A Fault Detection Method Based on Data Reliability and Interval Evidence Reasoning
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摘要: 为解决故障检测方法在处理数据不确定性问题上的不足, 本文提出一种基于数据可靠性和区间证据推理(Interval evidential reasoning, IER)的故障检测方法. 该方法通过融合专家知识与考虑可靠性的监测数据, 实现报警阈值区间的更新与优化, 从而提高故障检测的准确性. 首先基于信息一致性方法计算数据可靠度, 然后基于区间证据推理理论, 构建区间阈值的更新与优化模型, 最后基于投影协方差矩阵自适应进化策略算法求解优化模型, 得到故障检测误漏报率最小的最优报警阈值区间. 对石油管道泄漏实例和航天继电器加速寿命测试实例的故障检测问题进行了研究, 通过对比分析, 验证了所提方法的有效性.Abstract: In order to solve the problem of the fault detection method in dealing with data uncertainty, a fault detection method based on data reliability and interval evidence reasoning is proposed in this paper. In the proposed method, the interval threshold can be updated and optimized by integrating expert knowledge and reliability of monitoring data, and the accuracy of fault detection can be improved. Firstly, the data reliability based on the information consistency method is calculated. Then, the updating and optimization model of the interval threshold is established based on the interval evidence reasoning. Finally, the optimal alarm threshold interval with minimum false negatives and positives rate can be obtained by solving the optimization model based on projection covariance matrix adaptation evolution strategy algorithm. Two case studies of oil pipeline leak and aerospace relay accelerated life test are used to study the problem of fault detection. The effectiveness of the proposed method is verified by analyzing and comparing with several other methods.
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图 1 基于数据可靠性和IER的故障检测方法结构图
Fig. 1 Structure diagram of fault detection method based on data reliability and IER
表 1 初始阈值区间的区间置信度
Table 1 Interval belief degree of initial threshold interval
评价等级 区间置信度 $H_1$ $\left[ {0,0.0214} \right]$ $H_2$ $\left[ {0.7538,1} \right]$ $H_3$ $\left[ {0,0.2462} \right]$ 
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表 2 监测数据的区间置信度
Table 2 Interval belief degree of monitoring data
训练数据 H1 H2 H3 $x_1$ $\left[ {0.8571,0.8571} \right]$ $\left[ {0.1429,0.1429} \right]$ $\left[ {0,0} \right]$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $x_{300}$ $\left[ {0,0} \right]$ $\left[ {1,1} \right]$ $\left[ {0,0} \right]$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $x_{700}$ $\left[ {0,0} \right]$ $\left[ {0.9167,0.9167} \right]$ $\left[ {0.0823,0.0823}\right]$
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表 3 总体区间置信度更新过程
Table 3 The update process of overall interval belief degree
总体区间置信度 $H_1$ $H_2$ $H_3$ $\left[ {\min \beta _n ,\max \beta _n } \right]_1$ $\left[ {0,0} \right]$ $\left[ {0.7910,0.7963} \right]$ $\left[ {0.2037,0.2090} \right]$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\left[ {\min \beta _n ,\max \beta _n } \right]_{300}$ $\left[ {0,0} \right]$ $\left[ {0.8751,0.8816} \right]$ $\left[ {0.1184,0.1249} \right]$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\left[ {\min \beta _n ,\max \beta _n } \right]_{700}$ $\left[ {0,0} \right]$ $\left[ {0.9262,0.9507} \right]$ $\left[ {0.0493,0.0738} \right]$
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表 4 故障检测效果比较(%)
Table 4 Comparison of fault detection effects (%)
优化方法 阈值 误报率 漏报率 $G$ 未优化 $\left[ {0.8925,1.0477} \right]$ $0$ $9$ $9$ 神经网络方法 $\left[ {0.9832,1.0990} \right]$ $0$ $12$ $12$ IER方法 $\left[ {0.9510,0.9749} \right]$ $0.6$ $7.8$ $8.4$ IER$(r_i)$ $\left[ {0.9296,0.9443} \right]$ $4.8$ $1.8$ $6.6$
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表 5 第1组数据的总体区间置信度更新过程
Table 5 The overall interval confidence update process for the first set of data
总体区间置信度 $H_1$ $H_2$ $H_3$ $\left[ {\min \beta _n ,\max \beta _n } \right]_1$ $\left[ {0,0} \right]$ $\left[ {0.7093,0.7619} \right]$ $\left[ {0.2381,0.2907} \right]$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\left[ {\min \beta _n ,\max \beta _n } \right]_{100}$ $\left[ {0,0} \right]$ $\left[ {0.6842,0.7135} \right]$ $\left[ {0.2865,0.3158} \right]$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\left[ {\min \beta _n ,\max \beta _n } \right]_{300}$ $\left[ {0,0} \right]$ $\left[ {0.6547,0.7488} \right]$ $\left[ {0.2512,0.3453} \right]$
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表 6 第2组总体区间置信度更新过程
Table 6 The overall interval confidence update process for the second set of data
总体区间置信度 $H_1$ $H_2$ $H_3$ $\left[ {\min \beta _n ,\max \beta _n } \right]_1$ $\left[ {0,0} \right]$ $\left[ {0.7093,0.7619} \right]$ $\left[ {0.2381,0.2907} \right]$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\left[ {\min \beta _n ,\max \beta _n } \right]_{100}$ $\left[ {0,0} \right]$ $\left[ {0.6837,0.7156} \right]$ $\left[ {0.2844,0.3163} \right]$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\left[ {\min \beta _n ,\max \beta _n } \right]_{280}$ $\left[ {0,0} \right]$ $\left[ {0.6466,0.7402} \right]$ $\left[ {0.2598,0.3534} \right]$
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