Probabilistic Methods in Model Validation

Extensive experimentation over the past decade has shown that fabricated physical systems that are intended to be identical, and are nominally identical, in fact, differ from one another, and sometimes substantially. This fact makes it difficult to validate a mathematical model for any system and results in the requirement to characterize physical system behavior using the tools of uncertainty quantification. Further, because of the existence of system, component, and material uncertainty, the mathematical models of these elements sometimes seek to reflect the uncertainty. This presentation introduces some of the methods of probability and statistics, and shows how they can be applied in engineering modeling and data analysis. The ideas of randomness and some basic means for measuring and modeling it are presented. The ideas of random experiment, random variable, mean, variance and standard deviation, and probability distribution are introduced. The ideas are introduced in the framework of a practical, yet simple, example; measured data are included. This presentation is the third in a sequence of tutorial discussions on mathematical model validation. The example introduced here is also used in later presentations. Nomenclature