A grey-box modeling approach for the reduction of nonlinear systems

A novel model reduction methodology is proposed to approximate large-scale nonlinear dynamical systems. The methodology amounts to finding computationally efficient substitute models for an uncertain nonlinear system. Model uncertainty is incorporated by viewing the system as a grey-box or hybrid model with a mechanistic (first-principle) component and an empirical (black-box) component. The mechanistic part is approximated using proper orthogonal decomposition. Subsequently, the empirical part is identified by parameter estimation using the reduced order mechanistic part. As a consequence, the parameter estimation is computationally more efficient. An example with a distributed parameter system is provided.