Numerical method of estimation of parameters of the nonlinear differential operator of the second order

Abstract

The main problem of mathematical simulation is the problem of nonlinear estimation of parameters of the different physical systems. The article contains new numerical method of parameters estimation of the nonlinear differential operator of the second order with the dissipative force, proportional to n-motion speed level assessment. Mean square estimation of coefficients of the generalized regression model constructed taking into account the difference equations describing results of measurements of a pulse response of system is the cornerstone of the numerical method. Two landmark procedure of differentiated estimation of parameters of dynamic process realized in a method allow to provide high adequacy of the constructed model to data of an experiment. Application of the developed numerical method allows to increase significantly (several times) the accuracy of estimates of parameters of the nonlinear differential operator in comparison with the known methods due to elimination of the offset in estimates caused by use of approximation in case of simulation of an envelope of vibration amplitudes.

Keywords

• nonlinear differential operator
• dissipative force proportional
• difference equations
• generalized regression model
• nonlinear regression
• mean square estimation