Much of uncertainty quantification to date has focused on the propagation of uncertainties through computational models, for which the underlying uncertain parameters are modeled probabilistically, with known distributions. Propagation of uncertainty is very important in understanding the effect and impact that uncertainties have on performance measures, e.g. failure probabilities and mean or variances of solutions to partial differential equations. However, in many circumstances, the underlying uncertainty cannot be characterized exactly. We have developed a method to obtain sharp upper bounds on these performance measures of interests when the distributions of the underlying input variables of the system are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all. We also provide numerical techniques to efficiently compute these upper bounds.

K. Chowdhary, P. Dupuis. Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification. Submitted to ESAIM: Mathematical Modelling and Numerical Analysis. pdf

At the Sixteenth Mathematical and Statistical Modeling Workshop for Graduate Students, I worked on a problem in uncertainty quantification for Sandia National Labs. In this work, an acceleration switch has been proposed to detect events in a multi-stage rocket sled track test in order to activate instrumentation along the track. When the switch detects a desired acceleration profile, the switch closes to complete a circuit for instrument activation. Preliminary tests on the proposed switch has shown that statistical variations exist due to practical fabrication and assembly tolerances. It is supposed that the variations can lead to a switch that does not respond correctly to the desired acceleration. If the switch does not close at the proper time along the track, improper data may be collected or no data at all may be collected before destructive impact in the worst case. The objective of this project is to quantify the affect of uncertainity and to propose a switch design whose operation is insensitive to variation and uncertainty.

M. Brake, J. Massad, R. Smith, K. Chowdhary, et al. Uncertainty enabled design of an acceleration switch. IMECE 2011 Conference Proceedings. pdf