Performance Bounds for Neural Network Estimators: Applications in Fault Detection

TL;DR

This paper develops a method to quantify neural network robustness for fault detection by propagating confidence ellipsoids through the network, enabling improved threshold tuning and false alarm control in dynamical systems.

Contribution

It introduces a theory extension for propagating multiple confidence ellipsoids through neural networks, aiding in model-based anomaly detector tuning.

Findings

Effective bounds on false alarm rates under normal operation

Application to linear and nonlinear dynamical systems

Enhanced sensitivity analysis for neural network-based detectors

Abstract

We exploit recent results in quantifying the robustness of neural networks to input variations to construct and tune a model-based anomaly detector, where the data-driven estimator model is provided by an autoregressive neural network. In tuning, we specifically provide upper bounds on the rate of false alarms expected under normal operation. To accomplish this, we provide a theory extension to allow for the propagation of multiple confidence ellipsoids through a neural network. The ellipsoid that bounds the output of the neural network under the input variation informs the sensitivity - and thus the threshold tuning - of the detector. We demonstrate this approach on a linear and nonlinear dynamical system.