ABSTRACT
We often use empirical models in automaton applications. These may relate process output to inputs at steady state, describe the interrelation between easily measured variables to predict a less easily measured process characteristic (inferential or soft sensors), describe the dynamic process response to manipulated variables, or predict the impact of processing conditions on product attributes. Each of these models would predict an output value that is continuous. As well, we use models to classify conditions or faults that produce discrete or logical (0, 1) outputs. These may include classication of faults from process data, or classication of ¶ow regime (turbulent, laminar). Models are usually based on standard statistical regression equations of the form
y a bx cx dx= + + + + 2 3 (13.1)
Neural networks (NNs) can do the same modeling job, and can have advantages in ¶exibility and efciency. In a model such as that of Equation 13.1, the user has to explicitly choose the functional relation between y and x. In this case, a cubic relation is indicated. However, it could be reciprocal, logarithmic, or seasonal; and a user has to specify the right one. By contrast, in NNs the user does not have to specify the functional relations, and this convenience is often called the model-free attribute.
