Uncertainty Quantification Using Concentration-of-Measure Inequalities

• Main Author: Lucas, Leonard Joseph
• Format: Others
• Published: 2009
• Online Access: https://thesis.library.caltech.edu/2282/1/LeonardJosephLucasThesis.pdf; Lucas, Leonard Joseph (2009) Uncertainty Quantification Using Concentration-of-Measure Inequalities. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DRAM-H941. https://resolver.caltech.edu/CaltechETD:etd-05292009-165215 <https://resolver.caltech.edu/CaltechETD:etd-05292009-165215>

This work introduces a rigorous uncertainty quantification framework that exploits concentration–of–measure inequalities to bound failure probabilities using a well-defined certification campaign regarding the performance of engineering systems. The framework is constructed to be used as a tool for deciding whether a system is likely to perform safely and reliably within design specifications. Concentration-of-measure inequalities rigorously bound probabilities-of-failure and thus supply conservative certification criteria, in addition to supplying unambiguous quantitative definitions of terms such as margins, epistemic and aleatoric uncertainties, verification and validation measures, and confidence factors. This methodology unveils clear procedures for computing the latter quantities by means of concerted simulation and experimental campaigns. Extensions to the theory include hierarchical uncertainty quantification, and validation with experimentally uncontrollable random variables.