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.

翻译：数据驱动的、基于神经网络（NN）的异常检测和预测性维护是新兴研究领域。基于神经网络的时序数据分析可提供对过去行为的深刻洞察，并估计关键参数，如设备的剩余使用寿命（RUL）和电池的荷电状态（SOC）。然而，输入时间序列数据在通过传感器时可能遭受有意或无意的噪声干扰，因此需要对这些神经网络进行鲁棒的验证与确认。本文针对时序回归神经网络（TSRegNN），提出了一种基于集合形式化方法的鲁棒性验证案例研究。该方法侧重于利用变长度输入数据以简化输入操作并增强网络架构的泛化能力。该方法被应用于预测与健康管理（PHM）应用领域的两个数据集：（1）锂离子电池的SOC估计，（2）涡轮发动机的RUL估计。通过基于星的（star-based）可达性分析检查神经网络的鲁棒性，并采用多种性能指标评估输入中有界扰动对网络输出（即未来结果）的影响。总体而言，本文为现实应用中基于神经网络的时序数据分析的验证与确认提供了全面的案例研究，强调了鲁棒性测试对于准确可靠预测的重要性，尤其是考虑到噪声对未来结果的影响。