EXISTING MATHEMATICAL METHODS FOR UNCERTAINTY ASSESSMENT - Modelling Uncertainty in Flood Forecasting Systems - page 25

Chapter 3
EXISTING MATHEMATICAL METHODS
FOR UNCERTAINTY ASSESSMENT
Summary of Chapter 3
This chapter presents some existing mathematical methods for
uncertainty assessments. In particular four methods are presented:
Monte Carlo simulation, First-Order Second Moment method, fuzzy
Extension Principle and the expert judgement-based qualitative
method. The first two methods are based on probability theory and the
latter two are based on fuzzy set theory. Brief principles of two other
methods used in flood foresting problems are also presented. Primarily
based on Bayesian theory, these two methods are the Bayesian
Forecasting System and the Generalised Likelihood Uncertainty
Estimation. There are growing concerns in the hybrid use of
probability and possibility (or fuzzy set) theories to deal with the
problems where the uncertainty comes from both randomness and
vagueness. Various hybrid approaches are reported in the literature.
Two of such approaches, namely, the concept of fuzzy probability and
the concept of fuzzy-random variables are also presented. In dealing
with the situation where the presence of both random and vague
uncertainties is significant, the conversion from one representation to
another is an important issue. Although several methods of conversions
are reported, their acceptance in practical applications is yet to be seen.
Two transformation methods, one based on a simple normalisation and
another based on the principle of uncertainty invariance are also
presented. At the end of this chapter, discussion is presented to
illustrate some important distinctions and similarities of the uncertainty
assessment methods presented at the beginning of the chapter.
3.1 Probability theory-based methods
The assessment of uncertainty in a model output requires the propagation of different
sources of uncertainty through the model. The probability theory-based uncertainty
assessment methods involve either the propagation of probability distributions or the
moments of distributions (means and variances). Various methods exist both for the
propagation of distributions and propagation of moments of distributions. These methods
of uncertainty propagation can be broadly classified into three categories:
1. Analytical methods
2. Sampling methods
3. Approximation methods