  Advanced combustion technologies such as homogeneous charge compression
ignition (HCCI) engines have a narrow stable operating region defined by
complex control strategies such as exhaust gas recirculation (EGR) and variable
valve timing among others. For such systems, it is important to identify the
operating envelope or the boundary of stable operation for diagnostics and
control purposes. Obtaining a good model of the operating envelope using
physics becomes intractable owing to engine transient effects. In this paper, a
machine learning based approach is employed to identify the stable operating
boundary of HCCI combustion directly from experimental data. Owing to imbalance
in class proportions in the data, two approaches are considered. A re-sampling
(under-sampling, over-sampling) based approach is used to develop models using
existing algorithms while a cost-sensitive approach is used to modify the
learning algorithm without modifying the data set. Support vector machines and
recently developed extreme learning machines are used for model development and
results compared against linear classification methods show that cost-sensitive
versions of ELM and SVM algorithms are well suited to model the HCCI operating
envelope. The prediction results indicate that the models have the potential to
be used for predicting HCCI instability based on sensor measurement history.
