# The role of epistemic uncertainty of contact models in the design and optimization of mechanical systems with aleatoric uncertainty

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## Abstract

Epistemic uncertainty, the uncertainty in the physical model used to represent a phenomenon, has a significant effect on the predictions of simulations of mechanical systems, particularly in systems with impact events. Impact dynamics can have a significant effect on a system’s functionality, stability, wear, and failure. Because high-fidelity models of systems with impacts often are too computationally intensive to be useful as design tools, rigid body dynamics and reduced order model simulations are used often, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or penalty stiffness. The choice of impact model, though, can have significant ramifications on design predictions. The effects of both epistemic and aleatoric (parametric) uncertainty in the choice of contact model are investigated in this paper for a representative multiple-degree of freedom mechanical system. Six contact models are considered in the analysis: two different constant coefficient of restitution models, a piecewise-linear stiffness and damping (i.e., Kelvin–Voight) model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. Results show that the optimal mechanism design for each contact model appears extremely different. Further, the effects due to epistemic uncertainty are differentiated clearly in the response from the effects due to aleatoric uncertainty. Lastly, when the mechanisms are optimized to be robust against aleatoric uncertainty, the resulting designs show some robustness against epistemic uncertainty.

## Keywords

Impact mechanics Design optimization Epistemic uncertainty Aleatoric uncertainty Dynamics Contact## Notes

### Acknowledgments

The author gratefully acknowledges the support and collaboration of his colleagues, especially Dannelle Aragon, Doug VanGoethem, Anton Sumali, and Jill Blecke.

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