This paper is dedicated to control theoretically explainable application of
autoencoders to optimal fault detection in nonlinear dynamic systems.
Autoencoder-based learning is a standard method of machine learning technique
and widely applied for fault (anomaly) detection and classification. In the
context of representation learning, the so-called latent (hidden) variable
plays an important role towards an optimal fault detection. In ideal case, the
latent variable should be a minimal sufficient statistic. The existing
autoencoder-based fault detection schemes are mainly application-oriented, and
few efforts have been devoted to optimal autoencoder-based fault detection and
explainable applications. The main objective of our work is to establish a
framework for learning autoencoder-based optimal fault detection in nonlinear
dynamic systems. To this aim, a process model form for dynamic systems is
firstly introduced with the aid of control and system theory, which also leads
to a clear system interpretation of the latent variable. The major efforts are
devoted to the development of a control theoretical solution to the optimal
fault detection problem, in which an analog concept to minimal sufficient
statistic, the so-called lossless information compression, is introduced for
dynamic systems and fault detection specifications. In particular, the
existence conditions for such a latent variable are derived, based on which a
loss function and further a learning algorithm are developed. This learning
algorithm enables optimally training of autoencoders to achieve an optimal
fault detection in nonlinear dynamic systems. A case study on three-tank system
is given at the end of this paper to illustrate the capability of the proposed
autoencoder-based fault detection and to explain the essential role of the
latent variable in the proposed fault detection system