Optimization of incomplete dynamics for structural model refinement and damage assessment

Model refinement and damage assessment of engineering structures can be achieved by estimating the physical design parameters from the measured dynamic characteristics. The process is often posed as an optimization problem based on either modal data matching (MDM) or dynamic residual optimization (DRO). The MDM methods attempt to minimize a nonlinear error function between the analytical and measured modal properties. Conversely, the DRO methods attempt to minimize the dynamic residual between the analytical model and the measured modal properties. This research explores new approaches to model refinement and damage assessment applications based on the MDM and DRO formulations under incomplete measurement.; The initial effort of this research investigates the minimum rank perturbation theory (MRPT), which is a computationally attractive model update method that makes use of the dynamic residual. By introducing a new matrix property termed null symmetry, the MRPT is generalized to handle nonsymmetric system matrices in the equations of motion. A hybrid matrix update procedure that combines the MRPT and least squares estimation has also been extended in an iterative framework to deal with the incomplete measurement problem. The resulting algorithm minimizes the dynamic residual by implementing a form of repeated substitution. Then, the dynamic least squares method is developed to bypass the computation of the model matrix perturbation. The method solves a reduced linear least squares subproblem with quadratic inequality constraint in each major iteration.; Next, the theory of reduced dynamic sensitivity is developed along with several of its applications. The theory formulates the first and second derivatives of both the modal error function and the dynamic residual function. It supports various applications including structural dynamic sensitivity analysis, optimal sensor placement, parameter selection, damage localization, model refinement, and damage assessment. These applications are studied and demonstrated using simulation and experimental data. The proposed optimal sensor placement methods provide new instrumentation tools that are consistent with the MDM and DRO formulations.