Path planning is crucial for autonomous underwater vehicles (AUVs) and plays a vital role in ocean engineering. To improve the search efficiency and accuracy, this study proposed a three-dimensional path-planning method for AUVs based on the interval multi-objective secretary bird optimization algorithm (IMOSBOA). This method addressed path-planning challenges under imprecise current predictions and uncertain hazard source locations. First, the marine environment was modeled in three dimensions using the interval theory. Second, the danger levels and navigation times were set as the optimization objectives to construct a three-dimensional path-planning mathematical model. Finally, IMOSBOA was proposed and applied to solve the optimization problem. To verify the optimization performance of the new algorithm, its planning results were compared with those of the other algorithms. The simulation results demonstrated that the robustness and search capability of the proposed algorithm surpass those of comparative algorithms.

Rolling bearings constitute critical rotating components within rolling mill equipment. Production efficiency and the operational safety of the whole mechanical system are directly governed by their operational health state. To address the dual challenges of the over-reliance of conventional diagnostic methods on expert experience and the scarcity of fault samples in industrial scenarios, we propose a virtual–physical data fusion-optimized intelligent fault diagnosis framework. Initially, a dynamics-based digital twin model for rolling bearings is developed by leveraging their geometric symmetry. It is capable of generating comprehensive fault datasets through parametric adjustments of bearing dimensions and operational environments in virtual space. Subsequently, a symmetry-informed architecture is constructed, which integrates multi-scale convolutional neural networks with attention mechanisms and bidirectional gated recurrent units (MCNN-AT-BiGRU). This architecture enables spatiotemporal feature extraction and enhances critical fault characteristics. The experimental results demonstrate 99.5% fault identification accuracy under single operating conditions. It maintains stable performance under low SNR conditions. Furthermore, the framework exhibits superior generalization capability and transferability across the different bearing types.