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摘要: 针对缺乏有效的非完全失效故障（Loss of effect，LOE）可诊断性量化分析方法的现状，本文提出了一种基于距离相似度的系统非完全失效故障的实际可诊断性评价方法.通过将状态空间描述的动态系统转换为时间堆栈动态模型，使故障的可诊断性评估分析问题转化为多元分布的相似度问题.给出系统非完全失效故障可检测性与可隔离性的相关定义，并对故障的可诊断性进行量化.通过求取最小二乘解计算最小巴氏距离，增大了算法适用范围.最后，通过仿真实例验证评价方法的有效性，并通过所提出的可诊断性评估算法求取非完全失效故障的最大可诊断效能系数.Abstract: Due to the lack of efficient approaches to quantify actual loss of effect (LOE) fault diagnosability in dynamic systems, a novel presented is presented in this paper. Discrete-time state space models are modified into dynamic models with time window of certain length, and the similarity of different multivariate distributions, instead of fault diagnosability evaluation, is analyzed. The definitions of detectability and isolability of LOE fault are given. Diagnosability performance is quantified by the method based on minimum Bhattacharyya distance. Least-squares method is utilized to enhance applicability of the novel proposed approach. In addition, a simulation example is employed to show the validity of the proposed approach and to analyze maximum effectiveness coefficient of LOE fault in dynamic systems.1) 本文责任编委 胡昌华
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图 1 不同时间窗口长度对系统(16)故障可诊断性评价结果的影响
Fig. 1 Curves comparing computed distinguishability of dynamic systems (16) with different window length $s$
图 2 不同效能系数$\varepsilon$对系统(16)故障可检测性评价结果的影响
Fig. 2 Curves comparing computed detectability of dynamic systems (16) with different effectiveness coefficient $\varepsilon$
图 3 不同效能系数$\varepsilon$对系统(16)故障可检测性评价结果的影响
Fig. 3 Curves comparing computed isolability of dynamic systems (16) with different effectiveness coefficient $\varepsilon$
表 1 系统(16)在时间序列$\theta $的输入下的可诊断评价结果($\varepsilon = 0.8$, $s = 5$)
Table 1 Computed distinguishability of dynamic systems (16) with the given fault time profile $\theta $ ($\varepsilon = 0.8$, $s = 5$)
$F{D_\theta }/F{I_\theta }$ ${\rm NF}$ $f_1$ $f_2$ $f_3$ $f_1$ 155.022 0 84.110 3.0614 $f_2$ 274.632 131.22 0 111.20 $f_3$ 830.902 6.7403 126.05 0 
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表 2 系统(16)在时间序列$\theta $的输入下的可诊断评价结果($s = 3$)
Table 2 Computed distinguishability of dynamic systems (16) with the given fault time profile $\theta $ ($s = 3$)
$F{D_\theta }/F{I_\theta }$ ${\rm NF}$ $f_1$ $f_2$ $f_3$ $f_1$ 130.6592 0 0 0 $f_2$ 61.6940 0 0 0 $f_3$ 346.1748 0 0 0}
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表 3 系统(16)在时间序列$\theta $的输入下的可诊断评价结果($s = 6$)~($ \times {10^3}$)
Table 3 Computed distinguishability of dynamic systems (16) with the given fault time profile $\theta $ $(s = 6)~( \times {10^3})$
$F{D_\theta }/F{I_\theta }$ ${\rm NF}$ $f_1$ $f_2$ $f_3$ $f_1$ 0.3585 0 0.0853 0.0040 $f_2$ 0.5403 0.2581 0 0.1489 $f_3$ 1.3274 0.0225 0.2751 0}
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表 4 系统(16)在时间序列$\theta $的输入下的可诊断评价结果$(\varepsilon = 0.5)$ $( \times {10^3})$
Table 4 Computed distinguishability of dynamic systems (16) with the given fault time profile $\theta $ $(\varepsilon = 0.5)$ $( \times {10^3})$
$F{D_\theta }/F{I_\theta }$ ${\rm NF}$ $f_1$ $f_2$ $f_3$ $f_1$ 0.9689 0 0.5257 0.0191 $f_2$ 1.7164 0.8202 0 0.6950 $f_3$ 5.1931 0.0421 0.7878 0}
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表 5 系统(16)在时间序列$\theta $的输入下的最大可诊断效能系数$({p_i} = 0.3,{p_{i,j}} = 0.4)$
Table 5 Maximum effectiveness coefficient of dynamic systems (16) with the given fault time profile $\theta $ $({p_i} = 0.3,{p_{i,j}} = 0.4)$
$\varepsilon $ ${\rm NF}$ $f_1$ $f_2$ $f_3$ $f_1$ 0.45 0 0.36 0.36 $f_2$ 0.45 0.36 0 0.36 $f_3$ 0.45 0.36 0.36 0
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