Learning Domain-Generalizable Discriminative Representations by Mixing Euclidean Dynamics and Hilbert Statistics for Wind Turbine Blade Icing Detection

As wind energy grows in importance, blade icing threatens turbine efficiency and safety. Existing approaches based solely on convolutional neural networks (CNNs) for Euclidean-space feature extraction struggle with complex dynamics and domain shifts. To address this, we propose the domain-generalizable network for icing turbines via mixed Euclidean and Hilbert representations (DGMEHIT), which runs a CNN deep module and a Hilbert statistical module (HSM) in parallel to extract complementary local sequential and global statistical features from Euclidean-space and Hilbert space. Raw features are mapped into a high-dimensional Hilbert space to enhance global statistical separability and discriminate superficially similar signals. A channel–temporal mixer module further models dynamic dependencies by fusing multichannel and time-domain information. In addition, a maximum mean discrepancy loss is incorporated into the HSM to improve feature consistency across domains, enabling the learning of domain-generalizable representations and enhancing the model’s adaptability to varying geographical and climatic conditions. Experiments on ten public time-series datasets and one real-world icing dataset show DGMEHIT surpasses state-of-the-art methods, improving F1 by 6.4% and MCC by 12.7%, with generalization tests and online evaluations confirming practical robustness.