Identification Of Under-Determined Operating Modal Parameters Based On Sparse Component Analysis

With the development of high-speed,large-scale,complex,and intelligent structures,the problem of modal parameter identification under underdetermined conditions has become more and more common.Sparse Component Analysis(SCA)is used as a kind of The effective under-determined blind source separation method has attracted the attention of many researchers at home and abroad.Under under-determined conditions,it can identify more operating modal parameters from a limited number of sensors,and can break through the constraints of environment and cost.Structural performance evaluation,fault diagnosis and health monitoring,optimization design,power modification and integration,sensitivity analysis,etc.are of great significance.Based on the working modal analysis method based on sparse component analysis and under-determined blind source separation,this paper combines sliding window,transfer learning,improved density peak clustering and other methods to realize the time-invariance and slowness under under-determined conditions.Time-varying working modal parameter identification,the main research contents include:(1)A method for identifying under-determined operating modal parameters based on short-time Fourier transform based on sparse component analysis is proposed.First,the framework and process steps of working modal parameter identification based on sparse component analysis are established.After that,the signal purity is used to compare the modal parameter recognition effects of each sparse transformation method.Finally,the interpretation and evaluation of modalities,the number of identifiable modalities,modal omissions and false modalities,and the scope of adaptation of the method are discussed.The identification of working modal parameters in a 5-degree-of-freedom simulation data set shows that the working modal parameter identification method based on short-time Fourier transform can identify modal parameters that exceed the number of vibration response sensors,which is better than the independent component analysis method.If the number of recognized modes is less than or equal to the number of degrees of freedom,the recognition results are all true modes,and if the number of recognized modes is greater than the number of degrees of freedom,there are false modes in the recognition results.(2)A modal shape estimation method based on improved density peak clustering is proposed.This method introduces the density peak clustering method into the modal shape estimation.The specific method is to automatically select according to the change trend of the weight slope of the signal point.The clustering center(mode shape),to a certain extent,avoids the error caused by the manual decision diagram to select the mode shape in the traditional density peak clustering,and improves the recognition accuracy of the mode shape under the underdetermined situation.Anti-noise ability.The identification of working modal parameters under a5-degree-of-freedom simulation data set shows that,compared with K-mean,FCM,and DBSCAN clustering methods,the modal shape estimation method of improved density peak clustering has more advantages.High accuracy and noise immunity.(3)An online real-time identification method for working modal parameters of underdetermined linear time-varying structure with sliding window SCA based on transfer learning is proposed.The method is based on the assumption of short-term invariance and uses sliding window technology to decompose the underdetermined slow time-varying structure into Multiple time-invariant windows are transformed into multiple underdetermined time-invariant recognition problems.Secondly,in each time-invariant window,sparse component analysis is used to identify the corresponding modal parameters.Finally,due to the similarity of the response signal in the adjacent time-invariant recognition,the transfer learning method is used to transfer the modal shape that has been converged in the previous window to the mixing matrix estimation of the next window as the next modal vibration.The type estimates the initial value of the clustering iteration.The identification results of the slow time-varying three-degree-of-freedom spring oscillator structure simulation data set show that this method can effectively solve the problem of modal parameter identification of underdetermined linear slow time-varying structures,and can improve the accuracy and convergence speed of modal parameter identification.