Structural Identification and Vibration-Based Damage Detection Using Interval Arithmetic and Contractor Programming
Structural identification continues to gain increased attention as an applied technique for structural health monitoring and condition assessment. However, methods for structural identification through finite element model updating that have been developed over the last several decades fail to completely address pertinent challenges including computational efficiency, solution uniqueness, and the ability to incorporate measurement and modeling uncertainties in parameter identification and confidence quantification. To address many of the difficulties of past model updating approaches, this dissertation explores using constraint satisfaction with interval arithmetic and contractor programming for vibration-based model updating to facilitate the advancement of structural identification as a viable tool for performance-based condition assessment. The work presented within develops, verifies, and validates methodologies for parameter identification of continuous and multiple degree-of-freedom system models using a novel interval-based approach capable of structuring partially described and incompletely measured inverse eigenvalue problems as nonlinear constraint satisfaction problems and propagating measurement uncertainties to the parameter space. A methodology based on the Set Inversion Via Interval Arithmetic algorithm is first developed for determining the internal axial force and boundary restraints within in-service prismatic beam elements, including short cables, struts, bracing, and tie-rods, where bending stiffness and boundary conditions significantly affect natural frequencies. The framework offers the ability to completely enclose the feasible solution space for the unknown axial force and boundary restraints in prismatic beam and cable elements using a set of natural frequencies obtained from measurements of a single transducer with specified measurement uncertainties. The methodology is first demonstrated and verified on a numerical model and subsequently experimentally validated using dynamic measurements obtained from an axially loaded rod with progressively increased end restraint at one end. A second methodology is then developed for model updating of multiple degree-of-freedom system models that is based on formulating the structured inverse eigenvalue problem as a Constraint Satisfaction Problem. The approach of contractor programming with interval arithmetic is demonstrated to offer unique capabilities to fully enclose the feasible parameter space given specified measurement uncertainties as well as solve non-unique constructions of the inverse eigenvalue problem. These capabilities are first demonstrated and verified using synthetic data for a numerical six degree-of-freedom mass-spring model. The method is then experimentally validated using vibration measurements obtained from a laboratory shear building model and, furthermore, contrasted with probabilistic model updating to illustrate the unique capabilities of addressing the effects of measurement uncertainty on the parameter estimation. Subsequent extension of the methodology is then introduced to address challenges associated with scaling from small multiple degree-of-freedom models to much larger structures with significantly more uncertain parameters. Specifically, modifications to the methodology are developed to address the computational challenges resulting from the dramatic increase in dimensionality of the parameter space and the enforcement of eigenvalue inclusion constraints. The extended methodology is verified on a 45 degree-of-freedom, 45 member, 2D Pratt truss using partially described and incompletely measured modal properties acquired through hybrid testing. To demonstrate the vibration-based damage detection capabilities of the methodology, realistic damage, in the form of fracture and crack propagation in the net section rupture limit state is progressively introduced to the experimental member in the hybrid simulations. Through a matrix of experimental validation tests, the methodology is shown to be successful at not only identifying the damaged members of the truss in the presence of measurement uncertainty, but also capable of correctly quantifying the severity of damage, which provides an important contribution to damage diagnosis and prognostication.