Research Papers

Statistical Comparison of Feature Sets for Time Series Classification of Dynamic System Response

[+] Author and Article Information
Amit Banerjee

Pennsylvania State University Harrisburg,
777 West Harrisburg Pike, Middletown, PA 17057
e-mail: aub25@psu.edu

Juan C. Quiroz

Sunway University, Jakan Universiti,
Bandar Sunway, Petaling Jaya, Selangor 47500, Malaysia
e-mail: juanq@sunway.edu.my

Issam Abu-Mahfouz

Pennsylvania State University Harrisburg,
777 West Harrisburg Pike, Middletown, PA 17057
e-mail: iaa25@psu.edu

1Corresponding author.

Manuscript received January 28, 2016; final manuscript received April 27, 2016; published online August 19, 2016. Assoc. Editor: Ioannis Kougioumtzoglou.

ASME J. Risk Uncertainty Part B 2(4), 041006 (Aug 19, 2016) (8 pages) Paper No: RISK-16-1042; doi: 10.1115/1.4033542 History: Received January 28, 2016; Accepted April 28, 2016

The use of classification techniques for machine health monitoring and fault diagnosis has been popular in recent years. System response in the form of time series data can be used to identify the type of defect and severity of defect. However, a central issue with time series classification is that of identifying appropriate features for classification. In this paper, we explore a new feature set based on delay differential equations (DDEs). DDEs have been used recently for extracting features for classification but have never been used to classify system responses. The Duffing oscillator, Van der Pol–Duffing (VDP-D) oscillator, Lu oscillator, and Chen oscillator are used as examples for dynamic systems, and the responses are classified into self-similar groups. Responses with the same period should belong to the same group. Misclassification rate is used as an indicator of the efficacy of the feature set. The proposed feature set is compared to a statistical feature set, a power spectral coefficient feature set, and a wavelet coefficient feature set. In the work described in this paper, a density-estimation algorithm called DBSCAN is used as the classification algorithm. The proposed DDE-based feature set is found to be significantly better than the other feature sets for classifying responses generated by the Duffing, Lu, and Chen systems. The wavelet and power spectral coefficient data sets are not found to be significantly better than the statistical feature set for these systems. None of the feature sets tested is discerning enough on the VDP-D system.

