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Anomalies in time series in Xevents

Anomalies in time series in Xevents. DMA definition. Discrete mathematical analysis (DMA) is an approach to studying of multidimensional massifs and time series, based on modeling of limit in a finite situation, realized in a series of algorithms.

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Anomalies in time series in Xevents

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  1. Anomalies in time series in Xevents .... Vien, Austria

  2. DMA definition Discrete mathematical analysis (DMA) is an approach to studying of multidimensional massifs and time series, based on modeling of limit in a finite situation, realized in a series of algorithms. The basis of the finite limit was formed on a more stable character, compared to a mathematic character, of human idea of discontinuity and stochasticity. Fuzzy mathematics and fuzzy logic are sufficient for modeling of human ideas and judgments. That was reason why they became technical foundation of DMA. .... Vien, Austria

  3. DMA General Scheme Fuzzy comparisons ofpositive numbers Proximity in finite metrical space Limit in finite metrical space Density as limit measure Finite time series FTS Multidimensional Discrete spaces Smooth FTS: Equilibrium Monotonous FTS Predicationof FTS: Forecast Extremums on FTS Recognition of dense subsets: Crystal. Monolith. Convex FTS Clusterization: Rodin Anomalies on FTS: DRAS, FLARS, FCARS Recognition of linear structure: Tracing Fuzzy logic and geometry on FTS: Geometry measures .... Vien, Austria

  4. Classical Set • Classical set has a clear boundary between elements that do and don’t belong to the set. • If U is universal set, then a classical subset A  U is defined by the membership function μ(x) that takes only two values: μ(x) =1 for the elements belonging to A and μ(x) =0 for elements not belonging to A. .... Vien, Austria

  5. Fuzzy Set • A is a fuzzy set in U if there is a map μ: U 0,1, that showsthe degreeofinclusion of the element x into the fuzzy set A. μ(x) is called by membership function of the fuzzy set A. .... Vien, Austria

  6. .... Vien, Austria

  7. Fuzzy Sets Approach in Geophysics LoftiZadeh:A human being thinks not in terms of numbers, but rather in terms of fuzzy notions. Норберт Винер: По-видимому, главное преимущество человека перед компьютером – это его способность оперировать с нечетко очерченными понятиями. .... Vien, Austria

  8. FLASAR .... Vien, Austria

  9. La Fournaise volcano 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1998, 1992, 1991, 1990, 1985-88, 1983-84, 1981, 1979, 1977, 1977, 1976, 1975-76, 1973, 1973, 1972, 1966, 1964-65, 1964, 1963, 1961, 1960, 1959, 1958, 1957, 1955-57, 1954, 1953, 1952, 1951, 1950, 1950, 1949, 1948, 1947, 1946, 1945, 1944, 1943, 1942, 1941, 1938-39, 1938, 1937, 1936, 1935, 1933-34, 1932, 1931, 1930, 1929, 1926-27, 1925-26, 1924, 1924, 1921, 1920, 1917, 1915, 1913, 1910, 1909, 1908, 1907, 1905, 1904, 1903, 1902, 1901, 1901, 1900, 1899, 1898, 1898, 1897, 1894, 1890-91, 1889, 1884, 1882, 1878, 1876, 1875, 1874, 1874, 1872, 1871, 1870, 1869, 1868, 1865, 1863-64, 1861, 1860, 1859, 1858-59, 1852, 1851, 1850, 1849, 1848, 1847, 1846, 1845, 1844, 1843, 1842, 1832, 1830, 1824, 1824, 1821, 1820, 1817, 1816, 1815, 1815, 1814, 1813, 1812, 1810, 1809, 1807, 1802, 1801-02, 1800, 1797, 1795, 1794, 1792, 1791, 1789, 1787, 1786, 1784-85, 1776, 1775, 1774, 1772, 1771, 1768, 1766, 1760, 1759, 1753, 1751, 1734, 1734, 1733, 1721, 1709, 1708, 1703, 1672, 1671, 1669, 1649, 1640 .... Vien, Austria

