State estimation model for NOx storage reduction catalyst using modeling method based on machine learning

This report proposes a model that precisely estimates the state variable of NOx storage reduction (NSR) catalysts (i.e., the NOx storage amount) with a goal of improving fuel consumption by optimizing the control of an NSR catalyst. The proposed model combines neural networks (NNs) and a physical model, and uses mass conservation to estimate the NOx storage amount. Compared with a model that does not consider mass conservation (i.e., a model composed only of a NN), the proposed model reduces both the maximum and mean absolute error of the NOx storage amount by at least 80%. This result confirms the effectiveness of calculating the NOx storage amount based on mass conservation by combining NNs with a physical model. To implement the proposed model in an in-vehicle ECU, the model can use only variables that can be acquired from the vehicle as its input variables. The variables that cannot be acquired from the vehicle are the catalyst bed temperature and the CO concentration at the inlet. An unscented Kalman filter (UKF) was designed to estimate the catalyst bed temperature, which is then averaged in the flow direction with high accuracy while incurring a low computational load. The effect of removing the CO concentration at the inlet from the input variables was quantitatively evaluated. When the estimation accuracy was compared with actual engine test data, it was found that the catalyst bed temperature, averaged in the flow direction, could be estimated with reasonable accuracy. The maximum absolute error was 20.17°C (7.1% of the correct value) in all sections. By inputting the catalyst bed temperature (estimated using the UKF) into the proposed model, it was possible to estimate the NOx storage amount with reasonable accuracy. The maximum absolute error was 30.46 mg (2.2% of the correct value) in all sections. Furthermore, to take the distribution of the NSR catalyst temperatures in the flow direction into account, NNs were constructed to estimate the temperatures at the front, center, and rear ends of the NSR catalyst. These estimated NSR catalyst temperatures were then used as input variables for the proposed model. This improved the accuracy of the estimates of the NOx storage rate and NOx storage amount, relative to calculations using the averaged value in the flow direction of the NSR catalyst temperature, as estimated using a UKF. In particular, it was confirmed that the maximum absolute error for the NOx storage rate was roughly halved. As a result, even under the constraint of using only variables that can be acquired from the vehicle, it was possible to estimate the NOx storage amount with reasonable accuracy. The maximum absolute error was 30.08 mg (2.1% of the correct value) in all sections. The effectiveness of the proposed model was then confirmed using actual engine test data.