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By Wolfgang Fellin, Heimo Lessmann, Michael Oberguggenberger, Robert Vieider

This quantity comprehensively addresses the problem of uncertainty in civil engineering, from layout to building. present engineering perform usually leaves uncertainty matters apart, even though new medical instruments were constructed some time past a long time that let a rational description of uncertainties of every kind, from version uncertainty to information uncertainty. it's the goal of this quantity to take a serious examine present engineering hazard options with the intention to bring up knowledge of uncertainty in numerical computations, shortcomings of a strictly probabilistic defense idea, geotechnical types of failure and their building implications, genuine development, and obligation. additionally, the various new methods for modelling uncertainty are defined. The ebook is as a result a collaborate attempt of mathematicians, engineers and building managers who met usually in a post-graduate seminar on the collage of Innsbruck in past times years.

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10. 3 Fuzzy sets Degree of possibility Degree of possibility An even more robust non-probabilistic approach would employ fuzzy sets to describe the parameter uncertainties. The construction of a fuzzy set describing input variability may be based on an expert’s risk assessment of possible ranges of the angle of internal friction, say. A detailed discussion of the interpretation and the construction of fuzzy sets can be found in [13] and the references therein. An example of a triangular fuzzy number is given in Figure 11.

23], µϕ = 30◦ . If we want to account for a spacial averaging, we have to model the shear parameters as random fields [7]. For this we have to introduce a correlation function. This is another unknown in our calculations. A list of possible choices of the correlation function is given in [7]. We want to use the simplest correlation function, where the correlation is one within the correlation length δ and zero outside. With this simple rectangular function the coefficient of variation of the averaged parameter in the shear band of length l is Vµ = V δ l with δ

Second, what is probability? In engineering modeling, at least three interpretations can be identified. There is classical probability which assigns probabilities from combinatorial considerations (for example, the assertion that the number k of successes in a sequence of n trials has a binomial distribution). Then there is the frequentist interpretation in which probability is an approximation to relative frequencies of outcomes in large samples. For the practical purpose of determining confidence intervals and performing statistical tests for the parameters of a single random variable “large” means n ≥ 20.

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