Research on Fault Detection and Identification Method of Small PWR Based on Principal Component Analysis
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摘要: 故障检测和辨识对于小型压水堆的安全经济运行具有重要意义。反应堆中通常采用基于信号和专家知识经验的故障检测和辨识方法，操纵员往往不能从海量的故障数据信息中及时准确甄别故障类型，追溯故障原因。本文提出了采用主元分析进行小型压水堆故障检测和辨识的方法。首先利用RELAP5程序对小型压水堆建模，获得典型故障的样本数据。其次，基于主元分析理论对样本降维，并计算T2和Q两个统计量，通过判断是否超出阈值来检测反应堆运行状态。然后，利用贡献率图方法分析了过程变量对于统计量的贡献率，从而确定了对故障特征变化起主要作用的变量，实现对不同故障的辨识。最终和实际物理过程分析结果进行对比，验证了该方法的有效性。Abstract: Fault detection and identification are important for the safety and economy of small PWRs. The fault detection and identification method based on signal and expert knowledge and experience is usually applied in nuclear reactors. However, operators are often unable to identify the fault type and trace the fault cause in time and accurately from the massive fault data information. A method of fault detection and identification of small PWR based on principal component analysis is presented in this paper. First, the model of a small PWR is established by RELAP5 code, and the sample data of typical faults is obtained. Second, the dimension of sample data is reduced by using principle component analysis method. T2 and Q statistics are calculated to detect the reactor operation condition by judging whether the thresholds are exceeded. Then, the contribution rate of process variables to statistics is analyzed by using the contribution rate graph method, so as to determine the variables that play a major role in the change of fault characteristics and realize the identification of different faults. Finally, the effectiveness of the method is verified by comparing with the actual physical process analysis results.
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图 2 PCA方法故障检测和辨识流程图
Figure 2. Fault Detection and Identification Flow Chart Based on PCA Method
图 3 不同事故下T2和Q统计量计算结果
Figure 3. Calculation Results of T2 and Q under Different Accidents
图 4 不同事故工况主成分对T2统计量贡献率
Figure 4. Contribution Rate of Principal Component to T2 under Different Accidents
图 5 LOCA初期不同变量对T2和Q统计量贡献率分析
Figure 5. Analysis of Contribution Rate of Different Variables to T2 and Q under Initial Stage of LOCA
图 6 落棒事故初期不同变量对T2和Q统计量贡献率
Figure 6. Contribution Rate of Different Variables to T2 and Q under Initial Stage of Rod Drop Accident
图 7 LOCA后期不同变量对T2和Q统计量贡献率分析
Figure 7. Analysis of Contribution Rate of Different Variables to T2 and Q under Final Stage of LOCA
图 8 落棒事故后期不同变量对T2和Q统计量贡献率
Figure 8. Contribution Rate of Different Variables to T2 and Q under Final Stage of Rod Drop Accident
图 10 落棒事故下标准化变量随时间变化
Figure 10. Standardized Variables Vary with Time Under Rod Drop Accident
表 1 反应堆中选取的变量
Table 1. Variables Selected for Reactor
编号 变量名称 单位 1 反应堆功率 MW 2/3 冷却剂流量（环路1和环路2） kg/s 4/5 热段和冷段冷却剂温度（环路1） K 6/7 热段和冷段冷却剂温度（环路2） K 8 稳压器压力 MPa 9 稳压器水位 m 10/11 蒸汽发生器（SG1和SG2）蒸汽流量 kg/s 12/13 SG1和SG2给水流量 kg/s 14/15 SG1和SG2出口蒸汽温度 K 16/17 SG1和SG2水位 m 18/19 SG1和SG2出口蒸汽压力 MPa 
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表 2 特征值及累计方差贡献率
Table 2. Contribution Rate of Eigenvalues and Cumulative Variance
主成分 LOCA 落棒事故 λ σ/% λ σ/% PC1 6.86 36.09 6.12 32.20 PC2 6.01 67.74 4.82 57.58 PC3 2.82 82.58 4.02 78.76 PC4 1.53 90.64 1.33 85.78 PC5 0.56 93.61 1.07 91.42 PC6 0.52 96.34 0.76 95.41 PC7 0.39 98.38 0.46 97.86 PC8 0.16 99.24 0.25 99.15 PC9 0.08 99.65 0.09 99.62 PC10 0.05 99.90 0.04 99.82 PC11~PC19 特征较小，此处不继续列出
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表 3 不同事故的不同时期起主要贡献作用的变量
Table 3. Variables with Main Contribution under Different Periods of Different Accidents
事故类型 事故阶段 起主要贡献作用的变量及其编号 LOCA 前期 冷却剂流量（2和3） 稳压器水位（9） 后期 稳压器压力（8） 稳压器水位（9） 落棒事故 前期 功率（1） 冷却剂流量（2和3） 热段冷却剂温度（4和6） 稳压器压力和水位（8和9） 蒸汽发生器蒸汽流量（10） 后期 功率（1） 冷却剂温度（4，5和6） 稳压器压力和水位（8和9） 蒸汽流量（10） 给水流量（12，13） 蒸汽发生器水位（16）
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