Dr. Kim McAuley
Department of Chemical Engineering
Title: " Parameter Estimation in Continuous-Time Dynamic Models with Uncertainty "
Chemical engineers who develop fundamental dynamic models estimate model
parameters using noisy data. Often, modelers believe that their models
are imperfect due to simplifying assumptions. We have developed a new
parameter-estimation technique that explicitly considers model imperfections
and measurement errors. Our proposed method is based on Maximum-Likelihood (ML)
estimation. The likelihood criterion is approximated by means of spline-smoothing
and collocation techniques, which are used to discretize the differential
equations. The resulting objective function contains three parts that account
for measurement errors, model uncertainty and unknown initial conditions. The
method extends benefits of collocation techniques to stochastic dynamic models
with uncertain inputs and nonstationary disturbances. The ML formulation ensures
unbiased and consistent parameter estimates. Theoretical confidence intervals
agree with empirical confidence intervals from Monte Carlo simulations.