A wavelet-based clustering of multivariate time series using a Multiscale SPCA approach

Case study comprising the fault detection in a benchmark industrial process.Comprehensive and novel method for clustering multivariate time series.Multiscale approach provides improvement in clustering quality.Multiscale approach represents a useful technique in FDD problems.Results show the ability of the method in recognizing normal and fault patterns. Clustering and pattern recognition from data can be used as means to extract knowledge of a process which may be useful for control, predicting failures and supporting decision making, among other functions. This paper presents a method to recognize patterns in multivariate time series based on a combination of wavelet features, PCA (Principal Component Analysis) similarity metrics and fuzzy clustering. The signal analysis of some process variables is performed based on the Wavelet Transform (WT), and a Multiscale PCA Similarity factor (SPCAms) is proposed to consider the distances between objects (multivariate time series) according to a multi-resolution approach. A database extracted from the benchmark Tennessee Eastman (TE) process is used to show the efficiency of the method compared with traditional approaches in a fault detection and diagnosis problem. The clustering using SPCAms provides the recognition of a fault pattern which may be useful to support decision-making at the operational level allowing real-time monitoring of failure probability.

[1]  E. F. Vogel,et al.  A plant-wide industrial process control problem , 1993 .

[2]  Duygu Bayram,et al.  Wavelet based Neuro-Detector for low frequencies of vibration signals in electric motors , 2013, Appl. Soft Comput..

[3]  Chengjun Liu,et al.  Clustering-Based Discriminant Analysis for Eye Detection , 2014, IEEE Transactions on Image Processing.

[4]  Bernard Legube,et al.  Principal component analysis: an appropriate tool for water quality evaluation and management—application to a tropical lake system , 2004 .

[5]  T. Warren Liao,et al.  Clustering of time series data - a survey , 2005, Pattern Recognit..

[6]  James M. Keller,et al.  Fuzzy Models and Algorithms for Pattern Recognition and Image Processing , 1999 .

[7]  Frederico G. Guimarães,et al.  A cognitive system for fault prognosis in power transformers , 2015 .

[8]  Pierpaolo D’Urso,et al.  Autocorrelation-based fuzzy clustering of time series , 2009, Fuzzy Sets Syst..

[9]  Jun Lv,et al.  A robust approach for root causes identification in machining processes using hybrid learning algorithm and engineering knowledge , 2012, J. Intell. Manuf..

[10]  Claus Weihs,et al.  Variable window adaptive Kernel Principal Component Analysis for nonlinear nonstationary process monitoring , 2011, Comput. Ind. Eng..

[11]  George Karabatis,et al.  Discrete wavelet transform-based time series analysis and mining , 2011, CSUR.

[12]  Orestes Llanes-Santiago,et al.  Optimizing kernel methods to reduce dimensionality in fault diagnosis of industrial systems , 2015, Comput. Ind. Eng..

[13]  Hector Budman,et al.  Fault detection, identification and diagnosis using CUSUM based PCA , 2011 .

[14]  Dale E. Seborg,et al.  Evaluation of a pattern matching method for the Tennessee Eastman challenge process , 2006 .

[15]  Jinfang Zhang,et al.  Fault localization in electrical power systems: A pattern recognition approach , 2011 .

[16]  Fontes C.H.O,et al.  Multivariable correlation analysis and its application to an industrial polymerization reactor , 2001 .

[17]  János Abonyi,et al.  Correlation based dynamic time warping of multivariate time series , 2012, Expert Syst. Appl..

[18]  Junyi Shen,et al.  Classification of multivariate time series using two-dimensional singular value decomposition , 2008, Knowl. Based Syst..

[19]  V. Kavitha,et al.  Clustering Time Series Data Stream - A Literature Survey , 2010, ArXiv.

[20]  O. Kisi,et al.  Wavelet and neuro-fuzzy conjunction model for precipitation forecasting , 2007 .

[21]  Peter Trebuňa,et al.  Mathematical Tools of Cluster Analysis , 2013 .

[22]  E. L. Lima,et al.  Control strategies for complex chemical processes. Applications in polymerization processes , 2003, Comput. Chem. Eng..

[23]  Cyrus Shahabi,et al.  A PCA-based similarity measure for multivariate time series , 2004, MMDB '04.

[24]  Carlos Arthur Mattos Teixeira Cavalcante,et al.  Pattern recognition as a tool to support decision making in the management of the electric sector. Part II: A new method based on clustering of multivariate time series , 2015 .

[25]  Raghunathan Rengaswamy,et al.  A review of process fault detection and diagnosis: Part I: Quantitative model-based methods , 2003, Comput. Chem. Eng..

