Theoretical And Experimental Study On Blind Source Separation Based Operational Modal Analysis Methods

Due to its efficient and non-parametric properties,the Blind Source Separation(BSS)based Operational Modal Analysis(OMA)methods have been drawn wide attentions in mechanical systems and signal processing community recently,meanwhile,it also shows to be a promising tool for OMA in practical applications.The existing BSS based methods,however,suffer from the limitations of sensor number which is required to be more than or at least equal to that of active modes.This becomes a hindrance for its practical application.To overcome such a shortcoming,theoretical and experimental researches are carried out in the present work.Two popular blind separation algorithms,namely the Independent Component Analysis(ICA)and Second Order Blind Identification(SOBI),are considered firstly.Their performances are compared,and SOBI is finally identified as more suitable for modal identification problems.However,SOBI suffers the limitation that the number of sensors should not be less than that of sources.To overcome such a disadvantage,a new deflation second order blind identification algorithm(DSOBI)which minimizing the second order statistics by constructing the modal filter is proposed inhere.This new approach identifies the sources in a deflation way,with which only one source is identified in each iteration step,and then the corresponding modal contributions are then subtracted from the mixtures.The modal contribution can be estimated by Wiener-Hopf equation.The simulation results show that DSOBI exhibits some superiorities in BSS when the number of the sources can not be identified exactly,even it still can not solve the underdetermined BSS problem perfectly.Meanwhile,the analysis results show that the proposed method suffers the same drawbacks as other time domain methods.They all unable to distinguish the modal coordinates which have similar mode shapes.As a result,some frequency domain method must be proposed.To improve the efficiency of DSOBI,a frequency domain algorithm based on the minimization of spectral variance(FMSV)is proposed in the present work.It achieves the above minimization through the generalized Eigen-value decomposition.Thanks to the non-iteration essence,FMSV is more efficient than DSOBI.The simulation result show the proposed approach is more sensitive to noise and damping ratio.As a result,it can only work in OMA for the system which have high signal to noise ratio and lower damping.To improve the robustness of FMSV,another extended approach of FMSV is proposed,namely FGWCM,the parameters are optimized to make it as accurate as SOBI.The above two frequencydomain algorithms make it possible to solve the underdetermined BSS problems thanks to the sparsity of the sources in frequency domain.Then the failure causes of SOBI when it is used to solve underdetermined BSS are analyzed,some conclusions are obtained.Based on these conclusions a new approach is proposed which can identify the modal parameters in selected sub-frequency band.This new approach takes full advantage of the sparsity of virtual sources in frequency domain and requires the separation to be carried out in frequency domain.However,the proposed two frequency domain algorithms can not be used directly due to its robustness to noise and damping.To overcome such a problem,another algorithm which is called Frequency domain algorithm based on Joint Approximate Diagonalisation of Eigen-matrices(FJADE)is proposed.FJADE can be used to solve the underdetermined BSS problem,meanwhile,it is robust to noise and damping.The truth that some typical BSS algorithms such as SOBI and MSV are only particular cases of FJADE is also proved mathematically in present work.For the purpose of comparison,some numerical simulations are carried out using both SOBI and the four proposed algorithms.Parametric analyses are conducted to evaluate the influence of parameters such as noise,damping and the number of sources.Finally,realistic examples such as simply supported beam,rectangle plate and wind turbine blade are studied experimentally by utilizing the proposed algorithm for modal analysis.The experimental results of modal agree well with the theoretical results.Another noise identification experiment in which the noise is induced by Karman Vortex Street is carried out.The separated sources show more significant feature in frequency domain by comparing with the raw signal,which demonstrate the practicability of using DSOBI in this particular case.According to the simulation and experimental results,the proposed FJADE algorithm has been shown to be a more generalized algorithm which exhibits superiorities in solving the underdetermined BSS problem in OMA comparing with the existing BSS based methods.The other two frequency domain methods,namely FMSV and FGWCM can be two more efficient alternatives of the existing methods when the system has high signal to noise ratio.The four proposed algorithms can applied not only in OMA,but also in any circumstance in which the basic assumption is satisfied.