A Cost Efficient Algorithm for System Reliability Calculation with Aleatory and Epistemic Uncertainties Using Evidence Theory

Bin Suo(1*), Chao Zeng(2), Yong-Sheng Cheng(3), Jun Li(4)

(1) Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang, China, China
(2) Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang, China, China
(3) Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang, China, China
(4) Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang, China, China
(*) Corresponding author

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In reliability calculation of complex system, it is always in the situation that experimental data is inadequate, or information is not complete, which makes the system not only involving aleotory uncertainty, but also epistemic uncertainty. To reduce the cost of reliability calculation, an effective approach with evidence theory is developed. In this approach, the mean of belief and plausibility function is taken as the approximation of system reliability. The discretization methods for uncertain parameters are discussed when system involves only aleatory uncertainty, and involves aleatory and epistemic uncertainties simultaneously, respectively. Algorithms for belief and plausibility function evaluation are proposed for monotonic and non-monotonic system. Four numerical examples with different conditions are studied. Simulation results show that, the proposed method is much more effective than Monte Carlo method without sacrificing the accuracy of resulting reliability, and is a general method which is applicable for various systems with different types of information
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Reliability Calculation; Evidence Theory; Aleatory Uncertainty; Epistemic Uncertainty; Cost Efficient Algorithm

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I. H. M. Abdallah, F. H. Waleed, A. A. Fayez, Uncertainty and reliability analysis applied to slope stability, Structural Safety, vol.22 n. 2, June 2000, pp. 161-187.

G. Q. Li, J. J. Li, A semi-analytical simulation method for reliability assessments of structural systems, Reliability Engineering & System Safety, vol. 78 n. 3, December 2002, pp. 275-281.

J. Deng, D. S. Gu, X. B. Li, Z. Q. Yue, Structural reliability analysis for implicit performance functions using artificial neural network, Structural Safety, vol. 27 n. 1, January 2005, pp. 25-48.

S. Carbillet, F. Richard, L. Boubakar, Reliability indicator for layered composites with strongly non-linear behavior. Composites Science & Technology, vol. 69 n. 1, January 2009, pp. 81-87.

F. D. N. Mealier, L. Guillaumat, P. Arnoux, Reliability assessment of locking systems, Probabilistic Engineering Mechanics, vol. 25 n. 1, January 2010, pp. 67-74.

I. Kaymaz, C. A. McMahon, A response surface method based on weighted regression for structural reliability analysis, Probabilistic Engineering Mechanics, vol. 20 n. 1, May 2005, pp. 11-17.

S. C. Kang, H. M. Koh, J. F. Choo, An efficient response surface method using moving least squares approximation for structural reliability analysis. Probabilistic Engineering Mechanics, vol. 25 n. 4, October 2010, pp. 365-371.

M. Daoud, Q. H. Mahmoud, Monte Carlo simulation-based algorithms for estimating the reliability of mobile agent-based systems, Journal of Network and Computer Applications, vol. 31 n. 1, January 2008, pp. 19-31.

Xu, S.-Y., Chen, M., Ran, L., Probabilistic approach to reliability assessment of electric power system containing distributed generation, (2012) International Review of Electrical Engineering (IREE), 7 (1), pp. 3478-3485.

C. Luca, V. Paolo, Monte Carlo importance sampling optimization for system reliability applications, Annals of Nuclear Energy, vol. 31 n. 9, June 2004, pp. 1005-1025.

W. I. Guido, L. Tony, Efficient estimation and stratified sampling, Journal of Econometrics, vol. 74 n. 2, October 1996, pp. 289-318.

F. Zhang, Z.-Z. Lu, L.-J. Cui, S.-F. Song, Reliability Sensitivity Algorithm Based on Stratified Importance Sampling Method for Multiple Failure Modes Systems, Chinese Journal of Aeronautics, vol. 23 n. 6, March 2010, pp. 660-669.

W. L. Oberkampf, S. M. DeLand, B. M. Rutherford, Estimation of Total Uncertainty in Modeling and Simulation. Sandia National Laboratory, Albuquerque, SAND2000-0824, 2000.

J. C. Helton, Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty, Journal of Statistical Computation and Simulation, vol. 57 n. 3, March 1997, pp. 3-76.

W. L. Oberkampf, S.M. DeLand, B.M. Rutherford, K.V. Diegert, K. F. Alvin, Error and uncertainty in modeling and simulation, Reliability Engineering and System Safety, vol. 75 n. 3, March 2002, pp. 333-357.

A. P. Dempster, Upper and lower probabilities induced by a multi valued mapping, Annals Math Statist, vol. 38 n. 2, February 1967, pp. 325-339.

G. A. Shafer, Mathematical Theory of Evidence (Princeton University Press, 1976)

J. K. George, M. S. Richard, On measuring uncertainty and uncertainty-based information: recent development, Annals of Mathematics and Artificial Intelligence, vol. 32 n. 1-4, August 2001, pp. 5-33.

J. C. Helton, J. D. Johnson, W.L. Oberkampf, An exploration of alternative approaches to the representation of uncertainty in model predictions, Reliability Engineering and System Safety, vol. 85 n. 1-3, September 2004, pp. 39-71.

H. R. Bae, R. V. Grandhi, R. A. Canfield, Epistemic uncertainty quantification techniques including evidence theory for large-scale structures, Computers and Structures, vol. 82 n. 13-14, May 2004, pp. 1101-1112.

K. Sentz, S. Ferson, Combination of evidence in Dempster-Shafer theory, Sandia National Laboratories, Albuquerque, SAND2002-0835, 2002.

F. Tonon, Using random set theory to propagate epistemic uncertainty through a mechanical system, Reliability Engineering and System Safety, vol. 85 n. 1-3, June 2004, pp. 169-181.

W. M. Dong, H. C. Shah, Vertex Method for Computing Functions of Fuzzy Variable, Fuzzy Sets and Systems, vol. 24 n. 1, October 1987, pp. 65-78.

M. Hussaarts, J. K. Vrijling, H. D Looff, C. Blonk, The probabilistic optimization of revetment on the dikes along the Frisian coast, Proceedings of Coastal Structures ~ASCE PCS 2000~, March 17-19, 2005, Balkema, Rotterdam.

J. Hall, J. Lawry, Imprecise probabilities of engineering system failure from random and fuzzy set reliability analysis. Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications ~ ISIPTA ’01 ~, October 24-27, 2001, Ithaca, NY, USA.

Du, Y., Wang, K., Duan, W., Recognition method for key knowledge subjects in knowledge network, (2012) International Review on Computers and Software (IRECOS), 7 (5), pp. 2298-2307.


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