Sensitivity-based sparse Bayesian method for damage detection with unknown load input

Sparse Bayesian learning achieves great success in damage identification by employing a sparsity-inducing prior distribution on the sparse coefficients. However, if the input force is unknown, a sparse prior cannot be applied to both the damage and force parameters. In order to construct a sparse Bayesian learning model for damage and unknown load input identification, a sensitivity-based sparse Bayesian method for the damage detection with unknown input is proposed. An optimization equation is constructed on the basis of the dynamic response sensitivity to convert the complex non-linear relationships into linear equations. The prior information for the force and damage parameters is established using uniform and Gaussian priors, respectively, depending on the specific characteristics of each parameter. The Bayesian learning framework based on the sensitivity-based model is derived to compensate the linear truncation errors and measurement noise. The validation of the proposed approach is conducted using both a numerical frame structure and an experimental structure. Results indicate that this method can simultaneously identify both damage and forces, even when faced with significant measurement noise and limited sensor data.