Abstract
Multivariate statistical principles are introduced in this chapter as a basis for data-driven method for fault detection and isolation. Thus, Principal Component Analysis (PCA) properties for data projection and dimensionality reduction are exploited to model process behaviour based on historical data representing normal operating conditions. After formulating the PCA model in terms of projection and residual spaces, the method introduces the distance concept in both subspaces aiming to define fault detection criteria. Two statistics, Hotelling T\(^{2}\) and the square prediction error (SPE), are used with this purpose. Diagnosis functionalities are provided by the capability to describe the magnitude of both statistics in terms of contributions of the original variables. The chapter ends with an illustrative example of the method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Anderson, T.W.: An Introduction to Multivariate Statistical Analysis. Wiley, New York (1984)
Barta, C., Meléndez, J., Colomer, J.: Off line Diagnosis of Ariane Flights Using PCA, pp. 704–708. Elsevier, New York (2007)
Isermann, R., Ballé, P.: Trends in the application of model-based fault detection and diagnosis of technical processes. Control Eng. Pract. 5(5), 709–719 (1997). http://www.sciencedirect.com/science/article/pii/S0967066197000531
Jackson, J.E., Mudholkar, G.S.: Control procedures for residuals associated with principal component analysis. Technometrics 21(3), 341–349 (1979). https://doi.org/10.2307/1267757
Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Prentice-Hall, Upper Saddle River (1988)
Kourti, T.: Application of latent variable methods to process control and multivariate statistical process control in industry. Int. J. Adapt. Control Signal Process. 19(4), 213–246 (2005). https://doi.org/10.1002/acs.859
MacGregor, J.F.: Multivariate statistical approaches to fault detection and isolation. In: SAFEPROCESS (2003)
Nomikos, P., MacGregor, J.F.: Monitoring Batch Process Using Multiway Principal Componet Analysis. AIChE J. 40(8), 1361–1375 (1994). http://www3.interscience.wiley.com/journal/109063733/abstract
Qin, S.J., Dunia, R.: Determining the number of principal components for best reconstruction. J. Process Control 10, 245–250 (2000)
Russell, E.L., Chiang, L.H., Braatz, R.D.: Data-driven Methods for Fault Detection and Diagnosis in Chemical Processes (Advances in Industrial Control), 1st edn. Springer, Berlin (2000)
Wise, B.M., Gallagher, N.B., Bro, R., Shaver, J.M., Windig, W., Koch, R.S.: Chemometrics Tutorial for PLS \(\_\) Toolbox and Solo. Eigenvector Research Incorporated (2006)
Acknowledgements
This work has been developed within the eXiT (https://exit.udg.edu) research group (2017 SGR 1551) and supported by the CROWDSAVING project (Ref. TIN2016-79726-C2-2-R), funded by the Spanish Ministerio de Industria y Competitividad within the Research, Development and Innovation Program oriented toward the Societal Challenges.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Melendez i Frigola, J. (2019). Data-Driven Fault Diagnosis: Multivariate Statistical Approach. In: Escobet, T., Bregon, A., Pulido, B., Puig, V. (eds) Fault Diagnosis of Dynamic Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-17728-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-17728-7_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-17727-0
Online ISBN: 978-3-030-17728-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)