A Novel Friction Mean Effective Pressure Model for a Heavy-Duty Diesel Engine by Neural Network and Its Applications to Heat Release Rate Profile Optimization

<div>The prediction of friction mean effective pressure (FMEP) is important when engine performance is estimated in the model-based development process. The Chen–Flynn model as a function of the maximum in-cylinder pressure (P<sub>max</sub>) and mean piston speed (C<sub>m</sub>) is often used to predict FMEP because of its simplicity to utilize; however, this study inferred from the results of multiple regression analysis between FMEP and factors related to combustion phase and rate of heat release profile (ROHR) that the Chen–Flynn model may be difficult to accurately estimate FMEP in a modern diesel engine with common rail fuel injection system, which allows the control of fuel injection pressure (P<sub>inj</sub>) and combustion phase. In this study, a neural network with machine learning was applied to predict FMEP based on the expectation that the ROHR profile, which allows the reduction of FMEP may be possible to be found. 7666 points experimental results that include FMEP and combustion parameters in the heavy-duty single-cylinder diesel engine were utilized as training and validation data for machine learning. The pre-trained neural network prediction model for FMEP can predict the tendency of FMEP better than the Chen–Flynn model when start of combustion (SOC) and P<sub>inj</sub> were varied. The error between the predicted FMEP results by the pre-trained neural network and the experimental results of FMEP were within 4% of the experimental results when SOC was advanced from top dead center to −7 deg. ATDC. Whereas, the predicted FMEP by Chen-–Flynn model had a maximum error of 15% compare to the experimental results. Furthermore, the predicted FMEP by Chen–Flynn model had a maximum error of 9% compare to the experimental results when P<sub>inj</sub> was varied from 120 MPa to 200 MPa, whereas the error between the predicted FMEP results by the pre-trained neural network and the experimental results of FMEP were within 4% of the experimental results. The pre-trained neural network model was confirmed to be predictive better than the Chen–Flynn under the conditions that the combustion phase and P<sub>inj</sub> are changing. In addition, the parameter study using the pre-trained neural network prediction model for FMEP and a one-dimensional engine performance simulation tool was conducted to find the ideal ROHR profile that improve brake thermal efficiency (BTE). The result of parameter study suggests that the optimum ROHR profile to improve BTE under the same conditions of P<sub>max</sub> and the degree of constant volume combustion is to shorten combustion duration and to retard the peak of ROHR away from top dead center.</div>