Fuzzy Arithmetical Analysis of Multibody Systems with Uncertainties

Abstract

The consideration of uncertainties in numerical simulation is generally reasonable and is often indicated in order to provide reliable results, and thus is gaining attraction in various fields of simulation technology. However, in multibody system analysis uncertainties have only been accounted for quite sporadically compared to other areas. The term uncertainties is frequently associated with those of random nature, i.e. aleatory uncertainties, which are successfully handled by the use of probability theory. Actually, a considerable proportion of uncertainties incorporated into dynamical systems, in general, or multibody systems, in particular, is attributed to so-called epistemic uncertainties, which include, amongst others, uncertainties due to a lack of knowledge, due to subjectivity in numerical implementation, and due to simplification or idealization. Hence, for the modeling of epistemic uncertainties in multibody systems an appropriate theory is required, which still remains a challenging topic. Against this background, a methodology will be presented which allows for the inclusion of epistemic uncertainties in modeling and analysis of multibody systems. This approach is based on fuzzy arithmetic, a special field of fuzzy set theory, where the uncertain values of the model parameters are represented by socalled fuzzy numbers, reflecting in a rather intuitive and plausible way the blurred range of possible parameter values. As a result of this advanced modeling technique, more comprehensive system models can be derived which outperform the conventional, crisp-parameterized models by providing simulation results that reflect both the system dynamics and the effect of the uncertainties. The methodology is illustrated by an exemplary application of multibody dynamics which reveals that advanced modeling and simulation techniques using some well-thought-out inclusion of the presumably limiting uncertainties can provide significant additional benefit.