Page 84 - Neural Network Modeling and Identification of Dynamical Systems

72 2. DYNAMIC NEURAL NETWORKS: STRUCTURES AND TRAINING METHODS

the form of multiperceptrons with sigmoid ac- a relatively small subdomain of the values of
tivation functions. This allows us to most effec- state and control variables, and then, in the on-
tively meet the requirements, which are differ- line mode, an incremental learning process of
ent, generally speaking, for a priori and refin- the ANN model is performed, during which at
ing models. In particular, the main requirement each step a step-by-step extension of the sub-
for the a priori model is the ability to repre- region is performed. From here, the model is
sent complex nonlinear dependencies with the operational, in order to eventually expand the
required accuracy, while the time spent on learn- given subdomain to the full domain of the vari-
ing such a model is uncritical, since this train- ables.
ing is carried out in an autonomous (off-line) In the structural-parametric version of the in-
mode. At the same time, the refining model in cremental model formation procedure, at first,
its work must fit into the very rigid framework a “truncated” ANN model is constructed. This
of the real (or even advanced) time scale. For preliminary model has only a part of the state
this reason, in particular, in the vast majority of variables as its inputs, and it is trained on a
cases, the ANN architectures will be unaccept- dataset that covers only a subset of the domain
able, requiring full retraining, even with minor of definition. This initial model is then gradually
changes in the training data with which they expanded by introducing new variables into it,
work. In such a situation, an incremental ap- followed by further training.
proach to teaching and learning the ANN mod- For example, the initial model is the model of
els is more appropriate, allowing not to retrain the longitudinal angular motion of the aircraft,
the entire network, but only to correct those el- which is then expanded by adding trajectory
ements that are directly related to the changed longitudinal motion, after which lateral motion
components are added to it, that is, the model
training data.
is brought to the desired full model of the space
motion in a few steps.
2.3.3 Incremental Formation of ANN The structural-parametric variant of the in-
Models cremental formation of ANN models allows
us to start with a simple model, sequentially
One of the tools for adapting ANN models is
complicating it, for example, according to the
an incremental formation that exists in two vari-
ants: parametric and structural-parametric. scheme
With the parametric version of the incremen-
material point
tal formation, the structural organization of the
ANN model is set immediately and fixed, after ⇓
which it is incrementally adjusted (basic or ad-
rigid body
ditional learning) in several stages, for example,
to extend the domain of operation modes of the ⇓
dynamical system in which the model operates elastic body
with the required accuracy.
⇓
For example, if we take a full spatial model
of the aircraft motion, taking into account both a set of coupled rigid and/or elastic bodies
its trajectory and angular motion, then in accor-
dance with the incremental approach, first an This makes it possible to build up the model
off-line training of this model is carried out for step-by-step in a structural sense.