Reliability Analysis of Systems Characterized by Uncertain Parameters with Complex Dependencies
Speaker: James Hammond, NIA Visitor
Date: Thursday, October 27, 2022
Time: 10:00 am – 11:00 am
Abstract Talk 1
In this talk we present a method for reliability analysis based on a limited number observations of the uncertain parameter of a computational model. Rather than fitting a crisp distribution to the data, we use a probability box (p-box) of sliced-normal distributions spanning between the maximum likelihood estimate and the moment-bounded maximum entropy estimate. Sliced-normals are capable of characterizing multivariate distributions exhibiting complex parameter dependencies with minimal modeling effort. This p-box, which accounts for the effects of having a limited amount of data on the resulting reliability analysis, approaches a single distribution as the number of observations increases. Furthermore, we identify the slice-normal distributions leading to the maximal and the minimal failure probability estimates thereby complementing a point estimate with a bounding range.
Abstract Talk 2
Sliced distributions enable the characterization of complex multivariate data exhibiting multiple modes and strong parameter dependencies. In this talk we leverage the semi-algebraic nature of the sliced-normal distributions to identify the Most Likely Points (MLPs) of failure. When the failure domain is also semi-algebraic, this search is conducted by using semidefinite programming thereby providing a certificate of global optimality. The MLPs along with importance sampling enable the accurate and efficient estimation of small failure probabilities.
Bio
James Hammond is a Ph.D. candidate from Imperial College London, working in data-driven turbulence modelling for fluid topology optimization and UQ.
Have questions?
Mary Catherine Bunde
Senior Education Administrator
National Institute of Aerospace
mary.bunde@nianet.org