Uncontrollable Inaccuracy in Inverse Problems

Authors: Yu. Menshikov

Abstract:

In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solutions are analyzed. Several methods for removing the influence of uncontrollable inaccuracy have been suggested. 

Keywords: Inverse problems, uncontrollable inaccuracy, filtration.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1109103

References:

[1] A. Prilepko, D. Orlovsky, “About inverse problems for nonsteady systems”, Different. Equations and their Applications, Vilnus, no. 34, pp.85-92, 1983.
[2] Yu. L. Menshikov, “The inverse Problem of Astrodynamics”. Different. Equations and their Applications in Physics, Dniepropetrovsk, University, Dniepropetrovsk, Ukraine, pp.19-26, 1990.
[3] C. J. Radcliffe, Jr. C. D. Mote, “Identification and control of rotating disk Vibration”, Trans. ASME: Int. Symp. Syst., Meas. and Control, pp.120-128, 2002.
[4] St. Dubowsky, “Active control of mechanical systems: the state - of the art for robotics manipulators”, 26th Struct., Struct. Dyn. and Mater. Conf., Orlando, Fla, Apr.15-17, 1985, Pt. 2 .Coll. Techn. Pap. / New York, N.Y. pp.258-261, 1985.
[5] Yu. L. Menshikov, N. V. Polyakov, “Operative evaluation of unbalance characteristics of a deformable rotor”. In Proc.8th Int. Symp. on Technical Diagnostics (IMEKO), Dresden, 23-25 Sept. 1992, pp.399- 408.
[6] Yu. L. Menshikov, “The influence of uncontrollable inaccuracy of initial data on diagnostics results of mechanical objects”, Vibrodiagnostics of machines and mechanisms. The Methods and Tools. Zaporozhye, Ukraine, pp.65-66, 1985.
[7] Yu. L. Menshikov,“The Evaluation of the Unbalance Characteristics of a Rotor by the New Operative Method”, in Proc. of GAMM, 1996, vol.4, pp.103-105.
[8] G. Korn, T. Korn, Mathematical handbook for scientists and engineers, N.-Y., Toronto, London, 1961.