Franchek, Matthew A.2016-08-142016-08-14May 20142014-05http://hdl.handle.net/10657/1388Many non-destructive damage detection problems are presented with the challenge where limited sensor sets allow the measurement of fewer degrees of freedom than the analytical model. This study utilized damage residual expansion methods to determine the overall structural damage locations with reduced sensor sets. The new methods presented were the Modified Method of Expanded Dynamic Residuals and the Dot Product Damage Residual Expansion Method. Ritz vectors were also used with various sensor placement techniques to modify the sensor sets and focus the damage detection capabilities towards elements of interest. The results showed that the modified damage residual expansion methods were able to locate the damaged elements, while also simplifying the selection process, by employing the dot product method and the elemental disassembly. Additionally, the sensor set variations effectively focused the damage detection results towards elements of interest by modifying the Ritz vector loadings.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Damage DetectionMinimum Rank Perturbation TheoryDamage ResidualsMethod of Expanded Dynamic ResidualsModified Method of Expanded Dynamic ResidualsDot Product Damage Residual Expansion MethodRitz Vectors2016-08-14Thesisborn digital