Modal Identification And Its Error Analysis And Damage Detection In Structural Monitoring Systems Of Long-span Bridges

For structural health monitoring of long-span bridges, ambient responses with high Signal-Noise Ratio (SNR) measured on limited Degrees-Of-Freedom (DOFs) are used to detect damage. Several aspects of structural damage detection are deeply and systematically studied in this dissertation, and main innovation points are listed as follows:(1) The Natural Excitation Technique and Eigensystem Realization Algorithm (NExT-ERA) in the time domain are used and improved to identify structural modal parameters. NExT-ERA with two improvements including: a) defining and using a new-developed correlation estimation formula, b) arithmetically averaging modal parameters identified by different system orders related to the stabilization diagram, is proposed to enhance accuracy of modal parameters and named improved NExT-ERA. Finite sampling errors of modal parameters identified from structural ambient responses to Gaussian White Noises (GWN) excitations and contaminated by measuring GWN, are derived.(2) In improved NExT-ERA, a relationship between singular values and vectors of large-size Hankel matrixes and modal parameters is established by using author-defined equivalent singular values and vectors, on the premise that the modes are sparse and the damping ratios are low. Some existing error formulars are simplified after aplplying this relationship, and then the rules of finite sampling errors influenced by limited measuring time length, sampling rate, SNR, and singular values et al, are derived and analyzed. A stabilization diagram method and an equivalent singular value method are proposed for selecting high accuracy modes from the identified ones.(3) A new element modal strain energy index is defined basing on the complete modes at all DOFs and used to indicate both locations and extents of multiple damage from reductions in related bending stiffnesses for beam-system structures. For assumed cases of damage in the stiffening girder of the Xihoumen Suspension Bridge, damage detection capacities of this index, the Coordinate Modal Assurance Criterion (COMAC) and modal flexibility change constructed from complete modes, and Sum of Change Ratio (SCR) of wavelet packet component energy of responses, are studied and compared.(4) Three modal expansion methods are compared and used to expand incomplete modes at limited DOFs to complete DOFs, and then the expanded modes are used to construct'incomplete'modal strain energy damage indexes. The incomplete modal flexibility change index is directly constructed from incomplete modes. Damage detection with the two incomplete indexes is studied in Xihoumen suspension Bridge. Optimizing Sensor Locations (OSL) based on an improved Genetic Algorithm to make the two incomplete indexes most sensitive to possible damage is discussed, in addition, a Minimum Modal Variance (MMV) method for OSL is proposed. Damage detection based on the two incomplete indexes measured at optimized sensor locations is verified. All the work above is a systematical study of methods in aspects of damage detection.(5) Noise-contaminated ambient responses at limited DOFs of a beam-system finite element model and a plate-system finite element model with equivalent orthotropic plates and substructure method, are simulated. Capacities and errors of the above methods and the two incomplete indexes for detection of stiffness reductions in beam-system model and simulated cracking and corrosions in plate-system model are studied and discussed, respectively. Methods of selecting high accuracy modes are also verified to be effective and important.