An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 1-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first-and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.
Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives1
Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division July 20, 2001; revised manuscript received November 12, 2001. Associate Editor: G. Karniadakis.
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Putko, M. M., Taylor , , A. C., III, Newman, P. A., and Green, L. L. (November 12, 2001). "Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives." ASME. J. Fluids Eng. March 2002; 124(1): 60–69. https://doi.org/10.1115/1.1446068
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