Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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FAST BDD TRUNCATION METHOD FOR EFFICIENT TOP EVENT PROBABILITY CALCULATION

  • Published : 2008.12.31
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Abstract

A Binary Decision Diagram (BDD) is a graph-based data structure that calculates an exact top event probability (TEP). It has been a very difficult task to develop an efficient BDD algorithm that can solve a large problem since it is highly memory consuming. In order to solve a large reliability problem within limited computational resources, many attempts have been made, such as static and dynamic variable ordering schemes, to minimize BDD size. Additional effort was the development of a ZBDD (Zero-suppressed BDD) algorithm to calculate an approximate TEP. The present method is the first successful application of a BDD truncation. The new method is an efficient method to maintain a small BDD size by a BDD truncation during a BDD calculation. The benchmark tests demonstrate the efficiency of the developed method. The TEP rapidly converges to an exact value according to a lowered truncation limit.

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References

  1. C.Y. Lee, 'Representation of switching circuits by binarydecision programs,' Bell System Technical Journal, 38, pp. 985-999, 1959 https://doi.org/10.1002/j.1538-7305.1959.tb01585.x
  2. B. Akers, 'Binary Decision Diagrams,' IEEE Transactions on Computers, C-27(6), pp. 509-516, 1978 https://doi.org/10.1109/TC.1978.1675141
  3. R. Bryant, 'Graph Based Algorithms for Boolean Function Manipulation,' IEEE Transactions on Computers, C-35(8), pp. 677-691, August, 1986 https://doi.org/10.1109/TC.1986.1676819
  4. R. Bryant, 'Symbolic Boolean Manipulation with Ordered Binary Decision Diagrams,' ACM Computing Surveys, 24, pp. 293-318, September 1992 https://doi.org/10.1145/136035.136043
  5. O. Coudert and J.C. Madre, 'Implicit and Incremental Computation of Primes and Essential Primes of Boolean Functions,' Proceedings of the 29th ACM/IEEE Design Automation Conference, DAC' 92, June 1992
  6. A. Rauzy, 'New Algorithms for Fault Trees Analysis,' Reliability Engineering and System Safety, 40, pp. 203-211, 1993 https://doi.org/10.1016/0951-8320(93)90060-C
  7. O. Coudert and J.C. Madre, 'Fault Tree Analysis: 1020 Prime Implicants and Beyond,' Proceedings of the Annual Reliability and Maintainability Symposium, Atlanta, NC, USA, January 1993
  8. A. Rauzy and Y. Dutuit, 'Exact and Truncated Computations of Prime Implicants of Coherent and Non-coherent Fault Trees Within Aralia,' Reliability Engineering and System Safety, 58, pp. 127-144, 1997 https://doi.org/10.1016/S0951-8320(97)00034-3
  9. Y. Dutuit and A. Rauzy, 'Efficient Algorithms to Assess Component And Gate Importance in Fault Tree Analysis,' Reliability Engineering & System Safety, Volume 72, pp. 213-222, May 2001 https://doi.org/10.1016/S0951-8320(01)00004-7
  10. S. Epstein, A. Rauzy, 'Can we trust PRA,' Reliability Engineering & System Safety, Volume 88, pp. 195-205, June 2005 https://doi.org/10.1016/j.ress.2004.07.013
  11. S. Minato., 'Zero-suppressed BDDs for set manipulation in combinatorial problems,' Proc. of the 30th Int'l Conf. on Design Automation, pp. 272-277, 1993
  12. W.S. Jung, S.H. Han, J.J. Ha, 'A Fast BDD Algorithm for Large Coherent Fault Trees Analysis,' Reliability Engineering and System Safety, Vol. 83, pp. 369-374, 2004 https://doi.org/10.1016/j.ress.2003.10.009
  13. W.S. Jung, S.H. Han, J.J. Ha, 'Development of an Efficient BDD Algorithm to Solve Large Fault Trees,' Proceedings of the 7th International Conference on Probabilistic Safety Assessment and Management, June, Berlin, Germany, 2004
  14. W.S. Jung, S.H. Han, J.J. Ha, 'An Overview of the Fault Tree Solver FTREX,' 13th International Conference on Nuclear Engineering, Beijing, China, May 16-20, 2005
  15. B. Bollig and I. Wegener, 'Improving the variable ordering of OBDDs is NP complete,' IEEE Trans. Comput., Vol 45, pp. 993-1002, September 1996 https://doi.org/10.1109/12.537122
  16. S. J. Friedman and K. J. Supowit, 'Finding the Optimal Variable Ordering for Binary Decision Diagrams,' IEEE Transactions on Computers, Vol. C-39, No. 5, pp. 710-713, May 1990
  17. N. Ishiura, H. Sawada, and S. Yajima, 'Minimization of binary decision diagrams based on exchanges of variables,' International Conference on Computer Aided Design, pp. 472-475, November 1991
  18. R. Rudell, 'Dynamic variable ordering for ordered binary decision diagrams,' International Conference on Computer Aided Design, pp. 42-47, November 1993
  19. S. Panda, F. Somenzi, 'Who are the variable in your neighborhood,' International Conference on Computer Aided Design, pp. 74-77, November 1995
  20. C. Meinel and A. Slobodova, 'Speeding up variable reordering of OBDD,' in Int. Conf. Comput. Design, pp. 338-343, 1997
  21. R. Drechsler, W. Gunther, and F. Sornenzi, 'Using Lower Bounds During Dynamic BDD Minimization,' IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, Vol. 20, No. 1, January 2001
  22. W.S. Jung, J.E. Yang, and J.J. Ha, 'A New Method to Evaluate Alternate AC Power Source Effects in Multi-Unit Nuclear Power Plants,' Reliability Engineering and System Safety, Vol. 82, pp. 165-172, 2003 https://doi.org/10.1016/S0951-8320(03)00140-6

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