| Summary: | A system of interest usually consists of some unknown model parameters that affect its output. System diagnosis estimates these model parameters and track their evolution if the system is time-dependent. Subsequently, the prognosis predicts the system output at future inputs. An important challenge in diagnosis and prognosis is the presence of various uncertainty sources, such as natural variability, inadequate data, and approximate models. The first challenge is how to integrate the contributions of the different uncertainty sources towards the overall prediction uncertainty; dimension reduction is another challenge in the case of a large number of uncertainty sources; other challenges includes test design, computational efficiency, etc. This dissertation uses the Bayesian network and variance sensitivity analysis as major mathematical tools and develops multiple innovations to solve the aforementioned challenges in system diagnosis and prognosis. Regarding sensitivity analysis, this dissertation proposes a framework to incorporate both aleatory and epistemic uncertainty, and a new sample-based algorithm to significantly improve the computational efficiency. This leads to sensitivity analysis of the Bayesian network for dimension reduction. Regarding uncertainty integration, this dissertation proposes a roll-up method to incorporate the results from multiple uncertainty quantification activities, and a sensitivity-based optimization approach for test design. A dynamic Bayesian network is utilized for the diagnosis and prognosis of time-dependent systems, and illustrated with an aircraft wing digital model to monitor the health status of the wing. A fast Bayesian inference algorithm is also proposed to improve the computational efficiency, thus enabling real-time diagnosis and prognosis for decision support. In sum, this dissertation covers multiple topics in uncertainty quantification and system health monitoring, and the proposed methodologies/algorithms provide valuable breakthroughs for comprehensive uncertainty integration and higher computational efficiency without compromising accuracy.
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