NOx Emission Modeling in Diesel Engines

Oxides of nitrogen (NOx) emitted from diesel engines contribute significantly to atmospheric pollution and pose challenges for public health and climate targets. Accurate modelling of NOx formation within the combustion chamber is essential for engine design, calibration and real-time control systems. A spectrum of approaches has emerged, ranging from detailed three-dimensional computational fluid dynamics (CFD) simulations that resolve in-cylinder flows and chemical kinetics, through semi-empirical and phenomenological models that combine physical insight with simplified algebraic expressions, to data-driven techniques that exploit machine learning for rapid prediction under transient conditions. Each approach balances fidelity, computational cost and ease of integration into engine control units (ECUs). Recent work has emphasised virtual sensor development to replace costly hardware analysers, hybrid frameworks that marry physical submodels with neural nets, and advanced decomposition methods to isolate the multi-scale fluctuations inherent in transient NOx traces. Together, these advances support tighter emission legislation, improved fuel consumption and reduced development time, with clear practical applications in both light-duty and heavy-duty powertrains operating under real driving cycles worldwide.

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NOx Emission Modeling in Diesel Engines publication trend

The graph below shows the total number of articles in nox emission modeling in diesel engines across all publications each year (not limited to Nature Index journals).

Technical terms

NOx: Collective term for nitrogen oxides, primarily nitric oxide (NO) and nitrogen dioxide (NO2), produced during high-temperature combustion.

Semi-empirical model: A model combining fundamental physical laws with calibrated algebraic relations to predict engine emissions efficiently.

Virtual sensor: A software algorithm that estimates a physical parameter (e.g. NOx) from readily available measurements, eliminating the need for a hardware sensor.

CEEMDAN: Complete ensemble empirical mode decomposition with adaptive noise, a technique that decomposes non-stationary signals into intrinsic mode functions.

LSTM: Long short-term memory, a recurrent neural network architecture adept at learning temporal dependencies in sequential data.

References

1. Comparison of Physics-Based, Semi-Empirical and Neural Network-Based Models for Model-Based Combustion Control in a 3.0 L Diesel Engine. Energies (2019).
2. Development of a Real-Time Virtual Nitric Oxide Sensor for Light-Duty Diesel Engines. Energies (2017).
3. Prediction of Transient NOx Emission from Diesel Vehicles Based on Deep-Learning Differentiation Model with Double Noise Reduction. Atmosphere (2021).