Structural Vibration Modal Identification Based On Compressed Sensing

Compressed Sensing(CS)is a newly developed technology in recent decade,which provides a different sampling framework from traditional Nyquist by combining data sampling and data compression in one step and colecting data in a compressive manner.CS can simplify the data acquisition process,reduce the data size for acquisition and transmission and lower the requirement for data acquisition equipments.These features position CS at an advantage place in applications to the wireless sensor networks.However,in the structural health monitoring(SHM),most existing researches focus on the signal reconstruction using the known basis(such as Fourier basis,wavelet basis)and the intrinsic links between the CS and the vibrational modal analysis theory are yet to be investigated.This situation has hampered the CS from unleashing its potential to the full strength when applied to compress structural vibration signals.In this paper,studies of CS in SHM are explored in two aspects.On one hand,exploration and development of new methods are pursued to better use the compressed measurements for modal parameters identification.On the other hand,a compressive data acquisition circuit is developed for structural vibration sampling,so that the compressive sampling of vibrations can be implemented in a simple and easy strategy.The main research works are as follows:An improved orthogonal matching pursuit(IOMP)algorithm for vibration data reconstruction from its compressive measurements is presented by employing the Polar interpolation to mend the mismatch between the frequencies of Fourier basis and frequencies of the real signals.Based on the Fourier atoms optimally selected by the OMP algorithm in signal reconstitution,a frequency continuous dictionary is constructed by Polar interpolation in the vicinity of frequencies of those atoms.Then the convex optimization problem is solved to rectify the frequencies of those atoms,and thus reduce the signal reconstruction error.The improved method remedies the atoms obtained by the OMP at the cost of only a minimal additional computational effort.The performance of IOMP is verified through numerical simulation and laboratory model test,and the affecting factors to IOMP are discussed in the course of verification.It is shown that the signal reconstruction accuracy by IOMP is greatly enhanced.Meanwhile,IOMP is also compared with others classical algorithms through identifying modal parameters by the reconstructed signals,and it is conclude that the errors in reconstructed signals is not neglectable for the modal parameter extraction.For the vibration singals with less sparsity on Fourier basis,the CS reconstruction will cause significant errors and that will inevitably propagate to the subsequent modal analysis.So we develop two methods for modal parameters identification by direct use of the compressed measurements without requiring the CS reconstruction.Firstly,a Sparse Decompisition algoritm(SD)is proposed for modal parameter identification using the compressed measurement of free vibration of structures.As the the structure free vibration is shown to be the superposition of all modal responses,a redundant dictionary is constructured using the exponentially decayed sinusoid functions as atoms,and a two-step OMP optimization technique is proposed to decompose the compressed measurement sequences.The modal parameters are extracted from the spare coefficient matrix and the atoms produced in decomposition.The performance of SD is verified through numerical simulation and laboratory model test.In the course of verification,the affecting factors to SD are also discussed,and SD is compared with ERA which identifies modal parameters based on reconstructed vibration.For the cases of forced vibration,a compressed multivariate autoregressive algorithm(CMAR)is developed to directly identify modal parameters from compressed measurements of forced vibration.Resemblance between the multivariate autoregressive model(MAR)for multi-channel structure responses and the joint sparse model is revealed by comparing the equations of the two models,and the MAR model is proposed to be treated as a joint sparse model.Through designing a special compressive measurement matrix,a compressive MAR model is constructed from the compressed measurements,and the modal parameters are computed by establishing the state matrix of the system with the autoregressive parameter of the CMAR model.The performance of CMAR is verified through numerical simulation and laboratory model test.The affecting factors to CMAR are discussed in the course of verification.Meanwhile,CMAR is also compared with ERA which identifies modal parameters based on the reconstructed signals.A new method to discriminate false modes is proposed for the MAR model-based modal analysis and CMAR algorithm in this paper.Based on modal superposition equation,the relations between MAR models for structural responses and modal responses are first discussed.Then the auto-regression coefficients solved from structural responses are loaded on each modal response to construct MAR models for each mode with error terms.A criterion is put forward to discriminate the false modes by quantitatively evaluating the errors associated with each mode by its Euclidean norm,and modes with larger error terms are extruded as false modes.The stability diagram is used to identify real modes from the remaining modes in the end.The performance of proposed method is verified through numerical simulation and laboratory model test,and the proposed method is compared with traditional stability diagram.CS hardware circuit is the essential condition for applying CS algorithm.Regarding the absence of suitable CS hardware circuit in SHM,a digitized one is developed for compressive sampling of structural vibration.The structure responses are firstly sampled to digital signals with ADC.Then a FPGA chip computes the linear inner products between digital signals and measurement matrix as compressed measurements.The performance of hardware circuit is verified through laboratory model test,and the CMAR is used to extract modal parameters from the compressed measurements collected by the hardware circuit.