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Yang, J., Zhang, Y., and Zhu, Y., 2006, “Intelligent Fault Diagnosis of Rolling Element Bearing Based on SVMs and Fractal Dimension,” Mech. Syst. Signal Process., 21(5), pp. 2012–2024. 10.1016/j.ymssp.2006.10.005
Sanz, J., Perera, R., and Huerta, C., 2007, “Fault Diagnosis of Rotating Machinery Based on Auto-Associative Neural Networks and Wavelet Transforms,” J. Sound Vibr., 302(4–5), pp. 981–999. 10.1016/j.jsv.2007.01.006
Lui, B., 2006, “Selection of Wavelet Packet Basis for Rotating Machinery Fault Diagnosis,” J. Sound Vibr., 284(3–5), pp. 567–582.
Wong, M. L. D., Jack, L. B., and Nandi, A. K., 2006, “Modified Self-Organizing Map for Automated Novelty Detection Applied to Vibration Signal Monitoring,” Mech. Syst. Signal Process., 20(3), pp. 593–610. 10.1016/j.ymssp.2005.01.008
Ocak, H., Loparo, K. A., and Discenzo, F. M., 2007, “Online Tracking of Bearing Wear Using Wavelet Packet Decomposition and Probabilistic Modeling—A Method for Bearing Prognostics,” J. Sound Vibr., 302(4–5), pp. 951–961. 10.1016/j.jsv.2007.01.001
Lee, J., We, F., Zhao, W., Ghaffari, M., Liao, L., and Siegel, D., 2014, “Prognostics and Health Management Design for Rotary Machinery Systems—Reviews, Methodology and Applications,” Mech. Syst. Signal Process., 42(1–2), pp. 314–334. 10.1016/j.ymssp.2013.06.004
Lei, Y., He, Z., and Zi, Y., 2009, “Application of an Intelligent Classification Method to Mechanical Fault Diagnosis,” Expert Syst. Appl., 36(6), pp. 9941–9948. 10.1016/j.eswa.2009.01.065
Zhou, L., 2005, “Neural Networks Based on Fuzzy Clustering and Its Applications in Electrical Equipment’s Fault Diagnosis,” Proceedings of IEEE International Conference on Machine Learning and Cybernetics, Guangzhou, China, Vol. 7, pp. 3396–3999. 10.1109/ICMLC.2005.1527636
Chan, E. Y., Ching, W. K., Ng, M. K., and Huang, J. Z., 2004, “An Optimization Algorithm for Clustering Using Weighted Dissimilarity Measures,” Pattern Recognit., 37(5), pp. 943–952. 10.1016/j.patcog.2003.11.003
Saravanan, N., Cholairajan, S., and Ramachandran, K. I., 2009, “Vibration-Based Fault Diagnosis of Spur Bevel Gear Box Using Fuzzy Technique,” Expert Syst. Appl., 36(2), pp. 3119–3135. 10.1016/j.eswa.2008.01.010
Wang, X., Wang, Y., and Wang, L., 2004, “Improving Fuzzy C-Means Clustering Based on Feature-Weight Learning,” Pattern Recognit. Lett., 25(10), pp. 1123–1132. 10.1016/j.patrec.2004.03.008
Lei, Y., He, Z., Zi, Y., and Chen, X., 2008, “New Clustering Algorithm-Based Fault Diagnosis Using Compensation Distance Evaluation Technique,” Mech. Syst. Signal Process., 22(2), pp. 419–435. 10.1016/j.ymssp.2007.07.013
Yiakopoulos, C. T., Gryllias, K. C., and Antoniadis, I. A., 2011, “Rolling Element Bearing Fault Detection in Industrial Environments Based on a K-Means Clustering Approach,” Expert Syst. Appl., 38(3), pp. 2888–2911. 10.1016/j.eswa.2010.08.083
Lu, J., Chen, G., Cheng, D., and Celikovsky, S., 2002, “Bridge the Gap Between the Lorenz System and the Chen System,” Int. J. Bifurcation Chaos, 12(12), pp. 2917–2926. 10.1142/S021812740200631X
Chen, S., and Lu, J., 2002, “Synchronization of an Uncertain Unified Chaotic System via Adaptive Control,” Chaos Solitons Fractals, 14(4), pp. 643–647. 10.1016/S0960-0779(02)00006-1
Ueta, T., and Chen, G., 2000, “Bifurcation Analysis of Chen’s Equation,” Int. J. Bifurcation Chaos, 10(8), pp. 1917–1931. [CrossRef]
Esling, P., and Agon, C., 2012, “Time-Series Data Mining,” ACM Comput. Surv., 45(1), pp. 1–34. 10.1145/2379776
Nanopoulos, A., Alcock, R., and Manolopoulos, Y., 2001, “Feature-Based Classification of Time-Series Data,” Int. J. Comput. Res., 10(3), pp. 49–61.
Agrawal, R., Faloutsos, C., and Swami, A., 1993, “Efficient Similarity Search in Sequence Databases,” Proceedings of International Conference on Foundations of Data Organization and Algorithms, Springer, London, pp. 69–84.
Faloutsos, C., Ranganathan, M., and Manolopulos, Y., 1994, “Fast Subsequence Matching in Time-Series Databases,” Proceedings of ACM SIGMOD International Conference on the Management of Data, ACM Press, New York, NY, pp. 419–429. 10.1145/191843.191925
Struzik, Z. R., and Siebes, A., 1999, “Measuring Time Series Similarity Through Large Singular Features Revealed With Wavelet Transformation,” Proceedings of 10th International Workshop on Database and Expert Systems Applications, IEEE Computer Society, Los Alamitos, CA, pp. 162–166.
Janacek, G., Bagnall, A., and Powell, M., 2005, “A Likelihood Ratio Distance Measure for the Similarity Between the Fourier Transform of Time Series,” Advances in Knowledge Discovery and Data Mining (Lecture Notes in Computer Science, Vol. 3518), Springer, New York, pp. 737–743.
Vlachos, M., Yu, P., and Castelli, V., 2005, “On Periodicity Detection and Structural Periodic Similarity,” Proceedings of SIAM International Conference on Data Mining, Society for Industrial and Applied Mathematics, Philadelphia, PA, pp. 449–460. 10.1137/1.9781611972757.40
Papadimitriou, S., Sun, J., and Yu, P., 2006, “Local Correlation Tracking in Time Series,” Proceedings of International Conference on Data Mining, IEEE Computer Society, Los Alamitos, CA, pp. 456–465. 10.1109/ICDM.2006.99
Rafiei, D., and Mendelzon, A., 1997, “Similarity-Based Queries for Time Series Data,” Proceedings of ACM SIGMOD International Conference on the Management of Data, ACM Press, New York, NY, pp. 13–25. 10.1145/253260.253264
Lainscsek, C., and Sejnowsku, T. J., 2015, “Delay Differential Analysis of Time Series,” Neural Comput., 27(3), pp. 594–614. 10.1162/NECO_a_00706 [PubMed]
Judd, K., and Mees, A., 1998, “Embedding as a Modeling Problem,” Phys. D: Nonlinear Phenom., 120(3–4), pp. 273–286. 10.1016/S0167-2789(98)00089-X
Lainscsek, C., Rowat, P., Schettino, L., Lee, D., Song, D., Letellier, C., and Poizner, H., 2012, “Finger Tapping Movements of Parkinson’s Disease Patients Automatically Rated Using Nonlinear Delay Differential Equations,” Chaos, 22(1), pp. 0131191–01311913. 10.1063/1.3683444
Liao, T. W., “Clustering of Time Series Data—A Survey,” Pattern Recognit., 38(11), pp. 1857–1874. 10.1016/j.patcog.2005.01.025
Shaw, C. T., and King, G. P., 1992, “Using Cluster Analysis to Classify Time Series,” Physica D, 58(1–4), pp. 288–298. 0167-2789 10.1016/0167-2789(92)90117-6
Vlachos, M., Lin, J., Keogh, E., and Gunopulos, D., 2003, “A Wavelet-Based Anytime Algorithm for k-Means Clustering of Time Series,” Proceedings of Workshop on Clustering High Dimensionality Data and its Applications, SIAM International Conference on Data Mining, Society for Industrial and Applied Mathematics, Philadelphia, PA, pp. 23–30.
Jain, A. K., and Dubes, R. C., 1998, Algorithms for Clustering Data, Prentice Hall, Englewood Cliffs, NJ.
Ester, M., Krigel, H.-P., Sander, J., and Xu, X., 1996, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases With Noise,” Proceedings of International Conference on Knowledge Discovery and Data Mining, pp. 226–231.
Daniel, W., 1990, Applied Nonparametric Statistics, Duxbury Thomson Learning, Pacific Grove, CA.


