A Method for Projecting Uncertainty from Sparse Samples of Discrete Random Functions - Example of Multiple Stress-Strain Curves.

This paper describes a practical method for representing, propagating, and aggregating aleatory and epistemic uncertainties associated with sparse samples of discrete random functions and processes. An example is material strength variability represented by multiple stress-strain curves from repeated material characterization tests. The functional relationship underlying the stress-strain curves is not known─no identifiable parametric relationship between the curves exists─so they are here treated as non-parametric or discrete glimpses of the material variability. Hence, representation and propagation of the material variability cannot be accomplished with standard parametric uncertainty approaches. Accordingly, a novel approach which also avoids underestimation of strength variability due to limited numbers of material tests (small numbers of samples of the variability) has been developed. A methodology for aggregation of non-parametric variability with parametric variability is described.

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