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## Symbolic time series analysis via wavelet-based partitioning (2006)

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Venue: | Signal Processing |

Citations: | 75 - 42 self |

### Citations

3136 |
A wavelet tour of signal processing
- Mallat
- 1998
(Show Context)
Citation Context ... Ray / Signal Processing 86 (2006) 3309–3320 alleviates these difficulties via adaptive usage of long windows for retrieving low-frequency information and short windows for high-frequency information =-=[16,17]-=-. The ability to perform flexible localized analysis is one of the striking features of wavelet transform. In multi-resolution analysis (MRA) of wavelet transform, a continuous signal f 2 H, where H i... |

745 |
Nonlinear time series analysis
- Kantz, Schreiber
- 2003
(Show Context)
Citation Context ...s extraction of relevant information, imbedded in the measured time series data, to generate symbol sequences. Symbol generation requires partitioning of the data space to obtain the symbol sequences =-=[8,9]-=-. Various partitioning techniques have been suggested in literature for symbol generation, which include variancebased [10], entropy-based [11], and hierarchical clustering [12] methods. A survey of c... |

532 | The lifting scheme: A construction of second generation wavelets,” Jounnul on Murheimrical Analysis
- Sweldens
- 1998
(Show Context)
Citation Context ...ol generation for anomaly detection requires continued theoretical and experimental research. In this context, future research is recommended in the following areas: Exploration of lifting techniques =-=[23]-=- for wavelet customization; Extension of ME partitioning to multi-dimensional time series; Noise reduction in time series for robust anomaly/damage detection. ARTICLE IN PRESS V. Rajagopalan, A. Ray /... |

212 |
Nonlinear dynamics and chaos
- Thompson, Stewart
- 2002
(Show Context)
Citation Context ...is example demonstrates efficacy of the STSA method for anomaly detection in nonlinear systems. Experiments have been conducted on a laboratory apparatus [1] that emulates the forced Duffing equation =-=[21]-=-, modelled as d 2 y dy þ b dt2 dt þ yðtÞþy3ðtÞ A cosðOtÞ, (13) where the dissipation parameter b varies slowly with respect to the response of the dynamical system; b 0:1 represents the nominal con... |

199 |
A friendly guide to wavelets
- Kaiser
- 1994
(Show Context)
Citation Context ...particular scale a is given by the following formula [18,19]: f p F c , (4) aDt where Dt is the sampling interval. Fig. 1 depicts the center frequency associated with the Daubechies 4 wavelet ‘db4’ =-=[16,20]-=-. The power spectral density (PSD) of the signal provides the information about the frequency content of the signal. This information along with Eq. (4) can be used for scale selection. The procedure ... |

121 |
Symbolic dynamic analysis of complex systems for anomaly detection
- Ray
(Show Context)
Citation Context ...words: Symbolic time series analysis; Wavelets; Fault detection 1. Introduction The concept of symbolic time series analysis (STSA) has been recently proposed for anomaly detection in complex systems =-=[1]-=-. Several case studies [2–5] in anomaly detection show that STSA can be more effective than existing pattern recognition techniques (e.g., principal component analysis and neural networks). The STSA m... |

90 |
E.R.: A review of symbolic analysis of experimental data
- Daw, A, et al.
(Show Context)
Citation Context ...s extraction of relevant information, imbedded in the measured time series data, to generate symbol sequences. Symbol generation requires partitioning of the data space to obtain the symbol sequences =-=[8,9]-=-. Various partitioning techniques have been suggested in literature for symbol generation, which include variancebased [10], entropy-based [11], and hierarchical clustering [12] methods. A survey of c... |

64 |
Computational signal processing with wavelets
- Teolis
- 1998
(Show Context)
Citation Context ... Ray / Signal Processing 86 (2006) 3309–3320 alleviates these difficulties via adaptive usage of long windows for retrieving low-frequency information and short windows for high-frequency information =-=[16,17]-=-. The ability to perform flexible localized analysis is one of the striking features of wavelet transform. In multi-resolution analysis (MRA) of wavelet transform, a continuous signal f 2 H, where H i... |

47 |
Discrimination and clustering for multivariate time series
- Kakizawa, Shumway, et al.
- 1998
(Show Context)
Citation Context ... the symbol sequences [8,9]. Various partitioning techniques have been suggested in literature for symbol generation, which include variancebased [10], entropy-based [11], and hierarchical clustering =-=[12]-=- methods. A survey of clustering techniques is provided in [13]. In addition to these methods, another scheme of partitioning, based on symbolic false nearest neighbors (SFNN), was reported by Kennel ... |

39 |
Symbolic time series analysis of ultrasonic data for early detection of fatigue damage
- Gupta, Ray, et al.
(Show Context)
Citation Context ...n on a nonlinear electronic system apparatus [1]. Structural damage detection on a mechanical vibration system apparatus [3]. Damage detection in polycrystalline alloys on a fatigue testing apparatus =-=[5]-=-. Table 2 Distortion ratios s 0:05 s 0:1 dt 0.040 0.054 ds 0.006 0.010 ARTICLE IN PRESS V. Rajagopalan, A. Ray / Signal Processing 86 (2006) 3309–3320 3315 5.1. Anomaly detection in nonlinear syst... |

33 | Symbolic time series analysis for anomaly detection: a comparative evaluation - Chin, Ray, et al. |

