Investigation of Probabilistic Failure Predictions with Progressive Damage in Composites

Three probabilistic techniques are compared that allow for the estimation of sensitivity of a system to statistically distributed input parameters. These methods could be useful for estimating sensitivity of the system with an intractable response surface that must be calculated numerically using computational algorithms such as Monte Carlo experiments. All three methods estimate the baseline response using a Monte Carlo experiment. Two of the methods estimate the perturbed response using additional Monte Carlo experiments based on perturbed input parameters, generated either with a different seed or the same seed used to generate the instances of the input parameters for the baseline Monte Carlo experiment. The third method uses the ratio of the probability of occurrence of the perturbed and baseline input parameters to estimate the perturbed response. These techniques are demonstrated using a composite material progressive damage model with one, two, and three random input variables. This work explores the correlation between number of simulations in a Monte Carlo experiment and the variability in sensitivity. The same-seed Monte Carlo method is shown to be the most accurate method. The probability-ratio method is shown to be significantly less computationally expensive.