Online Nonlinear Dynamic System Identification With Evolving Spatial–Temporal Filters: Case Study on Turbocharged Engine Modeling

Vehicle control problems have been historically using simple control structures with lookup tables that were designed to use vehicle steady-state characterization to calibrate and are suited better for older systems with lower complexity/dimension. However, the increasing complexity of the vehicle systems and stringent regulations requires optimal control of the dynamic vehicle systems. In this brief, we present an efficient online identification methodology with a composite local model structure that will be critical to the new control paradigm. We first introduce the concept of evolving spatial-temporal filters (STFs) that dynamically transform an incoming input-output data stream into a nonlinear combination of local models. The local models are weighed by an array of weights corresponding to the compatibility of the input-output data to a set of ellipsoidal clusters that partition the input-output space. The filters exploit ellipsoidal-shape evolving clusters as function bases and a distance metric defined as a combination of Mahalanobis distance and scaled local model prediction error. Parameters of the filters and local models can be updated simultaneously online, making adaptive optimization a possibility for vehicle systems. Evolving clustering and recursive least square techniques are exploited to simultaneously update the cluster parameters and local linear models. We apply the developed algorithm to the modeling of a turbocharged internal combustion engine that is a highly nonlinear and complex system. Promising performance is demonstrated both in a high-fidelity simulator and on an experimental vehicle.