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A. N. Tikhonov and V. Y. Arsenin, “The Methods of Solution of the Incorrectly Formulated Problems,” Science, Moscow, 1979.

has been cited by the following article:

• TITLE: Identification of Rotor Unbalance as Inverse Problem of Measurement

  AUTHORS: Yuri Menshikov

  KEYWORDS: Mathematical Model; Unbalance Identification; Solution Estimation; Regularization; Numerical Test

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.9A, December 18, 2013

  ABSTRACT: In this paper, the problem of identification of the characteristics of the rotor unbalance on two supports is investigated as the inverse problem of measurement. The vibration of rotor supports in two mutually perpendicular directions used as the initial information. The inverse problem is considered, taking into account the error of the mathematical description of rotor-bearings system. To obtain estimates of real unbalance characteristics, the hypothesis as to the exact solutions is applied. The method of Tikhonov regularization is used to obtain stable results. Test calculations are given to illustrate the proposed approach.