass and a time-varying cantilever with a low density show that compared with the moving window fixed-step EASI and variable-step EASI,the proposed method have better time-varying tracking capabilities,higher identification accuracy and faster convergence speed.(3)A moving window incremental LLE based online and real-time operational modal parameter identification method for SLTV structures is studied.This method combines LLE algorithm in manifold learning,moving window and incremental learning,which makes it possible to delete old data recursively,update identification models and track time-varying characteristics.The Arnoldi method is used to calcalate the low dimensional emmbedding.The simulation results of a three-degree-of-freedom system with a slow time-varying mass and a time-varying cantilever with a low density show that using Arnoldi method,inverse iteration method and orthogonal iteration method,the idenfied modal shapes and natural frequencies of SLTV structures of the proposed moving window incremental LLE method have high accuracy.Compared with moving window LLE,the proposed method has less running time.