An ignition delay correlation encompassing the effects of temperature, pressure, residual gas, EGR, and lambda (on both the rich and lean sides) has been developed. The procedure uses the individual knocking cycle data from a boosted direct injection SI engine (GM LNF) operating at 1250 to 2000 rpm, 8-14 bar GIMEP, EGR of 0 to 12.5%, and lambda of 0.8 to 1.3 with a certification fuel (Haltermann 437, with RON=96.6 and MON=88.5). An algorithm has been devised to identify the knock point on individual pressure traces so that the large data set (of some thirty three thousand cycles) could be processed automatically. For lean and for rich operations, the role of the excess fuel, air, and recycled gas (which has excess air in the lean case, and hydrogen and carbon monoxide in the rich case) may be treated effectively as diluents in the ignition delay expression.

The combustion process after auto-ignition is investigated. Depending on the non-uniformity of the end gas, auto-ignition could initiate a flame, produce pressure waves that excite the engine structure (acoustic knock), or result in detonation (normal or developing). For the "acoustic knock" mode, a knock intensity (KI) is defined as the pressure oscillation amplitude. The KI values over different cycles under a fixed operating condition are observed to have a log-normal distribution. When the operating condition is changed (over different values of , EGR, and spark timing), the mean () of log (KI/GIMEP) decreases linearly with the correlationbased ignition delay calculated using the knock-point end gas condition of the mean cycle. The standard deviation  of log(KI/GIMEP) is approximately a constant, at 0.63. The values of  and  thus allow a statistical description of knock from the deterministic calculation of the ignition delay using the mean cycle properties