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.
Skip Nav Destination
Article navigation
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
Search for other works by this author on:
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
Download citation file:
Get Email Alerts
Cited By
A Novel Active Learning Kriging-Based Reliability Analysis Method for Aero-Engine Gear
ASME J. Risk Uncertainty Part B (September 2025)
An Efficient Statistical Inference Approach for Model Calibration Using Griddy Gibbs Sampling
ASME J. Risk Uncertainty Part B (September 2025)
Propagation of systematic sensor uncertainty into the frequency domain
ASME J. Risk Uncertainty Part B
Heuristic-based recommendation system for dealing with abnormal situations in industrial applications
ASME J. Risk Uncertainty Part B
Related Articles
Sensitivity Analysis of a Bayesian Network
ASME J. Risk Uncertainty Part B (March,2018)
Model-Form Calibration in Drift-Diffusion Simulation Using Fractional Derivatives
ASME J. Risk Uncertainty Part B (September,2016)
Effects of the Fractional Laplacian Order on the Nonlocal Elastic Rod
Response
ASME J. Risk Uncertainty Part B (September,2017)
Determining Probability of Importance of Features in a
Sketch
ASME J. Risk Uncertainty Part B (December,2017)
Articles from Part A: Civil Engineering
Multilevel Decomposition Framework for Reliability Assessment of Assembled Stochastic Linear Structural Systems
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering (March,2021)
Bayesian Methodology for Probabilistic Description of Mechanical Parameters of Masonry Walls
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering (June,2021)
Uncertainty Quantification of Power Spectrum and Spectral Moments Estimates Subject to Missing Data
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering (December,2017)
Dynamic Modeling for Analyzing Cost Overrun Risks in Residential Projects
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering (September,2022)
Related Proceedings Papers
Related Chapters
An Bayesian Assessment Model for Equipment Techonlogy State
International Conference on Software Technology and Engineering (ICSTE 2012)
On the Exact Analysis of Non-Coherent Fault Trees: The ASTRA Package (PSAM-0285)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
PSA Level 2 — NPP Ringhals 2 (PSAM-0156)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)