Operational Modal Parameter Identification Of Linear Structures Based On Manifold Learning

Operational modal analysis(OMA)has important engineering value,which has always been a research hotspots for domestic and overseas scholars.This proposes several solutions for one-dimensional linear time-invariant structure,three-dimensional linear time-invariant structures and linear slow time-varying structure.The major study context in this paper includes those:For one-dimensional linear time-invariant structure,we propose OMA methods based on self-iterative extraction(SIPCE)algorithm and Sanger neural network principal component extraction algorithm.Comparing with OMA method based on traditional principal component analysis(PCA),the OMA based on SIPCE avoid ill-posed problem and singular values problem in matrix decomposition,which has more identified accuracy and lower space-time cost.With the development of multi-core hardware and parallel computing and considering with the timelines of algorithm in practical application,we propose OMA method based on Sanger neural network principal component extraction algorithm.Comparing Sanger network with Oja network and APEX network,it not only extracts several principal components in parallel,but also there is actual physical meaning of weight matrix.The OMA method based on Sanger neural network principal component algorithm extracts principal components by learning rules,the algorithm is easy to be embed into multicore hardware,which has high engineering value.The identified modal parameter results in simulation and experiment of one-dimensional time-invariant simple supported beam show the OMA methods based on self-iterative extraction(SIPCE)algorithm and Sanger neural network principal component extraction algorithm are accurate and reliable.For three-dimensional linear time-invariant structures,we proposal three-dimensional OMA methods based on direct matrix-assemble SIPCE and isometric feature mapping(ISOMAP).At first,this paper analysis the different between one-dimensional linear time-invariant structures and three-dimensional linear time-invariant structures.Then,according to the deficiency of the inverse matrix substitution,we propose direct matrix-assemble method.That method solve the model after assembling the vibration response signals of three dimensions,which improves the identified accuracy.However,the direct matrix-assemble method will consume lots of computing resource and increase the polity of ill-posed problem.Solving the direct matrix-assemble model by SIPCE could avoid ill-posed problem and sharply reduce the space-time cost.Arming at the nonlinear characteristics in three-dimensional linear time-invariant structures,we propose three-dimensional OMA method based on ISOMAP.There is nonlinear characteristic in the vibration response data of three-dimensional,ISOMAP gets near neighbor relation between measuring points by near ground distance,which could express nonlinear characteristics well.The simulation results on a three-dimensional cylindrical shell show that the OMA methods based on SIPCE and ISOMAP are both has accuracy recognition performance for complex three-dimensional linear time-invariant structures.For linear slow time-varying structure,we propose OMA method based on moving window self-iterative extraction(MWSICPE).According to the theory of “Short time constant”,the time segment is divided into minimum time-window,and the structure could be regarded as time-invariant structure in each time-window.Then identifying the modal parameters of time-window's middle instant by SIPCE.The time-window slides with time,and in this way,we will get the modal parameters of every instant.In the end fitting the modal parameter of all instants,and the time-varying modal parameters will be identified.Simulation of a linear slow time-varying cantilever beam verify the correctness of OMA based on MWSIPCE,and a scientific explanation of modal exchange is proffered in the process of simulation experiment.