Propagation of uncertainties in deterministic systems

Abstract

This paper addresses the propagation of uncertainties in deterministic systems, i.e. the system definition is known but the system parameters and input to the system contain uncertain information. The effect of the uncertain information on the system response is to be assessed. Three models of uncertainties corresponding to differing degrees of knowledge about the uncertainty are considered: interval, fuzzy and random. A method to propagate uncertainties expressed as intervals is described; the method, called the Vertex method, is based on a generalization of combinatorial interval analysis techniques. It is shown how the Vertex method can be extended naturally to treat the propagation of uncertainties modeled as fuzzy sets. Finally, propagation of random uncertainties is described using the classical probabilistic technique of derived distribution functions. The computational implications of the three models of uncertainties and the corresponding methods of propagation are contrasted. It is suggested that when the available information is too crude to support a random definition, the interval or fuzzy model should be used to take advantage of the expediency with which interval and fuzzy uncertainties can be propagated and processed.

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