Uncertainty propagation in nonlinear systems.

This thesis examines the effects of uncertainty on a variety of different engineering systems. Uncertainty can be best described as a lack of knowledge for a particular system, and can come from a variety of different sources. Within this thesis the possibilistic branch of uncertainty quantification is used. A combination of simulated and real-life engineering systems are studied, covering some of the most popular types of computational models. An outline of various background topics is presented first, as these topics are all subsequently used within the thesis. The most important of these is the transformation method, a possibilistic uncertainty approach derived from fuzzy arithmetic. Most of the work here examines uncertain systems by implementing Ben-Haim's information gap theory. Uncertainty is deliberately introduced into the parameters of the various computational models to use the concept of “opportunity”. The basic rationale is that if some degree of tolerance can be accepted on a model prediction of a system, it is possible to obtain a lower value of prediction error than with a standard crisp-valued model. For the use of interval-valued computational models there is generally a trade-off to be made between minimising the prediction error of the model and minimising the range of predicted outputs, to reduce the tolerance on the solution. The studied models all use a “degree of uncertainty” parameter that allows any user to select the suitable trade-off level for their particular application. The thesis then concludes with a real-life engineering study, undertaken as a nine month placement on a European Union project entitled MADUSE. The work was done at Centro Ricerche Fiat, and examined the dynamic effects of uncertainties related to automotive spot welds. This study used both finite element modelling and experimental modal testing of manufactured specimens.