Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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Zero-suppressed ternary decision diagram algorithm for solving noncoherent fault trees in probabilistic safety assessment of nuclear power plants

  • Woo Sik Jung (Sejong University)
  • Received : 2023.08.04
  • Accepted : 2024.01.13
  • Published : 2024.06.25
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Abstract

Probabilistic safety assessment (PSA) plays a critical role in ensuring the safe operation of nuclear power plants. In PSA, event trees are developed to identify accident sequences that could lead to core damage. These event trees are then transformed into a core-damage fault tree, wherein the accident sequences are represented by usual and complemented logic gates representing failed and successful operations of safety systems, respectively. The core damage frequency (CDF) is estimated by calculating the minimal cut sets (MCSs) of the core-damage fault tree. Delete-term approximation (DTA) is commonly employed to approximately solve MCSs representing accident sequence logics from noncoherent core-damage fault trees. However, DTA can lead to an overestimation of CDF, particularly when fault trees contain many nonrare events. To address this issue, the present study introduces a new zero-suppressed ternary decision diagram (ZTDD) algorithm that averts the CDF overestimation caused by DTA. This ZTDD algorithm can optionally calculate MCSs with DTA or prime implicants (PIs) without any approximation from the core-damage fault tree. By calculating PIs, accurate CDF can be calculated. The present study provides a comprehensive explanation of the ZTDD structure, formula of the ZTDD algorithm, ZTDD minimization, probability calculation from ZTDD, strength of the ZTDD algorithm, and ZTDD application results. Results reveal that the ZTDD algorithm is a powerful tool that can quickly and accurately calculate CDF and drastically improve the safety of nuclear power plants.

Keywords

Acknowledgement

This work was supported by the Korea Foundation Of Nuclear Safety (KOFONS) grant funded by the Nuclear Safety and Security Commission(NSSC), Republic of Korea (Nos. 2106062-0323-SB110 and 2204017-0223-SB110).

References

  1. W.E. Vesely, F.F. Goldberg, N.H. Roberts, D.F. Haasl, Fault Tree Handbook, U.S. Nuclear Regulatory Commission, NUREG-0492, 1981.
  2. S. Minato, Zero-suppressed BDDs for set manipulation in combinatorial problems, in: Proceedings of the 30th International Conference on Design Automation, 1993, pp. 272-277.
  3. W.S. Jung, S.H. Han, J.J. Ha, A fast BDD algorithm for the reliability analysis of large coherent systems, Reliab. Eng. Syst. Saf. 83 (2004) 369-374.
  4. W.S. Jung, ZBDD algorithm features for an efficient probabilistic safety assessment, Nucl. Eng. Des. 239 (2009) 2085-2092.
  5. C.Y. Lee, Representation of switching circuits by binary-decision programs, Bell System Technical Journal 38 (1959) 985-999.
  6. B. Akers, Binary decision diagrams, IEEE Trans. Comput. C-27 (6) (1978) 509-516.
  7. R. Bryant, Graph-based algorithms for Boolean function manipulation, IEEE Trans. Comput. C-35 (8) (1986) 677-691.
  8. R. Bryant, Symbolic Boolean manipulation with ordered binary decision diagrams, ACM Comput. Surv. 24 (1992) 293-318.
  9. A. Rauzy, New algorithms for fault trees analysis, Reliab. Eng. Syst. Saf. 5 (59) (1993) 203-211.
  10. Y. Duituit, A. Rauzy, Efficient algorithms to assess component and gate importance in fault tree analysis, Reliab. Eng. Syst. Saf. 72 (2001) 213-222.
  11. A. Rauzy, BDD for reliability studies, in: K.B. Misra (Ed.), Handbook of Performability Engineering, Elsevier, Amsterdam, The Netherlands, 2008, pp. 381-396.
  12. R. Remenyte-Prescott, J. Andrews, An enhanced component connection method BDD, Reliab. Eng. Syst. Saf. 93 (2008) 1543-1550.
  13. O. Nusbaumer, A. Rauzy, Fault tree linking versus event tree linking approaches - a reasoned comparison, Journal of Risk and Reliability 227 (2013) 315-326.
  14. A. Rauzy, L. Yang, Decision diagram algorithms to extract minimal cutsets of finite degradation models, Information 10 (2019) 368.
  15. W.S. Jung, S.H. Han, J.E. Yang, Fast BDD truncation method for efficient top event probability calculation, Nucl. Eng. Technol. 40 (7) (2008) 571-580.
  16. T. Luo, K.S. Trivedi, An improved algorithm for coherent-system reliability, IEEE Trans. Reliab. 47 (1998) 73-78.
  17. T. Sasao, Ternary Decision Diagrams and Their Applications, Representations of Discrete Functions, 1996, pp. pp269-292 (Chapter 12).
  18. T. Sasao, Arithmetic ternary decision diagrams applications and complexity. Proceedings of the Fourth International Workshop on Applications of the Reed-Muller Expansion in Circuit Design, 1999.
  19. R. Remenyte-Prescott, J. Andrews, Analysis of non-coherent fault trees using ternary decision diagrams, Proc. Inst. Mech. Eng. O J. Risk Reliab. 222 (2) (2008).
  20. W.S. Jung, A new zero-suppressed ternary decision diagram algorithm, in: Probabilistic Safety Assessment and Management (PSAM) Topical, October 23-25, 2023. Virtual meeting.