Quantifying Robustness: A Benchmarking Framework for Deep Learning Forecasting in Cyber-Physical Systems

Cyber-Physical Systems (CPS) in domains such as manufacturing and energy distribution generate complex time series data crucial for Prognostics and Health Management (PHM). While Deep Learning (DL) methods have demonstrated strong forecasting capabilities, their adoption in industrial CPS remains limited due insufficient robustness. Existing robustness evaluations primarily focus on formal verification or adversarial perturbations, inadequately representing the complexities encountered in real-world CPS scenarios. To address this, we introduce a practical robustness definition grounded in distributional robustness, explicitly tailored to industrial CPS, and propose a systematic framework for robustness evaluation. Our framework simulates realistic disturbances, such as sensor drift, noise and irregular sampling, enabling thorough robustness analyses of forecasting models on real-world CPS datasets. The robustness definition provides a standardized score to quantify and compare model performance across diverse datasets, assisting in informed model selection and architecture design. Through extensive empirical studies evaluating prominent DL architectures (including recurrent, convolutional, attention-based, modular, and structured state-space models) we demonstrate the applicability and effectiveness of our approach. We publicly release our robustness benchmark to encourage further research and reproducibility.

Robustness and Generalization Performance of Deep Learning Models on Cyber-Physical Systems: A Comparative Study

Deep learning (DL) models have seen increased attention for time series forecasting, yet the application on cyber-physical systems (CPS) is hindered by the lacking robustness of these methods. Thus, this study evaluates the robustness and generalization performance of DL architectures on multivariate time series data from CPS. Our investigation focuses on the models' ability to handle a range of perturbations, such as sensor faults and noise, and assesses their impact on overall performance. Furthermore, we test the generalization and transfer learning capabilities of these models by exposing them to out-of-distribution (OOD) samples. These include deviations from standard system operations, while the core dynamics of the underlying physical system are preserved. Additionally, we test how well the models respond to several data augmentation techniques, including added noise and time warping. Our experimental framework utilizes a simulated three-tank system, proposed as a novel benchmark for evaluating the robustness and generalization performance of DL algorithms in CPS data contexts. The findings reveal that certain DL model architectures and training techniques exhibit superior effectiveness in handling OOD samples and various perturbations. These insights have significant implications for the development of DL models that deliver reliable and robust performance in real-world CPS applications.