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A framework for a new approach to modelling the cyclic pressure variations which occur in spark ignition engines, based on stochastic process theory, is discussed. The aim is to of establish a stochastic process model for the entire pressure/time history of cycle-by-cycle variation throughout the combustion period. Three types of model are discussed. In the first two it is possible to incorporate correlation across cycles, arising from “prior cycle effects”. In the third, simpler version, the individual cycles are treated as statistically independent. Through a statistical analysis of some pressure data acquired under typical engine conditions the basic characteristics of the stochastic process representations are illustrated.

A stochastic model for the entire pressure-time history of cycle-by-cycle cylinder pressure variations is obtained by fitting simple parametric models of cylinder pressure development to 506 cycles of continuous experimental data taken at four operating conditions. The cyclic variation is therefore encapsulated in a sequence of cyclically varying model parameters whose statistical properties then complete the stochastic description. Different model forms, (including computationally efficient linearised models), are compared for their degree of fit, and for the ease with which the statistics of the identified parameters can be defined. This approach, which typically accounts for 80-90% of the rms cyclic pressure variation, provides a more complete quantification of the phenomena than previously available, and a basis for simulating statistically identical pressure traces.