-
摘要:
为了分析在不确定性元器件失效率影响条件下动态系统的失效问题，提出了满足工作时间要求的系统失效概率和满足失效概率限制的系统正常工作时间的分析方法。同时，为了研究元器件失效率对动态系统失效的影响程度，提出了元器件失效率对系统失效概率以及系统正常工作时间不确定性影响的重要性分析方法，建立了元器件失效率对系统失效概率和系统正常工作时间方差贡献的重要性测度指标。首先给出了指标求解的直接蒙特卡罗方法，然后采用基于分数矩的极大熵方法来高效估计系统失效的概率密度函数，采用乘法降维积分建立了2种重要性测度指标的高效解法。阀门控制系统和民用飞机电液舵机系统的算例结果表明所提方法的合理性和算法的高效性。
Abstract:In order to study the failure of dynamic system when the failure rates of components are uncertain, a new method is proposed to analyze the system failure probability when function time is given and function time when the threshold of failure probability is shown in system. Meanwhile, a new importance measure technique is developed to estimate the impact of components' failure rates on system failure probability and function time in dynamic system. In this paper, the Monte Carlo procedure is given to solve the proposed indices. The fractional moments-based maximum entropy method is used to obtain failure probability density function in system efficiently. An efficient technique with multiplication dimensionality reduction is developed to estimate two importance measure indices. Valve control system and civil aircraft electro-hydraulic actuator system are presented to illustrate the rationality and efficiency of the proposed method.
-
图 1 系统失效概率随系统工作时间变化曲线
Figure 1. Variation of system failure probability with system function time
图 3 阀门控制系统失效概率的概率密度曲线
Figure 3. Probability density curves of failure probability of valve control system
图 4 阀门控制系统工作时间的概率密度曲线
Figure 4. Probability density curves of function time of valve control system
图 7 飞机电液舵机系统失效概率的概率密度曲线
Figure 7. Probability density curves of failure probability of aircraft electro-hydraulic actuator system
图 8 飞机电液舵机系统工作时间的概率密度曲线
Figure 8. Probability density curves of function time of aircraft electro-hydraulic actuator system
表 1 阀门控制系统元器件失效率分布参数
Table 1. Distribution parameters of components' failure rates in valve control system
λi 均值/10-2 方差/10-5 λ1 4 2 λ2 2 1 λ3 1 0.5 
下载: 导出CSV
表 2 阀门控制系统失效概率的概率密度函数特征
Table 2. Characteristics of probability density function about failure probability of valve control system
方法 μPf σPf 置信区间(95%) 计算量 MCS-KDE 0.489 3 0.045 1 [0.401 2, 0.578 0] 1×103 MaxEnt-FMD 0.489 4 0.045 6 [0.400 0, 0.578 8] 16
下载: 导出CSV
表 3 基于系统失效概率的元器件失效率重要性测度指标
Table 3. Importance measure indices of components' failure rates based on failure probability of system
方法 λ1 λ2 λ3 计算量 MCS 0.090 2 0.353 1 0.569 0 4×106 本文方法 0.089 8 0.354 0 0.567 1 181
下载: 导出CSV
表 4 阀门控制系统正常工作时间概率密度函数特征
Table 4. Characteristics of probability density function about function time of valve control system
方法 μt σt 置信区间(95%) 计算量 MCS-KDE 13.058 6 1.424 8 [10.266 0, 15.851 2] 142 172 MaxEnt-FMD 13.010 3 1.511 5 [10.047 8, 15.972 8] 2 279
下载: 导出CSV
表 5 基于系统正常工作时间的元器件失效率重要性测度指标
Table 5. Importance measure indices of components' failure rates based on function time of system
方法 λ1 λ2 λ3 计算量 MCS 0.060 2 0.201 2 0.786 5 2.36×108 本文方法 0.067 9 0.189 9 0.780 3 26 656
下载: 导出CSV
表 6 民用飞机电液舵机系统底事件失效率分布参数
Table 6. Distribution parameters of basic events' failure rates in civil aircraft electro-hydraulic actuator system
λi 均值/10-7 方差/10-14 λ1 3.5 2 λ2 2 1 λ3 3 1.5 λ4 10 5 λ5 6 5 λ6 2.5 1
下载: 导出CSV
表 7 民用飞机电液舵机系统失效概率的概率密度函数特征
Table 7. Characteristics of probability density function about failure probabilityof civil aircraft electro-hydraulic actuator system
方法 μPf σPf 置信区间(95%) 计算量 MCS-KDE 0.068 1 0.004 0 [0.060 3, 0.075 9] 1×105 MaxEnt-FMD 0.068 1 0.003 9 [0.060 5, 0.075 7] 31
下载: 导出CSV
表 8 底事件失效率重要性测度指标(t0=5 000 h)
Table 8. Importance measure indices of failure rates of basic events (t0=5 000 h)
方法 λ1 λ2 λ3 λ4 λ5 λ6 计算量 MCS 0.068 2 0.032 3 0.050 2 0.165 2 0.655 1 0.031 5 7×107 本文方法 0.065 2 0.032 6 0.048 9 0.162 9 0.651 7 0.032 0 811
下载: 导出CSV
表 9 民用飞机电液舵机系统正常工作时间的概率密度函数特征
Table 9. Characteristics of probability density function about function time of civil aircraft electro-hydraulic actuator system
方法 μt σt 置信区间(95%) 计算次数 MCS-KDE 3 111.78 207.21 [2 705.65, 3 517.91] 132 178 MaxEnt-FMD 3 115.26 203.46 [2 716.48, 3 514.04] 5 894
下载: 导出CSV
表 10 底事件失效率重要性测度指标(Pf0=0.01)
Table 10. Importance measure indices of failure rates of basic events (Pf0=0.01)
方法 λ1 λ2 λ3 λ4 λ5 λ6 计算量 MCS 0.040 8 0.031 2 0.059 2 0.145 2 0.621 1 0.031 5 5.97×109 本文方法 0.043 8 0.029 6 0.058 6 0.147 1 0.614 4 0.029 7 42 851
下载: 导出CSV
-
