# Engine Optimization Model for Accurate Prediction of Friction Model in Marine Dual-Fuel Engine
## 5 Conclusions and Further Research  
This study proposes an optimization method to predict the optimal coefficients of the Chen-Flynn correlation, employing advanced optimization techniques to accurately calculate the FMEP for a given engine, even in the absence of real data.  
The approach integrates a 1D engine simulation software with a nonlinear optimization algorithm implemented in MATLAB, creating a robust engine optimization model. This model predicts engine performance while determining the optimal values of critical parameters governing engine behavior across four operating points. Key outputs, including engine speed, FMEP, and P\({}_{\text{max}}\), are then incorporated into a specialized friction tool for data fitting and validation.  
The following has been concluded:  
1. The engine model facilitates maximizing the AFR by optimizing the turbocharger performance, injection system parameters, combustion characteristics, and the FMEP. This results in values of up to 68.89 at low-load operation, while maintaining combustion stability (R\({}^{2}\geq\) 0.9998).
2. The engine optimization model demonstrates excellent capability in meeting all predefined constraints, ensuring reliability and applicability under varying conditions.
3. The numerical model is computationally efficient and compatible with standard computer systems, offering fast simulation times while maintaining high accuracy in calculated results. It helps to match real engine performance with an error of less than 0.05% in brake power and BSFC, confirming both accuracy and efficiency.
4. The developed approach supports the precise determination of the Chen-Flynn correlation coefficients, enhancing the accuracy of engine performance predictions across the load diagram.  
This methodology provides a reliable approach to assessing engine friction behavior, particularly in scenarios where manufacturer-specific data is unavailable. These findings validate the model as a powerful tool for practical engine performance assessment and support its integration into advanced digital twin frameworks for marine propulsion systems.  
Future work could explore the performance simulation of dual-fuel engines operating with hydrogen as the primary fuel. Additionally, incorporating a life-cycle assessment (LCA) of emissions can help evaluate the full environmental impact of dual-fuel engines, particularly when transitioning to hydrogen-based fuels. This would provide a more comprehensive comparison between fuel options and support decision-making for sustainable marine propulsion. While this study focuses on steady-state operation, evaluating the  
Figure 7: Fitting curve of FMEP.  
model's performance under transient conditions, such as acceleration, deceleration, and load fluctuations, would further enhance its robustness and applicability to real-world marine engine operations. Incorporating transient simulations could also aid in control system development and engine calibration strategies.  
Such research aligns with global efforts toward net-zero emissions, positioning hydrogen as a key enabler of sustainable maritime and automotive propulsion systems.  
This research received no external funding.  
The data presented in this study is available on request from the corresponding author.  
The authors declare no conflicts of interest.