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Mathematical Problems in Engineering
Volume 2014, Article ID 427209, 10 pages
Research Article

Adaptive Fault Detection with Two Time-Varying Control Limits for Nonlinear and Multimodal Processes

1The Lab of Operation and Control, Shenyang University of Chemical Technology, Liaoning 110142, China
2The Key Laboratory of Networked Control Systems, Shenyang Institute of Automation, Chinese Academy of Sciences, Liaoning 110016, China
3The College of Information Engineering, Shenyang University of Chemical Technology, Liaoning 110142, China

Received 11 September 2013; Accepted 17 November 2013; Published 20 January 2014

Academic Editor: Jun Hu

Copyright © 2014 Jinna Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel fault detection method is proposed for detection process with nonlinearity and multimodal batches. Calculating the Mahalanobis distance of samples, the data with the similar characteristics are replaced by the mean of them; thus, the number of training data is reduced easily. Moreover, the super ball regions of mean and variance of training data are presented, which not only retains the statistical properties of original training data but also avoids the reduction of data unlimitedly. To accurately identify faults, two control limits are determined during investigating the distributions of distances and angles between training samples to their nearest neighboring samples in the reduced database; thus, the traditional -nearest neighbors (only considering distances) fault detection (FD-kNN) method is developed. Another feature of the proposed detection method is that the control limits vary with updating database such that an adaptive fault detection technique is obtained. Finally, numerical examples and case study are given to illustrate the effectiveness and advantages of the proposed method.