An improved entorpy-based representation for mixed uncertainty about intervals and points data

Abstract

In engineering design problems, intervals refer to any kind of lack of information. This paper presents an improved entorpy-based methodology for a probabilistic representation of a stochastic quantity for which only sparse point data and/or interval data may be available. The combined entropy function is used to measure the uncertainty in data, which is evaluated from the non-parametric probability density function for sparse point data and the cumulative distribution function for interval data, Wherein the entire non-parametric distribution can be discretized at a finite number of points and the probability density values at these points can be inferred using the principle of maximum-entropy, thus avoiding the assumption of any particular distribution. The proposed improved Entorpy-based methodology is then employed in the attempt of interval uncertainty propagation, with the results compared with previous studies. Examples are provided to demonstrate the effectiveness of present method. The study reveals great potentials of the probabilistic method for the treatment of the uncertainty in presence of the sparse point data and/or interval data.