Uncertain Random Variables Research Articles

Uncertain random programming with applications

Uncertain random variable is a tool to deal with a mixture of uncertainty and randomness. This paper presents an operational law of uncertain random variables, and shows an expected value formula by using probability and uncertainty distributions. This paper also provides a framework of uncertain random programming that is a type of mathematical programming involving uncertain random variables. Finally, some applications of uncertain random programming are discussed.

Uncertain random variables: a mixture of uncertainty and randomness

In many cases, human uncertainty and objective randomness simultaneously appear in a system. In order to describe this phenomena, this paper presents a new concept of uncertain random variable. To measure uncertain random events, this paper also combines probability measure and uncertain measure into a chance measure. Based on the tool of chance measure, the concepts of chance distribution, expected value and variance of uncertain random variable are proposed.

Analytical sensitivity of interpolatory quadrature in force‐based frame elements

AbstractRecent literature shows the choice of an integration method in the state determination of force‐based frame finite elements has a significant influence on the computed element response. To assess the modeling uncertainty associated with integration methods in force‐based elements, analytical sensitivity of one‐dimensional interpolatory quadrature is developed via direct differentiation of the governing Vandermonde equations. Comparisons with finite difference calculations show that the combination of the Vandermonde equation sensitivity with equations that govern force‐based element response sensitivity leads to an accurate approach to stand‐alone response sensitivity analysis. Consistent with previous findings for material, load, and geometric parameters in finite element response sensitivity analysis, sensitivity with respect to parameters associated with the integration method in force‐based elements improves the efficiency of gradient‐based algorithms where the locations and/or weights of the integration method are treated as uncertain random variables. Copyright © 2009 John Wiley & Sons, Ltd.

Estimating the uncertainty associated with Widmark's equation as commonly applied in forensic toxicology

No computation is performed more frequently by forensic toxicologists than that involving Widmark's equation. The equation is employed to estimate either the number of drinks consumed or the corresponding blood or breath alcohol concentration. Despite the wide use of Widmark's equation, rarely is an uncertainty estimate also provided. Estimates from Widmark's equation involve at least seven uncertain random variables. Uncertainty estimates are presented that rely on methods of general error propagation compared to a method developed by Widmark. Assuming reasonable variable and uncertainty estimates, the error propagation method yielded for N = 10.4 drinks, a combined uncertainty (standard deviation) of 1.3 drinks (CV = 12.3%). Similarly, estimating the blood alcohol concentration yielded for 0.120 g/100 ml, an uncertainty of 0.0255 g/100 ml (CV = 21.2%). Widmark's uncertainty method yielded 1.6 drinks (CV = 15.4%). The derivation of Widmark's uncertainty estimate is also presented, showing that he considered only ρ and β to be uncertain. Widmark estimates for the number of drinks should include a 2CV estimate of approximately 25% while the blood alcohol concentration estimate should include a 2CV estimate of approximately 42%. Including valid estimates of uncertainty should enhance the legal admissibility and confidence for Widmark estimations.

Parametric Uncertainty in Hydrologic Modeling

ABSTRACT <emph>I</emph>N most applications, parametric, hydrologic models are treated as deterministic. That is once the parameters are determined, the model always produces the same outputs for a given set of inputs. Parameters are generally treated as unknown constants. Once they are estimated, they are taken as constant. In fact, model parameters are generally estimated from observed data or from relationships that have been derived from observed data. The observed data generally includes some stochastic variables such as rainfall and runoff. Based on the premise that any function of a random variable is itself a random variable, this paper reviews theory and approaches enabling one to treat model parameters as uncertain random variables. The report is a review of parametric uncertainty in hydrologic modeling. Several aspects of the topic are introduced but not treated in great mathematical detail. Many references to additional work are given that will enable the interested reader to pursue various aspects of the topic in detail.