Henrik Steude

Alexander Windmann, Henrik Steude, Oliver Niggemann

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.

Lukas Moddemann, Henrik Sebastian Steude, Alexander Diedrich et al.

Consistency-based diagnosis is an established approach to diagnose technical applications, but suffers from significant modeling efforts, especially for dynamic multi-modal time series. Machine learning seems to be an obvious solution, which becomes less obvious when looking at details: Which notion of consistency can be used? If logical calculi are still to be used, how can dynamic time series be transferred into the discrete world? This paper presents the methodology Discret2Di for automated learning of logical expressions for consistency-based diagnosis. While these logical calculi have advantages by providing a clear notion of consistency, they have the key problem of relying on a discretization of the dynamic system. The solution presented combines machine learning from both the time series and the symbolic domain to automate the learning of logical rules for consistency-based diagnosis.

Henrik S. Steude, Lukas Moddemann, Alexander Diedrich et al.

In Cyber-Physical Systems (CPS) research, anomaly detection (detecting abnormal behavior) and diagnosis (identifying the underlying root cause) are often treated as distinct, isolated tasks. However, diagnosis algorithms require symptoms, i.e. temporally and spatially isolated anomalies, as input. Thus, anomaly detection and diagnosis must be developed together to provide a holistic solution for diagnosis in CPS. We therefore propose a method for utilizing deep learning-based anomaly detection to generate inputs for Consistency-Based Diagnosis (CBD). We evaluate our approach on a simulated and a real-world CPS dataset, where our model demonstrates strong performance relative to other state-of-the-art models.

Henrik Sebastian Steude, Alexander Diedrich, Ingo Pill et al.

Diagnostic processes for complex cyber-physical systems often require extensive prior knowledge in the form of detailed system models or comprehensive training data. However, obtaining such information poses a significant challenge. To address this issue, we present a new diagnostic approach that operates with minimal prior knowledge, requiring only a basic understanding of subsystem relationships and data from nominal operations. Our method combines a neural network-based symptom generator, which employs subsystem-level anomaly detection, with a new graph diagnosis algorithm that leverages minimal causal relationship information between subsystems-information that is typically available in practice. Our experiments with fully controllable simulated datasets show that our method includes the true causal component in its diagnosis set for 82 p.c. of all cases while effectively reducing the search space in 73 p.c. of the scenarios. Additional tests on the real-world Secure Water Treatment dataset showcase the approach's potential for practical scenarios. Our results thus highlight our approach's potential for practical applications with large and complex cyber-physical systems where limited prior knowledge is available.

Alexander Windmann, Henrik Steude, Daniel Boschmann et al.

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.

Henrik S. Steude, Alexander Windmann, Oliver Niggemann

Machine Learning (ML) has achieved great successes in recent decades, both in research and in practice. In Cyber-Physical Systems (CPS), ML can for example be used to optimize systems, to detect anomalies or to identify root causes of system failures. However, existing algorithms suffer from two major drawbacks: (i) They are hard to interpret by human experts. (ii) Transferring results from one systems to another (similar) system is often a challenge. Concept learning, or Representation Learning (RepL), is a solution to both of these drawbacks; mimicking the human solution approach to explain-ability and transfer-ability: By learning general concepts such as physical quantities or system states, the model becomes interpretable by humans. Furthermore concepts on this abstract level can normally be applied to a wide range of different systems. Modern ML methods are already widely used in CPS, but concept learning and transfer learning are hardly used so far. In this paper, we provide an overview of the current state of research regarding methods for learning physical concepts in time series data, which is the primary form of sensor data of CPS. We also analyze the most important methods from the current state of the art using the example of a three-tank system. Based on these concrete implementations1, we discuss the advantages and disadvantages of the methods and show for which purpose and under which conditions they can be used.