[26]  Tak-Chung Fu,et al.  A review on time series data mining , 2011, Eng. Appl. Artif. Intell..

[27]  Rubens Maciel Filho,et al.  Fuzzy cognitive approach of a molecular distillation process , 2011 .

[28]  Nitesh V. Chawla,et al.  Data Mining for Imbalanced Datasets: An Overview , 2005, The Data Mining and Knowledge Discovery Handbook.

[29]  K. I. Ramachandran,et al.  Incipient gear box fault diagnosis using discrete wavelet transform (DWT) for feature extraction and classification using artificial neural network (ANN) , 2010, Expert Syst. Appl..

[30]  Xiaogang Deng,et al.  Modified kernel principal component analysis based on local structure analysis and its application to nonlinear process fault diagnosis , 2013 .

[31]  Richard D. Braatz,et al.  Fault Detection and Diagnosis in Industrial Systems , 2001 .

[32]  Li Zhishu,et al.  The Similarity of Multivariate Time Series and Its Application , 2010, 2010 International Conference on Management of e-Commerce and e-Government.

[33]  Lifeng Xi,et al.  Fault diagnosis in assembly processes based on engineering-driven rules and PSOSAEN algorithm , 2011, Comput. Ind. Eng..

[34]  Sheng-Tun Li,et al.  Clustering spatial-temporal precipitation data using wavelet transform and self-organizing map neural network , 2010 .

[35]  Geeta Sikka,et al.  Recent Techniques of Clustering of Time Series Data: A Survey , 2012 .

[36]  Tiago J. Rato,et al.  Fault detection in the Tennessee Eastman benchmark process using dynamic principal components analysis based on decorrelated residuals (DPCA-DR) , 2013 .

[37]  D. Seborg,et al.  Clustering multivariate time‐series data , 2005 .

[38]  János Abonyi,et al.  On-line detection of homogeneous operation ranges by dynamic principal component analysis based time-series segmentation , 2012 .

[39]  Ali Cinar,et al.  Monitoring, fault diagnosis, fault-tolerant control and optimization: Data driven methods , 2012, Comput. Chem. Eng..

[40]  Bhavik R. Bakshi,et al.  Representation of process trends—III. Multiscale extraction of trends from process data , 1994 .

[41]  Farid Kadri,et al.  Improved principal component analysis for anomaly detection: Application to an emergency department , 2015, Comput. Ind. Eng..

[42]  Olatz Arbelaitz,et al.  An extensive comparative study of cluster validity indices , 2013, Pattern Recognit..

[43]  Elizabeth Ann Maharaj,et al.  Wavelets-based clustering of multivariate time series , 2012, Fuzzy Sets Syst..

[44]  田中 勝人.  D. B. Percival and A. T. Walden: Wavelet Methods for Time Series Analysis, Camb. Ser. Stat. Probab. Math., 4, Cambridge Univ. Press, 2000年，xxvi + 594ページ． , 2009 .

[45]  Marco S. Reis.  An integrated multiscale and multivariate image analysis framework for process monitoring of colour random textures: MSMIA , 2015 .

[46]  Xiao-Jun Zeng,et al.  Fuzzy C-means++: Fuzzy C-means with effective seeding initialization , 2015, Expert Syst. Appl..

[47]  N. Lawrence Ricker,et al.  Decentralized control of the Tennessee Eastman Challenge Process , 1996 .

[48]  Tapas K. Das,et al.  Wavelet-based multiscale statistical process monitoring: A literature review , 2004 .

[49]  Ying Wah Teh,et al.  Time-series clustering - A decade review , 2015, Inf. Syst..

[50]  Jin Wen,et al.  A model-based fault detection and diagnostic methodology based on PCA method and wavelet transform , 2014 .

[51]  Chee Peng Lim,et al.  Clustering and visualization of failure modes using an evolving tree , 2015, Expert Syst. Appl..

[52]  Hui Xiong,et al.  Clustering Validation Measures , 2018, Data Clustering: Algorithms and Applications.

[53]  Ping Zhang,et al.  A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process , 2012 .

[54]  Dimitrios Gunopulos,et al.  Indexing multi-dimensional time-series with support for multiple distance measures , 2003, KDD '03.

[55]  Jun Lv,et al.  Recognition of concurrent control chart patterns using wavelet transform decomposition and multiclass support vector machines , 2013, Comput. Ind. Eng..

[56]  Gülşen Aydın Keskin,et al.  A VARIANT PERSPECTIVE TO PERFORMANCE APPRAISAL SYSTEM FUZZY C MEANS ALGORITHM , 2014 .

[57]  Pierpaolo D'Urso,et al.  A Fuzzy Clustering Model for Multivariate Spatial Time Series , 2010, J. Classif..