Sensor layout optimization for blade tip timing measurement based on joint sparse Bayesian learning

The layout of blade tip timing (BTT) sensors critically influences the recovery of undersampled blade vibration signals. Existing layout strategies mainly optimize front-end surrogate metrics (such as coherence) and therefore remain only indirectly related to back-end identification performance. Starting from the perspective of efficient information acquisition, this paper proposes a joint sparse Bayesian learning (SBL)-based sensor layout optimization method for BTT measurement, aiming to establish consistency between front-end layout design and back-end reconstruction objectives. A greatest common divisor (GCD) expanded signal model is first introduced to separate the sampling matrix from the sparse representation matrix, thereby enabling explicit incorporation of layout variables into the reconstruction model. Subsequently, based on the posterior shrinkage property of SBL, a layout optimization objective is constructed within the Bayesian framework, where posterior information serves as the primary optimization target. Numerical simulation and experimental results demonstrate that the proposed method improves frequency identification accuracy compared with other layouts, and confirm that low-coherence structures do not guarantee stable recovery of sparse signals. The proposed layout optimization method provides a direct post-processing-oriented route for BTT sensor layout design.