## 1 Introduction  
Rapid development of the world economy brings a growing demand for transportation. Diesel engines have become the primary power source for surface transport due to their high thermal efficiency. However, their wide application is limited by high emission levels and high fuel consumption. In order to address the environmental pollution and energy crisis caused by diesel engines, alternative fuels are considered to be effective solutions. In the past decade, various types of alternative engine fuels such as hydrogen (H\({}_{2}\)), dimethyl ether (DME), alcohols, biofuels, compressed natural gas (CNG), liquefied petroleum gas (LPG), and some synthetic fuels have been extensively investigated. Among these candidates, hydrogen stands out as the most promising alternative fuel. The high burning rate of hydrogen improves the in-cylinder combustion process, while its wide combustion limit extends the lean limit of engine operation. Additionally, the only product of hydrogen combustion is water, which effectively reduces harmful emissions [1; 2]. Thus, hydrogen is strongly encouraged in the field of internal combustion engines. However, compression ignition (CI) of pure hydrogen is challenging due to its high auto-ignition temperature, which prevents its application in unmodified diesel engines. As a result, researchers have favored the use of diesel-hydrogen blends instead of pure hydrogen. The performance and emission characteristics of CI engines fueled with hydrogen-diesel blends have been extensively investigated. [PERSON] [3] reported a 14% increase in engine power at high engine speeds and a 70% increase in engine power at high air-fuel ratios when hydrogen addition reached 40%. [PERSON] et al. [4] investigated the combustion characteristics of a hydrogen-diesel dual-fuel engine and observed that as the hydrogen substitution rate increased, the heat release rate (HRR) and thermal efficiency increased simultaneously. [PERSON] et al. [5] examined the effect of hydrogen addition on engine combustion and revealed a significant decrease in combustion duration through hydrogen enrichment. [PERSON] et al. [6] stated that the introduction of hydrogen led to an increase in NOx emissions. [PERSON] et al. [7] proposed a combustion model to predict the emissions of a diesel-hydrogen dual-fuel engine and achieved good agreement between simulation and experimental data across various operating conditions, thus ensuring accurate predictions. [PERSON] et al. [8] conducted a numerical study of a diesel-hydrogen dual-fuel CI engine and showed that an optimized injection strategy could improve the thermal efficiency of a dual-fuel engine without worsening the emissions. In addition to the hydrogen substitution ratio, exhaust gas recirculation (EGR) can significantly influence the in-cylinder composition. [PERSON] et al. [9] examined a hydrogen-diesel direct injection (DI) engine with EGR and observed that increasing the EGR ratio led to higher peak HRR, combustion duration, and cyclic pressure fluctuation. [PERSON] et al. [10] explored a hydrogen-diesel dual-fuel CI engine by varying the engine load, fuel composition, and EGR ratio. The results showed that the engine emissions were reduced by adjusting the EGR rate in dual-fuel mode. [PERSON] et al. [11] simultaneously tuned the intake air temperature, fuel composition, and EGR ratio of a hydrogen-diesel engine by employing the classical Taguchi method. Through this approach, they were able to identify an optimal combination of parameters and achieved advancements in emissions, brake specific fuel consumption (BSFC), and brake thermal (BTE) efficiency. Furthermore, a comparative experimental investigation was carried out on a hydrogen-diesel dual-fuel engine, with variations in engine loads, EGR ratios, and intake air boosting conditions [12]. The results indicated that an appropriate level of hydrogen addition considerably mitigated both NOx and particulate emissions.