基于MDP的桥梁结构全寿命成本研究
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摘要
大型桥梁结构在服役期间由于受外界环境、荷载等因素的影响,性能不断退化。为了保障桥梁结构服役期间的安全与可靠,需对结构进行检测和维修。不恰当的维修决策将导致桥梁结构全寿命周期成本过高,或引起桥梁结构失效造成严重的经济损失,因此,开展桥梁结构的全寿命设计方法的研究具有重要的现实意义。本文基于马尔可夫决策过程(Markov Decision Processes,简记为MDP)对桥梁结构全寿命成本及桥梁结构的维修策略开展研究。本文主要内容如下:
首先,针对隐式极限状态方程且非线性程度较高时,响应面法求解可靠指标的误差大,而采用Monte Carlo抽样包括重要抽样方法,虽然精度高但计算效率低,对于结构有限元分析进行抽样几乎不能实现的状况,本文提出采用Kriging插值技术建立极限状态超曲面的代理模型,在验算点处应用Monte Carlo重要抽样方法对代理模型抽样进而求得结构的失效概率。结果表明:方法在隐式极限状态方程且非线性程度较高时精度良好,同时较Monte Carlo抽样或重要抽样效率高。
其次,建立了基于MDP的全寿命成本分析方法,采用值迭代法得到结构寿命周期最优维修策略。研究结构的自身转移矩阵、维修决策影响矩阵及状态综合转移矩阵的确定方法,并以此为基础建立桥梁结构性能退化的马尔可夫模型及桥梁结构全寿命最优维修决策模型。
最后,以桥梁结构全寿命总成本最小为目标,以可靠指标为约束建立桥梁结构全寿命总成本评价模型;采用基于MDP的全寿命分析方法确定一般桥梁结构的最优初始抗力和全寿命周期内的最优维修策略,研究初始抗力、抗力衰减规律、折现率、失效费用对桥梁结构全寿命周期内可靠指标、总成本及维修决策的影响规律。
Large bridges are deteriorating continuously during their service lives, because of external environment, load and other factors. Necessary maintenance and inspection should be taken on bridge structures for ensuring safety and reliability during service. However, irrelevancy maintenance policies may lead to high life-cycle cost or structural failure, cause enormous economic loss. Life-cycle design of bridge structure has great research significance. This dissertation focuses on investigation of life-cycle cost and maintenance policy of bridge structure by using a Markov Decision Processes-based (MDP) modeling approach. The main contents are as follows:
Firstly, a new method based on Kringing technology and Monte Carlo important sampling was proposed for structural reliability analysis. Kriging technology can be used to alleviate the computational burden as well as response surface method (RSM). However, surrogate model constructed by Kriging technology is more accurate than that constructed by RSM, especially when the limit state function is strong nonlinear. Monte Carlo important sampling was used to obtain the failure probability of this surrogate model. The results show that the proposed method has excellent accuracy and is more efficient than the direct Monte Carlo sampling and important sampling.
Then, a life cycle design method based on MDP was proposed and value iteration method was used to identify optimal maintenance policy. In order to build the Markov degradation model of bridge structures and determine the optimal maintence policy, the methods used to determine the self-transition matrix, decision-effect matrix and joint-transition matrix were researched.
Finally, holding the objective of minimization of expected life-cycle cost, the economic model of bridge life-cycle design was developed to satisfy the reliability index. A MDP modeling approach was used to identify optimal structural initial resistance and their associated maintenance policies. The effects of initial resistance, resistance deterioration, discount rate and failure loss on bridge life-cycle costs, reliability index and maintenance policy were discussed.
