Lightweight off-grid Bayesian inference: A low-complexity and high-precision sparse reconstruction method

Blade tip timing (BTT) is an effective non-contact vibration measurement method for monitoring the condition of rotating blades owing to its high efficiency and long service life. However, due to its limitations in the number of sensors and measurement principles, the BTT signal is often severely undersampled. Although some sparse Bayesian learning-based methods have offered a promising solution to this problem, they either suffer from basis mismatch due to predefined frequency grids or involve computationally intensive matrix inversions, hindering high-precision and real-time BTT signal analysis. To overcome these limitations simultaneously, we develop a lightweight off-grid Bayesian inference (LOGBI) approach for BTT signal post-processing. First, by integrating variational inference with the majorization-minimization principle, we adopt a quadratic surrogate of the original likelihood term in the Bayesian formulation. Under the variational expectation–maximization framework, the posterior covariance is approximated in a diagonal form, thereby avoiding explicit matrix inversion process. Meanwhile, the corresponding M-step is equivalent to a standard convex quadratic optimization problem, resulting in a tighter surrogate and improved inference stability. Then, to compensate for the weakened suppression of highly correlated atoms caused by the diagonal transformation, a Bayesian information criterion-guided peak selection strategy is further introduced to filter out spurious peaks and provide reliable coarse frequency initialization results. Subsequently, a Levenberg–Marquardt-based local refinement strategy is applied to calibrate the identified frequency candidates and achieve high-precision parameter estimation. Finally, extensive numerical simulations and experiments demonstrate that LOGBI effectively mitigates basis mismatch while significantly reducing the computational cost of classic Bayesian methods.