Kim, K. and Ghandhi, J., "Preliminary Results from a Simplified Approach to Modeling the Distribution of Engine Knock," SAE Technical Paper 2012-32-0004, 2012, doi:10.4271/2012-32-0004.
In this paper, three models for the prediction of knock onset timing are compared: an ignition-integral model using a simple ignition delay correlation, an ignition-integral model using a pre-computed lookup table of ignition delays, and the direct integration of a detailed chemical kinetic mechanism. All three models were found to compare well with experimentally measured results; the correlation-based knock-integral model was found to be as accurate as the other methods and was computationally far more efficient. The direct integration approach correlated very well with the experimental data but was delayed by 1-2 crank angles. The simplified models have been used in conjunction with a Monte-Carlo approach to assess the cycle-by-cycle variations in knock onset timing. A statistical comparison between the Monte-Carlo predictions and experimental results showed a good prediction of the distribution widths, and some modest phasing issues over a wide range of ignition timing.