Development of Improved Uncertainty Analysis Methods for Hydrosystem Engineering Problems

Point estimate methods (PEMs) are one of uncertainty analysis methods, which are proved to be more computationally efficient than the Monte-Carlo simulation. Application of uncertainty analysis and risk assessment has gained more popularity these days. In the first part of this study, we apply uncertainty analysis to discrete time Markov chain with an attempt to improve the discrete time Markov chain from a deterministic model to a stochastic model. And in the second part, the traditional output(s) of a stochastic model are often expressed using a region of expected value plus and minus a standard deviation. The above expression is based on an underlying assumption that the output distribution is symmetric. To extend the output distribution to an asymmetric distribution, we introduce the Gram-Charlier (GC) type-A series. The GC type-A series utilizes the statistical moments of a random variable to determine an appropriate distribution. It is more straightforward to use GC type-A series to revise the shape of distribution. Additionally, the third and fourth order statistical moments of the Perturbance moments method are made available for the use of the GC type-A series. An example of the hydraulic jump problem is presented to analyze the stochastic output of the flow depth after the jump. Finally, the PMM is improved to consider the correlation of each uncertain variable using the orthogonal transformation to the principal axis of uncertain variables. An example of particle settling is proposed to quantify the uncertainty of settling velocity of a particle.