Many phenomena as well as complex and safety critical systems can be studied and analysed only by using virtual prototypes and predictive mathematical models. One of the greatest challenges of virtual prototyping is to improve the fidelity of the computational analysis. This can only be achieved by explicitly including variability and uncertainties from different sources. Variability is inherent in many natural systems, and therefore cannot be reduced. Uncertainty is also always present since it is not possible to perfectly model or predict future events for which no real-world data are available. Although stochastic methods offer a much more realistic approach for analysis and design, their utilization in practical applications remains quite limited. One of the reasons is the difficult to propagate different representation of the uncertainties. Another reason is the computational cost of stochastic analysis that it is often by orders of magnitude higher than the deterministic analysis. This paper presents a powerful and unified representation of the uncertainty and an efficient computational framework. The computational tools satisfy the industry requirements regarding numerical efficiency, flexibility, scalability and analysis of detailed models that can be used to analyse a wide range of engineering and scientific problems.
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