Ranking-Based Parameter Subset Selection for Nonlinear Dynamics with Stochastic Disturbances under Limited Data

The modeling procedure for a production-scale plant includes a parameter estimation (PE) problem based on the measured data. However, when only the nominal operation data are available, however, it is often impossible to estimate all model parameters, as the PE problem becomes ill-conditioned. In this situation, it is preferable to estimate only an estimable subset of the model parameters to prevent the model from overfitting the given data, which results in poor prediction accuracy. This study suggests an algorithm for selecting and estimating a parameter subset of a stochastic model when only limited data are available. A target system is represented by stochastic differential equations with additive stochastic terms. Using a mean-squared-error-based parameter subset selection method, state disturbances and measurement errors are estimated simultaneously with the model parameters to reduce the effects of uncertainties on the PE. A virtual plant representing a fed-batch bioreactor, with 12 model parameters to be estimated, is selected for a numerical illustration. The simulation results show that the proposed method effectively manages the overfitting problem owing to the ill-conditioned PE and improves the model prediction accuracy compared to cases where all of the model parameters are estimated.