Multifractal approach to the description and wavelet analysis of the fatigue damage
DSpace at Ternopil State Ivan Puluj Technical University
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Multifractal approach to the description and wavelet analysis of the fatigue damage
|
|
| Creator |
Zainetdinov, R. I.
|
|
| Contributor |
Moscow State University of Railway Communication, Moscow, Russia
|
|
| Description |
A phenomenological model for the multifractal description of the fatigue damage accumulation has been introduced. The multifractal approach gives probabilistic evidence for the existence of a constructive process hidden in the temporal pattern of damage accumulation. It is shown that a series of Bernoulli trials results in multiplicative bi- or polynomial process that recursively generates the multifractal probability measure. Connection between parameter of the Bernoulli trials and multifractal spectrum is considered. A technique for revealing the multifractal properties of the damage accumulation is proposed. For the approbation of the technique, a computer simulation study has been done. The wavelet transform has been used for revealing the intrinsic temporal structure of data sets obtained from numerical simulation, tests, empirical observations and measurements. |
|
| Date |
2016-06-05T07:01:10Z
2016-06-05T07:01:10Z 2006-09-25 2006-09-25 |
|
| Type |
Article
|
|
| Identifier |
Zainetdinov R. I. Multifractal approach to the description and wavelet analysis of the fatigue damage / R. I. Zainetdinov // Механічна втома металів. Праці 13-го міжнародного колоквіуму (МВМ-2006), 25-28 вересня 2006 року — Т. : ТДТУ, 2006 — С. 192-197. — (Фізичні та феноменологічні підходи до опису втомного пошкодження).
966-305-027-6 http://elartu.tntu.edu.ua/handle/123456789/16784 Zainetdinov R. I. (2006) Multifractal approach to the description and wavelet analysis of the fatigue damage. Mechanical Fatigue of Metals: Proceeding of the 13-th International Colloquium (MFM) (Tern., 25-28 September 2006), pp. 192-197 [in English]. |
|
| Language |
en
|
|
| Relation |
ⅩⅢ міжнародний колоквіум „Механічна втома металів“
ⅩⅢ Internation Colloquium "Mechanical fatigue of metals" 1. E.Lewis, Introduction to Reliability Engineering, Wiley, New York, 1987. 2. J.Feder, Fractals, Plenum Press, New York, 1989. 3. C.J.G.Evertsz and B.B.Mandelbrot, Multifractal Measures. In Chaos and Fractals: New frontiers of science, by H.O.Peitgen, H.Jurgens, and D.Saupe, pp. 921-953, Springer-Verlag, New York, 1992. 4. Р.И.Зайнетдинов, Представление результатов испытаний Бернулли в виде мультифрактала, Методы менеджмента качества, № 3, с. 36 - 41, Москва, 2000. 5. A.Arneodo, Wavelet analysis of fractals: from the mathematical concepts to experimental reality. In Wavelets: Theory and Applications, ed. by G.Erlebacher, Y.Hussaini and L.Jameson, pp. 349-502, Oxford University Press, New York, 1996. 6. J.Buckheit and D.Donoho, WaveLab and Reproducible Research. In Wavelets and Statistics, ed. by A.Antoniadis and G.Oppenheim, pp. 55-81, Springer, New York, 1995. 7. Л.А.Сосновский, Механика усталостного разрушения: Словарь-справочник, НПО “Трибофатика”, Гомель, 1994. 8. R.I.Zainetdinov, Wavelet Analysis of Statistical Data on Reliability for Exploring the Multifractal Properties of Failure-Cascading Process. In Wavelets and Multiscale Methods, INRIA, Paris, Tangier, 1998. 9. R.I.Zainetdinov, Wavelet Analysis of Statistical Data on Reliability Reveals the Multifractal Nature of the Flow of Failures. In Yong-In Songdam College Journal, Issue 2, pp. 301-311, Yong-In, South Korea, 1999. 10. Z.W.Birnbaum, S.C.Saunders, R.C.McCarty, R.Elliott, A Statistical Theory of Life-Length of Materials, Boeing Airplane Company, Document No. D2-1325, Sept. 15, 1950. 11. J.Bogdanoff and F.Kozin, Probabilistic Models of Cumulative Damage, Wiley, New York, 1985. 1. E.Lewis, Introduction to Reliability Engineering, Wiley, New York, 1987. 2. J.Feder, Fractals, Plenum Press, New York, 1989. 3. C.J.G.Evertsz and B.B.Mandelbrot, Multifractal Measures. In Chaos and Fractals: New frontiers of science, by H.O.Peitgen, H.Jurgens, and D.Saupe, pp. 921-953, Springer-Verlag, New York, 1992. 4. R.I.Zainetdinov, Predstavlenie rezultatov ispytanii Bernulli v vide multifraktala, Metody menedzhmenta kachestva, No 3, P. 36 - 41, Moskva, 2000. 5. A.Arneodo, Wavelet analysis of fractals: from the mathematical concepts to experimental reality. In Wavelets: Theory and Applications, ed. by G.Erlebacher, Y.Hussaini and L.Jameson, pp. 349-502, Oxford University Press, New York, 1996. 6. J.Buckheit and D.Donoho, WaveLab and Reproducible Research. In Wavelets and Statistics, ed. by A.Antoniadis and G.Oppenheim, pp. 55-81, Springer, New York, 1995. 7. L.A.Sosnovskii, Mekhanika ustalostnoho razrusheniia: Slovar-spravochnik, NPO "Tribofatika", Homel, 1994. 8. R.I.Zainetdinov, Wavelet Analysis of Statistical Data on Reliability for Exploring the Multifractal Properties of Failure-Cascading Process. In Wavelets and Multiscale Methods, INRIA, Paris, Tangier, 1998. 9. R.I.Zainetdinov, Wavelet Analysis of Statistical Data on Reliability Reveals the Multifractal Nature of the Flow of Failures. In Yong-In Songdam College Journal, Issue 2, pp. 301-311, Yong-In, South Korea, 1999. 10. Z.W.Birnbaum, S.C.Saunders, R.C.McCarty, R.Elliott, A Statistical Theory of Life-Length of Materials, Boeing Airplane Company, Document No. D2-1325, Sept. 15, 1950. 11. J.Bogdanoff and F.Kozin, Probabilistic Models of Cumulative Damage, Wiley, New York, 1985. |
|
| Rights |
© Тернопільський державний технічний університет імені Івана Пулюя
|
|
| Format |
192-197
6 |
|
| Coverage |
25-28 вересня 2006 року
25-28 September 2006 Україна, Тернопіль Ukraine, Ternopil |
|
| Publisher |
ТДТУ
TDTU |
|