Parameter estimation with improved model prediction for over-parametrized nonlinear systems

Abstract

Parameter estimation is a crucial step in system modeling. In practice, the fundamental models developed by chemical engineers are often complex. There may be parameters that have no or little effect on the model prediction. Also, some parameters may have an impact on model prediction related to other parameters. In this case, it is difficult to estimate all the parameters. The general approach to address this issue is to select a subset of parameters to estimate, and fix the rest at the initial value. Here, a reduced Hessian and statistical criterion-based parameter estimation approach is proposed for improving model prediction. The proposed method considers the influence of the initial parameter values on model prediction. In the process of selecting the optimal subset of transformed parameters based on the mean square error (MSE) of output, the sensitivity matrix is replaced by the reduced Hessian matrix, which can save computational cost of MSE calculation. After obtaining the optimal transformed parameter subset, the optimal initial values are selected based on the statistical criterion. The large difference between the model prediction and the actual model output caused by the arbitrary initial values can be avoided. The numerical results show the effectiveness of the proposed approach.