Grahic Jump Location
Fig. 4

Schematic of the two-population evolutionary algorithm to optimize structure and time delays

Grahic Jump Location
Fig. 5

Core, border, and outlier points as defined in DBSCAN.

Grahic Jump Location
Fig. 3

(a) Phase space portrait for the standard Chen attractor: a=35, b=28, c=3. (b) Phase space portrait for Chen attractor: a=35, b=20.2, c=3. (c) Phase space portrait for Chen-type C attractor: a=35, b=24, c=3. (d) Phase space portrait for the Transverse 8 type-S Chen attractor: a=35, b=28.2, c=3.

Grahic Jump Location
Fig. 2

Phase space portrait (displacement versus velocity) for VDP-D oscillator, for F=0.35, ω=1.4, μ=0.1, α=−0.5, β=0.5. The Poincaré points indicate that the response is chaotic.

Grahic Jump Location
Fig. 1

(a) Phase space portrait (displacement versus velocity) for Duffing oscillator, for F=1.5, ω=2.0, μ=0.1, α=0.5, β=1. The Poincaré point indicates that the response is periodic of period 1. (b) Phase space portrait (displacement versus velocity) for Duffing oscillator, for F=0.35, ω=1.4, μ=0.1, α=−0.5, β=0.5. The Poincaré points indicate that the response is chaotic.




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