Lambda-Guided Bounded Scale Adaptation for A Physics-Guided Virtual Mass-Airflow Estimator: A BMW M30B35 Simulation Study

The virtual mass-airflow (VMA) estimation for the BMW M30B35 engine was tested practically in simulation. The estimator combines a speed-density model with a (513-parameter) residual network. There is an online feedback loop for a single bounded scale parameter provided by the measurement of the injector voltage levels and lambda without a reference airflow sensor. The nominal mean absolute error (MAE) was reduced by 69.9% using residual learning and normalised root mean square error (NRMSE) for post-shift (scale adaptation after a simulated change in the plant) was reduced from 0.0152 to 0.0079. The four-stage supervisor did not significantly improve upon simpler policies on the original final test, and failed to satisfy the predeclared false-update criterion. Original results were then inspected and another fault test, exploratory, was conducted. For this purpose, it evaluates seven different feedback conditions with 60 run–seed pairs for each condition for 12 different load sequences and 5 frozen networks. Relative to validity-only adaptation (Holm-adjusted p = 0.0103), adaptation root-mean-square error (RMSE) was found to be 8.023 during a brief +15% lambda fault, versus 6.750 during acceptance during a similar error window in the later part of the hour, with no false updates, compared to 60 during the validity-only run. During this high of +15% there were 181 false updates in C2 and C3 each. Other recursive methods like random phase recurring fault did not give much benefit and recursive least squares (RLS) showed lower adaptation RMSE when the input was healthy feedback. This meant that only if the fault occurred after the window opened (and the feedback was accurate) did the benefit of later acceptance come. Before a practical, deployment, engine measurements, embedded timing tests and electrical compatibility checks need to be performed.