- Menshikov, Yu., Identification of Rotor Unbalance as Inverse Problem of Measurement. Advances in Pure Mathematics, 2013, 3, 20-25. DOI: 10.4236/apm.2013.39A1004
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.
- Menshikov, Yu., Inverse problems for dynamic systems: classification and solution methods. Journal Advances in Pure Mathematics, 2013, v.3, n.4, p.390-393.
The inverse problems for dynamic systems the motions of which are described by system of the ordinary differential equations are examined. The classification of such type of inverse problems is given. It was shown that inverse problems can be divided into two types: synthesis inverse problems and inverse problems of measurement (recognition). Each type of inverse problems requires separate approach to statements and solution methods. The regularization method for obtaining of stable solution of inverse problems was suggested. In some cases, instead of recognition inverse problems solution can be used the estimation of solution. Within the framework of this approach two practical inverse problems of measurement are considered.
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