Extended State Dependent Parameter modelling with a Data-Based Mechanistic approach to nonlinear model structure identification. (June 2018) - Mindham, David A.; Tych, Wlodzimierz; Chappell, Nick A.
Abstract: A unified approach to Multiple and single State Dependent Parameter modelling, termed Extended State Dependent Parameters (ESDP) modelling, of nonlinear dynamic systems described by time-varying dynamic models applied to ARX or transfer-function model structures. Crucially, the approach proposes an effective model structure identification method using a novel Information Criterion (IC) taking into account model complexity in terms of the number of states involved. In ESDP, model structure involves not only the model orders, but also selection of the states driving the parameters, which effectively prevents the use of most current IC. This leads to a powerful methodology for investigating nonlinear systems building on the Data-Based Mechanistic (DBM) philosophy of Young and expanding the applications of the existing DBM methods. The methodologies presented are tested and demonstrated on both simulated data and on high frequency hydrological observations, showing how structure identification leads to discovery of dynamic relationships between system variables. Highlights: Extension of Data-Based Mechanistic modelling of non-linear systems. Identification of model structure for a significant class of non-linear systems. State-Dependent Parameters extended for irregularly spaced data. Application to environmental systems – water quality dynamics.