Uncertainty evaluation through mapping identification in intensive dynamic simulations

Authors:
Yan Wan;Sandip Roy;Bernard Lesieutre
Affiliations:
Department of Electrical Engineering, University of North Texas, Denton, TX;School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA;Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI and Lawrence Berkeley National Laboratory, Berkeley, CA
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special issue on model-based diagnostics
Year:
2010

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Abstract

We study how the dependence of a simulation output on an uncertain parameter can be determined when simulations are computationally expensive and so can only be run for very few parameter values. Specifically, the methodology that is developed--known as the probabilistic collocation method (PCM)--permits selection of these few parameter values, so that the mapping between the parameter and the output can be approximated well over the likely parameter values, using a low-order polynomial. Several new analyses are developed concerning the ability of PCM to predict the mapping structure, as well as output statistics. A holistic methodology is also developed for the typical case where the uncertain parameter's probability distribution is unknown, and instead, only depictive moments or sample data (which possibly depend on known regressors) are available. Finally, the application of PCM to weather-uncertainty evaluation in air traffic flow management is discussed.