基于自适应MCMC和子集模拟的非能动系统热工水力可靠性评估
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摘要
基于修正Metropolis-Hastings(MMH)算法的子集模拟(SS)方法在较低失效率水平下候选样本接受率降低、失效率估计误差增大、稳健性较差。为进一步提高SS用于反应堆非能动系统热工水力可靠性评估的精度、效率和稳健性,引入一种基于自适应条件采样(aCS)的马尔可夫链蒙特卡罗(MCMC)方法,提出了一种基于自适应MCMC和SS的非能动系统热工水力可靠性评估方法。以某型核动力装置二次侧非能动余热排出试验系统为例,给出了基于aCS的子集模拟(aCS-SS)与基于MMH的子集模拟(MMH-SS)在不同失效率水平下的性能比较。计算结果表明:较低失效率水平下aCS-SS能更好地使候选样本接受率在目标值附近保持稳定,失效率估计的精度和稳健性均高于MMH-SS。
For the commonly used subset simulation(SS) method based on modified Metropolis-Hastings(MMH) algorithm, the acceptance rate of candidate samples decreases and the error of failure probability estimate increases at lower failure probability level, and the algorithm's robustness is also poor. For the accurate, efficient and robust evaluation of thermal-hydraulic reliability of passive system using SS, a new Markov chain Monte Carlo(MCMC) method based on adaptive conditional sampling(aCS) was introduced and a reliability evaluation method based on adaptive MCMC and SS was proposed. Taking the experimental facility of a secondary side passive residual heat removal system as an example, the performance comparison of SS based on MMH(MMH-SS) and SS based on aCS(aCS-SS) was given at different failure probability levels. Calculation results show that, under lower failure rate level, aCS-SS can make the acceptance rate of candidate samples stably near the target value, and accuracy and robustness of the failure probability estimate are higher than those of MMH-SS.
For the commonly used subset simulation(SS) method based on modified Metropolis-Hastings(MMH) algorithm, the acceptance rate of candidate samples decreases and the error of failure probability estimate increases at lower failure probability level, and the algorithm's robustness is also poor. For the accurate, efficient and robust evaluation of thermal-hydraulic reliability of passive system using SS, a new Markov chain Monte Carlo(MCMC) method based on adaptive conditional sampling(aCS) was introduced and a reliability evaluation method based on adaptive MCMC and SS was proposed. Taking the experimental facility of a secondary side passive residual heat removal system as an example, the performance comparison of SS based on MMH(MMH-SS) and SS based on aCS(aCS-SS) was given at different failure probability levels. Calculation results show that, under lower failure rate level, aCS-SS can make the acceptance rate of candidate samples stably near the target value, and accuracy and robustness of the failure probability estimate are higher than those of MMH-SS.
引文
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[13] AU S K. On MCMC algorithms for subset simulation[J]. Probabilistic Engineering Mechanics, 2016, 43: 117-120.
[14] CHIB S, GREENBERG E. Understanding the Metropolis-Hastings algorithm[J]. American Statistician, 1995, 49(4): 327-335.
[15] ZUEY K M, BECK J L, AU S K, et al. Bayesian post-processor and other enhancements of subset simulation for estimating failure probabilities in high dimensions[J]. Computers and Structures, 2012, 92-93(3): 283-293.
[16] 于雷,谢海燕,蔡章生. 非能动余热排出系统数学模型研究与运行特性分析[J]. 核科学与工程,2008,28(3):233-243. YU Lei, XIE Haiyan, CAI Zhangsheng. Mathematic model research and operating characteristic analysis of passive residual heat removal system[J]. Chinese Journal of Nuclear Science and Engineering, 2008, 28(3): 233-243(in Chinese).
[17] 饶彧先,于雷,傅晟威. PRS换热器蒸汽凝结换热模型研究[J]. 核动力工程,2016,37(1):34-37. RAO Yuxian, YU Lei, FU Shengwei. Study on steam condensation model of a PRS heat exchanger[J]. Nuclear Power Engineering, 2016, 37(1): 34-37(in Chinese).
[18] 蒋立志,蔡琦,张永发. 核动力装置非能动系统可靠性及参数敏感性分析[J]. 核动力工程,2017,38(5):91-95. JIANG Lizhi, CAI Qi, ZHANG Yongfa. Reliability and parameter sensitivity analysis of passive system in nuclear power plants[J]. Nuclear Power Engineering, 2017, 38(5): 91-95(in Chinese).
