Optimal Estimation of Gasoline LP-EGR via Unscented Kalman Filtering with Mixed Physics-based/Data-driven Components Modeling

We propose a novel optimal estimation methodology for gasoline engine LP (low-pressure) EGR (exhaust gas recirculation) air-path system, which allows us to implement virtual sensors for oxygen mass fraction at the intake manifold and EGR mass flow rate at the LP-EGR valve, real sensors for them too expensive to deploy in production cars. We first decompose the LP-EGR air-path system into several sub-components; and opportunistically utilize physics-based modeling or data-driven modeling for each component depending on their model complexity. In particular, we apply the technique of MLP (multi-layer perceptron) as a means for data-driven modeling of LP-EGR/throttle valves and engine cylinder valve aspiration dynamics, all of which defy accurate physics-based modeling, that is also simple enough for real-time running. We further optimally combine these physics-based and data-driven modelings in the framework of UKF (unscented Kalman filtering), and also manifest via formal analysis that this mixed physics-based/data-driven modeling renders our estimator much faster to run as compared to the case of full data-driven MLP modeling. In doing so, we also extend the standard UKF theory to the more general case, where the system contains non-additive uncertainties both in the measurement and process models with cross-correlations and state-dependent variances, which stems from the inherent peculiar structure of our mixed physics-based/data-driven modeling approach, for the UKF formulation. Experiments are also performed to show the theory.