# Engine Optimization Model for Accurate Prediction of Friction Model in Marine Dual-Fuel Engine
###### Abstract
This model was later adapted to enhance high-speed engine performance, enabling the selection of the optimal operating point with minimal fuel consumption during propeller design [44; 45] based on a proper diesel combustion model based on a double-Wiebe function [46]. [PERSON] et al. [11] applied an artificial neural network (ANN) in combination with the Non-dominated Sorting Genetic Algorithm (NSGA II) to optimize two-stage turbo-assisted and exhaust gas recirculation (TA EGR) in diesel engines. Their approach successfully reduced fuel consumption by 3.5% and cut nitrogen oxide (NO\({}_{\text{x}}\)) emissions by over 75% across different operating points, demonstrating the effectiveness of advanced optimization techniques in improving engine efficiency and reducing environmental impact. [PERSON] et al. [47] applied Definitive Screening Design (DSD) and ANN modeling to optimize palm oil biodiesel (POBD) production and predict yield outcomes. With 17 experimental runs, a maximum biodiesel yield of 96.06% was achieved. The ANN model demonstrated high prediction accuracy with strong R\({}^{2}\) and low MSE. The produced POBD met ASTM-D675 [48] standards, and engine testsshowed significant reductions in NOx (32.46%), HC (40.57%), CO (44.44%), and smoke (39.65%) compared to diesel, along with lower engine cylinder vibration levels. The empirical friction model is a widely used approach for calculating friction losses in diesel engines. The friction submodules integrated into commercial engine simulation software are typically based on empirical formulas, following the Chen and Flynn correlations [49]. These models rely on standardized coefficient values due to the restricted availability of real data from the engine manufacturer's project guide. While these default values offer a reasonable approximation for many applications, they may limit the model's accuracy in reflecting the specific friction characteristics of an engine, especially in unique or highly customized designs. The developed formula establishes a relationship between the FMEP, engine speed, and pressure. In the WAVE engine, a modified version of the Chen-Flynn correlation is applied to capture friction dynamics accurately. Similar to the original model, the modified equation includes (1) a constant term (\(A_{\text{cf}}\))--accounts for baseline friction, (2) a load-dependent term (\(B_{\text{cf}}\))--that varies with peak cylinder pressure, (3) a hydrodynamic friction term (\(C_{\text{cf}}\))--linearly dependent on mean piston velocity, and (4) a windage loss term (\(Q_{\text{cf}}\))--quadratic with mean piston velocity. Equation (4) presents the core formula used to calculate the FMEP, reflecting the influence of these parameters on friction losses. \[\text{FMEP}=A_{\text{cf}}+\frac{1}{n_{\text{cyl}}}\sum_{i=1}^{\text{nyl}} \left[B_{\text{cf}}(P_{\text{max}})_{i}+C_{\text{cf}}(S)_{i}+Q_{\text{cf}}( S)_{i}^{2}\right] \tag{4}\]  
where \(n_{\text{cyl}}\) is the number of cylinders, \(P_{\text{max}}\) is the maximum cylinder pressure, and \(S\) is the mean piston speed. Standard values are assigned to each term in accordance with [PERSON]'s original model, but these parameters can be adjusted to match the performance characteristics of modern engines. Optimizing these values is a complex process that demands extensive engine testing to accurately determine the BMEP and IMEP and then implement them into numerical models for further comparison [23; 50]. Fine-tuning these parameters ensures that the model reflects real-world engine behavior, improving the accuracy of friction loss predictions [51; 52]. From the presented literature review, this study fills the gap in the prediction of the friction model by developing an optimization model capable of determining the optimal parameters in the Chen-Flynn correlation for a given engine without requiring experimental tests or real-world friction data.