Bayesian Calibration of Engine-out NOx Models for Engine-to-Engine Transferability

2025-11-22

AI Summary

To address poor cross-engine generalization of engine NOₓ prediction models caused by sensor biases and operating-condition disparities, this paper proposes a retraining-free Bayesian calibration framework. The method integrates Gaussian process regression (GPR) with approximate Bayesian computation (ABC), enabling automatic inference and correction of sensor biases and input shifts from the posterior predictive distribution of a pre-trained model—using only a small number of target-engine measurements. Compared to conventional adaptive GPR approaches, it significantly improves prediction accuracy on unseen engines, reducing mean absolute error by 32%, while maintaining strong robustness even under extreme data scarcity (≤5 calibration samples). Its core innovation lies in embedding ABC within the GPR calibration pipeline, facilitating decoupled bias identification and plug-and-play transfer. This yields a scalable, Bayesian solution for multi-source, heterogeneous engine emission modeling.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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 with approximate Bayesian computation to infer and correct sensor biases. Starting with a pre-trained 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.

Problem

• Calibrating NOx prediction models for engine transferability with minimal adjustments
• Addressing sensor biases and input variations across different engines
• Improving model generalization without retraining for unseen engine data

Innovation

• Bayesian calibration framework corrects sensor biases
• Gaussian processes infer engine-specific biases without retraining
• Posterior predictive distributions improve NOx prediction accuracy