• The Journal of the Korea Contents Association
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• v.10 no.9
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• pp.97-106
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• 2010

Various time series representation methods have been suggested in order to process time series data efficiently and effectively. SAX is the representative time series representation method combining segmentation and discretization techniques, which has been successfully applied to the time series classification task. But SAX requires a large number of segments in order to represent the meaningful dynamic patterns of time series accurately, since it loss the dynamic property of time series in the course of smoothing the movement of time series. Therefore, this paper suggests a new time series representation method that combines PIPs detection and Persist discretization techniques. The suggested method represents the dynamic movement of high-diemensional time series in a lower dimensional space by detecting PIPs indicating the important inflection points of time series. And it determines the optimal discretizaton ranges by applying self-transition and marginal probabilities distributions to KL divergence measure. It minimizes the information loss in process of the dimensionality reduction. The suggested method enhances the performance of time series classification task by minimizing the information loss in the course of dimensionality reduction.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.707-719
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• 2018

Various time series representation methods have been proposed for efficient time series clustering and classification. Lin et al. (DMKD, 15, 107-144, 2007) proposed a symbolic aggregate approximation (SAX) method based on symbolic representations after approximating the original time series using piecewise local mean. The performance of SAX therefore depends heavily on how well the piecewise local averages approximate original time series features. SAX equally divides the entire series into an arbitrary number of segments; however, it is not sufficient to capture key features from complex, large-scale time series data. Therefore, this paper considers data-adaptive local constant approximation of the time series using the unbalanced Haar wavelet transformation. The proposed method is shown to outperforms SAX in many real-world data applications.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1107-1120
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• 2004

This study proposes a new scheme for the sampled-data representation of nonlinear systems with time-delayed multi-input. The proposed scheme is based on the Taylor-series expansion and zero-order hold assumption. The mathematical structure of a new discretization scheme is explored. On the basis of this structure, the sampled-data representation of nonlinear systems including time-delay is derived. The new scheme is applied to nonlinear systems with two inputs and then the delayed multi-input general equation is derived. The resulting time-discretization provides a finite-dimensional representation of nonlinear control systems with time-delay enabling existing controller design techniques to be applied to them. In order to evaluate the tracking performance of the proposed scheme, an algorithm is tested for some of the examples including maneuvering of an automobile and a 2-DOF mechanical system.

• International Journal of Control, Automation, and Systems
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• v.4 no.3
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• pp.293-301
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• 2006

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well-known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.

• Journal of Mechanical Science and Technology
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• v.18 no.8
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• pp.1297-1305
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• 2004

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sampled-data representation of a non-affine nonlinear system with constant input time-delay. The mathematical expressions of the discretization scheme are presented and the ability of the algorithm is tested for some of the examples. The proposed scheme provides a finite-dimensional representation for nonlinear systems with time-delay enabling existing controller design techniques to be applied to them. For all the case studies, various sampling rates and time-delay values are considered.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.125-127
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• 2005

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sample-data representation of a nonlinear system with constant state tine-delay. The mathematical expressions of the discretization scheme are presented and the effect of the time-discretization method on key properties of nonlinear control system with state tine-delay, such as equilibrium properties and asymptotic ability, is examined. The proposed scheme provides a finite-dimensional representation for nonlinear systems with state time-delay enabling existing controller design techniques to be applied to then. The performance of the proposed discretization procedure is evaluated using a nonlinear system. For this nonlinear system, various sampling rates and time-delay values are considered.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.327-332
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• 2003

A new discretization method for nonlinear system with time-delay is proposed. It is based on the well-known Taylor series expansion and the zero-order hold (ZOH) assumption. We know that a discretization of linear system can be obtained with the ZOH assumption and within the sampling interval. A similar line of thinking is available in nonlinear case. The mathematical structure of the new discretization method is explored and under the structure, the sampled-data representation of nonlinear system including time-delay is computed. Provided that the discrete form of the single input nonlinear system with time-delay is derived, this result is easily extended to nonlinear system with multi-input time-delay. For simplicity two inputs are considered in this study. It is enough to generalize that of multiple inputs. Finally, the time-discretization of non-affine nonlinear system with time-delay is investigated for apply all nonlinear system

• Smart Structures and Systems
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• v.29 no.1
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• pp.93-103
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• 2022

With the wider availability of sensor technology through easily affordable sensor devices, several Structural Health Monitoring (SHM) systems are deployed to monitor vital civil infrastructure. The continuous monitoring provides valuable information about the health of the structure that can help provide a decision support system for retrofits and other structural modifications. However, when the sensors are exposed to harsh environmental conditions, the data measured by the SHM systems tend to be affected by multiple anomalies caused by faulty or broken sensors. Given a deluge of high-dimensional data collected continuously over time, research into using machine learning methods to detect anomalies are a topic of great interest to the SHM community. This paper contributes to this effort by proposing a relatively new time series representation named "Shapelet Transform" in combination with a Random Forest classifier to autonomously identify anomalies in SHM data. The shapelet transform is a unique time series representation based solely on the shape of the time series data. Considering the individual characteristics unique to every anomaly, the application of this transform yields a new shape-based feature representation that can be combined with any standard machine learning algorithm to detect anomalous data with no manual intervention. For the present study, the anomaly detection framework consists of three steps: identifying unique shapes from anomalous data, using these shapes to transform the SHM data into a local-shape space and training machine learning algorithms on this transformed data to identify anomalies. The efficacy of this method is demonstrated by the identification of anomalies in acceleration data from an SHM system installed on a long-span bridge in China. The results show that multiple data anomalies in SHM data can be automatically detected with high accuracy using the proposed method.

• Journal of Mechanical Science and Technology
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• v.20 no.7
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• pp.950-960
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• 2006

An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.

• Journal of The Korean Association For Science Education
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• v.21 no.5
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• pp.841-854
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• 2001

The purpose of this study was to find the effect of these variables on the duration of the momentum effect. To examine the momentum effect for gravitational field concepts, an intensive time series design was used. We collected data every day except Sundays and holidays for 50 days; 5 days for baseline, 30 days for intervention, and 15 days for the follow up We adopted cognitive levels and styles as students characteristics and two item characteristics(quantity versus quality, and word versus picture) as the item representation patterns. In this study, the momentum effect was influenced by students characteristics and item representation patterns. The results showed that two variables, cognitive style and quantity/quality, were the most influential factors for the duration of momentum effect. Field independent students showed a longer duration than field dependent students did. In addition, students showed a longer duration in quality items than in quantity items. However, students cognitive levels(formal or preformal) and word/picture presentations seemed to have relatively weak effect on the duration of the momentum effect.