A new way of modelling dynamic systems and processes is sought,The prime motive for such modelling in the context of control engineering and time series analysis is the requirement to predict dynamic behaviour. Conventionally, the solution to this prediction problem is to use mathematical models based on differential or difference equations. The parameters in these equations are normally few in number and thus constitute a very efficient representation of a dynamic process. For systems which may be described accurately as linear these explicitly parameterised models are readily identified and form the basis for a general, tractable control theory. These qualities, on the other hand, do not extend to nonlinear systems.
When computers are used as aids to system modelling the succinctness of parameterised models is no longer essential because there is now access to abundant, cheap memory. Probabilistic descriptions of dynamic objects provide a general modelling procedure which can exploit this memory. These descriptions require no a priori assumptions regarding linearity or model structure.
With non-gaussian input signals the output PDF of a particular linear system is unique to that system thus making parameter estimation possible for both linear systems and nonlinear 'sandwich' type systems. This property of the prosaic marginal PDF is impressive in its own right but in this context its real value lies in the confirmation of its potential for conveying dynamics information. This potential increases with the order of the joint and conditional density functions which relate to system input and output signals and the essence of the predictive properties conveyed by them is summarised in the conditional expection function. The conditional expectation of a process output engendered by a knowledge of the current dynamic state constitutes a very general minimum variance prediction for linear and nonlinear systems alike.
The real concern is determining this function and storing it in a manner which leads to a tractable prediction and control process.
Dynamic systems are modelled by a discrete, multidimensional array of conditional expectations which in the first instance is filled out in an off-line learning process. The fitting of an hypersurface to this array and subsequent interpolation enhance prediction accuracy whilst using only moderate amounts of memory in an efficient way. This modelling process lends itself to a one-step-ahead control strategy which in second order form out-performs an optimised PID controller when each is used with a selection of linear and nonlinear control objects. On-line adaptive control of nonlinear systems is also possible.
In the time series analysis context attention is centred on the problem of detecting the onset of boiling in the sodium cooling loop of a nuclear reactor by studying the acoustic noise in the loop. A strategy based on the prediction error resulting from a conditional expectation array learnt under normal plant operating conditions is compared with a frequency-domain approach, itself novel, based on a differentiation or a differencing process. Both strategies are shown to be demonstrably superior to simple mean square signal level monitoring in the boiling detection problem. In this and the control problem the use of the conditional expectation array requires no a priori knowledge of the process to be observed save that of the ranges of the relevant signals.