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Data-driven, neural network (NN) based anomaly detection and predictivemaintenance are emerging research areas. NN-based analytics of time-series dataoffer valuable insights into past behaviors and estimates of criticalparameters like remaining useful life (RUL) of equipment and state-of-charge(SOC) of batteries. However, input time series data can be exposed tointentional or unintentional noise when passing through sensors, necessitatingrobust validation and verification of these NNs. This paper presents a casestudy of the robustness verification approach for time series regression NNs(TSRegNN) using set-based formal methods. It focuses on utilizingvariable-length input data to streamline input manipulation and enhance networkarchitecture generalizability. The method is applied to two data sets in thePrognostics and Health Management (PHM) application areas: (1) SOC estimationof a Lithium-ion battery and (2) RUL estimation of a turbine engine. The NNs'robustness is checked using star-based reachability analysis, and severalperformance measures evaluate the effect of bounded perturbations in the inputon network outputs, i.e., future outcomes. Overall, the paper offers acomprehensive case study for validating and verifying NN-based analytics oftime-series data in real-world applications, emphasizing the importance ofrobustness testing for accurate and reliable predictions, especiallyconsidering the impact of noise on future outcomes.

Robustness Verification of Deep Neural Networks using Star-Based Reachability Analysis with Variable-Length Time Series Input