Estimation of parameters in models for viscoplastic and creep materials
Ola Wall and Jan Holst
Centre for Mathematical Sciences
Lund Institute of Technology,
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.