Statistical characterization of the dual-autoencoder residual

Develop a statistical characterization of the fault-detection residual produced by the dual-autoencoder framework for nonlinear dynamical systems, accounting for finite data, measurement noise, and operating variability.

Background

The proposed fault-detection method decides whether a nonlinear dynamical system has undergone a parametric change by comparing the norm of a residual, obtained from complementary coordinates learned by a dual autoencoder, against a threshold estimated from nominal data. The residual is affected by finite sample size, measurement noise, approximation errors in the Koopman representation, uncertainty in the learned mappings, and variability in operating conditions. The paper reports empirical performance on simulated and experimental systems but does not derive a statistical model or rigorous calibration procedure for the residual under these sources of uncertainty. A statistical characterization would support principled threshold selection and more reliable control of false-alarm and missed-detection rates.