Application of a hybrid-driven framework based on sensor optimization placement for the thermal error prediction of the spindle-bearing system

The precise thermal error prediction of spindle-bearing systems (SBSs) necessitates a comprehensive analysis of information gathered from multi-source sensors. However, limited data availability due to structural constraints poses challenges to fully characterize the system state. In this study, we introduce a data-model hybrid-driven framework based on sensor optimization placement for accurate thermal error prediction of SBSs. Firstly, a thermal hypernetwork method is developed to consider uneven temperature distribution and establish a unified information fusion model for state estimation. Secondly, based on an analysis of the rapidity and robustness, robust geodesic distance-based fuzzy c-medoid clustering with a simulated annealing algorithm (RGDFCMSA) is proposed to optimize sensor placement by minimizing the information entropy of the system. Next, uncertain parameters with estimability are selected based on SIAN and Sobol's sensitivity indicator under optimal sensor placement. Furthermore, a multilayer particle filter (MLPF) is proposed to estimate temperature fields and predict the thermal error of SBSs by fusing information from multiple sources with different fidelity. Finally, experiments under different working conditions are conducted to validate the effectiveness and accuracy of the proposed method. The result indicates that the proposed framework is capable of an accurate estimation of the global temperature field, uncertain thermal parameters and thermal errors.