[1] PARRY G W, WINTER P W.Characterization and evaluation of uncertainty in probabilistic risk analysis.Nuclear Safety, 1981, 22(1):251-263. https://www.mendeley.com/research-papers/characterization-evaluation-uncertainty-probabilistic-risk-analysis/ [2] HOFFMAN F O, HAMMONDS J S.Propagation of uncertainty in risk assessments:The need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability.Risk Analysis, 1994, 14(5):707-712. doi: 10.1111/risk.1994.14.issue-5 [3] ELDRED M S, SWILER L P, TANG G.Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation.Reliability Engineering & System Safety, 2011, 96(9):1092-1113. https://www.researchgate.net/publication/251621497_Mixed_aleatory-epistemic_uncertainty_quantification_with_stochastic_expansions_and_optimization-based_interval_estimation [4] KELLY E J, CAMPBELL K.Separating variability and uncertainty in environmental risk assessment—Making choices.Human and Ecological Risk Assessment, 2000, 6(1):1-13. doi: 10.1080/10807030091124419 [5] BARALDI P, ZIO E, COMPARE M.A method for ranking components importance in presence of epistemic uncertainties.Journal of Loss Prevention in the Process Industries, 2009, 22(5):582-592. doi: 10.1016/j.jlp.2009.02.013 [6] ZAFIROPOULO E P, DIALYNAS E N.Reliability and cost optimization of electronic devices considering the component failure rate uncertainty.Reliability Engineering & System Safety, 2004, 84(3):271-284. http://www.sciencedirect.com/science/article/pii/S0951832003002734 [7] BLANKS H S.Arrhenius and the temperature dependence of non-constant failure rate.Quality and Reliability Engineering International, 1990, 6(4):259-265. doi: 10.1002/(ISSN)1099-1638 [8] BORGONOVO E.A new uncertainty importance measure.Reliability Engineering & System Safety, 2007, 92(6):771-784. http://paris.utdallas.edu/IJPE/Vol05/Issue03/VOL5N3P2FLGR.pdf [9] SALTELLI A, MARIVOET J.Non-parametric statistics in sensitivity analysis for model output:A comparison of selected techniques.Reliability Engineering & System Safety, 1990, 28(2):229-253. https://www.researchgate.net/publication/223733810_Non-parametric_statistics_in_sensitivity_analysis_for_model_output_A_comparison_of_selected_techniques [10] SOBOL I M.Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates.Mathematics and Computers in Simulation, 2001, 55(1):271-280. https://www.researchgate.net/publication/222535147_Global_sensitivity_indices_for_nonlinear_mathematical_models_and_their_Monte_Carlo_estimates [11] NOVI INVERARDI P L, TAGLIANI A.Maximum entropy density estimation from fractional moments.Communications in Statistics-Theory and Methods, 2003, 32(2):327-345. doi: 10.1081/STA-120018189 [12] DENG J, PANDEY M D.Estimation of the maximum entropy quantile function using fractional probability weighted moments.Structural Safety, 2008, 30(4):307-319. doi: 10.1016/j.strusafe.2007.05.005 [13] ZHANG X, PANDEY M D.Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method.Structural Safety, 2013, 43(9):28-40. https://www.researchgate.net/publication/257007041_Structural_reliability_analysis_based_on_the_concepts_of_entropy_fractional_moment_and_dimensional_reduction_method [14] CREMERS D, OSHER S J, SOATTO S.Kernel density estimation and intrinsic alignment for shape priors in level set segmentation.International Journal of Computer Vision, 2015, 69(3):335-351. doi: 10.1007/s11263-006-7533-5 [15] 张磊刚, 吕震宙, 陈军.基于失效概率的矩独立重要性测度的高效算法.航空学报, 2014, 35(8):2199-2206. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201408013.htmZHANG L G, LYU Z Z, CHEN J.An efficient method for failure probability-based moment-independent importance measure.Acta Aeronautica et Astronautica Sinica, 2014, 35(8):2199-2206(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201408013.htm [16] LEIBLER R A, KULLBACK S.On information and sufficiency.Annals of Mathematical Statistics, 1951, 22(1):79-86. doi: 10.1214/aoms/1177729694 [17] 尹晓伟, 钱文学, 谢里阳.系统可靠性的贝叶斯网络评估方法.航空学报, 2008, 29(6):1482-1489. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB200806013.htmYIN X W, QIAN W X, XIE L Y.A method for system reliability assessment based on bayesian networks.Acta Aeronautica et Astronautica Sinica, 2008, 29(6):1482-1489(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB200806013.htm [18] 袁朝辉, 崔华阳, 侯晨光.民用飞机电液舵机故障树分析.机床与液压, 2006(11):221-223. doi: 10.3969/j.issn.1001-3881.2006.11.075YUAN C H, CUI H Y, HOU C G.Fault tree analysis of civil aircraft electro-hydraulic actuator.Machine Tool & Hydraulics, 2006(11):221-223(in Chinese). doi: 10.3969/j.issn.1001-3881.2006.11.075 -
下载:
点击查看大图
计量
- 文章访问数: 837
- HTML全文浏览量: 169
- PDF下载量: 537
- 被引次数: 0
