Bearing fault diagnosis in modern industrial applications frequently encounters severe challenges due to data privacy fragmentation, domain shifts induced by varying working conditions, and the insufficiency of single-sensor information. To address these critical bottlenecks, this paper proposes a multi-modal domain generalization federated learning framework. Specifically, a dual-branch 1D-CNN feature extraction network is constructed to independently process horizontal and vertical vibration signals, which are then integrated using multi-scale convolutional blocks and a Squeeze-and-Excitation (SE) channel attention mechanism for robust feature fusion. Furthermore, to mitigate the client drift issue caused by non-IID data distributions across different rotational speeds and loads, a FedProx-based federated optimization strategy with a dynamic proximal term regularization is implemented. Extensive experiments conducted on the XJTU-SY bearing dataset demonstrate that the proposed framework achieves an overall classification accuracy of 67.20% and an F1-score of 67.32% under strict differential privacy constraints (DP-SGD noise multiplier = 0.05). Compared with the baseline federated model, the optimized version provides a significant performance gain of +12.37% in diagnostic accuracy. The proposed approach successfully strikes an optimal balance between data privacy protection and cross-condition domain generalization, offering a reliable paradigm for distributed industrial intelligent maintenance.

The report gives a very clear, systematic exposition of the major shortcomings in current Large Language Model (LLM)-based automated reward design methods for reinforcement learning, and after a careful analysis of EUREKA and LEARN-Opt, it naturally and elegantly identifies two fundamental issues: dependence on environment source code and absence of mathematical guarantees for policy optimality. In view of the existing limitations, this paper proposes a well-designed framework that combines Vision-Language Models (VLMs) for visual observation, Graph-of-Thoughts for hierarchical task decomposition, and Potential - based Reward Shaping for theoretical safety guarantees, hence naturally solving the problem of code dependency by using pure visual feedback and reducing generation variance by structured decomposition. The paper presents a method that achieves policy invariance by means of mathematically constrained reward generation, and accordingly gives a clear, logically organized discussion of the problem analysis, theoretical background, proposed approach, implementation architecture, current results, and experimental validation plan. It makes a very natural and important contribution to building robust, generalizable, and theoretically sound automated reward design systems.