Title: Structural Identification, Health Monitoring and Uncertainty Quantification under Incomplete Information with Minimal Requirements for Identifiability
Description: Structural identification is the inverse problem of estimating the physical parameters, e.g. element masses and stiffnesses, of a model representing a structural system, using response measurements obtained from the actual structure subjected to operational or well-defined experimental excitations. It is one of the principal focal areas of modal testing and structural health monitoring, with the identified model finding a wide variety of applications, from obtaining reliable response predictions to timely detection of structural damage (location and severity) and consequent planning and validating of maintenance/retrofitting operations. However, incomplete instrumentation of the monitored system and ambient vibration testing generally result in spatially incomplete and arbitrarily normalized measured modal information, often making the inverse problem ill-conditioned and resulting in non-unique identification results. The problem of parameter identifiability addresses the question of whether or not a parameter set of interest can be identified from the available information.

The identifiability of any parameter set of interest depends on the number and location of sensors on the monitored system. In this dissertation we study the identifiability of the mass and stiffness parameters of shear-type systems, including 3-dimensional laterally-torsionally coupled rigid floor systems, with incomplete instrumentation, simultaneous to the development of algorithms to identify the complete mass and stiffness matrices of such systems. Both input-output and output-only situations are considered, and mode shape expansion and mass normalization approaches are developed to obtain the complete mass normalized mode shape matrix, starting from the incomplete modal parameters identified using any suitable experimental or operational modal analysis technique. Methods are discussed to decide actuator/sensor locations on the structure which will ensure identifiability of the mass and stiffness parameters. Several possible minimal and near-minimal instrumentation set-ups are also identified.

The minimal a priori information necessary in output-only situations is determined, and different scenario of available a priori information are considered. Additionally, tests for identifiability are discussed for both pre- and post-experiment applications. The different theoretical discussions are illustrated using numerical simulations and experimental data. It is shown that the proposed identification algorithms are able to obtain reliably accurate physical parameter estimates even under the constraints of minimal instrumentation, minimal a priori information, and unmeasured input. The different actuator/sensor placement rules and identifiability tests are useful for both experiment design purposes, to determine the necessary number and location of sensors, as well as in identifying possibilities of multiple solutions post-experiment. The parameter identification methods are applied for structural health monitoring using experimental data, and an approach is discussed for probabilistic characterization of structural damage location and severity.

A perturbation based uncertainty propagation approach is also discussed for the identification of the distributions of mass and stiffness parameters, reflecting the variability in the test structure, using very limited measured and a priori information.