Study Of Load Identification Technique Based On Green Fuction And Regularation Method

Load Identification problem belongs to the second inverse problem of mechanical dynamics,which has serious Ill-posed characters,and solving difficulty coefficient is large,and has important science research significance and engineering application value,involving to multiple disciplines,including structural mechanics,numerical analysis,structural health monitoring(SHM),and signal testing et,al.In order to solve structural dynamic load effectively and accurately,it is a feasible way to perform to identify load based on the regularization method.Firstly,load identification problem of the system was established according to the time domain method theory,and the forward problem equation is established by Green kernel function,and the dynamic load was represented by a series of impulse superposition functions,and the dynamic response of a structure was expressed as a convolution integral form between the input load and the Green kernel function response.Because of the kernel function ill-posedness and the dynamic response of the structure with noise pollution,the forward problem equation is discretized into the form of linear equations to discuss its ill-posedness and its specific methods to solve the ill-conditioned equation.Secondly,the problem was solved by adding additional boundary constraints,which was introducing regularization method to deal with ill-posedness problem,including Tikhonov method,Truncated singular value decomposition method and LSQR method et,al.Meanwhile,this progress was involved to choose regularization parameters,and the merits and demerits of these parameters affect the accuracy and validity of this regularization solution,seriously.The methods of finding a regularization parameter were mainly L curve criterion and generalized cross validation method(GCV).Thirdly,this paper performed numerical verification through two structural examples and four kinds of loads.The results showed that through L curve criterion combining to Tikhonov method had certain identification ability,which was still more sensitive to noise,because of it was mainly due to the over-processing of singular values of Tikhonov regularization method,and even filtering out the better singular values.However,generalized cross validation method combining to the Truncated singular value decomposition method was ideal for the one-dimensional and two-dimensional structural load identification,which was less sensitive to noise and could improve the ill-posedness of inverse problem,effectively.Finally,this paper performed experiment to verify load identification methods.The sine load was applied to the cantilever structure by exciter and reversing the load.The experimental results showed that the effect of the load identification method was good,and this method had certain validity and reliability for the load identification of the actual structure.But there were some errors in some data points,which showed that the singular value was different from the actual noise the amplification effect was obvious.The results showed that the load identification method based on Green function and regularization technique had a good ability to identify load in the simulation cases and the load of the structure in the real field.The whole relative error of the identification load was small and the correlation coefficient was large.