Modelling Time-Varying Industrial Processes Using MLP Networks

Abstract

The modelling of time-invariant systems using a multilayer perceptron (MLP) network has been studied. As MLPs have been demonstrated to be universal approximators — given sufficient hidden processing elements within the hidden layers and a suitable input vector — a time-invariant systems output can be predicted by an MLP trained to functionally approximate the system given current input and historic input and output information, thus $$\hat{y}=f(y, u)$$ if the system is an infinite impulse response system.Experimental modelling of the nonlinear startup regime of a real industrial process using this method met with poor results. One explanation for this failure is that the system is time-varying in that at any stage of operation, the output of the process is functionally dependant not only upon previous input and output measurements, but also on time. Thus an estimate for y will be $$\hat{y}=g(y, u, t)$$ and an MLP will need to be provided with a representation for time in its input vector in order to approximate this function. However, many industrial processes are not smoothly dependant upon time as would be an MLP with time as an input. Study of the industrial process revealed several distinct phases of operation within its startup regime; stages characterised by the switching in and out of various process components and changes in control set points which alter the underlying operation of the process. As each stage of operation was time-invariant in isolation, the system can be described as being piecewise time-invariant overall. Thus the system is more disjointedly dependant upon time, and attempting to model it using an MLP with time as an input provided no greater success than before.An alternative, where it is possible to clearly distinguish between several stages of execution in the operation of a system, is to treat each stage as a function in its own right and attempt to model each with a separate MLP. This would result in a cascade of MLPs which it should be possible to switch between during the normal running of the process to provide a continuous input-output mapping (Figure 1). This method met with far greater success for the industrial process.A mechanism for modelling a time-varying process with n identifiable stages of operation.