Numerical Investigation Of Probability Measures Utilized In A Maximum Entropy Approach

The quantification of uncertainty is an important aspect in modern design. One relatively new technique to quantify this uncertainty is the maximum entropy approach. This approach characterizes the physical system in terms of random matrices. The random matrices are generated to have a mean value of the nominal system and the variance is controlled by a single dispersion parameter. The determination of the dispersion parameter is done by creating the maximum likelihood estimate. This estimate requires a numerical probability measure for any real world system since an analytical distribution cannot be determined. This paper investigates the effect of multiple sampling techniques and multiple probability measurements. The investigation is performed on a planar frame truss with uncertainty introduced due to a reduced model using different reduction techniques. This technique is a systematic method that produces repeatable results that can be used in model simulations to produce a stochastic output range that is verified to the desired truth data.