In general, the behavior of science and engineering is predicted based on nonlinear math models. Imprecise knowledge of the model parameters alters the system response from the assumed nominal model data. One proposes an algorithm for generating insights into the range of variability that can be expected due to model uncertainty. An automatic differentiation tool builds the exact partial derivative models required to develop a state transition tensor series (STTS)-based solution for nonlinearly mapping initial uncertainty models into instantaneous uncertainty models. The fully nonlinear statistical system properties are recovered via series approximations. The governing nonlinear probability distribution function is approximated by developing an inverse mapping algorithm for the forward series model. Numerical examples are presented, which demonstrate the effectiveness of the proposed methodology.
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December 2016
Research Papers
Semi-Analytic Probability Density Function for System Uncertainty
Ahmad Bani Younes,
Ahmad Bani Younes
Assistant ProfessorMem. ASME Department of Aerospace Engineering,
Khalifa University
, P. O. Box 127788, Abu Dhabi
, UAE
e-mail: ahmad.younes@kustar.ac.ae
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James Turner
James Turner
Visiting ProfessorMem. ASME Department of Aerospace Engineering,
Khalifa University
, P. O. Box 127788, Abu Dhabi
, UAE
e-mail: james.turner@kustar.ac.ae
Search for other works by this author on:
Ahmad Bani Younes
Assistant ProfessorMem. ASME Department of Aerospace Engineering,
Khalifa University
, P. O. Box 127788, Abu Dhabi
, UAE
e-mail: ahmad.younes@kustar.ac.ae
James Turner
Visiting ProfessorMem. ASME Department of Aerospace Engineering,
Khalifa University
, P. O. Box 127788, Abu Dhabi
, UAE
e-mail: james.turner@kustar.ac.aeManuscript received January 28, 2016; final manuscript received June 13, 2016; published online August 19, 2016. Assoc. Editor: Athanasios Pantelous.
ASME J. Risk Uncertainty Part B. Dec 2016, 2(4): 041007 (7 pages)
Published Online: August 19, 2016
Article history
Received:
January 28, 2016
Revision Received:
June 13, 2016
Accepted:
June 13, 2016
Citation
Younes, A. B., and Turner, J. (August 19, 2016). "Semi-Analytic Probability Density Function for System Uncertainty." ASME. ASME J. Risk Uncertainty Part B. December 2016; 2(4): 041007. https://doi.org/10.1115/1.4033886
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