School: California Institute of Technology

Began Rickover Fellowship: September 2005

Lab Assignment: Bettis, May 2006 - Sept. 2006, June 2007 through Sept. 2007

Lab Mentor: Dr. David Jones

Degree(s):
BS - Mechanical Engineering - Carnegie Mellon, 2004
MS - Mechanical Engineering - California Institute of Technology

Expected Graduation Date: June 2009

University Advisor: Dr. Michael Ortiz

Field of Study: Uncertainty Quantification

Email Address: lenny.lucas@gmail.com

Summary of Research:
The current focus of my research is to apply the Concentration-of-Measure (CM) phenomenon inequalities to uncertainty quantification, specifically for verification of engineering systems. We calculate statistical measures of the system uncertainty in a rigorous framework and apply them to the CM inequalities, which provide upper bounds for the probability-of-failure. The implementation of this framework includes many global optimizations over high numbers of random variables for different applications, including hypervelocity impact, robot control, and electrical circuits.

Publications:

1. Lucas, L.J.; Owhadi, H.; Ortiz, M.; Rigorous Verification, Validation, Uncertainty Quantification, and Certification through Concentration-of-Measure Inequalities. Accepted to CMAME July 2008.