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Research on a Diagnosis Method Based on a correlation integral

International Journal of Plant Engineering and Management 2003年第2期8卷 65-73页

作者： ZHAOHong XIAYong LIANGXiao-guo DepartmentofComputerScienceandEngineering NorthwesternPolytechnicalUniversityXi‘an710072P.R.China The4thResearchInstituteofSecondArtilleryGroups Beijing100085P.R.China CollegeofAstronautics NorthwesternPolytechnicalUniversityXi’an710072P.R.China

For the first time, the diagnosis idea based on a correlation integral isproposed, which regard's the correlation integral as a feature set. The correlation dimension iscontained in the double-log curve of the correlation integral to scale, so extracting featuresdirectly from the correlation integral can avoid the bottleneck problem of determining the range ofnon-scale length. Several features extracted from the correlation integral are better than thesingle feature of the correlation dimension when describing the signal. It is obvious that thismethod utilizes more information of the signal than does the correlation dimension. The diagnosisexamples verify that this method is more accurate and more effective.

关键词： diagnosis correlation dimension correlation integral range of non-scale

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Gorkha earthquake (MW7.8) and aftershock sequence: A fractal approach

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Earthquake Science 2022年第3期35卷 193-204页

作者： Ram Krishna Tiwari Harihar Paudyal Central Department of Physics Tribhuvan UniversityKirtipurKathmandu 44618Nepal Birendra Multiple Campus Tribhuvan UniversityBharatpurChitwan 44200Nepal

On April 25, 2015, Nepal was struck by the MW7.8 Gorkha earthquake followed by an intense aftershock sequence. It was one of the most destructive earthquakes in the Himalayan arc, causing more than 8900 fatalities. In this study, we analyzed the dataset (429 events, magnitude of completeness (Mc) ≥ 4.2 local magnitude) of the first 45 days after the Gorkha earthquake to estimate the seismicity parameters b-value, D-value, and p-value. We used the maximum likelihood method to estimate the b-value and Omori-Utsu parameters, whereas the correlation integral method was applied to estimate the fractal dimension (D-value). The analysis was carried out using running and sliding window techniques. The lowest b-value (0.57 ± 0.04) and the highest D-value (1.65 ± 0.02) were computed at the time of the Gorkha earthquake, after which the b-value significantly increased to a maximum of 1.57. It again dropped to 0.93 at the time of the major aftershock on May 12, 2015. The D-value showed an initial quick drop and then decreased in a wavy pattern until the end of the study period, indicating the clustering and scattering of earthquakes in a fault region. The b-value contour map identified the eastern part of the study area as a high stress region (b = ~0.8), implying that the stress shifted to that region. The D-value contour map reveals that the seismogenic structure shifted from linear to planar in the region. The rate of aftershock decay (p = 0.86 ± 0.04) for a short period reflects that the level of stress decreased rapidly. This study helps to understand the level of stress and seismicity pattern of a region, which could be useful for aftershock studies.

关键词： Omori-Utsu law correlation integral fractal dimension b-value central Himalaya

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Selection of Optimal Embedding Parameters Applied to Short and Noisy Time Series from Rossler System

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Journal of Modern Physics 2017年第9期8卷 1607-1632页

作者： Olivier Delage Alain Bourdier Department of Physics The University of La ReunionSaint DenisFrance Department of Physics and Astronomy The University of New MexicoAlbuquerqueNMUSA

Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.

关键词： Phase Space Reconstruction Embedding Window Rossler System Time Series correlation integral Delay Time

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