 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| << Previous article | Volume 45, Issue 1 / 2010 | Next article >> |
| V.A. Postnov, "Use of Tikhonov's Regularization Method for Solving Identification Problem for Elastic Systems," Mech. Solids. 45 (1), 51-56 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
1 |
Pages |
51-56 |
| DOI |
10.3103/S0025654410010085 |
| Title |
Use of Tikhonov's Regularization Method for Solving Identification Problem for Elastic Systems |
| Author(s) |
V.A. Postnov (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr-t 61, St. Petersburg, 199178 Russia) |
| Abstract |
We present a method for solving nonlinear inverse problems, which also include identification problems for elastic systems. The problems whose initial data contain an error are usually solved by regularization methods [1-5]. In the present paper, we give preference to Tikhonov's regularization method, which has been widely used in the recent years in practice to increase the stability of computational algorithms for solving problems in various areas of mechanics [6-9].
The identification problem for elastic systems is posed in the variational setting. We obtain an unconditional optimization problem, which is solved by the Newton method. We present a numerical example of identification of a single-span beam. An analysis of the obtained numerical results shows that it is necessary to solve the identification problems for elastic systems by regularization methods. |
| Keywords |
regularization, identification, inverse problem, ill-posed problem |
| References |
| 1. | A. N. Tikhonov,
"On the Stability of Inverse Problems,"
Dokl. Akad. Nauk SSSR
39 (5), 195-198 (1943). |
| 2. | A. N. Tikhonov,
"On the Solution of Ill-Posed Problems and the Method of Regularization,"
Dokl. Akad. Nauk SSSR
151 (3), 501-504 (1963). |
| 3. | A. N. Tikhonov and V. Ya. Arsenin,
Methods for Solving Ill-Posed Problems
(Nauka, Moscow, 1979)
[in Russian]. |
| 4. | V. A. Morozov,
Regularization Methods for Ill-Posed Problems
(Nauka, Moscow, 1987; CRC Press, Florida, 1993). |
| 5. | G. I. Marchuk,
Methods of Numerical Mathematics
(Nauka, Moscow, 1980; Springer, New York, 1982). |
| 6. | K. Kunish,
"Iterative Choices of Regularization Parameters in Linear Inverse Problems,"
Inverse Probl.
14, 1247-1264 (1998). |
| 7. | E. Habert, U. M. Ascher, and D. Oldenburg,
"On Optimization Techniques for Solving Nonlinear Inverse Problems,"
Inverse Probl.
16, 1263-1280 (2000). |
| 8. | H. W. Park, S. Shin, and H. S. Lee,
"Determination of Optimal Regularization Factor in System Identification with Tikhonov Regularization for Linear Elastic Continua,"
Int. J. Num. Meth. Engng
51, 1211-1230 (2001). |
| 9. | U. Tautenhahn and Jin Qi-nian,
"Tikhonov Regularization and a Posteriori Rules for Solving Nonlinear Ill-Posed Problems,"
Inverse Probl.
19, 1-21 (2003). |
| 10. | V. A. Postnov,
"Tikhonov's Regularization Method to Identification of Elastic System,"
in Proc. XXXV Summer School Conf. "Advance Problems of Mechanics," St. Petersburg, 2007
(St. Petersburg, 2007),
pp. 356-365. |
| 11. | V. A. Postnov,
"Damage Identification in Elastic Systems by Mathematical Treatment of Experimentally Obtained Frequency Spectra,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 155-160 (2000)
[Mech. Solids (Engl. Transl.)
35 (6), 129-133 (2000)]. |
| 12. | V. A. Postnov and G. A. Tumashik,
"Use of the Newton Method for Solving the Problems of Identification of Beam Systems,"
in Problems of Strength and Plasticity,
MezhVUZov. Sb. Lobachevskii NNGU,
No. 68 (2006)
[in Russian],
pp. 86-94. |
|
| Received |
26 November 2007 |
| Link to Fulltext |
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