Data-Based In-Cylinder Pressure Model with Cyclic Variations for Combustion Control: A RCCI Engine Application

TL;DR

The paper addresses the challenge of predicting full in-cylinder pressure and cycle-to-cycle variations for advanced combustion control. It presents a data-driven framework that couples Principle Component Decomposition with Gaussian Process Regression to map in-cylinder conditions to pressure traces, capturing both mean behavior and CCV via a stochastic weight model. The approach demonstrates that eight principal components plus Matérn-3/2 kernels yield competitive mean and variability predictions on a RCCI engine using Diesel and E85 fuels, enabling pressure shaping and potential safety-aware optimization. This work provides a practical, control-oriented tool for combustion management and highlights areas for improvement, such as incorporating correlations between output weights to better predict CCV under varying operating conditions.

Abstract

Cylinder pressure-based control is a key enabler for advanced pre-mixed combustion concepts. Besides guaranteeing robust and safe operation, it allows for cylinder pressure and heat release shaping. This requires fast control-oriented combustion models. Over the years, mean-value models have been proposed that can predict combustion measures (e.g., Gross Indicated Mean Effective Pressure, or the crank angle where 50% of the total heat is released) or models that predict the full in-cylinder pressure. However, these models are not able to capture cyclic variations. This is important in the control design for combustion concepts, like Reactivity Controlled Compression Ignition, that can suffer from large cyclic variations. In this study, the in-cylinder pressure and cyclic variation are modelled using a data-based approach. The model combines Principle Component Decomposition and Gaussian Process Regression. A detailed study is performed on the effects of the different hyperparameters and kernel choices. The approach is applicable to any combustion concept, but most valuable for advance combustion concepts with large cyclic variation. The potential of the proposed approach is demonstrated for an Reactivity Controlled Compression Ignition engine running on Diesel and E85. The prediction quality of the evaluated combustion measures has an overall accuracy of 13.5% and 65.5% in mean behaviour and standard deviation, respectively. The peak-pressure rise-rate is traditionally hard to predict, in the proposed model it has an accuracy of 22.7% and 96.4% in mean behaviour and standard deviation, respectively. This Principle Component Decomposition-based approach is an important step towards in-cylinder pressure shaping. The use of Gaussian Process Regression provides important information on cyclic variation and provides next-cycle controls information on safety and performance criteria.

Figures (7)

• Figure 1: Schematic of the single cylinder PACCAR MX13 engine equipped with acr:egr (acr:egr), acr:di (acr:di) and acr:pfi (acr:pfi).
• Figure 2: Distribution of the in-cylinder conditions of the training (black) and validation data (red)
• Figure 3: Four most relevant resulting from the used training data
• Figure 4: Prediction error of combustion metrics for the validation data set using different numbers of Principle Components $n_\text{PC}$. The box plot shows the minimum, maximum, median, first and third quartile, while the crosses show outliers.
• Figure 5: Average and cycle-to-cycle variation of important combustion measures (black) and the measured distribution (red) for different values of $\text{SOI}_\text{DI}$ and the nominal conditions shown in Table \ref{['tab:soisweep_nominal']} using the hyperparameters as shown in Table \ref{['tab:mdl_hp']}.