Fault Detection and Diagnosis Using Principal Component Analysis - Literature review Example

?Fault Detection Using Q and T2 Statistics PCA is highly effective in reducing the overall dimensions of varied input data for analysis. Over time, PCA has been adopted for use in different applications such as fault monitoring and diagnosis, signal processing, recognition of patterns, data compression and other similar tasks (Zhu, Bai and Yang, 2010). PCA allows projecting large streams of input data onto a smaller dimensional space, so that the projected data is uncorrelated when compared to the original data. The various elements of such projected data are better known as the principal components (Mdlazi et al., 2007). PCA has been employed with genetic algorithms (GA) in order to reduce data dimensionality for use in fault diagnosis of induction motors. PCA was employed to remove relative features, after which GA was employed to select the irrelative features and to optimise the ANN (Yang, Han and Yin, 2006). Fault detection and diagnosis of plant subsystems have also been attempted using PCA. Normal plant operation decomposed through PCA was compared to faulty operation data through PCA decomposition to create thresholds for taking corrective actions. Real time monitoring of plant operation data was compared to both data sets with thresholds settled through Q statistics in order to detect faults (Villegas, Fuente and Rodriguez, 2010). Vibration monitoring of helicopter transmissions has been attempted using tri-axial accelerometers and PCA processing of the obtained data. The three different dimensions of acceleration data obtained using accelerometers were reduced to a single dimension using PCA for simpler processing. This approach is seen to provide a simpler and computationally robust technique for vibration monitoring in highly complex systems (Tumer and Huff, 2002). Independent PCA models suffer due to the control limits required for the Q and T2 statistics. Also, the limits are produced assuming that the process data is Gaussian in character, which may lead to complications if the process data is not actually Gaussian in character. Probabilistic techniques have been used in conjunction with PCA (PPCA) in order to handle both Gaussian and non-Gaussian process data for fault detection and diagnosis in a process control environment. Outcomes signified improvement over simple PCA based control schemes, but certain areas still required improvement under the PPCA based control scheme (He et al., 2012). PCA applications to process control are growing over time. Polyester film process monitoring has been attempted using Q and T2 statistics through a PCA approach for multivariate quality control (MQC). When compared to other techniques, PCA provided a more robust model for fault detection although diagnosis was not highly reliable. It could be inferred that PCA standalone approaches are best suited to fault detection since fault diagnosis requires the application of other techniques for established reliability (Qin, 2003). A combined index consisting of statistics Q and T2 has been developed in order to minimise the index when faulty variables are being isolated. This provides a better solution than applying the conventional approach of using statistics Q and T2 separately (Chen, Lee and Liu, 2011). It must be noted that PCA provides a simple reduction of dimensionality, but PCA processing is not suited to data streams with a large amount of outliers. A robust PCA (ROBPCA) method has been suggested for dealing with large dimension data using projection pursuit in combination with robust estimation of lower dimensions. Classification of outliers has been made possible through diagnostic plots (Hubert and Engelen, 2004). ROBPCA has been employed for fault detection and isolation in various theoretical situations in order to prove its worth over PCA. The findings signify that ROBPCA provides better results than PCA with its inherent ability to process large data sets (Tharrault et al., 2008). PCA has also been applied together with acoustic emission testing (AET) to deal with vibration monitoring of automobile engines. The use of acoustic variables for monitoring and control with PCA application allowed a strong process control with accuracy levels of 70% and more. It can be seen that PCA could be used with non-conventional monitoring variables in order to determine vibration characteristics of operating machines. Hence, PCA could find system-wide variable monitoring for applications as diverse as automobile engines (Kabiri and Makinezhad, 2010). Dimensional reduction is the key reason that makes PCA well suited to fault detection and identification (FDI). PCA projects the data for analysis