Fault Isolability Evaluation Based on Zonotope
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摘要: 针对包含幅值有界而分布形式未知的故障及输入干扰项的线性离散系统, 提出了一种新的系统故障可分离性的量化评价方法. 故障可分离性是故障可诊断性中的重要部分, 针对现有方法中基于方向相似度的故障可分离性评价方法存在的不足加以补充, 提出了利用中心对称多胞体对故障可分离性进行分析, 将中心对称多胞体集合转化为多面体的表示形式, 以达到对故障可分离性量化评价的目的, 同时给出了具体评价原理和评价指标. 最后, 通过数值仿真算例, 验证了该方法的有效性和优越性.Abstract: This paper proposes a new quantitative evaluation method for fault isolability of the linear discrete systems subject to faults and input disturbances which are bounded but with unknown distributions. Fault isolability evaluation is an important part of fault diagnosis. In order to improve the existing direction similarity-based method, we propose a new fault isolability method via using zonotopes. To achieve the quantitative evaluation of fault isolability, zonotopes are converted into polytopes. Specific evaluation principles and indices are provided. Finally, numerical examples demonstrate the effectiveness and advantages of the proposed method.
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Key words:
- Dynamic system /
- zonotope /
- fault isolability /
- directional similarity
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图 1 各个故障模式组合下系统输出结果
Fig. 1 System output results under the combination of various fault modes
表 1 基于方向相似度可分离性评价结果
$(s=5)$ Table 1 Fault isolability evaluation results based on directional similarity
$(s=5)$ 次数 评价结果 次数 评价结果 次数 评价结果 1 0.0977 6 0.7662 11 0.9239 2 0.7345 7 0.0191 12 0.3114 3 0.1380 8 0.7235 13 0.6323 4 0.4580 9 0.1939 14 0.3153 5 0.2760 10 0.4178 15 0.2760 
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表 2 基于方向相似度可分离性评价结果
$(s=500)$ Table 2 Fault isolability evaluation results based on directional similarity
$(s=500)$ 次数 评价结果 次数 评价结果 次数 评价结果 1 0.6481 6 0.6836 11 0.6811 2 0.6480 7 0.6885 12 0.6734 3 0.6380 8 0.6654 13 0.6559 4 0.6294 9 0.6294 14 0.6289 5 0.6698 10 0.6168 15 0.6610
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表 3 数据分散程度评价
Table 3 Evaluation of data dispersion
窗口长度 极差($R$) 标准差($\sigma$) 窗口长度 极差($R$) 标准差($\sigma$) 5 0.9128 0.2577 225 0.1669 0.0349 10 0.7519 0.1758 250 0.1335 0.0297 50 0.3501 0.0882 375 0.1213 0.0278 100 0.2941 0.0604 450 0.0914 0.0259 175 0.1898 0.0514 500 0.0718 0.0226
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表 4 基于方向相似度可分离性评价结果(
$s=500$ )Table 4 Fault isolability evaluation results based on directional similarity (
$s=500$ )故障 $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_{1}$ NULL 1.0000 0.9236 0.4780 $f_{2}$ 1.0000 NULL 0.9236 0.4780 $f_{3}$ 0.9236 0.9236 NULL 0.6411 $f_{4}$ 0.4780 0.4780 0.6411 NULL
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表 5 基于中心对称多胞体可分离性评价结果(
$s=500$ )Table 5 Fault isolability evaluation results based on Zonotope (
$s=500$ )故障 $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_1$ NULL 1.0000 0.4464 0.1508 $f_2$ 1.0000 NULL 0.4463 0.1508 $f_3$ 0.4463 0.4463 NULL 0.3380 $f_4$ 0.1508 0.1508 0.3380 NULL
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表 6 基于中心对称多胞体可分离性评价结果(
$s=5$ )Table 6 Fault isolability evaluation results based on Zonotope (
$s=5$ )故障 $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_1$ NULL 1.0000 0.3665 0.2961 $f_2$ 1.0000 NULL 0.3665 0.2961 $f_3$ 0.3665 0.3665 NULL 0.3645 $f_4$ 0.2961 0.2961 0.3645 NULL
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