安全性要求下系统失效概率及其灵敏度分析  

Systematic failure probability on the required safety and its sensitivity analysis

作　　者：阚丽娟[1] 徐吉辉 陈玉金 宋晓博 KAN Li-juan;XU Ji-hui;CHEN Yu-jin;SONG Xiao-bo(Equipment Management and Unmanned Aerial Vehicle Engineering College,Air Force Engineering University,Xi'an 710051,China)

机构地区：[1]空军工程大学装备管理与无人机工程学院,西安710051

出　　处：《安全与环境学报》2022年第5期2342-2351,共10页Journal of Safety and Environment

基　　金：国家自然科学基金项目(52074309)。

摘　　要：针对部附件失效率不确定性对系统安全性的影响问题,探讨了安全性要求下系统失效概率及其灵敏度分析方法。首先,给出安全性要求下系统失效概率的定义,并运用Monte Carlo数值模拟法,分析了安全性要求下系统失效概率的取值规律及特点;其次,依据Borgonovo矩独立灵敏度分析思想,提出了一种新的安全性要求下系统失效概率的全局灵敏度指标,用来度量部附件失效率不确定性对安全性要求下系统失效概率的影响程度;之后,为有效减少Monte Carlo数值模拟法求解指标的计算成本,运用贝叶斯公式将灵敏度指标转化为求解相应的条件概率密度和无条件概率密度,并与Kriging自适应代理模型相结合,提出了指标的高效算法。并通过工程算例,验证了新灵敏度指标的可行性和算法的经济高效性。To study the influence of uncertain component failure rates on system safety,this work studies the systematic failure probability on the required safety and the method of its sensitivity analysis.Firstly,the concept of systematic failure probability on the required safety is established,as a measure of system safety under uncertain failure rates.The index measures the safety degree of the system by the probability that the system failure probability is greater than the given system safety requirement.Monte Carlo numerical simulation method is used to analyze the value rules and characteristics of the systematic failure probability on the required safety;secondly,according to the theory of moment-independent sensitivity analysis proposed by Borgonovo,a new global sensitivity index is established based on system failure probability on the required safety.The index measures the influence of the uncertain component failure rates on the system failure probability on the required safety by comparing the difference of absolute value between unconditional systematic failure probability and conditional systematic failure probability;moreover,aiming to reduce the cost of solving the sensitivity index by Monte Carlo numerical simulation method,an efficient algorithm of sensitivity index based on Kriging and Bayesian estimation is proposed.The algorithm uses the Bayesian formula to transform the sensitivity index into solving the corresponding conditional probability density and unconditional probability density and uses the adaptive Kriging surrogate model to construct the corresponding output surrogate model,to further obtain the conditional samples of the component failure rates.The conditional probability density is estimated by combining the kernel density estimation method with the conditional samples of the component failure rates,and the final sensitivity index is obtained by further solving.The results of examples show that the sensitivity analysis index based on the system failure probability on the required safety

关 键 词：安全工程 系统失效概率 灵敏度指标 贝叶斯估计 Kriging代理模型 

分 类 号：X949[环境科学与工程—安全科学]