Data-driven nonlinear system identification of blood glucose behaviour in Type I diabetics

Data-driven nonlinear system identification with sparse regression is a promising method to represent nonlinear dynamics in the form of a rigorous model description. Therefore, nonlinear functional structure identification and parameter estimation are performed simultaneously. Classical identification methods require functional structures that are manually derived using process knowledge either from first principles or practical experience. However, the effort required to provide these structures is time-consuming, labour-intensive, and in connection with operational trials in production plants, also associated with high costs. In addition, the latest sparse regression solution for nonlinear system identification does not offer an analytical solution due to the properties of the L1 norm. For this reason, sparse regression with smoothed L1 regularisation is proposed for nonlinear system identification. For this purpose, a nonlinear library function is first constructed based on the extended dynamic mode decomposition theory (eDMD), which contains all possible nonlinear bijective function candidates. For the process description, the most suitable functions with the related weighting parameters are selected using the regularisation properties. The performance of the method is demonstrated using the blood glucose behaviour from Type I Diabetes. The validation of the method is performed for a simulation study with and without noise influence and applied to experimental data of two patients in a Python simulation. It can be shown that the identification is successful for both studies with a performance limit for a signal-to-noise ratio (SNR) of 0.45 (3.46 dB).