Last 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 | http://link.aip.org/link/?JMD/134/100911 |
| Doi | http://dx.doi.org/10.1115/1.4007389 |