Page 174 - Neural Network Modeling and Identification of Dynamical Systems

CHAPTER
5

Semiempirical Neural Network Models

of Controlled Dynamical Systems

5.1 SEMIEMPIRICAL ANN-BASED the ANN model, while preserving its flexibility
APPROACH TO MODELING OF at the same time.
DYNAMICAL SYSTEMS So, both traditional theoretical and empir-
ical modeling approaches have certain flaws.
Theoretical (“white box”) modeling approach Manually designed theoretical models often lack
relies on the knowledge of some fundamental the required accuracy, because it is difficult to
relationships (such as the laws of mechanics, take all the factors into account. Moreover, such
thermodynamics, etc.), as well as the knowledge models are not suited for real-time adaptation.
of the simulated system structure. Theoretical Hence, any changes in a simulated system or
models might lack the required accuracy due its operating environment lead to a decrease in
to incomplete and inaccurate knowledge of the model accuracy. On the other hand, empirical
properties of the simulated system and environ- models require the acquisition and preprocess-
ment in which it operates. Moreover, such mod- ing of an extensive amount of experimental data.
els are unable to adapt to changes in the simu- Also, a poor choice of the family of empirical
lated system properties. models will likely result in a nonparsimonious
Empirical (“black box”) modeling approach, model with low generalization ability due to
described in Chapters 3 and 4, relies only on overfitting. We propose a hybrid semiempiri-
experimental data for the behavior of the sim- cal (“gray box”) modeling approach that utilizes
ulated system. This approach has its benefits, both theoretical domain-specific knowledge and
and it is the only possible option in cases when experimental data of system behavior [1–3].
there is no a priori knowledge of the nature In this book, we assume that the mentioned
of the system being modeled, of its operational domain-specific knowledge about the object of
mechanisms, and of essential aspects of its be- modeling is presented in the form of ODEs.
havior. However, the results presented in this There is also an extension of this approach to the
chapter show that empirical ANN-based mod- case of subject knowledge in the form of DAEs
els of dynamical systems have severe limitations [4–6]. This approach can be extended for the case
on the complexity level of the problems being when the object of modeling is described by par-
solved. In order to overcome these limitations, tial differential equations (PDEs), but we do not
we need to reduce the number of parameters of consider this variant in our book.

Neural Network Modeling and Identification of Dynamical Systems
https://doi.org/10.1016/B978-0-12-815254-6.00015-0 165 Copyright © 2019 Elsevier Inc. All rights reserved.