Multi-objective optimization of brake thermal efficiency, NO_x emissions, and hydrogen slip in a direct-injection hydrogen engine toward future emission standards

Nitrogen oxides (NO_x) emissions from hydrogen internal combustion engines (H₂ICEs) are subject to increasingly stringent regulations, while unburned hydrogen (UH₂) emissions, reported as high as 6 g/kWh, have received limited attention. This study investigates NO_x and UH₂ characteristics of a direct-injection (DI) H₂ICE over a wide operating range and develops a Gaussian Process Regression (GPR)-based surrogate modeling and optimization framework to quantify the brake thermal efficiency (BTE)–NO_x–UH₂ trade-off under Worldwide Harmonized Light Vehicles Test Cycle (WLTC)-relevant regulatory constraints. Latin Hypercube Sampling is applied to generate 300 experimental operating points covering WLTC-relevant operating conditions. Considering the challenge of accurately predicting emissions in H₂ICEs, a GPR model with R² ≥ 0.9869 is developed to predict BTE, NO_x, and UH₂ using five operating parameters—engine speed, BMEP, excess air ratio (λ), start of injection, and crank angle at 50% heat release. Shapley Additive Explanations (SHAP) analysis is used to examine the key marginal effects of operating parameters and support model interpretation, after which the Non-dominated Sorting Genetic Algorithm III is applied to identify WLTC-oriented calibration strategies. Compared with the fixed-parameter control strategy, evolutionary optimization reduces hydrogen consumption by 2.49% and NO_x emissions by 72.88%, satisfying the Euro 7 NO_x limit of 60 mg/km, but increasing UH₂ emissions to 122.48 mg/km. The results quantify the WLTC-level BTE–NO_x–UH₂ trade-off and show that lean-burn NO_x control may shift the system-level burden toward hydrogen slip, highlighting the need for coordinated in-cylinder calibration and aftertreatment strategies for DI H₂ICEs.