Applications of Possibility and Evidence Theory in Civil Engineering

Abstract

This article is devoted to applications of fuzzy set theory, possibility theory and evidence theory in civil engineering, presenting current work of a group of researchers at the University of Innsbruck. We argue that these methods are well suited for analyzing and processing the parameter uncertainties arising in soil mechanics and construction management. We address two specific applications here: finite element computations in foundation engineering and a queueing model in earth work.Keywords: Engineering applications, finite element methods, queueing models, imprecise parameters, possibility and evidence theory, fuzzy probabilities. Int. J. Unc. Fuzz. Knowl. Based Syst. 2000.08:295-309. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/21/15. For personal use only.

Approximated Computation of Belief Functions for Robust Design Optimization

“…Authors like Oberkampf et al 1 demonstrated the potentiality of Evidence Theory to model both epistemic and aleatory uncertainties in the design of engineering systems. Similar examples can be found in the work of Agarwal et al 2 or in the work of Bae et al 3 , Fetz et al 4 He et al 5 and Mourela et al 6 , mainly with applications to structural design. Denoeux proposed a technique to compute an inner and outer approximation of Belief and Plausibility functions 7 .…”

Random sets of probability measures in slope hydrology and stability analysis

“…If fuzzy sets are thought of as nested families of sets (i.e., consonant random sets) they can also be handled in random set theory, providing a convenient link between probability theory, possibility theory and fuzzy sets. A random set approach is attractive in the context of geotechnical analysis, as has previously been argued by Fetz et al [2] and Tonon et al [4], because information tends to be scarce and may only be available in the form of interval bounds on unknown quantities or vague testimony of experts. When interval measurements are available from several sources under certain circumstances their combination can be thought of as a (not necessarily consonant) random set.…”

“…As a consequence there is often considerable uncertainty in predictions of slope stability. Research on stochastic versions of geotechnical models has yielded interesting theoretical insights [1] but is seldom applied in practice because the sample data requirements at a site are so much in excess of what is typically available [2].…”

Clouds, p-boxes, Fuzzy Sets, and Other Uncertainty Representations in Higher Dimensions

“…As the inner level of problem (30), i.e., equation (29), maximizes the objective which is sought to be minimized for the design optimization in the outer level (i.e., one seeks the design with minimal worst-case), the term anti-optimization has been proposed for this approach.…”