Mathematics of uncertain multi-body systems

Abstract

As a consequence, numerous branches of simulation technology are warming up to the idea of taking uncertainties into account in numerical simulation, which is both reasonable and frequently necessary for producing trustworthy results. However, uncertainties have only been sometimes taken into consideration in multibody system analysis. Uncertainties are often thought of as being of a random character, or aleatory uncertainties, which may be effectively managed by using probability theory. So-called epistemic uncertainties, such as those attributable to a lack of knowledge, to subjectivity in numerical implementation, and to simplification or idealization, actually account for a significant portion of the uncertainties built into dy amical systems in general, or multibody systems in particular. As a result, a suitable theory is needed to describe epistemic uncertainty in multibody systems, which is still a challenging problem. In light of this, an approach will be introduced that incorporates epistemic uncertainty into multibody system modelling and analysis. Based on fuzzy arithmetic, a subfield of fuzzy set theory, this strategy uses fuzzy numbers to represent the uncertain values of the model's parameters, which is a relatively straightforward and realistic representation of the fuzzy range of potential parameter values. By giving simulation results that account for the dynamics of the system as well as the impact of the uncertainties, this cutting-edge modelling approach allows for the derivation of more complete system models that surpass the conventional, crisp-parameterized models.