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Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities

Lucas, L. J. and Owhadi, H. and Ortiz, M. (2008) Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities. Computer Methods in Applied Mechanics and Engineering, 197 (51-52). pp. 4591-4609. ISSN 0045-7825. https://resolver.caltech.edu/CaltechAUTHORS:LUCcmame08

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Abstract

We apply concentration-of-measure inequalities to the quantification of uncertainties in the performance of engineering systems. Specifically, we envision uncertainty quantification in the context of certification, i.e., as a tool for deciding whether a system is likely to perform safely and reliably within design specifications. We show that concentration-of-measure inequalities rigorously bound probabilities of failure and thus supply conservative certification criteria. In addition, they supply unambiguous quantitative definitions of terms such as margins, epistemic and aleatoric uncertainties, verification and validation measures, confidence factors, and others, as well as providing clear procedures for computing these quantities by means of concerted simulation and experimental campaigns. We also investigate numerically the tightness of concentration-of-measure inequalities with the aid of an imploding ring example. Our numerical tests establish the robustness and viability of concentration-of-measure inequalities as a basis for certification in that particular example of application.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.cma.2008.06.008DOIUNSPECIFIED
ORCID:
AuthorORCID
Owhadi, H.0000-0002-5677-1600
Ortiz, M.0000-0001-5877-4824
Additional Information:Copyright © 2008 Elsevier. Received 11 August 2007; revised 27 May 2008; accepted 4 June 2008. Available online 1 July 2008. The authors gratefully acknowledge the support received from NSF through an ITR grant on Multiscale Modeling and Simulation and Caltech’s Center for Integrative Multiscale Modeling and Simulation.
Funders:
Funding AgencyGrant Number
National Science FoundationUNSPECIFIED
Center for Integrative Multiscale Modeling and Simulation, CaltechUNSPECIFIED
Subject Keywords:Uncertainty quantification; Quantification of margins and uncertainities; Verification and validation; Certification; Concentration of measure inequalities
Issue or Number:51-52
Record Number:CaltechAUTHORS:LUCcmame08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:LUCcmame08
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12554
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:12 Dec 2008 19:28
Last Modified:24 Feb 2020 10:30

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