Numerical method for structural and parametric identification of a mathematical model of incomplete inverse deformation of creep strain

A new numerical method for parametric and structural identification of the physically nonlinear theory of reversibility of creep strain, valid within the first and second stages, has been developed. A series of stationary creep curves is used as basic experimental information. The problem is reduced to nonlinear regression analysis of determining estimates of random parameters based on time series of a sequence of observations of creep deformation at various constant stresses using difference equations. The obtained relationships between the coefficients of the difference equation and the parameters of nonlinear regression allow us to reduce the problem of estimating the coefficients of a linear-parametric discrete model. Corresponding iterative algorithms for refining parameter estimates with any given accuracy have been developed. Parametric and structural identification of the theory of incomplete reversibility of creep deformation has been carried out for steel EI736 (500 $^{\circ}$C) and alloys EI437A (700 $^{\circ}$C), VZh98 (900 $^{\circ}$C), EP693 (700 $^{\circ}$C). Numerical values of model parameter estimates for these alloys are given. The adequacy of the constructed mathematical models was checked, and the relation between the calculated and experimental data was observed. Experimental data for all materials considered belong to the corresponding calculated confidence intervals for creep deformation, which indicates the reliability of the obtained estimates of the model parameters.