基于D-S证据理论的β因子估算方法

β Factor Estimation Method Based on D-S Evidence Theory

β因子法是定量评估共因失效的常用方法,为解决IEC 61508中评分表法估算β时可能存在不确定性的问题,通过分析估算过程中的不确定性类型,提出一种基于D-S证据理论的因子估算方法。该方法首先建立β不同取值范围的辨识框架,然后对被分析系统进行评估,并分配辨识框架中各基元的初始BPA(基本信任分配函数),最后通过证据理论融合各专家评分意见得到由信任函数和似然函数构成的β因子不确定区间。其中针对传统证据合成规则难以处理高度冲突证据的不足,提出了基于改进折扣系数的证据理论合成方法,该方法在证据融合之前,首先计算证据间的相似度以获取每个证据的支持度,同时结合专家权重,按一定的规则融合两者形成权重并将其作为折扣系数对初始BPA进行加权修正,以降低证据间的冲突程度。实例结果表明:与传统证据合成规则、Murphy法、折扣系数法相比,所提出的方法对目标结果的识别速度优于其他方法,且合成结果的不确定度0.0804是所有方法中最低的。

βFactor Method is a common method for quantitative evaluation of CCF(common cause failure).To solve the problem of the uncertainty that may exist in the evaluation ofβby scoring table in IEC 61508,aβfactor estimation method based on D-S evidence theory is proposed.Firstly,the identification framework of different value ranges is established.Secondly,the system to be analyzed is evaluated and the initial BPA(Basic Probability Assignment,BPA)of each primitive in the identification framework is assigned.Lastly,experts'evaluation opinions are fused through evidence theory to obtain the uncertain region ofβfactor composed of belief function and plausibility function.Aiming at the deficiency that the traditional evidence synthesis rules are difficult to deal with highly conflicting evidence,an evidence theory synthesis method based on improved discount coefficient is proposed.Before evidences are fused,the method calculates the similarity between evidences first to obtain the support of each evidence.At the same time,combined with expert weights,the two are fused according to certain rules to form weights,which are used as discount coefficients to weight and modify the initial BPA,so as to reduce the degree of conflict between evidences.The example results show that:compared with the traditional evidence synthesis rule,Murphy method and discount coefficient method,the proposed method has faster recognition speed than other methods,and the uncertainty 0.0804 of the synthesis result is the lowest of all methods.