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Anomalies in time series in Xevents
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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.
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Density as limit measure
DMA General SchemeFuzzy comparisons of
positive numbers
Proximity in finite metrical space
Limit in finite metrical space
MultidimensionalDiscrete spaces
Finite time seriesFTS
Recognition of dense subsets:
Crystal. Monolith.
Clusterization:Rodin
Recognition of linear structure:
Tracing
Smooth FTS:Equilibrium
Monotonous FTS
Predicationof FTS:
Forecast
Extremums onFTS
Anomalies on FTS:DRAS, FLARS,
FCARS
ConvexFTS
Fuzzy logic andgeometry on FTS:
Geometry measures12 May 2009
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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.
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Fuzzy Set
• A is a fuzzy set in U if there is a map μ: U 0,1, that shows the degree of inclusion
of the element x into the fuzzy set A.μ(x) is called by membership function of the
fuzzy set A.
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Fuzzy Sets Approach in Geophysics
Lofti Zadeh: 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.
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FLASAR
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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
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Monitoring of La Fournais volcano, Reunion, France
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DON
300 mV/km
NS
EW
DOS
300 mV/kmNS
EW
MAV
1500 mV/km
NS
EW
27-02-98 01-03-98 03-03-98 05-03-98 07-03-98 09-03-98 11-03-98 13-03-98
Извержение
Recognition SP- anomalyes, connected with volcanic activity
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Eruption
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FCARS: three vision for one time series
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-40
-35
-30
-25
Regression
02-07-0712:00
03-07-0700:00
03-07-0712:00
04-07-0700:00
04-07-0712:00
-40
-35
-30
-25
Length
-40
-35
-30
-25
Energy
nT
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FCARS: universality
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Agreement “Equilibrium” and “Forecast”
Real time series
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Extremums on time series
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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, -619012 May 2009
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Algorithm “Monolith”. Etna volcano
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Interferogram
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Smooth points1st iteration
470 475 480 485 490 495 500 505 510 515 520
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2nd iteration
470 475 480 485 490 495 500 505 510 515 520
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3rd iteration
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4th iteration
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Borders
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Algorithm “Monolith”. Etna volcano. Final result
470 475 480 485 490 495 500 505 510 515 520
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0102030405060708090100110120130140150160170180190200210220
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GIS
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GIS
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Цифровая модель высот (разрешение 30")
Площадная гидрография, Гидрорельеф, Естественные формы рельефа, Изогоны (1:33 000 000)
Фрагмент карты почв (1:1 000 000)
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Literature on DMA to Xevents list
12 May 2009
Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.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., Bogoutdinov Sh.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.
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Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.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., Bogoutdinov Sh.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. Bogoutdinov Sh.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.
Literature on DMA to Xevents list
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Gvishiani A.D., Agayan S.M., Bogoutdinov Sh.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., Bogoutdinov Sh.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
Literature on DMA to Xevents list
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