An Alternative to Monte Carlo Simulation Method

Jorge S. Ballaben, Hector E. Goicoechea, Marta B. Rosales


The quantification and propagation of uncertainty is a growing discipline, with applications within practically all sciences. Uncertainties are present in every prediction model of each discipline (natural, structural, biological, etc), since an exact and perfect definition of geometry, boundary conditions, material properties, initial conditions and excitations (among others) is rarely possible. A common and robust approach to perform the propagation of uncertainties is the Monte Carlo method, which usually implies running a large number of simulations. Complex systems, where uncertainty propagation is particularly interesting, require time expensive computations, and large memory and storage capacities in order to process such amount of data. Even thousands of runs of a slightly non-linear model with a few degrees of freedom could take a considerable time, despite the use of state-of-the-art solvers and parallelization techniques. In this work, a methodology that could allow the reduction of the number of simulations is discussed. The idea of the method is to perform a parametric sweep for a certain parameter X to be considered stochastic, then assign probabilities (according to a previously selected cumulative probability density function) to the values of X, and finally map the corresponding probability values to the target variables. Hence, the probability density function of the target variables could be estimated. Within this work, the theory and implementation of the proposed method are discussed and application examples are provided.

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