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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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Figures

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.

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. 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. 4

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

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Fig. 5

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

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