Ensemble methods for nonlinear system identification with uncertainty quantification using the example of locally linear-affine multi-models

Nonlinear system identification is commonly used to determine dynamic models that provide a single output value ('single value prediction') for each requested point in time. However, in order to take into account the reliability or uncertainty of the predicted value when making decisions, a predictor should provide confidence information in addition to the predicted single value. Uncertainties in modelling can arise with regard to model structure, model parameter values, measured values/observations, and initial values. The treatment of structural uncertainties in particular is considered challenging.

This project aims to investigate ensemble methods for quantifying uncertainty in prediction in nonlinear system identification, using locally affine discrete-time multi-models of the Takagi-Sugeno type as an example. Firstly, improved estimation and initialisation strategies for single-value prediction of Takagi–Sugeno models as ensemble members or base learners are investigated. Subsequently, these base learners will be extended to predict uncertainty. Next, methods are designed for the composition and interaction of the ensemble members. The extension to other modelling approaches is also investigated. As formal proofs are not feasible for general nonlinear systems and realistic random processes, the properties of the methods are evaluated statistically using a portfolio of around ten different dynamic systems, including the applicant's test benches. This avoids selective statements and establishes a basis for transferability to other systems.

Dipl.-Ing. Konrad Lange

April 2025 - March 2028

Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number 541311230