Browsing by Subject "Singular Value Decomposition"
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Item Advancing Engine Control Performance with Adaptive Feedforward Strategies(2023-04) Sonstegard, JackAn adaptive feedforward control strategy that enables real-time online learning of engineinputs and outputs for a unmanned arial vehicle (UAV) drone was improved and expanded upon in this work. Through the use of recursive least squares for online learning, a variable-direction forgetting factor was used to enhance tracking while ensuring forgetting is only applied to the information-rich subspace. Compared to uniform forgetting methods, the variable-direction method was shown to improve tracking and to bound the singular values of the covariance matrix when a signal was not persistently exciting. Additionally, a detection method for large environmental disturbances was used for covariance resetting where this resetting significantly helped the system adapt to disturbances. In order to use the variable-direction forgetting, a gradient flow approach was used to compute the singular value decomposition of the covariance matrix efficiently. In simulation, this iterative method was shown to converge and to track the singular values with low error. Furthermore, improvements to the algorithm included the use of multiresolution techniques where a fine and coarse mesh were combined using a mixing coefficient to smooth out the response of the engine. This allowed for a simpler representation of the system to contribute the majority of the input when the system was in an unexplored region of the learned map. The improved algorithm was then used to learn a higher dimensional model. To evaluate the safety of the system, a one dimensional drone model was used to monitor the position of the drone based upon the inputs provided by the engine. In order to search this higher dimensional engine map, a new search algorithm was devised that considered constraints of combustion phasing and indicated mean effective pressure as well as a minimization of fuel mass input. In simulation, the position of the drone was shown to track the desired trajectory well. With this work, a foundation for future research in active learning of the engine map is motivated.Item Development and Testing of Decision Support Tools in Gait Analysis(2016-04) Rozumalski, AdamObjectives Clinical gait analysis, as commonly prescribed for children with Cerebral Palsy, is a complex set of procedures which include examining data from several sources. The tools developed with this project will use that data to provide robust, repeatable, evidence-based guidance to highlight the most effective treatments for children with CP. These tools will also supply objective measures that can be included in outcome analysis. Methods Several mathematical techniques are used to find patterns within the gait date including: singular value decomposition of kinematic and kinetic data to measure gait pathology; k-means cluster analysis of those results to find recurring patterns; principal components analysis of physical exam findings to relate the gait patterns to physical function; and non-negative matrix factorization of electromyography data to measure motor control. Results The decomposition and scaling of the kinematic and kinetic data resulted in a set of indexes that are able to quantify gait pathology. The k-means cluster analysis reveals that there are repeatable patterns within the gait pathology. These patterns are related to clinical findings as calculated from principal components analysis. Clinical interpretations of motor control can be quantified as muscle synergies using non-negative matrix factorization. Interpretation These tools have proven to provide important quantitative information on treatment outcomes. When implemented in routine clinical gait analysis, these tools have the ability to provide evidence based guidance in treatment decisions.