Bayesian Full-Field Response Reconstruction via Expectation-Maximization Algorithm from Sparse Sensor Data

This study proposes a Bayesian full-field dynamic response reconstruction framework, comprising two key components. First, a Bayesian framework is proposed to determine the means and covariance of the predicted structural responses. The modal responses and measurement noise are modeled as stationary Gaussian processes and Gaussian white noise, respectively. Utilizing the modal superposition principle, variance vectors (i.e. hyperparameters) are formulated, thereby enabling uncertainty quantification within this probabilistic framework. Second, hyperparameters in the Bayesian framework require estimation through the expectation-maximization (EM) algorithm. This approach iteratively treats modal responses as latent variables, utilizing sensor data and mode shapes as inputs, and converges to optimal hyperparameter estimates through successive iterations. To address reconstruction challenges under underdetermined case, a novel band-limited source decomposition technique is introduced. Numerical and experimental validations demonstrate the proposed framework’s capability to achieve high-accuracy full-field reconstruction.