Blaschke learning machine: A novel and efficient continual learning classifier toward intelligent fault diagnosis

In the field of mechanical fault diagnosis, identifying the mapping relationship between signal features and labels is a core issue for achieving accurate and reliable diagnostics. Existing methods are often characterized by high complexity and are typically constrained to static environments, relying heavily on historical datasets. To address these challenges, this paper presents Blaschke Approximation Theorem and, based on this foundation, proposes a novel classifier with continuous learning capabilities for fault diagnosis: Blaschke Learning Machine (BLM). BLM decomposes inputs by generating dynamic Blaschke systems through Blaschke nodes, effectively modeling the input–output mapping relationship and demonstrating excellent generalization ability. Furthermore, BLM is highly flexible; when the initial model fails to adequately capture the mapping, it can dynamically adjust Blaschke system without the need for retraining. It is worth noting that BLM can efficiently update the model based on new data and support three types of incremental learning: data increment, class increment, and condition increment, enabling real-time diagnostics for mechanical equipment. Finally, the effectiveness of BLM is validated on two industrial fault diagnosis datasets. Compared with seven state-of-the-art continual learning methods, BLM achieves consistent improvements of 5.07–21.7% in average diagnosis accuracy while requiring fewer parameters and computational than typical deep learning baselines. Experimental results demonstrate that BLM not only excels in fault diagnosis under non-stationary conditions but also exhibits robust continual learning capabilities, making it particularly suitable for real-world mechanical fault diagnosis systems with limited computational resources.