Sparse Regularization-based Detection On Moving Force And Structural Damage Of Bridges

Moving force identification（MFI）and structural damage detection（SDD）are two important issues in the field of bridge structural health monitoring（SHM）.Combining the concept of sparse representation,this study aims at research works in both MFI and SDD.The main contents can be summarized as follows:1).There is lack of qualitative analysis in existing force reconstruction（FR）methods.To get insight into qualitative understanding of FR,a new concept,named source-image pair,is firstly introduced.Herein,source means external forces and initial conditions;image represents structural responses caused by sources.A source-image pair is expressed as a collection whose elements are source and the corresponding image.A linear vibration system can be packaged as a black box whose input and output are formed by some source-image pairs.Some derivative concepts,such as zero source,non-zero source,orthogonal sources,non-orthogonal sources,similar sources,scaling factor and similar coefficient,are defined for describing the packaged system.Physical meanings of the new concepts are discussed by qualitative analysis.Some qualitative conclusions are made for FR inverse problem.2).A novel sparse representation-based method is proposed for solving the MFI problem with considering influence of unknown initial conditions.The proposed method is a logical framework containing two steps,i.e.response decomposition and force reconstruction.To make the logical framework as a practical algorithm,two strategies called L₁-norm regularization and truncated feature method（TFM）are introduced for implementing response decomposition and force reconstruction,respectively.The measured responses will be compressed twice to make sure that the identified results are stable.Both similarities and differences among the proposed method,Tikhonov regularization method and L₁-norm regularization method are discussed from theoretical analysis.Numerical simulations on a simply-supported beam are carried out for assessing the effectiveness and feasibility of the proposed method.Illustrated results show that the proposed method can identify the moving forces with a strong robustness.3).A steel beam is designed and constructed in laboratory.Two preliminary experiments,i.e.static experiment and experimental modal analysis（EMA）,are performed for calibrations of strain gauges and for updating finite element model,respectively.A series of experiments are conducted for MFI.Several cases are selected for MFI calculation.Illustrated results show that the proposed sparse representation-based MFI method is effective and feasible.4).An output-only SDD method based on sparse singular value is proposed.A transmissibility matrix between two sensor sets is formulated by using the least square principle-based FR analysis.Singular value decomposition（SVD）technology is performed for the transmissibility matrix,and the corresponding singular vectors are used for decomposing the measured responses.Some response components,whose signal energies are relatively large,are extracted for estimating the measured singular values.Status of structure is then classified by detecting variations of the measured singular values.In order to assess the accuracy and feasibility of the proposed method,a simply-supported beam is taken as an example for numerical simulations,as well as a cantilever beam is used for experimental studies.Illustrated results show that the proposed method can be used for detecting whether the structure is damage or not,and it has a well robustness.5).A hybrid self-adaptive Firefly-Nelder-Mead（SA-FNM）algorithm is proposed based on classical Firefly algorithm and Nelder-Mead（NM）algorithm.In order to preferably balance exploitation and exploration ability of the SA-FNM,as well as make a well balance between computational efficiency and accuracy,three effective strategies,i.e.random walk strategy,improved information exchange strategy and self-adaptive control strategy for key parameters,are introduced into the framework of SA-FNM.Then a novel SDD method with considering sparse constraints is proposed based on SA-FNM.Numerical simulations of a simply-supported beam and experimental studies of a steel beam are carried out for assessing the effectiveness and feasibility of the proposed method.Illustrated results show that,a)the proposed method can accurately identify structural damage;b)Sparse constraints can effectively reduce the influences from measured noise and can highlight sparsity of structural damage vector.6).Based on L_1/2-norm regularization and moving average Tikhonov regularization methods,a novel output-only MFI-SDD method is proposed for identifying both moving forces and structural damages.The sensors installed on a structure are divided into two sets and the relationship between them is expressed by a transmissibility matrix.An optimization problem,which takes damage factors as the optimal variables,is firstly formulated by combining the transmissibility matrix and L_1/2-norm regularization.Matlab optimization toolbox is used for solving this problem.As the structural damage has been estimated,the MFI-SDD problem will be changed into a MFI problem.The local average values of the time history of moving force are relatively stable in time domain.In order to take this character into consideration,an improved regularization method called moving average Tikhonov regularization method is proposed for solving the remaining MFI problem.Numerical simulations of a simply-supported beam are carried out for assessing the effectiveness and feasibility of the proposed method.Illustrated results show that the proposed method can simultaneously identify both moving forces and structural damages with a good accuracy and a better robustness to noise.