[2] MICHEL M, PIGNATEL J F, SAIGNES P, et al. Methodology for the reliability evaluation of a passive system and its integration into a probabilistic safety assessment[J]. Nuclear Engineering and Design, 2005, 235(24): 2 612-2 631.
[3] AU S K, BECK J L. A new adaptive importance sampling scheme for reliability calculations[J]. Structural Safety, 1999, 21: 135-158.
[4] 王宝生,王冬青,姜晶,等. 基于自适应重要抽样法非能动系统功能故障概率评估[J]. 核动力工程,2012,33(2):30-36. WANG Baosheng, WANG Dongqing, JIANG Jing, et al. Estimation of functional failure probability of passive systems based on adaptive importance sampling method[J]. Nuclear Power Engineering, 2012, 33(2): 30-36(in Chinese).
[5] AU S K, BECK J L. Importance sampling in high dimensions[J]. Structural Safety, 2003, 25: 139-163.
[6] AU S K, BECK J L. Estimation of small failure probabilities in high dimensions by subset simulation[J]. Probabilistic Engineering Mechanics, 2001, 16(4): 263-277.
[7] ZIO E, PEDRONI N. Estimation of the functional failure probability of a thermal-hydraulic passive system by subset simulation[J]. Nuclear Engineering and Design, 2009, 239(3): 580-599.
[8] 王冬青,王宝生,姜晶,等. 基于子集模拟法非能动系统功能故障概率评估[J]. 原子能科学技术,2012,46(1):43-50. WANG Dongqing, WANG Baosheng, JIANG Jing, et al. Estimation of functional failure probability of passive systems based on subset simulation method[J]. Atomic Energy Science and Technology, 2012, 46(1): 43-50(in Chinese).
[9] AU S K, BECK J L. A new adaptive importance sampling scheme for reliability calculations[J]. Structural Safety, 1999, 21: 135-158.
[10] ROBERTS G O, ROSENTHAL J S. Optimal scaling for various Metropolis-Hastings algorithms[J]. Statistical Science, 2001, 16(4): 351-367.
[11] ANDRIEU C, THOMS J. A tutorial on adaptive MCMC[J]. Statistics and Computing, 2008, 18(4): 343-373.
[12] PAPAIOANNOU I, BETZ W, ZWIRGLMAIER K, et al. MCMC algorithms for subset simulation[J]. Probabilistic Engineering Mechanics, 2015, 41: 89-103.
[13] AU S K. On MCMC algorithms for subset simulation[J]. Probabilistic Engineering Mechanics, 2016, 43: 117-120.
[14] CHIB S, GREENBERG E. Understanding the Metropolis-Hastings algorithm[J]. American Statistician, 1995, 49(4): 327-335.
[15] ZUEY K M, BECK J L, AU S K, et al. Bayesian post-processor and other enhancements of subset simulation for estimating failure probabilities in high dimensions[J]. Computers and Structures, 2012, 92-93(3): 283-293.
[16] 于雷,谢海燕,蔡章生. 非能动余热排出系统数学模型研究与运行特性分析[J]. 核科学与工程,2008,28(3):233-243. YU Lei, XIE Haiyan, CAI Zhangsheng. Mathematic model research and operating characteristic analysis of passive residual heat removal system[J]. Chinese Journal of Nuclear Science and Engineering, 2008, 28(3): 233-243(in Chinese).
[17] 饶彧先,于雷,傅晟威. PRS换热器蒸汽凝结换热模型研究[J]. 核动力工程,2016,37(1):34-37. RAO Yuxian, YU Lei, FU Shengwei. Study on steam condensation model of a PRS heat exchanger[J]. Nuclear Power Engineering, 2016, 37(1): 34-37(in Chinese).
[18] 蒋立志,蔡琦,张永发. 核动力装置非能动系统可靠性及参数敏感性分析[J]. 核动力工程,2017,38(5):91-95. JIANG Lizhi, CAI Qi, ZHANG Yongfa. Reliability and parameter sensitivity analysis of passive system in nuclear power plants[J]. Nuclear Power Engineering, 2017, 38(5): 91-95(in Chinese).
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