Trajectory Parallel Measure Method for Measuring the Degree of Deterministic Property in the Observed Time Series Data

Fujimoto, Yasunari; Iokibe, Tadashi; TANIMURA, Takayoshi

doi:10.3156/jfuzzy.9.4_580

Cited by 11 publications

(4 citation statements)

References 10 publications

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“…If the correlation dimension is small, this suggests that the motion may be described by a small number of variables, even when the original system has many degrees of freedom [36]. x(t i,1 +δ t) proposed by Kaplan and Glass [24], Wayland et al [60], and Fujimoto et al [10]. We propose a simple method to evaluate parallelness degrees of the adjacent trajectories quantitatively.…”

Section: Estimated Results Of the Correlation Dimensionmentioning

confidence: 99%

“…Here, we use the least-square algorithm to estimate the Jacobian matrix A, which minimizes the summation of the squared error norm between z i and Ay i as follows: 10) where V and C are m × m matrices, v k,l and c k,l are the (k, l) components of matrices V and C, respectively, and A = C V −1 . Using matrix A, the following expression for the prediction is obtained:…”

Section: L) (43)mentioning

confidence: 99%

“…If the decision is wrong, there is a possibility of wrong time series analysis or construction of a wrong model. Therefore, detecting determinism in a time series is very important, and numerous studies have focused on this problem [4,5,10,12,18,24,29,33,40,42,[45][46][47]51,54,55,60]. The purpose of the present research is closely related to this problem.…”

Section: Introductionmentioning

confidence: 96%

“…Methods that can distinguish deterministic time series and stochastic time series by estimating parallelness degrees of adjacent reconstructed trajectories were proposed by Kaplan and Glass [24], Wayland et al [60], and Fujimoto et al [10]. In this study we propose a simple method to evaluate parallelness degrees of the adjacent trajectories quantitatively.…”

Section: Introductionmentioning

confidence: 98%

See 3 more Smart Citations

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

Ueno

Fan

2012

Japan J. Indust. Appl. Math.

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This paper describes similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos, with particular emphasis on the geometric characteristics of trajectories reconstructed in m-dimensional phase space from measured scalar time series data with a time-delay coordinate system. In this study, the time series data of ship roll angle in irregular waves were analyzed as an example of the narrow-band response of a resonant system. These time series data were measured by one of the authors in Tokyo Bay. The similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos are verified by numerical simulation data.

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Section: Estimated Results Of the Correlation Dimensionmentioning

confidence: 99%

Section: L) (43)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

Ueno

Fan

2012

Japan J. Indust. Appl. Math.

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Failure diagnosis by trajectory parallel measure on attractor

Iokibe

Fujimoto²

1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98C

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Recently, the study of chaos is attracting attention, and a wide range of academic fields is actively involved.On the other hand, Aihara proposed the term "chaos enginee~g" to describe the application of chaos theory for engineering purposes, and its possibilities have been demonstrated. The approaches to the engineering applications of chaos are generally classified, into two groups: (1) creative methods and (2) analytical methods. In the former, chaos conditions, consistent with the particular application, are produced in any case, and this behavior is used in a positive manner. In the latter, a phenomenon is examined to see whether it is chaotic or not, and if it is a deterministic chaos, the latent rules involved are extracted and used for a practical purpose. Applications based on the creative methods include chaos computing, chaotic memory, chaos cipher communications, chaos art, applications using chaos fluctuations, chaos circuits, non-linear engineering systems, etc. Applications using the analytical methods include failure diagnosis, deterministic non-hear shortterm forecasting, identifying chaos, modeling, biochaos, etc. This paper first describes approaches of chaotic diagnosis. Next, trajectory parallel measue method for diagnosis is described. Finally, fault diagnosis is discussed as a prospective industrial application using practical examples.In Japan, in 1991, the Bio-information Application System Study Committee (Chaired by K. Aihara) was organized by the Japan Electronic Industry Development Association. The committee surveyed possible engineering applications of chaos, and a report titled "Questionnaire Survey on the Prospects of Chaos Engineering" was published in 1992 [l]. This report used the word "chaos engineering" for the first time in Japan, and since then, R&D on chaos applications has been more widely implemented.Considering the human centered machine system, fault diagnosis is one of the most important functions and also one of the possible applications in chaos engineering field. The approaches of fault diagnosis based on chaos theory are categorized into two groups, one is focused on the changes of dynam~cs in the observed time series by calculation of the suitable embedding dimension and delay time, the maximum Lyapunov exponent and fractal dimension [2], the other is focused on the amount of mixed random noise.For the latter approach, several measures have been proposed to examine whether an observed time series is random noise or chaos. Recently, Kaplan and Glass have proposed the coarse-grained embedding of time series [3], in which the complexity of trajectories embedded in a state space is calculated statistically. With the Kaplan and Glass' algorithm, the state space should be well divided into hypercubes, so it may be necessary to do comprehensive preparatory work, and to do heavy calculation.Under these circumstances, we propose the Trajectory Parallel Measure method (TPM method) [4]. One of the essential points of this method is, similar to the Kaplan and Glass' algorith...

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