Uncertainty estimation of reliability redundancy in complex systems based on the Cross-Entropy method

다국어 초록 (Multilingual Abstract)

The article aims to estimate the uncertainty of possible failure events of redundancy systems based on the crossentropy (CE) method. Failure events of subsystems and components always result in the incomplete or complete failure of engineering systems, yet optimal condition monitoring of a complex system is heavily dependent on the accuracy analysis of all the failure events of subsystems and components and their interaction effects. The CE method is a versatile tool for estimating probabilities of rare events in complex systems with the least bias beyond conditional constraints. In this paper we introduce the CE method for analyzing the system reliability with the highest uncertainty among all possibilities satisfying supplied moment constraints, and developed numerical CE algorithms capable of estimating the

uncertainty of failure modes in an M-dimensional redundancy system domain with moment constraints of order up to N. A general computational framework of event estimation and condition monitoring of redundancy systems is illustrated in which the Monte Carlo simulations and CE optimization algorithms are combined. Numerical results indicate potential improvements in the measure of the uncertainty of redundancy systems that would lead to the best-fit analysis of all the complete or incomplete failure events.

참고문헌 (Reference)

1 C. K. Mechefske, "Using fuzzy linguistics to select optimum maintenance and condition monitoring strategies" 17 (17): 305-316, 2003

2 A. D. Kiureghian, "The geometry of random vibrations and solutions by FORM and SORM" 15 (15): 81-90, 2000

3 R. Y. Rubinstein, "The crossentropy method: a united approach to combinatorial optimization, Monte-Carlo simulation and machine learning" Springer 2004

4 R. Y. Rubinstein, "The Cross-Entropy Method for Continuous Multi-Extremal Optimization" 8 (8): 383-407, 2006

5 R. Y. Rubinstein, "The Cross-Entropy Method for Combinatorial and Continuous Optimization" 1 (1): 127-190, 1999

6 H. B. Liu, "Target Setting and Cascading for Design of Complex Engineering Systems under Uncertainty" Northwestern University 2006

7 I. Kopylov, "Subjective probabilities on “small” domains" 133 (133): 236-265, 2007

8 G. Levitin, "Structure optimization of power system with bridge topology" 45 (45): 201-208, 1998

9 Y. M. Zhan, "Robust detection of gearbox deterioration using compromised autoregressive modeling and Kolmogorov-Smirnov test statistic - Part II: Experiment and application" 21 (21): 1988-2011, 2007

10 P. Robert, "Risk analysis using stochastic reliability methods applied to two cases of deterministic water quality models" 34 (34): 153-170, 2000

11 S. K. Au, "Reliability-based design sensitivity by efficient simulation" 83 (83): 1048-1061, 2005

12 S. K. Au, "Reliability of uncertain dynamical systems with multiple design points" 21 (21): 113-133, 1999

13 K. Žiha, "Redundancy and robustness of systems of events" 15 (15): 347-357, 2000

14 D. Lieber, "Rare Events Estimation Via Cross- Entropy and Importance Sampling" 1999

15 D. Lieber, "Quick Estimation of Rare Events in Stochastic Networks" 46 (46): 254-265, 1997

16 R. Y. Rubinstein, "Optimization of Computer Simulation Models with Rare Events" 99 (99): 89-112, 1997

17 D. P. Kroese, "Network reliability optimization via the Cross-Entropy method" 56 (56): 275-287, 2007

18 N. F. G. Martin, "Mathematical Theory of Entropy" Addison-Wesley Publishing Company 1981

19 J. Ching, "Local estimation of failure probability function and its confidence interval with maximum entropy principle" 22 (22): 39-49, 2004

20 G. Levitin, "Joint redundancy and maintenance optimization for multistate series - parallel systems" 64 (64): 33-42, 1999

21 J. Ching, "Hybrid subset simulation method for reliability estimation of dynamic systems subject to stochastic excitations" 20 (20): 199-214, 2005

22 J. Lin, "Extraction of periodic components for gearbox diagnosis combining wavelet filtering and cyclostationary analysis" 126 : 449-451, 2004

23 K. Žiha, "Event oriented analysis of series structural systems" 23 (23): 1-29, 2001

24 S. K. Au, "Estimation of small failure probability in high dimensions by subset simulation" 16 (16): 263-277, 2001

25 J. D. Fast, "Entropy: The significance of the concept of entropy and its applications in science and technology" Philips Technical Library 1962

26 B. MÖller, "Engineering computation under uncertainty-Capabilities of non-traditional models" 86 (86): 1024-1041, 2008

27 O. Moralesa, "Eliciting conditional and unconditional rank correlations from conditional probabilities" 93 : 699-710, 2008

28 R. Y. Rubinstein, "Combinatorial optimization, cross entropy, ants and rare events, Stochastic Optimization: Algorithm and Applications" Kluwer 2001

29 H. J. Pradlwarter, "Assessment of low probability events of dynamical systems by controlled Monte Carlo simulation" 14 (14): 213-227, 1999

30 E. Y. Chow, "Analytical Redundancy and the Design of Robust Failure Detection Systems" 29 (29): 603-614, 1984

31 P. T. D. Boer, "A tutorial on the cross-entropy method" 134 : 19-67, 2005

32 C. C. Lin, "A neural network application for reliability modeling and condition-based predictive maintenance" 25 (25): 174-179, 2005

33 D. Dubois, "A definition of subjective possibility" 48 (48): 352-364, 2008

34 Tae Won Lee, "A Study for Robustness of Objective Function and Constraints in Robust Design Optimization" 대한기계학회 20 (20): 1662-1669, 2006

35 M. Kalsi, "A Comprehensive robust design approach for decision tradeoffs in complex systems design" 123 (123): 1-10, 2001