Approximation of Probabilistic Distributions Using Selected Discrete Simulations

Abstract

The goal of this research is to find a computationally efficient and easy to use alternative to current approximation of direct Monte Carlo methods for robust design. More specifically, a new technique is sought to use selected deterministic analyses to obtain probability distributions for analyses with large inherent uncertainties. Two techniques for this task are investigated. The first uses a design of experiments array to find key points in the algorithm space upon which deterministic analyses will be performed. An expectation value error minimization routine is then used to assign discrete probabilities to the individual runs in the array based on the joint probability distribution of the inputs. This creates a representative distribution that can be used to estimate expectation values for the output distribution. The second technique uses a similar error minimization algorithm, but this time alters the location of the points to be sampled from the function space. This means that for every change in input variable distribution, the algorithm will generate a table of runs at input locations that minimize the error in expectation values. The advantages of these techniques include a small time savings over approximation or direct Monte Carlo methods as well as elimination of numerical noise due to random number generation. This noise will be shown to be a hindrance when converging multiple Monte Carlo analyses. In additional, when the variable location sampling point algorithm is used, this takes away the arbitrary task of defining levels for the input variables and provides enhanced accuracy.