基于Kullback-Leibler距离的闭环系统传感器微小故障诊断
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摘要
在闭环控制系统中,当故障幅值较小时,由故障带来的影响会被控制量所掩盖.因此,闭环系统中的微小故障诊断实现更为复杂.本文针对闭环系统中的传感器故障,提出了基于Kullback-Leibler(KL)距离的微小故障在线检测与估计方法.本文首先介绍了KL距离的定义及其在多变量故障检测中的应用,然后提出了结合KL距离与快速移动窗口主成分分析(MWPCA)的在线微小故障检测与估计模型.在高斯分布的假设下,利用系统输入输出残差构造MWPCA的数据矩阵,然后通过在线更新数据矩阵主成分的均值与方差实现KL距离的在线更新,最终实现闭环系统中传感器的在线故障检测与估计.仿真实验表明,该方法能有效实现具有低故障—噪声比(FNR)特性的微小故障诊断.
Due to the feedback control law in the closed-loop control system, changes caused by incipient faults could be covered especially when the fault amplitude is small. Accordingly, it is more complicated for the diagnosis of incipient faults in the closed-loop system. In this paper, a novel online fault detection and estimation method utilizing the KullbackLeibler divergence(KLD) is proposed for sensors in the closed-loop system. First, the definition of the KL divergence and corresponding applications in the monitoring of multivariable systems are introduced. Combined with the KLD and fast moving window principal component analysis(MWPCA) method, the model of online incipient detection and estimation is established. Under the hypothesis of Gaussian distribution, the data matrix is constituted by residuals of system inputs and outputs. Then the value of KLD is updated online through computing the mean and variance of score vectors of selected principal components. Last, utilizing the proposed detection and estimation model, the online incipient fault detection and estimation for sensors in the closed-loop system are obtained. In the simulation, it is shown that the proposed method can deal with the incipient fault with lower fault-to-noise ratio(FNR) more efficiently.
Due to the feedback control law in the closed-loop control system, changes caused by incipient faults could be covered especially when the fault amplitude is small. Accordingly, it is more complicated for the diagnosis of incipient faults in the closed-loop system. In this paper, a novel online fault detection and estimation method utilizing the KullbackLeibler divergence(KLD) is proposed for sensors in the closed-loop system. First, the definition of the KL divergence and corresponding applications in the monitoring of multivariable systems are introduced. Combined with the KLD and fast moving window principal component analysis(MWPCA) method, the model of online incipient detection and estimation is established. Under the hypothesis of Gaussian distribution, the data matrix is constituted by residuals of system inputs and outputs. Then the value of KLD is updated online through computing the mean and variance of score vectors of selected principal components. Last, utilizing the proposed detection and estimation model, the online incipient fault detection and estimation for sensors in the closed-loop system are obtained. In the simulation, it is shown that the proposed method can deal with the incipient fault with lower fault-to-noise ratio(FNR) more efficiently.
引文
[1] ZHOU Donghua, LIU Yang, HE Xiao. Review on fault diagnosis techniques for closed-loop systems. Acta Automatica Sinica, 2013,39(11):1933–1943.(周东华,刘洋,何潇.闭环系统故障诊断技术综述.自动化学报,2013, 39(11):1933–1943.)
[2] LI Juan, ZHOU Donghua, SI Xiaosheng, et al. Review of incipient fault diagnosis methods. Control Theory&Applications, 2012,29(12):1517–1529.(李娟,周东华,司小胜,等.微小故障诊断方法综述.控制理论与应用, 2012, 29(12):1517–1529.)
[3] LI X, YANG G. Adaptive fault detection and isolation approach for actuator stuck faults in closed-loop systems. International Journal of Control Automation&Systems, 2012, 10(4):830–834.
[4] SIMANDL M, PUNCOCHAR I. Active fault detection and control:Unified formulation and optimal design. Automatica, 2009, 45(9):2052–2059.
[5] QIU Tian, BAI Xiaojing, ZHENG Xiyu, et al. Incipient fault detection of multivariate exponentially weighted moving average principal component analysis. Control Theory&Applications, 2014, 31(1):19–26.(邱天,白晓静,郑茜予,等.多元指数加权移动平均主元分析的微小故障检测.控制理论与应用, 2014, 31(1):19–26.)
[6] ZENG J, KRUGER U, GELUK J, et al. Detecting abnormal situations using the Kullback-Leibler divergence. Automatica, 2014, 50(11):2777–2786.
[7] JI H, HE X, SHANG J, et al. Incipient sensor fault diagnosis using moving window reconstruction-based contribution. Industrial&Engineering Chemistry Research, 2016, 55(10):2746–2759.
[8] HARMOUCHE J, DELPHA C, DIALLO D. Incipient fault detection and diagnosis based on Kullback-Leibler divergence using principal component analysis:Part II. Signal Processing, 2015, 109(1):334–344.
