Moving window incremental multidimensional scale analysis-based operational modal analysis for linear slow time varying structure

In order to solve the problems of low precision and high time cost in operational modal analysis for linear slow time-varying (LSTV) structures, a moving window incremental multidimensional scale analysis (MWIMDS) method is proposed in this paper. Based on the time-freezing theory and the moving window technique, in each window, the non-stationary random vibration signals are regarded as stationary random time series, and the LSTV structure is regarded as linear time-invariant structure. Firstly, the low dimensional matrix corresponding to the modal coordinate response matrix is obtained by using multidimensional scale analysis (MDS) for stationary random vibration response signals. Then, the natural frequencies are identified from the modal coordinate response matrix by using the single degree of freedom technique. Secondly, the least square generalized inverse is used to substitute the identified modal coordinate response matrix into the vibration response signal to estimate the modal shape matrix. Finally, when the fixed-length window is moved to the next window, the increment is applied to the MDS by removing the first time series point data, adding the latest time vibration response signal data, and calculating the distance between the new time point and other sequence points without recalculating all sequence points. Incremental can greatly reduce the time complexity of the algorithm. MDS is a linear global dimension reduction algorithm. Identification results on simulation dataset of three-dimensional cylindrical shell structure and the experiment dataset of steel cantilever beam structure verify that the MDS-based operational modal analysis has the advantages of good robustness and high identification accuracy. Identification results on the simulation dataset of mass slow time-varying with three degrees of freedom verify that MWIMDS-based operational modal analysis can identify modal shapes and natural frequencies only from non-stationary random vibration signals for LSTV structure well, and the identification accuracy of modal shapes is better than the moving window principal component analysis method and moving window neighborhood preserving embedding. The time and space cost of MWIMDS-based operational modal analysis are lower than that of the moving window multidimensional scale analysis based operational modal analysis without incremental.