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This paper is dedicated to control theoretically explainable application ofautoencoders to optimal fault detection in nonlinear dynamic systems.Autoencoder-based learning is a standard machine learning method and widelyapplied for fault (anomaly) detection and classification. In the context ofrepresentation learning, the so-called latent (hidden) variable plays animportant role towards an optimal fault detection. In ideal case, the latentvariable should be a minimal sufficient statistic. The existingautoencoder-based fault detection schemes are mainly application-oriented, andfew efforts have been devoted to optimal autoencoder-based fault detection andexplainable applications. The main objective of our work is to establish aframework for learning autoencoder-based optimal fault detection in nonlineardynamic systems. To this aim, a process model form for dynamic systems isfirstly introduced with the aid of control theory, which also leads to a clearsystem interpretation of the latent variable. The major efforts are made on thedevelopment of a control theoretic solution to the optimal fault detectionproblem, in which an analog concept to minimal sufficient statistic, theso-called lossless information compression, is introduced and proven fordynamic systems and fault detection specifications. In particular, theexistence conditions for such a latent variable are derived, based on which aloss function and further a learning algorithm are developed. This learningalgorithm enables optimally training of autoencoders to achieve an optimalfault detection in nonlinear dynamic systems. A case study on three-tank systemis given at the end of this paper to illustrate the capability of the proposedautoencoder-based fault detection and to explain the essential role of thelatent variable in the proposed fault detection system.

Control theoretically explainable application of autoencoder methods to fault detection in nonlinear dynamic systems