Incipient fault detection and diagnosis based on Kullback-Leibler divergence using principal component analysis: Part II

Most of fault indicators are devoted to detect deviations related to specific features but they fail to detect and estimate unpredictable slight distortions often caused by incipient faults. The Kullback-Leibler divergence is characterised with a high sensitivity to incipient faults that cause unpredictable small changes in the process measurements. This work has two main objectives: first estimate the amplitude of incipient faults in multivariate processes based on the divergence and second evaluate, through detection error probabilities, the performance of the divergence in the detection of incipient faults in noisy environments.Throughout all the paper, the Fault-to-Noise Ratio (FNR) has been referred to as a comparative criterion between the fault level and noise; particularly the region around 0 dB of FNR is of interest in the evaluation. A theoretical study is developed to derive an analytical model of the divergence that considers the presence of Gaussian noise and allows obtaining a theoretical estimate of the fault amplitude. After application on a simulated AR process, the fault amplitude estimate turns out to be an overestimation of the actual amplitude, therefore guaranteeing a safety margin for monitoring. Accurate fault severity estimation for an eddy currents application shows the effectiveness of this approach. HighlightsWe propose to enhance the fault detection approach based on the KLD modelling with the introduction of the noise.Based on the aforementioned model an estimator of the fault amplitude is developed and validated.The performances of the detection are studied in a noisy environment with the introduction of the Fault to Noise Ratio (FNR).The robustness of the proposed method is evaluated with the computation of the miss-detection and false alarms probabilities.A performed validation of this approach with a simulated AR model is given.

[1]  H. G. ter Morsche,et al.  Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem , 2006 .

[2]  Theodora Kourti,et al.  Statistical Process Control of Multivariate Processes , 1994 .

[3]  L. Ren,et al.  Single-Sensor Incipient Fault Detection , 2011, IEEE Sensors Journal.

[4]  I. Jolliffe.  Principal Component Analysis , 2002 .

[5]  Ying Liu,et al.  A Selective Kernel PCA Algorithm for Anomaly Detection in Hyperspectral Imagery , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[6]  Rolf Isermann,et al.  Supervision, fault-detection and fault-diagnosis methods — An introduction , 1997 .

[7]  Alfred O. Hero,et al.  Decomposable Principal Component Analysis , 2009, IEEE Transactions on Signal Processing.

[8]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[9]  Zhihuan Song,et al.  Fault detection behavior and performance analysis of principal component analysis based process monitoring methods , 2002 .

[10]  S. Sinanovic,et al.  Anomaly detection using the Kullback-Leibler divergence metric , 2008, 2008 First International Symposium on Applied Sciences on Biomedical and Communication Technologies.

[11]  D. Diallo,et al.  Faults diagnosis and detection using principal component analysis and Kullback-Leibler divergence , 2012, IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society.

[12]  B. Upadhyaya,et al.  Model Based Approach for Fault Detection and Isolation of Helical Coil Steam Generator Systems Using Principal Component Analysis , 2006, IEEE Transactions on Nuclear Science.

[13]  Luis Eduardo Mujica,et al.  A study of two unsupervised data driven statistical methodologies for detecting and classifying damages in structural health monitoring , 2013 .

[14]  Michèle Basseville,et al.  Divergence measures for statistical data processing - An annotated bibliography , 2013, Signal Process..

[15]  Raghunathan Rengaswamy,et al.  A review of process fault detection and diagnosis: Part III: Process history based methods , 2003, Comput. Chem. Eng..

[16]  Jyrki Kullaa,et al.  Distinguishing between sensor fault, structural damage, and environmental or operational effects in structural health monitoring , 2011 .

[17]  Steven X. Ding,et al.  A Review on Basic Data-Driven Approaches for Industrial Process Monitoring , 2014, IEEE Transactions on Industrial Electronics.

[18]  Janos J. Gertler,et al.  Analytical Redundancy Methods in Fault Detection and Isolation , 1991 .

[19]  B. Upadhyaya,et al.  Incipient fault detection and isolation in a PWR plant using principal component analysis , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[20]  Yann Le Bihan,et al.  Non destructive evaluation of small defects using an eddy current microcoil sensor array , 2008 .

[21]  Charles W. Champ,et al.  A multivariate exponentially weighted moving average control chart , 1992 .

[22]  Ali Cinar,et al.  Diagnosis of process disturbances by statistical distance and angle measures , 1997 .

[23]  Raghunathan Rengaswamy,et al.  A review of process fault detection and diagnosis: Part I: Quantitative model-based methods , 2003, Comput. Chem. Eng..

[24]  Jianbo Yu,et al.  Fault Detection Using Principal Components-Based Gaussian Mixture Model for Semiconductor Manufacturing Processes , 2011, IEEE Transactions on Semiconductor Manufacturing.

[25]  Michael B. Wakin,et al.  Modal Analysis With Compressive Measurements , 2014, IEEE Transactions on Signal Processing.

[26]  Harald Haas,et al.  Kullback-Leibler Divergence (KLD) Based Anomaly Detection and Monotonic Sequence Analysis , 2011, 2011 IEEE Vehicular Technology Conference (VTC Fall).

[27]  Janos Gertler,et al.  Principal Component Analysis and Parity Relations - A Strong Duality , 1997 .

[28]  J. E. Jackson.  A User's Guide to Principal Components , 1991 .

[29]  Michèle Basseville,et al.  On-board Component Fault Detection and Isolation Using the Statistical Local Approach , 1998, Autom..

[30]  Rolf Isermann,et al.  Process fault detection based on modeling and estimation methods - A survey , 1984, Autom..

[31]  Michèle Basseville,et al.  Detection of Abrupt Changes: Theory and Applications. , 1995 .

[32]  Athena Vakali,et al.  A new approach to web users clustering and validation: a divergence-based scheme , 2009, Int. J. Web Inf. Syst..

[33]  M. Basseville.  Distance measures for signal processing and pattern recognition , 1989 .

[34]  Smiley W. Cheng,et al.  Single Variables Control Charts: an Overview , 2006, Qual. Reliab. Eng. Int..

[35]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[36]  S. Qin,et al.  Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to Other Methods† , 1999 .

[37]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[38]  Tao He,et al.  Process Fault Detection and Diagnosis Based on Principal Component Analysis , 2006, 2006 International Conference on Machine Learning and Cybernetics.

[39]  Yann Le Bihan,et al.  Study and experimental validation of the calculation of the ECT signal induced by a minute crack using a FEM-BIM combination , 2006 .

[40]  Shrikanth S. Narayanan,et al.  Average divergence distance as a statistical discrimination measure for hidden Markov models , 2006, IEEE Transactions on Audio, Speech, and Language Processing.

[41]  Manabu Kano,et al.  A new multivariate statistical process monitoring method using principal component analysis , 2001 .

[42]  Qiang Liu,et al.  Decentralized Fault Diagnosis of Continuous Annealing Processes Based on Multilevel PCA , 2013, IEEE Transactions on Automation Science and Engineering.

[43]  Douglas M. Hawkins,et al.  Multivariate Exponentially Weighted Moving Covariance Matrix , 2008, Technometrics.

[44]  S. Joe Qin,et al.  Subspace approach to multidimensional fault identification and reconstruction , 1998 .