This paper proposes the use of radial basis function (RBF) networks in the modelling of non-linear engine processes. A pertinent application of such a model is the reconstruction of cylinder pressure based upon the instantaneous angular velocity of the engine crankshaft. Distinction is made between parametric and non-parametric models and applications to which each is suited. The structure of an RBF model is presented and the use of this model in combustion pressure reconstruction is discussed. The paper concludes with a treatment of the practicalities associated with the implementation of an RBF model to typify a non-linear engine process.Keywords: angular speed, cylinder pressure measurement, non-parametric engine model, radial basis function network, regressor selection, regularization
NON-LINEAR ENGINE MODELSMany of the systems and processes operating within internal combustion engines are inherently non-linear; because of this, simple but accurate analytical models cannot be derived for them. A classic example of a non-linear engine process is the cyclic pressure variation within a combusting diesel engine cylinder. Owing to its practical importance, cylinder pressure estimation has been used as the process upon which to develop the non-linear modelling techniques illustrated in this paper. Combustion pressure waveform measurement and analysis play an important role in the improvement of performance, emissions control and condition monitoring in internal combustion engines. Conventional techniques are inapplicable for reliable, high-resolution cylinder pressure measurement on a routine or in-service basis. For these reasons an alternative approach to cylinder pressure estimation, based on easy-to-measure variables, is attractive. This paper introduces a family of non-parametric models, radial basis function (RBF) networks, which may be applied to the task of reconstructing cylinder pressure based on easy-to-obtain measurements of instantaneous crankshaft angular velocity and cylinder head vibration.At this stage it is worthwhile formally distinguishing between parametric and non-parametric models. Parametric models are differentiated from non-parametric models by the inference which may be drawn from their coefficients. In the case of the former, the aim is to arrive at values for a select few terms that are meaningful in the real world. It is assumed that a set of deterministic mathematical models of the system can be derived using physical laws. The system can then usually be written as a set of ordinary differential equations and algebraic equations: y= f (q, q; , q,x,t,) (where q represents the degrees of freedom, y the observed output variables, x the input variables and t the explicit time. Vector represents the unknown model parameters. Sufficient initial conditions must be supplied to arrive at values for q and its first and second derivatives. In order to determine the model parameters, , it is necessary to substitute the measured time histories of all variables. This assumes that the m...