首先,针对隐式极限状态方程且非线性程度较高时,响应面法求解可靠指标的误差大,而采用Monte Carlo抽样包括重要抽样方法,虽然精度高但计算效率低,对于结构有限元分析进行抽样几乎不能实现的状况,本文提出采用Kriging插值技术建立极限状态超曲面的代理模型,在验算点处应用Monte Carlo重要抽样方法对代理模型抽样进而求得结构的失效概率。结果表明:方法在隐式极限状态方程且非线性程度较高时精度良好,同时较Monte Carlo抽样或重要抽样效率高。
其次,建立了基于MDP的全寿命成本分析方法,采用值迭代法得到结构寿命周期最优维修策略。研究结构的自身转移矩阵、维修决策影响矩阵及状态综合转移矩阵的确定方法,并以此为基础建立桥梁结构性能退化的马尔可夫模型及桥梁结构全寿命最优维修决策模型。
最后,以桥梁结构全寿命总成本最小为目标,以可靠指标为约束建立桥梁结构全寿命总成本评价模型;采用基于MDP的全寿命分析方法确定一般桥梁结构的最优初始抗力和全寿命周期内的最优维修策略,研究初始抗力、抗力衰减规律、折现率、失效费用对桥梁结构全寿命周期内可靠指标、总成本及维修决策的影响规律。
Large bridges are deteriorating continuously during their service lives, because of external environment, load and other factors. Necessary maintenance and inspection should be taken on bridge structures for ensuring safety and reliability during service. However, irrelevancy maintenance policies may lead to high life-cycle cost or structural failure, cause enormous economic loss. Life-cycle design of bridge structure has great research significance. This dissertation focuses on investigation of life-cycle cost and maintenance policy of bridge structure by using a Markov Decision Processes-based (MDP) modeling approach. The main contents are as follows:
Firstly, a new method based on Kringing technology and Monte Carlo important sampling was proposed for structural reliability analysis. Kriging technology can be used to alleviate the computational burden as well as response surface method (RSM). However, surrogate model constructed by Kriging technology is more accurate than that constructed by RSM, especially when the limit state function is strong nonlinear. Monte Carlo important sampling was used to obtain the failure probability of this surrogate model. The results show that the proposed method has excellent accuracy and is more efficient than the direct Monte Carlo sampling and important sampling.
Then, a life cycle design method based on MDP was proposed and value iteration method was used to identify optimal maintenance policy. In order to build the Markov degradation model of bridge structures and determine the optimal maintence policy, the methods used to determine the self-transition matrix, decision-effect matrix and joint-transition matrix were researched.
Finally, holding the objective of minimization of expected life-cycle cost, the economic model of bridge life-cycle design was developed to satisfy the reliability index. A MDP modeling approach was used to identify optimal structural initial resistance and their associated maintenance policies. The effects of initial resistance, resistance deterioration, discount rate and failure loss on bridge life-cycle costs, reliability index and maintenance policy were discussed.
引文
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2秦权.基于时变可靠度的桥梁检测与维修方案优化.公路.2002, 9(9):17~25
3王光远.结构软设计理论初探.哈尔滨:哈尔滨建筑工程学院, 1987
4王光远.工程软设计理论.北京:科学出版社, 1992
5 H. Bonstedt. Life Cycle Cost Analysis for Bridges: In Search of Better Investment and Engineering Decisions. http://www.pcap.org/presentations, 2003
6 E. Gabler. Transportation Asset Management: The Role of Engineering Economic Analysis. Faderal Highway Administration. 2003
7 M. Hastak, A. Mirniran, R. Deepak. A Framework for Life-Cycle Cost Assessment of Composites: in Construction. Journal of Reinforced Plastics and Composites. 2003, 22(15): 1409~1422
8 R.F. Chandler. Life-Cycle Cost Model for Evaluating the Sustainability of Bridge Decks: A Comparison of Conventional Concrete Joints and Engineered Cementitious Composite Link Slabs. University of Michigan, Report No. CSS04-06, 2004
9李惠,欧进萍.斜拉桥结构健康监测系统的设计与实现(I):系统设计,土木工程学报, 2006, 39(4): 29~44
10李惠,欧进萍.斜拉桥结构健康监测系统的设计与实现(II):系统实现,土木工程学报, 2006,.39(4): 45~53
11 D,M, Frangopol, K.Y. Lin. Life-cycle cost design of deteriorating structures. Journal of Structural Engineering. 1997, 36(10):1390-1401
12 M.A. Hassanain, R.E. Loov. Cost optimization of concrete bridge infrastructure. Canadian Journal of Civil Engineering. 2003, 30(5): 841~849
13 A. Miyamoto, K. Kawamura, H. Nakamura. Bridge management system and maintenance optimization for existing bridge. Computer-aided Civil and Infrastructure Engineering. 2005
14 Y.J. Lee, L.M. Chang. Rehabilitation decision analysis and life-cycle costingof the infrastructure system. Construction Research. 2003
15 J.S. Kong, D.M. Frangopol. Life-cycle reliability-based maintenance cost optimization of deteriorating structures with emphasis on bridges. Journal of Structural Engineering. 2003, 129(6):818-828
16 J.S. Kong, D.M. Frangopol. Cost-reliability interaction in Life-cycle cost optimization of deteriorating structures. Journal of Structural Engineering. 2004, 130(11):1704-1712
17 Y. Mori, B.R. Ellingwood. Maintaining Reliability of Concrete Structures. II:Optimization Inspection/Repair. Journal of Structural Engineering. 1994, 120(3):846-862
18 T.S. William, M.G. Douglas. Models for Bridge Maintenance Management. Journal of Transportation Engineering. 1994, 120(1): 37~51
19 Zongwei Tao, B.C. Ross, J. Hugh Ellis. Reliability-based bridge design and life cycle management with Markov decision processes. Structural Safety. 1994, 16:111~132
