Bayesian calibration of engine-out NOx models for engine-to-engine transferability

Abstract

Accurate prediction of engine-out NOx is essential for meeting stringent emissions regulations and optimizing engine performance. Traditional approaches rely on models trained on data from a small number of engines, which can be insufficient in generalizing across an entire population of engines due to sensor biases and variations in input conditions. In real world applications, these models require tuning or calibration to maintain acceptable error tolerance when applied to other engines. This highlights the need for models that can adapt with minimal adjustments to accommodate engine-to-engine variability and sensor discrepancies. While previous studies have explored machine learning methods for predicting engine-out NOx, these approaches often fail to generalize reliably across different engines and operating environments. To address these issues, we propose a Bayesian calibration framework that combines Gaussian processes (GP) with approximate Bayesian computation to infer and correct sensor biases. Starting with a pretrained model developed using nominal engine data, our method identifies engine specific sensor biases and recalibrates predictions accordingly. By incorporating these inferred biases, our approach generates posterior predictive distributions for engine-out NOx on unseen test data, achieving high accuracy without retraining the model. Our results demonstrate that this transferable modeling approach significantly improves the accuracy of predictions compared to conventional non-adaptive GP models, effectively addressing engine-to-engine variability and improving model generalizability.