Last Tuesday, I defended my thesis entitled Efficient, Accurate, and Non-Gaussian Statistical Error Propagation Through Nonlinear, Closed-Form, Analytical System Models.
Basically, my thesis uses a Taylor series expansion to estimate the distribution of system model outputs resultant from propagating error in system inputs through a system model. I show how variance can be propagated more efficiently and accurately, producing fourth-order accuracy with only second-order computational cost. I also show that output skewness and kurtosis can be estimated.
All of my committee members thought I did really well, and were very impressed by my presentation, the quality and clarity of my writing, and the research work I have done. One of my committee members, Dr. Chase, was particularly excited about my work. He’s in his seventies (he retired last year, but still continues teaching as an adjunct faculty) and has spent his entire career in the field of assembly uncertainty and tolerance analysis. He’s really excited about the contributions I’ve made to uncertainty analysis and its applicability to tolerance analysis. He said mine was one of the best defenses he’s ever been to ("And I’ve been here a lot of years!"), and he asked for a copy of my defense presentation to use as an example for all his current and future grad students.
Since my work was so math-intensive (not very advanced math, but a lot of it), I’ve had Dr. Fullwood, who has his Ph.D. in math, review my papers before I submitted them for publication. He said I’m an exceptional writer. My advisor, Dr. Mattson, said there’s not a single thing that could’ve gone better in my presentation.