Research On Structural Damage Identification Method Based On Sparse Reconstruction

Finite element model updating is one of effective damage identification methods on the basis of structural vibration properties.Worldwide researchers have conducted comprehensive studies in this field during the past decades.In recent years,sparse recovery theory and compressed sensing theory have been developed and applied in structural health monitoring.In a practical structure,the number of damaged elements is much less than the number of elements of the entire structure.Therefore the damage vector of the structure,represented by the elemental stiffness reduction,is a sparse vector with most of items being zero except those damaged elements.However,the conventional l₂ regularized finite element model updating method generally leads to over-smoothy damage identification results and cannot identify the real sparse damage.Therefore,this Master study will propose a new l₁ regularization method and iteratively reweighted l₁ regularization method to identify the location and severity of structural sparse damage,on the basis of the sparse recovery theory and finite element model updating method.The main research contents of the thesis include following aspects:1.The l₁ regularization and iteratively reweighted l₁ regularization damage identification method are proposed with combination of the one-step model updating method and the sparse damage identification method.Two different criteria are considered,namely,the frequencies and the combination of frequencies and mode shapes.The first order sensitivity matrix of eigenvalue?natural frequency?and eigenvector?modal shape?are derived.The selection method of regularization parameter?and the optimization iteration method are also discussed.2.Modal experiments were carried out on a cantilever beam and a space frame scaled models to measure the modal parameters?natural frequencies and modal shapes?before and after structural damage.3.A modal analysis program and the damage identification program were compiled in MATLAB.The programs are used to study the damage identification method.4.The modal parameters obtained from the structural modal experiments are applied to the developed l₁ regularization methods for identifying the structural damage.The results are also compared with those using the widely used l₂ regularization method.It shows that the proposed method can accurately identify the sparse structural damage,while the l₂ counterpart cannot.5.A regularization parameter selection method is also developed.The parameters?such as the number of measurement data,the measurement error,the severity of damage and so on?are investigated through simulation data.Suggestions on the practical damage identification application are provided.