Uncertain Nonlinear Process Monitoring Using Interval Ensemble Kernel Principal Component Analysis
Xianrui Wang*, Guoxin Zhao*,, Yu Liu*, and Shujie Yang**
*College of Information Engineering, Beijing Institute of Petrochemical Technology
No.19 Qingyuan North Road, Daxing District, Beijing 102617, China
**School of Marine Engineering Equipment, Zhejiang Ocean University
No.1 Haida South Road, Dinghai District, Zhoushan, Zhejiang 336022, China
To solve uncertainties in industrial processes, interval kernel principal component analysis (IKPCA) has been proposed based on symbolic data analysis. However, it is experimentally discovered that the performance of IKPCA is worse than that of other algorithms. To improve the IKPCA algorithm, interval ensemble kernel principal component analysis (IEKPCA) is proposed. By optimizing the width parameters of the Gaussian kernel function, IEKPCA yields better performances. Ensemble learning is incorporated in the IEKPCA algorithm to build submodels with different width parameters. However, the multiple submodels will yield a large number of results, which will complicate the algorithm. To simplify the algorithm, a Bayesian decision is used to convert the result into fault probability. The final result is obtained via a weighting strategy. To verify the method, IEKPCA is applied to the Tennessee Eastman (TE) process. The false alarm rate, fault detection rate, accuracy, and other indicators used in the IEKPCA are compared with those of other algorithms. The results show that the IEKPCA improves the accuracy of uncertain nonlinear process monitoring.
-  G. Wang, J. Jiao, and Z. Ge, “A Kernel Least Squares Based Approach for Nonlinear Quality-Related Fault Detection,” IEEE Trans. Ind. Electron, Vol.64, No.4, pp. 3195-3204, 2019.
-  S. J. Qin, “Survey on data-driven industrial process monitoring and diagnosis,” Annual Reviews in Control, Vol.36, No.2, pp. 220-234, 2012.
-  M. Harkat, G. Mourot, and J. Ragot, “An improved PCA scheme for sensor FDI: Application to an air quality monitoring network,” J. of Process Control, Vol.16, No.6, pp. 625-634, 2006.
-  B. Schölkopf, A. Smola, and K. R. Müller, “Nonlinear Component Analysis as a Kernel Eigenvalue Problem,” Neural Computation, Vol.10, No.5, pp. 1299-1299, 1998.
-  J. Huang and X. Yan, “Quality-Driven Principal Component Analysis Combined with Kernel Least Squares for Multivariate Statistical Process Monitoring,” IEEE Trans. Control Systems Technol., Vol.27, No.6, pp. 2688-2695, 2019.
-  B. Zhou and X. Gu, “Multi-block statistics local kernel principal component analysis algorithm and its application in nonlinear process fault detection,” Neurocomputing, Vol.376, pp. 222-231, 2020.
-  Y. Wang, Y. Si, B. Huang, and Z. Lou, “Survey on the theoretical research and engineering applications of multivariate statistics process monitoring algorithms,” The Canadian J. of Chemical Engineering, Vol.96, No.10, pp. 2073-2085, 2018.
-  J. Zhao, Y. Li, and T. Qiu, “A method for sensor fault diagnosis based on wavelet transform and neural network,” J. Qinghua University, Vol.53, No.2, pp. 205-209+221, 2013.
-  S. Ferson, V. Kreinovich, J. Hajagos, W. Oberkampf, and L. Ginzburg, “Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty,” Sandia Report, SAND2007-0939, Sandia National Laboratories, 2007.
-  F. Palumbo and C. N. Lauro, “A PCA for interval-valued data based on midpoints and radii,” K. Shigemasu, Y. Kano, and J. J. Meulman (Eds.), “New Developments in Psychometrics,” Springer, pp. 641-648, 2003.
-  C. Chakour, A. Benyounes, and M. Boudiaf, “Diagnosis of uncertain nonlinear systems using interval kernel principal components analysis: Application to a weather station,” ISA Trans., Vol.83, pp. 126-141, 2008.
-  T. Ait-Izem, M. Harkat, M. Djeghaba, and F. Kratz, “On the application of interval PCA to process monitoring: A robust strategy for sensor FDI with new efficient control statistics,” J. of Process Control, Vol.63, pp. 29-46, 2018.
-  M. Mansouri, M. F. Harkat, M. Nounou, and H. Nounou, “Midpoint-radii principal component analysis-based EWMA and application to air quality monitoring network,” Chemometrics and Intelligent Laboratory Systems, Vol.175, pp. 55-64, 2018.
-  M. F. Harkat, M. Mansouri, M. Nounou, and H. Nounou, “Fault detection of uncertain nonlinear process using interval-valued data-driven approach,” Chemical Engineering Science, Vol.205, pp. 36-45, 2019.
-  B. Scholkopf, A. Smola, and K. Muller, “Kernel principal component analysis,” W. Gerstner, A. Germond, M. Hasler, and J.-D. Nicoud (Eds.), “Artificial Neural Networks – ICANN’97,” Lecture Notes in Computer Science, Vol.1327, pp. 583-588, 2005.
-  Y. Liu and Z. Ge, “Weighted random forests for fault classification in industrial processes with hierarchical clustering model selection,” J. Process Control, Vol.64, No.4, pp. 62-70, 2018.
-  C. Chakour, “Diagnostic et surveillance des procédés industriels et de leur environnement sur la base de l’analyse de données,” Ph.D. Thesis, Badji Mokhtar-Annaba University, 2016.
-  P. Cui, C. Zhan, and Y. Yang, “Improved nonlinear process monitoring based on ensemble KPCA with local structure analysis,” Chemical Engineering Research and Design, Vol.142, pp. 355-368, 2019.
-  S. Gajjar, M. Kulahci, and A. Palazoglu, “Real-time fault detection and diagnosis using sparse principal component analysis,” J. Process Control, Vol.67, pp. 112-128, 2018.
-  M. T. Amin, S. Imtiaz, and F. Khan, “Process system fault detection and diagnosis using a hybrid technique,” Chemical Engineering Science, Vol.189, pp. 191-211, 2018.