Two types of uncertainty exist in engineering. Aleatory uncertainty comes from inherent variations while epistemic uncertainty derives from ignorance or incomplete information. The former is usually modeled by the probability theory and has been widely researched. The latter can be modeled by the probability theory or nonprobability theories and is much more difficult to deal with. In this work, the effects of both types of uncertainty are quantified with belief and plausibility measures (lower and upper probabilities) in the context of the evidence theory. Input parameters with aleatory uncertainty are modeled with probability distributions by the probability theory. Input parameters with epistemic uncertainty are modeled with basic probability assignments by the evidence theory. A computational method is developed to compute belief and plausibility measures for black-box performance functions. The proposed method involves the nested probabilistic analysis and interval analysis. To handle black-box functions, we employ the first order reliability method for probabilistic analysis and nonlinear optimization for interval analysis. Two example problems are presented to demonstrate the proposed method.
Skip Nav Destination
e-mail: dux@umr.edu
Article navigation
September 2008
Research Papers
Unified Uncertainty Analysis by the First Order Reliability Method
Xiaoping Du
Xiaoping Du
Department of Mechanical and Aerospace Engineering,
e-mail: dux@umr.edu
Missouri University of Science and Technology
, 1870 Miner Circle, Rolla, MO 65409
Search for other works by this author on:
Xiaoping Du
Department of Mechanical and Aerospace Engineering,
Missouri University of Science and Technology
, 1870 Miner Circle, Rolla, MO 65409e-mail: dux@umr.edu
J. Mech. Des. Sep 2008, 130(9): 091401 (10 pages)
Published Online: August 8, 2008
Article history
Received:
May 9, 2006
Revised:
May 27, 2007
Published:
August 8, 2008
Citation
Du, X. (August 8, 2008). "Unified Uncertainty Analysis by the First Order Reliability Method." ASME. J. Mech. Des. September 2008; 130(9): 091401. https://doi.org/10.1115/1.2943295
Download citation file:
Get Email Alerts
Related Articles
An Approach for Testing Methods for Modeling Uncertainty
J. Mech. Des (September,2006)
A Bayesian Approach to Reliability-Based Optimization With Incomplete Information
J. Mech. Des (July,2006)
Robustness of Design Through Minimum Sensitivity
J. Mech. Des (June,1992)
Reliability-Based Design Optimization of Microstructures With Analytical Formulation
J. Mech. Des (November,2018)
Related Proceedings Papers
Related Chapters
Performance-Based Expert Judgement Weighting Using Moment Methods (PSAM-0264)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
Threat Anticipation and Deceptive Reasoning Using Bayesian Belief Networks
Intelligent Engineering Systems through Artificial Neural Networks
Study on Probability Distribution of Shear Strength Parameters of Sliding Zone in Three Gorges Reservoir Zone Based on Multiple Test Methods
Geological Engineering: Proceedings of the 1 st International Conference (ICGE 2007)