[9] CHAI Y, TAO S, MAO W, et al. Online incipient fault diagnosis based on Kullback-Leibler divergence and recursive principle component analysis. Canadian Journal of Chemical Engineering, 2018, 96(2):426–433.
[10] TAO S, CHAI Y, VI N Q. Incipient fault online estimation based on Kullback-Leibler divergence and fast moving window PCA. The 43rd Annual Conference of the IEEE Industrial Electronics Society. Beijing, China:IECON, 2017:8065–8069.
[11] KULLBACK S, LEIBLER R A. On Information and sufficiency. Annals of Mathematical Statistics, 1951, 22(1):79–86.
[12] TAO S, LI N, WEI B, CHAI Y. Weighted window sliding multivariate empirical mode decomposition for online multichannel filtering.IEEE Access, 2018, 6:43170–43178.
[13] CALLIER F M, DESOER C A. Linear System Theory. New York:Springer, 1991.
[14] ZHU Xuefeng, XIAO Shujun, WANG Xiu. A new practical method for closed-loop identification with PI control. Control Theory&Applications, 2010, 27(9):1240–1244.(朱学峰,肖术骏,王秀.一种新的实用PI控制闭环辨识方法.控制理论与应用, 2010, 27(9):1240–1244.)
[15] WANG X, UWE KRUGERK A, IRWIN G W. Process monitoring approach using fast moving window PCA. Industrial&Engineering Chemistry Research, 2005, 44(15):5691–5702.
[16] WILLIAMS R L, LAWRENCE D A. Linear State-Space Control Systems. New Jersey:John Wiley&Sons, 2007.
[2] LI Juan, ZHOU Donghua, SI Xiaosheng, et al. Review of incipient fault diagnosis methods. Control Theory&Applications, 2012,29(12):1517–1529.(李娟,周东华,司小胜,等.微小故障诊断方法综述.控制理论与应用, 2012, 29(12):1517–1529.)
[3] LI X, YANG G. Adaptive fault detection and isolation approach for actuator stuck faults in closed-loop systems. International Journal of Control Automation&Systems, 2012, 10(4):830–834.
[4] SIMANDL M, PUNCOCHAR I. Active fault detection and control:Unified formulation and optimal design. Automatica, 2009, 45(9):2052–2059.
[5] QIU Tian, BAI Xiaojing, ZHENG Xiyu, et al. Incipient fault detection of multivariate exponentially weighted moving average principal component analysis. Control Theory&Applications, 2014, 31(1):19–26.(邱天,白晓静,郑茜予,等.多元指数加权移动平均主元分析的微小故障检测.控制理论与应用, 2014, 31(1):19–26.)
[6] ZENG J, KRUGER U, GELUK J, et al. Detecting abnormal situations using the Kullback-Leibler divergence. Automatica, 2014, 50(11):2777–2786.
[7] JI H, HE X, SHANG J, et al. Incipient sensor fault diagnosis using moving window reconstruction-based contribution. Industrial&Engineering Chemistry Research, 2016, 55(10):2746–2759.
[8] HARMOUCHE J, DELPHA C, DIALLO D. Incipient fault detection and diagnosis based on Kullback-Leibler divergence using principal component analysis:Part II. Signal Processing, 2015, 109(1):334–344.
[9] CHAI Y, TAO S, MAO W, et al. Online incipient fault diagnosis based on Kullback-Leibler divergence and recursive principle component analysis. Canadian Journal of Chemical Engineering, 2018, 96(2):426–433.
[10] TAO S, CHAI Y, VI N Q. Incipient fault online estimation based on Kullback-Leibler divergence and fast moving window PCA. The 43rd Annual Conference of the IEEE Industrial Electronics Society. Beijing, China:IECON, 2017:8065–8069.
[11] KULLBACK S, LEIBLER R A. On Information and sufficiency. Annals of Mathematical Statistics, 1951, 22(1):79–86.
[12] TAO S, LI N, WEI B, CHAI Y. Weighted window sliding multivariate empirical mode decomposition for online multichannel filtering.IEEE Access, 2018, 6:43170–43178.
[13] CALLIER F M, DESOER C A. Linear System Theory. New York:Springer, 1991.
[14] ZHU Xuefeng, XIAO Shujun, WANG Xiu. A new practical method for closed-loop identification with PI control. Control Theory&Applications, 2010, 27(9):1240–1244.(朱学峰,肖术骏,王秀.一种新的实用PI控制闭环辨识方法.控制理论与应用, 2010, 27(9):1240–1244.)
[15] WANG X, UWE KRUGERK A, IRWIN G W. Process monitoring approach using fast moving window PCA. Industrial&Engineering Chemistry Research, 2005, 44(15):5691–5702.
[16] WILLIAMS R L, LAWRENCE D A. Linear State-Space Control Systems. New Jersey:John Wiley&Sons, 2007.
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