Evaluating Epistemic Uncertainty from Random Variables at the Terminal Branches of a Logic Tree
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 3
Abstract
We present solutions for a combined probability density function computed as the weighted sum of individual probability density functions at the terminal branches of a logic tree. Logic trees are commonly utilized to quantify epistemic uncertainty in system analysis and can be computationally expensive when many branches and variables are included. The information provided herein can reduce those computational demands. We first derive closed-form expressions for the first two moments of the combined probability density function and subsequently derive expressions for the probability density function in cases where the mean value of the individuals is either normally or uniformly distributed and the variance is constant.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published paper.
Acknowledgments
This research significantly benefited from interactions and discussions with Jonathan P. Stewart. This technical note was prepared as part of a research project sponsored by the California Department of Transportation (Caltrans) through the UCLA John B. Garrick Institute of Risk Sciences (GIRS) under Task Order 3 through contract number 65A0780. Any opinions, findings, and conclusions or recommendations expressed in this report are those of the authors and do not necessarily reflect the views of acknowledged individuals, Caltrans or GIRS.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10 • Issue 3 • September 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Nov 1, 2023
Accepted: Feb 20, 2024
Published online: May 16, 2024
Published in print: Sep 1, 2024
Discussion open until: Oct 16, 2024
ASCE Technical Topics:
- Analysis (by type)
- Closed form solutions
- Computing in civil engineering
- Continuum mechanics
- Dynamics (solid mechanics)
- Ecosystems
- Engineering fundamentals
- Engineering mechanics
- Environmental engineering
- Mathematics
- Motion (dynamics)
- Probability
- Solid mechanics
- System analysis
- Trees
- Uncertainty principles
- Vegetation
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