Uncertainty quantification and propagation based on hybrid experimental, theoretical, and computational treatment. (15th January 2021) - Elishakoff, I.; Fang, T.; Sarlin, N.; Jiang, C.
Highlights: Beginning with given scarce experimental data, the method first obtains the convex hull of the experimental data and then enclosing the data by various figures, namely the convex hull, box, parallelepiped, ellipsoid and super-ellipsoid with minimal volume, all containing the data. An inflating Chebyshev's ellipsoid is then calculated based on the data and given probability level. Thus the transformed uncertainty domain is obtained by enlarging the original minimal volume figures based on the so-called 'Chebyshev's ellipsoid' so that the specified probability level of uncertainty domain can be ensured. The method is applied to a ten-bar truss under three uncertain loads for response analysis. Abstract: This paper extends two companion studies (Elishakoff and Sarlin, 2016a, b) into three-dimensional case. Beginning with given scarce experimental data, the method first obtains the convex hull of the experimental data and then enclosing the data by various figures, namely the convex hull, box, parallelepiped, ellipsoid and super-ellipsoid with minimal volume, all containing the data. An inflating Chebyshev's ellipsoid is then calculated based on the data and given probability level. Thus the transformed uncertainty domain is obtained by enlarging the original minimal volume figures based on the so-called 'Chebyshev's ellipsoid' so that the specified probability level of uncertainty domain can be ensured. Finally, this method is applied to a ten-bar truss under three uncertain loads for response analysis.