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Mechanical Engineering « Travis V. Anderson

Engineer by day, Superhero by night — Amazing all the time

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Publication in the Journal of Mechanical DesignLast September, ASME’s Journal of Mechanical Design published a technical paper I wrote as part of my mechanical engineering master’s research.

This peer-reviewed paper is about error propagation through design models. Essentially, a Taylor series is often used to propagate error through closed-form engineering models. However, designers typically assume outputs are Gaussian, and neglect any higher-order statistics (such as skewness and kurtosis). This paper shows that skewness and kurtosis can also be propagated using a Taylor series with little additional computational cost, but tremendous improvements in overall accuracy.

Title Propagating Skewness and Kurtosis Through Engineering Models for Low-Cost, Meaningful, Non-Deterministic Design
Abstract System models help designers predict actual system output. Generally, variation in system inputs creates variation in system outputs. Designers often propagate variance through a system model by taking a derivative-based weighted sum of each input’s variance. This method is based on a Taylor series expansion. Having an output mean and variance, designers typically assume the outputs are Gaussian. This paper demonstrates that outputs are rarely Gaussian for nonlinear functions, even with Gaussian inputs. This paper also presents a solution for system designers to more meaningfully describe the system output distribution. This solution consists of using equations derived from a second-order Taylor series that propagate skewness and kurtosis through a system model. If a second-order Taylor series is used to propagate variance, these higher-order statistics can also be propagated with minimal additional computational cost. These higher-order statistics allow the system designer to more accurately describe the distribution of possible outputs. The benefits of including higher-order statistics in error propagation are clearly illustrated in the example of a flat rolling metalworking process used to manufacture metal plates.
Journal Journal of Mechanical Design
Publication Date October 2012
Volume 134
Issue 10
Publication URL
Written by Travis Anderson on January 4th, 2013 , Mechanical Engineering, Patents & Publications, Statistics

Publication in the Journal of Mechanical DesignThis month, ASME’s Journal of Mechanical Design published a technical paper I wrote as part of my mechanical engineering master’s research.

This peer-reviewed paper is about error propagation through design models. The formula typically used to analytically propagate error is based on a first-order Taylor series expansion, and consequently, it can be wrong by one or more orders of magnitude for nonlinear systems. Using a higher-order Taylor series does improve the accuracy of the approximation, but this comes at higher and higher computational cost. This paper presents a technique for error propagation that achieves higher-order accuracy but without the additional higher-order cost. This is accomplished by predicting the Taylor series truncation error and applying a “correction factor” to the lower-order model.

Title Efficient Propagation of Error Through System Models for Functions Common in Engineering
Abstract System modeling can help designers make and verify design decisions early in the design process if the model’s accuracy can be determined. The formula typically more
Journal Journal of Mechanical Design
Publication Date January 4, 2012
Volume 134
Issue 1
Publication URL

Thesis Defense PresentationLast 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.

Written by Travis Anderson on July 31st, 2011 , Downloads, Mechanical Engineering, Patents & Publications, Statistics Tags: , ,

Library of Congress Data ViewerThere are a lot of different fields within mechanical engineering, but the one that I’m most interested in is engineering design. This last spring term, a professor at BYU sponsored a research project looking at historical trends in engineering design publications. I applied and was selected to be on the team of three.

Basically, we gathered and analyzed data from the Library of Congress and identified some major trends in engineering design publications. We created a video (below) to show our findings. The video’s not the best quality, but I only had a week to do all the filming (with an inexpensive camcorder and no external microphone… Sorry!), get the photos, put in all the effects with the graphs, and do all the editing. But I still think it turned out pretty well:

The History of Engineering Design (according to the Library of Congress)

The Library of Congress provides an API to facilitate search queries of its database. This API (implemented through a number of different REST webservices) allows a user to perform a search query and retrieve the query results. I wrote a script to consume these webservices and obtain the information we desired. I even used some multi-threaded programming in the script. It would monitor its own progress, and as appropriate, spawn new threads to asynchronously process multiple search queries at the same time. AWhen the work-load became too much for the network and/or computer to handle, threads were killed off as the results were processed. Since the data was all stored in a central location, multiple instances of the script could be run simultaneously, if desired, even on different computers. Even still, it took a few days to get all the data we needed.

In all, we obtained over 150,000 books published on the topic of engineering design, but only about 100,000 of them had a known publication date and a publication language. I built a quick data viewer that uses Google’s Charts API to quickly show the results, accessible at

It was a really fun project to work on, and I really learned a lot!

Written by Travis Anderson on June 21st, 2011 , Mechanical Engineering, Software Development Tags: ,

This last semester I took a product development class. The first week of class, we were divided into design teams and given the task to design an improved model of a Hitachi impact driver such that it would fill some unmet market needs.

My design team decided to create a new cordless hand power tool capable of drilling holes, driving screws, and hammering nails, all with a single device. The operating function is changed simply by changing from a drill or screw bit to a specially designed hammer bit. After creating our design, we had to manufacture a functional prototype, which actually works surprisingly well!

The technology we developed is pretty cool (if I do say so myself :) ). It changes from a rotational motion to a back-and-forth hammering impact just by changing the bit. The Technology Transfer Office at BYU has started the process of filing for a provisional patent and then they will present our design to manufacturers. If any of them bite, we’ll work out a licensing deal for them to lease our technology.

Hammer-Drill Video Demonstration on YouTube

It has been a really fun project to work on! I learned a lot, and am really excited and happy about our results!

Hammer-Drill Storyboard