Modeling with Neural Networks: Principles and Model Design Methodology - Neural Networks: Methodology and Applications - page 168

algorithm). Directed and semidirected algorithms also apply, with the addition
of a third type of training: undirected training.

2.7.4 What to Do in Practice? A Real Example of Dynamic
Black-Box Modeling

In the first sections of this chapter, we emphasized the questions related to
the design of a black-box static model, such as

• preprocessing and selection of relevant variables,

• choice of the complexity of the model (e.g., number of hidden neurons).

The design a dynamic models involves the following additional choices:

• choice of the representation (input-output or state),

• choice of the noise assumption (state noise, output noise, state and output

noise),

• choice of the order of the model.

If no prior knowledge on the process is available, all combinations of assump-
tions and representations should be tested, and models of increasing order
should be designed, until a satisfactory model is found. However, the follow-
ing arguments should alleviate the designer's task:

• State-space models are more general and more parsimonious, but more

di cult to train, than input-output models; therefore, it is recommended
to first design input-output models, then, if the latter turn out to be
unsatisfactory, try state-space models.

• Prior knowledge, however cursory, may give useful hints as to the influence

of noise on the process.

• Similarly, a cursory analysis of the process response to typical inputs may

provide valuable insights into the order of the model.

In order to illustrate the design methodology discussed above, the example of
the black-box modeling of the hydraulic actuator of a robot arm is presented.
Experimental data was gathered by the Linkoping University (Sweden), and
black-box modeling was performed by several groups (see for instance [Sjoberg
1995; Norgaard 2000]).
The control input is the opening of the liquid admission valve in the ac-
tuator, the output is the resulting hydraulic pressure. Sequences of input and
output data are available for training (512 points) and testing (512 points).
Figure 2.47(a) shows the available input data, and Fig. 2.47(b) shows the
corresponding responses.
Because no validation set was provided, the performances reported here
are the best performances obtained on the test set.
First, it appears clearly that he model must be nonlinear in order to ac-
count for the observations: input variations by a factor of 2 (for instance