Full Function Sampling of Uncertain Correlations

Abstract

Empirically-based correlations are commonly used in modeling and simulation but rarely have rigorous uncertainty quantification that captures the nature of the underlying data. In many applications, a mathematical description for a parameter response to some input stimulus is often either unknown, unable to be measured, or both. Likewise, the data used to observe a parameter response is often noisy, and correlations are derived to approximate the bulk response. Practitioners frequently treat the chosen correlation — sometimes referred to as the “surrogate” or “reduced-order” model of the response — as a constant mathematical description of the relationship between input and output. This assumption, as with any model, is incorrect to some degree, and the uncertainty in the correlation can potentially have significant impacts on system responses. Thus, proper treatment of correlation uncertainty is necessary. In this paper, a method is proposed for high-level abstract sampling of uncertain data correlations. Whereas uncertainty characterization is often assigned to scalar values for direct sampling, functional uncertainty is not always straightforward. A systematic approach for sampling univariable uncertain correlations was developed to perform more rigorous uncertainty analyses and more reliably sample the correlation space. This procedure implements pseudo-random sampling of a correlation with a bounded input range to maintain the correlation form, to respect variable uncertainty across the range, and to ensure function continuity with respect to the input variable.