Robustness Verification of Deep Neural Networks using Star-Based
  Reachability Analysis with Variable-Length Time Series Input
Neelanjana Pal Diego Manzanas Lopez Taylor T Johnson
Data-driven, neural network (NN) based anomaly detection and predictive
maintenance are emerging research areas. NN-based analytics of time-series data
offer valuable insights into past behaviors and estimates of critical
parameters like remaining useful life (RUL) of equipment and state-of-charge
(SOC) of batteries. However, input time series data can be exposed to
intentional or unintentional noise when passing through sensors, necessitating
robust validation and verification of these NNs. This paper presents a case
study of the robustness verification approach for time series regression NNs
(TSRegNN) using set-based formal methods. It focuses on utilizing
variable-length input data to streamline input manipulation and enhance network
architecture generalizability. The method is applied to two data sets in the
Prognostics and Health Management (PHM) application areas: (1) SOC estimation
of a Lithium-ion battery and (2) RUL estimation of a turbine engine. The NNs'
robustness is checked using star-based reachability analysis, and several
performance measures evaluate the effect of bounded perturbations in the input
on network outputs, i.e., future outcomes. Overall, the paper offers a
comprehensive case study for validating and verifying NN-based analytics of
time-series data in real-world applications, emphasizing the importance of
robustness testing for accurate and reliable predictions, especially
considering the impact of noise on future outcomes.