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 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.

翻译：准确预测发动机氮氧化物(NOx)排放对于满足严格排放法规和优化发动机性能至关重要。传统方法依赖基于少量发动机数据训练的模型，由于传感器偏差和输入条件差异，此类模型难以推广至整个发动机群体。在实际应用中，当模型应用于其他发动机时，需要通过调整或标定来维持可接受的误差容限，这凸显了开发能够通过最小调整量适应发动机间差异和传感器偏差的自适应模型的必要性。尽管已有研究探索了利用机器学习方法预测发动机NOx排放，但这些方法往往无法可靠地在不同发动机和运行环境中泛化。为解决上述问题，我们提出一种结合高斯过程(GP)与近似贝叶斯计算的贝叶斯标定框架，用于推断并修正传感器偏差。该方法从基于标称发动机数据预训练的模型出发，识别特定发动机的传感器偏差并据此重新校准预测值。通过整合推断出的偏差，我们的方法在未见过测试数据上生成发动机NOx排放的后验预测分布，无需重新训练模型即可实现高精度。结果表明，与传统非自适应高斯过程模型相比，这种可迁移建模方法显著提升了预测精度，有效解决了发动机间变异性问题并增强了模型泛化能力。