A Class of Simple and Effective UQ Methods for Sparse Replicate Data applied to the Cantilever Beam End-to-End UQ Problem~1

摘要

When very few samples of a random quantity are available from a source distribution or probability density function (PDF) of unknown shape, it is usually not possible to accurately infer the PDF from which the data samples come. Then a significant component of epistemic uncertainty exists concerning the source distribution of random or aleatory variability. For many engineering purposes, including design and risk analysis, one would normally want to avoid inference related under-estimation of important quantities such as response variance, and failure probabilities. Recent research has established the practicality and effectiveness of a class of simple and inexpensive UQ Methods for reasonable conservative estimation of such quantities when only sparse samples of a random quantity are available. This class of UQ methods is explained, demonstrated, and analyzed in this paper within the context of the Sandia Cantilever Beam End-to-End UQ Problem, Part A. 1. Several sets of sparse replicate data are involved and several representative uncertainty quantities are to be estimated: A) beam deflection variability, in particular the 2.5 to 97.5 percentile "central 95%" range of the sparsely sampled PDF of deflection; and B) a small exceedance probability associated with a tail of the PDF integrated beyond a specified deflection tolerance.