29 | A maximum variance cluster algorithm
- Veenman, Reinders, et al.
- 2002
(Show Context)
Citation Context ...tion requires partitioning of the data space to obtain the symbol sequences [8,9]. Various partitioning techniques have been suggested in literature for symbol generation, which include variancebased =-=[10]-=-, entropy-based [11], and hierarchical clustering [12] methods. A survey of clustering techniques is provided in [13]. In addition to these methods, another scheme of partitioning, based on symbolic f... |

16 |
Estimating good discrete partitions form observed data: Symbolic false nearest neighbors
- Kennel, Buhl
- 2003
(Show Context)
Citation Context ... A survey of clustering techniques is provided in [13]. In addition to these methods, another scheme of partitioning, based on symbolic false nearest neighbors (SFNN), was reported by Kennel and Buhl =-=[14]-=-. The objective of SFNN partitioning is to ensure that points that are close to each other in the symbol space are also close to each other in the phase space. Partitions that yield a smaller proporti... |

16 |
Ondelettes et turbulence. Multirésolutions, algorithmes de décomposition, invariance d'échelles, Paris: Diderot Editeur
- Abry
- 1997
(Show Context)
Citation Context ...d the center frequency F c that has the maximum modulus in the Fourier transform of the wavelet [18]. The pseudo-frequency f p of the wavelet at a particular scale a is given by the following formula =-=[18,19]-=-: f p F c , (4) aDt where Dt is the sampling interval. Fig. 1 depicts the center frequency associated with the Daubechies 4 wavelet ‘db4’ [16,20]. The power spectral density (PSD) of the signal prov... |

12 | Pattern discovery by residual analysis and recursive partitioning
- Chau, Wong
- 1999
(Show Context)
Citation Context ...ioning of the data space to obtain the symbol sequences [8,9]. Various partitioning techniques have been suggested in literature for symbol generation, which include variancebased [10], entropy-based =-=[11]-=-, and hierarchical clustering [12] methods. A survey of clustering techniques is provided in [13]. In addition to these methods, another scheme of partitioning, based on symbolic false nearest neighbo... |

9 |
Wavelet-based space partitioning for symbolic time series analysis
- Rajagopalan, Ray
- 2005
(Show Context)
Citation Context ...-mentioned shortcomings and is particularly effective with noisy data from high-dimensional dynamical systems. Usage of wavelet transform for symbolization has been recently introduced by the authors =-=[1,15]-=-. This paper elaborates the concept of wavelet-based partitioning for STSA and its major features are delineated below. Selection of the wavelet basis and scale range. Noise mitigation in the measured... |

5 | Anomaly detection in aircraft gas turbine engines - Tolani, Yasar, et al. - 2006 |

4 | Detection of fatigue crack anomaly: a symbolic dynamics approach
- Khatkhate, Ray, et al.
- 2004
(Show Context)
Citation Context ...d via experimentation on the following laboratory apparatuses: Anomaly detection on a nonlinear electronic system apparatus [1]. Structural damage detection on a mechanical vibration system apparatus =-=[3]-=-. Damage detection in polycrystalline alloys on a fatigue testing apparatus [5]. Table 2 Distortion ratios s 0:05 s 0:1 dt 0.040 0.054 ds 0.006 0.010 ARTICLE IN PRESS V. Rajagopalan, A. Ray / Sign... |

4 |
Clustering of time series data—a survey, Pattern Recognition Society
- Liao
- 2005
(Show Context)
Citation Context ...ve been suggested in literature for symbol generation, which include variancebased [10], entropy-based [11], and hierarchical clustering [12] methods. A survey of clustering techniques is provided in =-=[13]-=-. In addition to these methods, another scheme of partitioning, based on symbolic false nearest neighbors (SFNN), was reported by Kennel and Buhl [14]. The objective of SFNN partitioning is to ensure ... |

1 |
Incipient fault detection in mechanical power transmission systems
- Bhatnagar, Rajagopalan, et al.
- 2005
(Show Context)
Citation Context ... techniques (e.g., principal component analysis and neural networks). The STSA method has also been demonstrated for fault detection in electromechanical systems, such as three-phase induction motors =-=[6]-=- and helical gearbox in rotorcraft [7]. $ This work has been supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under Grant No. DAAD19-01-1-0646. Corresponding au... |

1 |
Early detection of voltage imbalances in induction machines
- Samsi, Rajagopalan, et al.
- 2005
(Show Context)
Citation Context ... analysis and neural networks). The STSA method has also been demonstrated for fault detection in electromechanical systems, such as three-phase induction motors [6] and helical gearbox in rotorcraft =-=[7]-=-. $ This work has been supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under Grant No. DAAD19-01-1-0646. Corresponding author. Tel.: +1 814 865 63 77; fax: +1 ... |

1 |
A symbolic dynamics approach for early detection of slowly evolving faults in nonlinear systems
- Rajagopalan, Samsi, et al.
- 2004
(Show Context)
Citation Context ...on is to identify small changes in the parameter b as early as possible and well before it manifests a drastic change in the system dynamics. The details of the experimental apparatus are provided in =-=[22]-=-. Time series data of the signal yðtÞ from the experimental apparatus is used for symbolic analysis. The first step in the analysis is selection of the wavelet basis. The time series data of the signa... |