Fuzzy uncertainty in forward dynamics simulation using variational integrators

Abstract

AbstractIn engineering applications, dynamic simulations are usually carried out with precisely defined input parameters. In this contribution, forward dynamics with epistemic parameter‐uncertainty is considered and α‐level discretisation in combination with α‐level optimisation is used to determine the output of the dynamical system – a fuzzy function. A new numerical method for an efficient realisation of α‐level optimisation in this context is developed, which combines forward dynamics steps and local optimisations. A variational integrator, which exhibits special structure preserving properties, is used as the underlying time integration scheme. However, the method can be combined with any time stepping scheme. In detail, an approximative description of the output as a function of the uncertain parameters is developed, which can be used to reduce the complexity of the developed algorithm.