Independent Slow Feature Analysis Modelling Method and Its Application in Dynamic Fault Detection
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摘要: 故障检测与诊断技术是保证复杂装备或工业过程正常运行的技术支撑和有效手段, 独立成分分析(Independent component analysis, ICA)作为一种典型的多元统计过程监测(Multivariate statistical process monitoring, MSPM)方法, 可充分挖掘数据的高阶统计信息. 传统ICA方法在预处理阶段采用主成分分析(Principle component analysis, PCA)进行白化和降维, 但PCA的静态性质导致ICA在动态过程监测中的效果不太理想. 为解决这一问题, 提出一种独立慢特征分析(Independent-slow feature analysis, ISFA)建模方法. ISFA以原始观测矩阵和白化矩阵为自变量构造双目标优化函数, 基于牛顿迭代法求解目标函数, 使用网格搜索优化权重系数, 利用指数加权移动平均(Exponentially weighted moving average, EWMA)修正统计量并构建综合检测指标; 最后, 利用数值仿真和电动伺服机构实验验证所提方法的有效性.Abstract: Fault detection and diagnosis technologies serve as critical technical supports and effective means to ensure the normal operation of complex equipment or industrial processes. As a typical multivariate statistical process monitoring (MSPM) method, independent component analysis (ICA) can fully exploit high-order statistical information from data. Conventional ICA methods employ principal component analysis (PCA) for whitening and dimensionality reduction during the pre-processing stage. However, the static nature of PCA compromises ICA＇s effectiveness in dynamic process monitoring. To address this issue, an independent-slow feature analysis (ISFA) modelling method is approached. Specifically, ISFA constructs a dual-objective optimization function using the original observation matrix and whitening matrix as independent variables, solves the objective function via Newton＇s iteration method, optimizes weight coefficients through grid search, modifies statistical metrics using exponentially weighted moving average (EWMA), and establishes a comprehensive detection index. Finally, numerical simulations and electric servo mechanism experiments are conducted to validate the effectiveness of the proposed method.
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Key words:
- Independent-slow feature /
- dynamic process /
- fault detection /
- grid search
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图 9 电动伺服机构故障1的检测效果图
Fig. 9 Detection effect diagram of electric servo mechanism fault 1
图 11 电动伺服机构故障3的检测效果图
Fig. 11 Detection effect diagram of electric servo mechanism fault 3
图 10 电动伺服机构故障2的检测效果图
Fig. 10 Detection effect diagram of electric servo mechanism fault 2
表 1 各变量零延迟相关系数表
Table 1 Zero delay correlation coefficient table for each variable
变量 $ E_1 $ $ E_2 $ $ E_3 $ $ E_4 $ $ E_5 $ $ E_1 $ 1 — — — — $ E_2 $ −0.13 1 — — — $ E_3 $ −0.09 −0.62 1 — — $ E_4 $ −0.12 0.76 −0.17 1 — $ E_5 $ 0.43 0.22 0.14 −0.02 1 
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表 2 数值仿真故障检测的FARs和FDRs (%)
Table 2 FARs and FDRs for fault detection of numerical simulation (%)
算法 DICA SICA PCA ISFA 故障 FAR FDR FAR FDR FAR FDR FAR FDR 1 0.00 33.69 0.00 63.33 0.00 7.97 0.00 83.81 2 0.00 91.19 0.00 97.02 0.00 93.45 0.00 98.81 3 0.00 96.78 0.00 99.88 0.00 99.40 0.00 99.76 平均 0.00 73.89 0.00 86,74 0.00 66.94 0.00 94.13
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表 3 电动伺服机构变量表
Table 3 Variable table of electric servo mechanism
序号 变量描述 序号 变量描述 1 时标(高字) 2 时标(低字) 3 A通道位置反馈 4 B通道位置反馈 5 A通道速度反馈 6 B通道速度反馈 7 A通道q轴电流反馈 8 B通道q轴电流反馈 9 A通道d轴电流反馈 10 B通道d轴电流反馈 11 A通道喷管摆角 12 B通道喷管摆角 13 A通道电机转角 14 B通道电机转角 15 +10 V供电状态 16 −10 V供电状态 17 +15 V供电状态 18 −15 V供电状态 19 +5 V供电状态 20 28 V电压 21 28 V电流
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表 4 电动伺服机构故障检测的FARs和FDRs (%)
Table 4 FARs and FDRs for fault detection of electric servo mechanisms (%)
算法 DICA SICA PCA ISFA 故障 FAR FDR FAR FDR FAR FDR FAR FDR 1 0.21 99.85 0.89 100.00 2.50 99.85 0.00 100.00 2 0.72 99.01 0.24 97.69 1.44 1.32 0.00 98.69 3 0.00 36.18 0.00 4.67 0.93 33.89 0.84 53.33 平均 0.31 78.35 0.38 77.19 2.87 34.03 0.28 84.01
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