onto a lower dimensional space, and this allows it to acquire the chief reasons behind variation in any process. However, PCA is limited in the sense that causes may change due to faulty processes. Such limitations may be dealt with using hybrid PCA models such as multi-scale PCA (MSPCA), adaptive PCA (APCA), recursive PCA, exponentially weighted PCA (EWPCA), dynamic PCA and non-linear PCA (Garc?a-Alvarez, 2009). The PCA method discovers various linear combinations of different variables that can be used in order to describe the significant facets of a group of data. The variables that are described by the data are orthogonally decomposed based on the covariance matrix of the subject variables. This also gives directions that provide an explanation for maximum discrepancy in the provided data. In the simplest terms, PCA allows reduction of the dimensional space of the originally recorded data for simpler analysis (Chiang, Russell and Braatz, 2000). PCA with neural network algorithms (PCANNA) has been utilised in computer systems to detect intrusion on computer networks such as through denial of service (DoS) attacks (Lakhina, Joseph and Verma, 2010). PCA has been used in condition monitoring applications to reduce the size of input space provided to the neural network for processing (Mdlazi et al., 2007). When using the PCA method, the faulty signal is detected by either the T2 or the Q statistic. The use of either statistic is not enough to provide the root cause of the fault, which must be determined using contribution plots. It must be kept in mind that the contribution of the Q statistic is easier to determine compared to the T2 statistic. Theoretically, if only a single principal component is recognised, which is responsible for a fault, the T2 statistic could be used with ease. However, practically this is not possible since practical application requires the use of multiple scores that are connected to a fault (Kano et al., 2000). Multi-way PCA (MPCA) has been employed to monitor batch processes by observing three dimensions of data that are batch number, process variables and measured observations at reference sample times (Hong and Zhang, 2010). Kernel PCA (KPCA) has been widely implemented in the chemical processing industry for fault monitoring. KPCA has been improved through feature vector selection (FVS) based on geometrical contemplation for large sample sizes. Moreover, Fisher discriminant analysis (FDA) is also adopted to improve KPCA performance (Cui, Li and Wang, 2008). KPCA has also been employed in order to reduce features in hyper spectral image analysis. Compared to PCA, it was found that KPCA was able to produce better results since higher order extraction was possible with KPCA and not with PCA (Fauvel, Chanussot and Benediktsson, 2006). Contribution Plots It must be kept in mind that PCA can be used independently in order to classify faults if historical data is available for comparison. In case that there is no historical data for fault comparison and classification, contributions plots must be used to classify faults. The contribution of different variable, or their groups, to a monitored index can be used in order to recognise variables that are causing the monitored index to reach out of bound values. There is a growing school of thought that tends to favour the use of contribution plots in comparison to PCA alone or PCA combined with other methods for fault identification. This method has been expressed as ‘DISSIM’ and is known to operate better than conventional PCA methods (Kano et al., 2001). Contribution plots can provide what variable is most strongly related to the observed fault. Typical batch processing operations utilise Q and T2 statistics in order to identify the presence of faults. In turn, contribution plots are used to decipher what variables have the greatest role to play in the observed fault. It must be noted that this conventional method cannot apply if the identified variable(s) is the cause for or merely connected to the fault. Progressive PCA modelling has been used in batch operations to successively eliminate variables for progressive fault variable identification (Hong and Zhang, 2010). Process control has been attempted through contribution plot application for fault diagnosis. A hybrid partial least squares (PLS) and T2 statistic index was developed in order to allow monitoring of variables through a contribution plot. The Tennessee Eastman Process was controlled using the hybrid index with contribution plots. The results were encouraging as robust process control was achieved (Gang et al., 2009). Contribution plots have been applied to quality and process variables in an attempt to decipher fault causing variables for a