Statistical methods for providing the stability of the solutions of inverse problems and their application to decrease rotor vibroactivity

Abstract

Many machine design problems relate to the class of inverse problems, whose solution is reduced to the solution of systems of linear algebraic equations. The relation between the matrix conditionality number of such systems and solution errors is shown in this article. The application of the least square method to improve the accuracy of solutions is justified. A method for providing the stability of solutions of systems of linear algebraic equations based on the use of additional information by increasing the number of measurements of initial parameters is proposed. The approach and statistical algorithm for achieving a given accuracy of the solution of poorly specified systems of linear algebraic equations are developed. The results of using the offered methods for the identification of eccentricities and elastic inertial parameters in the problem of decreasing the vibroactivity of the rotor of turbine pump are given.