20 G Morcus. Performance Prediction of Bridge Deck Systems Using Markov Chains. ASCE, 2006.
21贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(1).建筑结构学报. 2002, 23(4): 2~9
22 A.M. Hasofer, N.C. Lind. Exact and Invariant Second-moment Format. Journal of Engineering Mechanics Division. ASCE, 1974, 100(1): 111~121
23赵国藩,金伟良,贡金鑫.结构可靠度理论.北京:中国建筑工业出版社. 2000
24 K. Breitung. Asymptotic Approximations for Multinormal Integrals. Journal of Engineering Mechanics. ASCE, 1984, 110(3): 357~366
25 R.Y. Rubinstein, D.P. Kroese. Simulation and the Monte-Carlo Method. 2nd edition. New York: Wiley, 2007
26 G. Augusti, A. Baratta, Casciati F. Probabilistic Methods in Structural Engineering. London: Chapman and Hall, 1984
27中国科学院计算中心概率统计组.概率统计计算.北京:科学出版社, 1979
28中华人民共和国国家标准.港口工程结构可靠度设计统计标准(GB 50158-92).北京:中国计划出版社, 1992
29 Y. Ben-Haim. A Non-Probabilistic Concept of Reliability. Structural Safety. 1994, 14(4): 227~245
30 Y. Ben-Haim. A Non-Probabilistic Measure of Reliability of Linear Systems Based on Expansion of Convex Models. Structural Safety. 1995, 17(2): 91~109
31 Y. Ben-Haim. Robust Reliability in The Mechanical Sciences. Berlin: Springer-Verlag, 1996
32郭书祥,吕震宙.结构非概率可靠性方法和概率可靠性方法的比较.应用力学学报. 2003, 20(3): 107~110
33中华人民共和国国家标准.工程结构可靠度设计统一标准(GB50153-92).北京:中国计划出版社. 1992
34 M.R. Rajashekhar, B.R. Ellingwood. A New Look at the Response Surface Approach for Reliability Analysis. Structrual Safety. 1993, 12: 205~220
35 S.H. Kim, S.W. Na. Response Surface Method Using Vector Projected Sampling Points. Structural Safety. 1997, 19(1): 3~19
36 X.L Guan, R.E. Melchers. Effect of Response Surface Parameter Variation on Structural Reliability Estimates. Structural Safety. 2001, 23: 429~444
37 B.D. Youn, K.K Choi. A New Response Surface Methodology for Reliability-based Design Optimization. Computers and Structures. 2004, 82: 241~256
38 L. Faravelli. A Response Surface Approach for Reliability Analysis. Journal of Engineering Mechanics, ASCE. 1989, 115(12): 2763~2781
39 C.G. Bucher, U. Bourgund. A Fast and Efficient Response Surface Approach for Structural Reliability Problems. Structural Safety. 1990, 7: 57~66
40 G.I. Schu?ller, C.G. Bucher, U. Bourgund, W. Ouypornprasert. On Efficient Computational Schemes to Calculate Structural Failure Probabilities. Probabilistic Engineering Mechanics 1989, 4(1): 10~18
41 Y.W. Liu, F. Moses. A Sequential Response Surface Method and Its Application in the Reliability Analysis of Aircraft Structrual Systems. Structural Safety. 1994, 16: 39~46
42庄镇泉.神经网络与神经计算机.北京:科学出版社, 1994
43 P.D. Wasserman. Advanced Methods in Neural Computing. New York: Van Nostrand Reinhold, 1993
44 K.I. Diamantaras. Principal Component Neural Networks-Theory and Appliaction. A Wiley-Interscience Publication, John Wiley & Sons, Inc., 1996
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