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Uncertainty Quantification Using Concentration-of-Measure Inequalities


Lucas, Leonard Joseph (2009) Uncertainty Quantification Using Concentration-of-Measure Inequalities. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DRAM-H941.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:certification; concentration of measure; uncertainty quantification; validation; verification
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ortiz, Michael
Thesis Committee:
  • Ortiz, Michael (chair)
  • Owhadi, Houman
  • Marsden, Jerrold E.
  • Lapusta, Nadia
Defense Date:4 May 2009
Non-Caltech Author Email:lenny.lucas (AT)
Record Number:CaltechETD:etd-05292009-165215
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2282
Deposited By: Imported from ETD-db
Deposited On:02 Jun 2009
Last Modified:26 Nov 2019 19:13

Thesis Files

PDF (LeonardJosephLucasThesis.pdf) - Final Version
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