Formal Probabilistic Risk Assessment using Theorem Proving with Applications in Power Systems
Bibliographic record
Abstract
The central inquiry in many safety-critical systems is to assess the probability of all possible risk consequences that can occur in a system and its subsystems. In this research, we use theorem proving to formalize Event Trees (ET), Cause Consequence Diagrams (CCD) and Functional Block Diagrams (FBD), which are efficient techniques for probabilistic risk assessment at system and subsystem levels. Our approach provides the reasoning support with verified mathematical formulations that can analyze multi-level ETs, FBDs for complex systems, Cause Consequence Diagrams (CCD) based on Fault Trees (FT) as well as on Reliability Block Diagrams (RBD), as a novel approach. Also, the proposed formalizations of ETs/CCDs/FBDs allowed us to accurately determine of reliability indices, such as System/Customer Average Interruption Frequency and Duration (SAIFI, SAIDI and CAIDI) at system and subsystem levels. Moreover, we develop FBD and ET Modeling and Analysis (FETMA) software, which provides user-friendly features and graphical interfaces for industrial planners/designers. We applied our methods and tools on several realistic case studies from the power systems sector, i.e., the standard IEEE 3/39/118-bus electrical power generation/transmission/distribution networks, Quebec-New England High Voltage Direct Current (HVDC) transmission coupling system, multiple interconnected Micro-Grids, a nuclear power plant, transmission distance protection and a smart automated substation. Experimental results showed improvements compared to all existing reliability analysis methods in terms of scalability, expressiveness, accuracy and time.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.026 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".