polyethylene reactor (Kourti and MacGregor, 1996). Investigation revealed that contribution plots do not decipher abnormality causing faults directly but allow identification of variables that caused the abnormality. Similarly, contribution plots have been applied to industrial batch processes based on a hierarchical classification of variables into various blocks and groups (Nomikos, 1996; Kourti and MacGregor, 1996; Choi and Lee, 2005; Qin et al., 2001). Classification of variables into blocks and groups based on process knowledge allowed easier fault isolation since blocks and groups of variables were investigated instead of all variables put together (Chen et al., 2011). Contribution plots have been applied after PCA in order to detect sensor faults on a localised scale. PCA was used in order to detect faults while contribution plots were created in order to locate the fault on a local scale. The contribution plots were applied through a hierarchical scheme that allowed processing blocks and groups of variables for fault diagnosis (Benaicha et al., 2010). Bibliography Benaicha, A., Guerfel, M., Bouguila, N. & Benothman, K., 2010. New PCA based methodology for sensor fault detection and localization. 8th International Conference of Modeling and Simulation. Ilammamet, Tunisia. Chen, D.-S., Lee, M.-W. and Liu, J., 2011. Isolating multiple sensor faults based on self-contribution plots with adaptive monitoring. China Steel Technical Report, 24, pp. 64–73. Chiang, L., Russell, E. and Braatz, R., 2000. Fault Detection and diagnosis in industrial systems. New York: Springer. Choi, S. W. and Lee, I. B., 2005. Multiblock PLS-based localized process diagnosis. Journal of Process Control, 15, p. 295. Cui, P., Li, J. and Wang, G., 2008. Improved kernel principal component analysis for fault detection. Expert Systems with Applications, 34, pp. 1210–19. Fauvel, M., Chanussot, J. and Benediktsson, J. A., 2006. Kernel principal component analysis for feature reduction in hyperspectrale image analysis. Proceedings of the 7th Nordic Signal Processing Symposium. Rejkjavik. Gang, L., Si-Zhao, Q., Yin-Dong, J. and Dong-Hua, Z., 2009. Total PLS based contribution plots for fault diagnosis. ACTA Automatica Sinica, 35(6), pp. 759–65. Garc?a-Alvarez, D., 2009. Fault detection using principal component analysis (PCA) in a wastewater treatment plant (WWTP). Proceedings of the International Student’s Scientific Conference. He, B., Yang, X., Chen, T. & Zhang, J., 2012. Reconstruction-based multivariate contribution analysis for fault isolation: A branch and bound approach. Journal of Process Control, 22(7), p.1228–1236. Hong, J. J. and Zhang, J., 2010. Progressive PCA modeling for enhanced fault diagnosis in a batch process. International Conference on Control, Automation and Systems 2010. Gyeonggi-do, Korea. Hubert, M. and Engelen, S., 2004. Robust PCA and classi?cation in biosciences. Bioinformatics, 20(11), pp. 1729–35. Kabiri, P. and Makinezhad, A., 2010. Using PCA in acoustic emission condition monitoring to detect faults in an automobile engine. European Working Group on Acoustic Emission. Vienna. Kano, M., Hasebe, S., Hashimoto, I. and Ohno, H., 2001. Fault detection and identification based on dissimilarity of process data. Preprints of European Control Conference (ECC). Porto, Portugal. Kano, M. et al., 2000. Contribution plots for fault identification based on the dissimilarity of process data. AIChE Annual Meeting. Los Angeles. Kourti, T. and MacGregor, J. F., 1996. Multivariate SPC methods for process and product monitoring. Journal of Quality Technology, 28, p. 409. Lakhina, S., Joseph, S. and Verma, B., 2010. 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International Journal of Mathematics and Computer Science, 18(4), pp. 429–42. Tumer, I. Y. and Huff, E. M., 2002. Principal components analysis of triaxial vibration data from helicopter transmissions (2002). Machinery failure prevention technology to improve the bottom line. Proceedings of the 56th meeting of the Society for Machinery Failure Prevention Technology. Villegas, T., Fuente, M. J. and Rodriguez, M., 2010. Principal Component analysis for fault diagnosis: experience with a pilot plant. CIMMACS' 10 proceedings of the 9th WSEAS International Conference on Computational Intelligence, Man-Machine Systems and Cybernetics. Yang, B.-S., Han, T. and Yin, Z.-J., 2006. Fault diagnosis system of induction motors using feature extraction, feature selection and classification algorithm. JSME International Journal, 49(3), pp. 734–41. Zhu, D., Bai, J. and Yang, S. X., 2010. A multi-fault diagnosis method for sensor systems based on principle component analysis. Sensors, 10, pp. 241–53. 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