Estimation of parameters in models for viscoplastic and creep materials

Ola Wall and Jan Holst

Abstract:: Estimation of parameters in time and rate dependent materials is frequently performed by least squares regression.
Time and rate dependent material models are represented mathematically by systems of differential equations. As predictions of dynamical systems are history dependent, the residuals produced by regression estimators are dependent random variables and the estimates may therefore be biased. A new approach using time series analysis methods, which offers a way to circumvent the problems related to dependent residuals, is presented. With the new approach, the residuals are obtained via a continuous-discrete time Kalman filter. A simulation study, with models suitable for both high temperature creep and transient loading has been performed. A comparison between the
proposed methods and standard least squares regression shows that the model parameters are estimated with up to 40% higher precision. An analysis of the residuals clearly shows that the residuals of the new estimator form an independent sequence of random variables. The results also indicate that the proposed estimator remains unbiased whereas the regression estimator may be biased when the excitation increases.