### Abstract

Evidence theory provides an alternative to probability theory for the representation of epistemic uncertainty in model predictions that derives from epistemic uncertainty in model inputs, where the descriptor epistemic is used to indicate uncertainty that derives from a lack of knowledge with respect to the appropriate values to use for various inputs to the model. The potential benefit, and hence appeal, of evidence theory is that it allows a less restrictive specification of uncertainty than is possible within the axiomatic structure on which probability theory is based. Unfortunately, the propagation of an evidence theory representation for uncertainty through a model is more computationally demanding than the propagation of a probabilistic representation for uncertainty, with this difficulty constituting a serious obstacle to the use of evidence theory in the representation of uncertainty in predictions obtained from computationally intensive models. This presentation describes and illustrates a sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Preliminary trials indicate that the presented strategy can be used to propagate uncertainty representations based on evidence theory in analysis situations where naïve sampling-based (i.e., unsophisticated Monte Carlo) procedures are impracticable due to computational cost.

Original language | English (US) |
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Pages (from-to) | 3980-3998 |

Number of pages | 19 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 196 |

Issue number | 37-40 SPEC. ISS. |

DOIs | |

State | Published - Aug 1 2007 |

### Keywords

- Dempster-Shafer theory
- Epistemic uncertainty
- Evidence theory
- Monte Carlo
- Numerical uncertainty propagation
- Sensitivity analysis
- Uncertainty analysis

### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications

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## Cite this

*Computer Methods in Applied Mechanics and Engineering*,

*196*(37-40 SPEC. ISS.), 3980-3998. https://doi.org/10.1016/j.cma.2006.10.049