Evaluation of Probabilistic Point Estimate Methods in Uncertainty Analysis for Environmental Engineering Applications

This paper begins with a comprehensive review of various point estimate methods, with an emphasis on their differences and similarities in theory and application. The Rosenblueth probabilistic point estimate method is a computationally straightforward technique for the uncertainty analysis of engineering problems. It is capable of estimating a statistical moment of any order of a model output involving several stochastic variables that are correlated or uncorrelated, symmetric, or asymmetric. However, in multivariate problems with more than two stochastic variables involved, the Rosenblueth method is not able to provide a unique solution, rather an approximate solution to indeterminate problems. This is attributed to the fact that the number of unknowns to be solved is larger than the number of governing equations provided. An improved modified Rosenblueth point estimate method is proposed to circumvent the drawback of the nonunique solution of the original Rosenblueth method and to increase the computational efficiency in modeling. One example application on the particle terminal velocity computation is presented for illustration. A quantitative performance index is introduced to assess the performance of various point estimate methods. It is concluded in this study that the modified Rosenblueth method has a comparable performance to the Rosenblueth method and yet resolves the nonuniqueness problem in solutions.