  10. Monitoring of La Fournais volcano, Reunion, France .... Vien, Austria

  11. Recognition SP-anomalyes, connected with volcanic activity Eruption .... Vien, Austria

  12. FCARS: three vision for one time series .... Vien, Austria

  13. FCARS: universality .... Vien, Austria

  14. Agreement “Equilibrium” and “Forecast” Real time series .... Vien, Austria

  15. Extremumson time series .... Vien, Austria

  16. Etna volcano 2005, 2004, 2003, 2002, 2001, 1994, 1993, 1991, 1989, 1988, 1987, 1986, 1985, 1984, 1983, 1981, 1980, 1979, 1978, 1975, 1974, 1971, 1968, 1966, 1959, 1958, 1957, 1955, 1953, 1951, 1950, 1949, 1947, 1946, 1945, 1942, 1940, 1935, 1934, 1931, 1930, 1929, 1928, 1926, 1924, 1923, 1919, 1918, 1917, 1913, 1912, 1911, 1910, 1908, 1899, 1893, 1892, 1891, 1886, 1884, 1883, 1879, 1878, 1874, 1869, 1868, 1865, 1864, 1863, 1857, 1852, 1843, 1842, 1838, 1833, 1832, 1828, 1827, 1822, 1819, 1816, 1811, 1810, 1809, 1803, 1802, 1797, 1792, 1791, 1787, 1781, 1780, 1776, 1770, 1767, 1766, 1764, 1763, 1758, 1755, 1752, 1747, 1744, 1735, 1732, 1723, 1702, 1693, 1689, 1688, 1682, 1669, 1654, 1651, 1646, 1643, 1640, 1634, 1633, 1614, 1610, 1609, 1607, 1603, 1595, 1579, 1578, 1566, 1554, 1550, 1541, 1540, 1537, 1536, 1535, 1533, 1494, 1470, 1447, 1446, 1444, 1408, 1381, 1350, 1334, 1333, 1329, 1321, 1284, 1250, 1222, 1194, 1175, 1169, 1164, 1160, 1157, 1063, 1044, 1004, 0911, 0859, 0814, 0812, 0644, 0604, 0560, 0500, 0417, 0410, 0400, 0252, 0165, 0080, 0072, 0050, 0039, 0010, -0010, -0032, -0036, -0044, -0049, -0056, -0061, -0122, -0126, -0135, -0141, -0350, -0396, -0425, -0479, -0565, -0695, -0735, -1050, -1470, -1500, -2330, -3050, -3390, -3510, -4150, -5150, -6190 .... Vien, Austria

  17. Interferogram Smooth points 1stiteration 2nditeration 4thiteration Borders 3rditeration Algorithm“Monolith”.Etna volcano .... Vien, Austria

  18. Algorithm“Monolith”.Etna volcano. Final result .... Vien, Austria

  19. GIS .... Vien, Austria

  20. GIS Цифровая модель высот (разрешение 30") Фрагмент карты почв (1:1 000 000) Площадная гидрография, Гидрорельеф, Естественные формы рельефа, Изогоны (1:33 000 000) .... Vien, Austria

  21. Literature on DMA to Xevents list Gvishiani A.D., Agayan S.M., BogoutdinovSh.R., Ledenev A., Zlotnicki J., Bonnin J. Mathematical Methods of Geoinformatics. II. The algorithms of fuzzy logic in the problem of anomalies recognition in time series / / Cybernetics and system analysis. 2003. № 4. p.103-111. Gvishiani A.D., Agayan S.M., BogoutdinovSh.R., Zlotnicki J. Algorithms of fuzzy logic in the problem of anomalies recognition in time series / / Sketches of Geophysical Research. By the 75 th anniversary of the Joint Institute of Physics of the Earth RAS. O.Y Schmidt. M.: OIFZ RAS. 2003. p.257-262. Zlotnicki J., Agayan S., Gvishiani A., Bogoutdinov Sh. Telematics and artificial intelligence tools in monitoring of volcanoes // WISTCIS Newsletter. 2003. Vol. 3. November 2002-May 2003. p.58-60. Zlotnicki J., Le Mouel J.-L., Gvishiani A., Agayan S., Mikhailov V., Bogoutdinov Sh., Kanwar R., Yvetot P. Automatic fuzzy-logic recognition of anomalous activity on long geophysical records: Application to electric signals associated with the volcanic activity of La Fournaise volcano (Reunion Island) // Earth and Planetary Science Letters. 2005. Vol. 234. p.261-278. .... Vien, Austria

  22. Literature on DMA to Xevents list Gvishiani A.D., Agayan S.M., BogoutdinovSh.R., Tikhotsky S.A., Hinderer J., Bonnin J., Diament M. Algorithm FLARS and recognition of time series anomalies // System Research & Information Technologies. 2004. №. 3. p.7-16. Agayan S.M., BogoutdinovSh.R., Gvishiani A.D., Graeva E.M., Zlotnicki J., Rodkin M.V. Investigation of the morphology of the signal based on the algorithms of fuzzy logic / / Geophysical Research. M.: IFZ RAS. 2005. Vol.1. p. 143-155 Zlotnicki J., LeMouel J.-L., Gvishiani A., Agayan S., Mikhailov V., Bogoutdinov Sh. Automatic fuzzy-logic recognition of anomalous activity on long geophysical records. Application to electric signals associated with the volcanic activity of la Fournaise volcano (Réunion Island) // Earth and Planetary Science Letters. 2005. Vol.234. P.261-278. BogoutdinovSh.R., Agayan S.M., Gvishiani A.D., Graeva E.M., Rodkin M.V., Zlotnicki J., Le Mouël J.L. Fuzzy logic algorithms in the analysis of electrotelluric data with reference to monitoring of volcanic activity // Izvestiya, Physics of the Solid Earth. MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC . 2007. Vol. 43. p. 597-609. .... Vien, Austria

  23. Literature on DMA to Xevents list Gvishiani A.D., Agayan S.M., BogoutdinovSh.R. Fuzzy Recognition of Anomalies in Time Series / / Doklady Earth Sciences, June-July 2008, Vol. 421, № 5, p. 838-843. Gvishiani A.D., Agayan S.M., BogoutdinovSh.R., Zlotnicki J., Bonnin J. Mathematical Methods of Geoinformatics. III. Fuzzy comparison and recognition of anomalies in time series / / Cybernetics and system analysis. 2008, Vol. 44, № 3, p. 3-18 .... Vien, Austria

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