SUN Hong-bin, WU Zi-yan, LIU Shu-kui. A Dynamic Bayesian Network Model for Structural Time-Dependent Reliability Analysis of Resistance Deterioration[J]. Applied Mathematics and Mechanics, 2014, 35(1): 102-110. doi: 10.3879/j.issn.1000-0887.2014.01.011
 Citation: SUN Hong-bin, WU Zi-yan, LIU Shu-kui. A Dynamic Bayesian Network Model for Structural Time-Dependent Reliability Analysis of Resistance Deterioration[J]. Applied Mathematics and Mechanics, 2014, 35(1): 102-110.

# A Dynamic Bayesian Network Model for Structural Time-Dependent Reliability Analysis of Resistance Deterioration

##### doi: 10.3879/j.issn.1000-0887.2014.01.011
Funds:  The National Natural Science Foundation of China（51278420）
• Rev Recd Date: 2013-11-01
• Publish Date: 2014-01-15
• A dynamic Bayesian network (DBN) model was proposed for timedependent reliability analysis of structures in deterioration. The structural resistance deterioration was modeled as a gamma process while the loads as random variables. The stochastic deterioration process was discretized in time domain as deterioration models. A DBN was established and comprised of the reliability model, deterioration model and observation model. Node elimination algorithm and discretization were applied to modify the DBN into a network with only discrete variables. Exact inferences with the DBN were presented to estimate the 3 structural states at present (filtering), in the future (prediction) and in the past (smoothing), respectively. The structural timedependent reliability was updated with the reestimated deterioration model when measurements were available. The proposed model was validated through the timedependent reliability analysis of a onebay example frame in resistance deterioration.
•  [1] 吕大刚, 樊学平, 蒋伟. 结构时变可靠度方法的对比分析研究[C]//全国工程结构设计安全与可持续发展研讨会. 宁波, 2010. (Lü Da-gang, FAN Xue-ping, JIANG Wei. Structural time-dependent reliability method research[C]// Seminar of National Engineering Structure Design Safety and Sustainable Development.Ningbo, 2010.(in Chinese)) [2] 王正, 谢里阳. 不确定性载荷作用下的零件时变可靠性模型[J]. 航空学报, 2009,30(7): 1243-1247.(WANG Zheng, XIE Li-yang. Time-variant reliability model of components under uncertain loads[J]. Acta Aeronautica et Astronautica Sinica,2009,30(7): 1243-1247.(in Chinese)) [3] Stewart M G, Mullard J A. Spatial time-dependent reliability analysis of corrosion damage and the timing of first repair for RC structures[J]. Engineering Structure,2007,29(7): 1457-1464. [4] Kuniewski S P, Van der Weide J A M, Van Noortwijk J M. Sampling inspection for the evaluation of time-dependent reliability of deteriorating systems under imperfect defect detection[J]. Reliability Engineering & System Safety,2009,94(9): 1480-1490. [5] Liu M, Frangopol D M. Time-dependent bridge network reliability: novel approach[J]. Journal of Structural Engineering,2005,131(2): 329-337. [6] Van Noortwijk J M, Van der Weide J A M, Kallen M J, Pandey M D. Gamma processes and peaks-over-threshold distributions for time-dependent reliability[J]. Reliability Engineering & System Safety,2007,92(12): 1651-1658. [7] 张连文, 郭海鹏. 贝叶斯网引论[M]. 北京: 科学出版社, 2006.(ZHANG Lian-wen, GUO Hai-peng. Introduction to Bayesian Networks [M]. Beijing: Science Press, 2006.(in Chinese)) [8] Jensen F V, Nielsen T D. Bayesian Networks and Decision Graphs [M]. 2nd ed. Berlin: Springer, 2007. [9] Abdel-Hameed M. A gamma wear process[J]. IEEE Transactions on Reliability,1975,24(2): 152-153. [10] Ellingwood B R, Mori Y. Probabilistic methods for condition assessment and life prediction of concrete structures in nuclear power plants[J]. Nuclear Engineering and Design,1993,142(2/3): 155-166. [11] Shachter R D. Evaluating influence diagrams[J]. Operations Research,1986,34(6): 871-882. [12] Straub D. Stochastic modeling of deterioration processes through dynamic Bayesian networks[J]. Journal of Engineering Mechanics,2009,135(10): 1089-1099. [13] Der Kiureghian A. First- and second-order reliability methods[C]//Nikolaidis E, Ghiocel D M, Singhal S, eds. Chap14. Engineering Design Reliability Handbook.Boca Raton, Florida: CRC Press, 2005.

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