Inverse simulation is an inverse process of a direct simulation. During the process, unknown simulation input variables are identified for a given set of known simulation output variables. Uncertainties such as random parameters may exist in engineering applications of inverse simulation. An optimization method is developed in this work to estimate the probability distributions of unknown input variables. The first order reliability method is employed and modified so that the inverse simulation is embedded within the reliability analysis. This treatment avoids the separate executions of reliability analysis and inverse simulation and consequently maintains high efficiency. In addition, the means and standard deviations of the unknown input variables can also be obtained. A particle impact problem is presented to demonstrate the proposed method for inverse simulation under uncertainty.

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