Performance Bounds for Neural Network Estimators: Applications in Fault Detection
This work addresses fault detection in dynamical systems, but it is incremental as it builds on existing robustness results and applies them to specific tuning scenarios.
The authors tackled the problem of tuning neural network-based anomaly detectors by providing upper bounds on false alarm rates, using a theory extension to propagate confidence ellipsoids through neural networks, and demonstrated it on linear and nonlinear dynamical systems.
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.