1. Fault Tree Analysis Based on Dynamic Uncertain Causality Graph
Zhenxu Zhou
Prof. Qin Zhang
Institute of Nuclear and New Energy Technology (INET)
Tsinghua University

2. Outline Background Intro to DUCG Methodology Examples
Summary and Conclusion

3. Background-Fault Tree Analysis (FTA)
A deductive method consists of qualitative analysis and quantitative analysis
Commonly used tools in PSA
Widely applied in
nuclear power plants (NPP)
space systems
chemical plants
A fault tree

4. Background-Some Problems in FTA
1. Dependencies and circular loops(CLs)
Dependencies are caused by
shared components
shared utilities
among and within FTs
CLs are caused by
mutual or circular dependencies
In NPPs, mainly dependencies of support systems
not major concerns not well explored

5. Background-Some Problems in FTA
2. Large scales
increase in the exponential order
3. Repeated representations
additional calculations
4. Non-deterministic causalities
may be uncertain
not well addressed

6. Background-Other approaches
Binary Decision Diagram
(BDD)
Bayesian Network
(BN)
Petri Net
(PN)
Dependencies
CLs
Non-deterministic causalities
Efficiency~Order~NP Complete
Dependencies
CLs
Non-deterministic causalities
Efficiency~Conditional Probability Tables
Dependencies
CLs
Non-deterministic causalities
Efficiency~ State Reachability Graphs

7. Outline Background Intro to DUCG Methodology Examples
Summary and Conclusion

8. repeated representations deterministic causalities
Intro to DUCG
Dynamic Uncertain Causality Graph (DUCG) is proposed by Prof. Qin Zhang
DUCG can deal with
dynamics
uncertainties
CLs
has been applied in
NPPs
space systems
chemical plants
medical expert system
An example of DUCG
Able to analyze FTs and solve the issues:
dependency
CLs
large scales
repeated representations deterministic causalities

9. Outline Background Intro to DUCG Methodology Examples
Summary and Conclusion

10. Methodology-Mapping Algorithm
Algorithm 1 mapFaultTreeIntoDUCG
01. for each Event in FaultTree do 02. if Event.Type == Basic || Event.Type == Undeveloped then 03. if flow_add.sourceRef.type !=B do 04. currentDUCG.addNode(new XVariable(name=Event.name, probability=Event.probability)) 05. elseif Event.Type == Intermediate || Event.Type == Top then 06. currentDUCG.addNode(new XVariable(name=Event.name, probability= Event.probability)) 07. elseif Event.Type == House then 08. currentDUCG.change(Event.Logic,Event.UpperLogic) 09. endfor 10. for each LogicGate in FaultTree do 11. currentDUCG.addGate(LogicGate.Type, LogicGate.In, LogicGate.Out ) 12. endfor

11. Methodology-Event MappingFT
DUCG
No direct mapping relation.

12. Methodology-Numerical Mapping
House events:
commonly used to control whether some special events happen or not
have a fixed probability of 0 or 1, expected to occur
have direct effects on its logic gates

13. Methodology-Logic Mapping
OR Gate
AND Gate
2/3 Gate
NOT Gate

14. Methodology-Modelling Improvements
Break Circular Loops (CLs)
Assumption 4 in DUCG:
Any state of a variable cannot be the cause of any state of the same variable at the same time.
A fault tree with CL

15. Methodology-Modelling Improvements
Common Cause Failures (CCF)
Represent CCF Gates
Adding a NOT Gate (the output of given CCF Gate as its input) to the input of TE
Modifying the corresponding P variable with parameter LCCF
CCF AND Gate

16. Methodology-Modelling Improvements
Multi-state Events
Use M-DUCG instead
Statistically Dependencies
Are removed because of logic operations before numerical calculations
Non-deterministic Causalities
Specify the probabilities with Pn;i or Fn;i

17. Methodology-Analysis Improvements
Importance Analysis
Extend importance measures to
entire system.

18. Methodology-Analysis Improvements
Failure Prediction
Fault Diagnosis

19. Outline Background Intro to DUCG Methodology Examples
Summary and Conclusion

20. Example 1 How? If we replace house event B1 with a basic event:
If B10 occurs and B21 doesn’t occur, X61 won’t occur.
Corresponding logic gate will be removed which leading to X61 = B51.
House event with AND-AND Gate
How?
Use Z-type variable and modifying LGSs accordingly.

21. Example 2 A feed-control system
Disjoint Sum of Products
A feed-control system
The importance measurements of each basic events

22. Outline Background Intro to DUCG Methodology Examples
Summary and Conclusion

23. Summary and Conclusion
Compared to classical FTA
when dependencies/CLs exist, the results are exact
involves uncertainties
extends to multi-state variables
handles CCF
shows how to conduct importance analysis
base of online fault diagnosis and failure prediction

24. Thank you for your attention!