Convex Identification of Minimal Function Bases for Cylinder Pressure by Using Pressure Values as Basis Weights

Estimating cylinder individual pressures using flywheel angular measurements is difficult, foremost because several input signals must be estimated from one single measurement signal. Since the pressures cannot vary arbitrary, estimation can still be possible, but it leaves little room for robustness. To take most use of data and models, it is suggested here to parameterize pressures using a function basis. For a general physics-based engine model, it is shown how the information content in the angular measurement is limited, implying that only a few parameters per cylinder can be estimated. If small deviations in the combustion are to be identified, a very parameter efficient basis is, therefore, needed. By showing that the basis can be chosen such that its weights are pressures at distinct angles, a convex optimization problem to determine optimal basis functions is derived. The method is applied to extensive cylinder pressure data for a six-cylinder diesel engine in a case study with induced combustion faults. The result is that only three to four free parameters per cylinder are needed to achieve a close fit, and a provided analysis suggests that this may enable the design of robust estimators.