Nonparametric bayesian based on mixture of dirichlet process in application of fault detection
LUO Lin 1, SU Hong ye1, BAN Lan2
1. Institute of Cyber System & Control, Zhejiang University, Hangzhou 310027, China;2. School of Mechanical Engineering, University of Science and Technology Beijing,Haidian District 100083, China
A nonparametric Bayesian fault detection method based on Dirichlet process mixture model was proposed to resolve the issues of Gaussian mixture model, i.e., noisy model size estimates and overfitting proneness in the model estimation. The construction of Dirichlet process mixture model was constructed baseed on the stick breaking method and the redefinition of the mixing weight in Gaussian mixture model. The parameters and latent variables was approximatively infered by an efficient truncated variational Bayesian inference algorithm. The resulting posterior distribution was utilized to the estimation of fault model. The monitoring statistic was proposed to measure the variation inside the posterior. The results on the non isothermal continuous stirred tank reactor and Tennessee Eastman chemical plant simulation show that the performances of fault diagnosis by the presented method are superior to that by kernel principal component analysis with higher accuracy．
LUO Lin, SU Hong ye, BAN Lan. Nonparametric bayesian based on mixture of dirichlet process in application of fault detection. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2015, 49(11): 2230-2236.
［1］ VENKATASUBRAMANIAN V, RENGASWAMY R, YIN K., et al. A review of process fault detection and diagnosis part I: Quantitative model based methods ［J］. Computers and Chemical Engineering, 2003, 27(3): 293-311．
［2］ VENKATASUBRAMANIAN V, RENGASWAMY R, KAVURI S N. A review of process fault detection and diagnosis part II: Qualitative models and search strategies ［J］. Computers and Chemical Engineering, 2003, 27(3): 313-326．
［3］ VENKATASUBRAMANIAN V, RENGASWAMY R, KAVURI S N, et al. A review of process fault detection and diagnosis part III: Process history based methods ［J］. Computers and Chemical Engineering, 2003, 27(3): 327-346．
［4］ QIN S J. Survey on data driven industrial process monitoring and diagnosis ［J］. Annual Reviews in Control, 2012, 36(2): 220-234．
［5］ SHEN Y, STEVEN X D, ADEL H, et al. A comparison study of basic data driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process ［J］. Journal of Process Control, 2012, 22(9): 1567-1581．
［6］ LIN L, HONGYE S, BAOFEN Z, et al. Generalized convexity based inexact projection method for multiple kernel learning ［J］. Journal of Intelligent and Fuzzy Systems, 2014, 27(4): 1825-1835．
［7］ YU J, QIN S J. Multimode process monitoring with Bayesian inference based finite Gaussian mixture models ［J］. American Institute of Chemical Engineers, 2008, 54(7): 1811-1829．
［8］ TAO C, JIE Z. On line multivariate statistical monitoring of batch processes using Gaussian mixture model ［J］. Computers and Chemical Engineering, 2010, 34(4)：500-507．
［9］ MCLACHLAN G, PEEL D. Finite mixture models ［M］. John Wiley & Sons: New York, USA, 2000．
［10］ RUSSELL E L, CHIANG L H, BRAATZ R D. Fault detection in industrial processes using canonical variate analysis and dynamic principal component analysis ［J］. Chemometrics and Intelligent Laboratory Systems, 2000, 51(1): 81-93．
［11］ CHATZIS S P, KOSMOPOULOS D, VARVARIGOU T. Signal modeling and classification using a robust latent space model based on t distributions ［J］. IEEE Transactions on Signal Processing, 2008, 56(3)：949-963．
［12］ DAVID B. Bayesian Reasoning and Machine Learning ［M］. Cambridge University Press: New York, USA, 2012．
［13］ ATTIAS H. A variational bayesian framework for graphical models ［C］∥ Advances in Neural Information Processing Systems. Denver: MIT Press, 2000: 209215．
［14］ LIN L, LEI X, KRUGER U, et al. A novel Bayesian robust model and its application for fault detection and automatic supervision of nonlinear process ［J］. Industrial & Engineering Chemistry Research. 2015, 54 (18): 5048-5061.
［15］ CHEN Q, KRUGER U, MERONK M, et al. Synthesis of T2 and Q statistics for process monitoring ［J］, Control Engineering Practice, 2004, 12(6): 745-755．
［16］ FIGUEIREDO M, JAIN A K. Unsupervised learning of finite mixture models ［J］. IEEE Transaction on Pattern Analysis and Machine Intelligence. 2002, 24(3): 381-396．
［17］ CHO J H, LEE J M, CHOI S W, et al. Fault identification for process monitoring using kernel principal component analysis ［J］. Chemical Engineering Science, 2005, 60(1): 279-288．
［18］ RICKER NL. Decentralized control of the tennessee eastman challenge process ［J］. Journal of Process Control, 1996, 6(4): 205-221．
［19］ ZHIQIANG G, ZHIHUAN S. Performance driven ensemble learning ICA model for improved non Gaussian process monitoring ［J］. Chemometrics and Intelligent Laboratory Systems, 2013, 123: 1-8．
［20］ LEI X, XIAOZHONG L, JIUSUN Z. Shrinking principal component analysis for enhanced process monitoring and fault isolation ［J］. Industrial & Engineering Chemistry Research, 2013, 52 (49): 17475-17486．
［21］ LARSSON T, HESTETUN K, HOVLAND E, et al. Self Optimizing control of a large scale plant: the Tennessee Eastman process ［J］. Industrial & Engineering Chemistry Research, 2001, 40(22): 4889-4901．
