Structural damage identification with limited modal measurements and ultra‐sparse Bayesian regression

Summary This paper proposes a novel approach for structural damage identification with a limited number of modal measurements and ultra‐sparse Bayesian regression. An iterative Cross Modal Strain Energy (CMSE) method is proposed for establishing the linear regression model. It can be applied to enlarge the number of available modes, thus alleviating the problem of insufficient mode orders. In addition, the proposed approach can also be used to solve the identification of incomplete measurements by combining with a dynamic condensation process. The condensed system matrices of the damaged structure are updated iteratively by the identified damage severity vector. A major contribution of this study is that the most advanced Bayesian linear regression estimator, called Horseshoe (HS), is first introduced to provide an ultra‐sparse regularization. Owning to the particular choice of a half‐Cauchy prior to the global and local scale hyper‐parameters, using HS can provide a sparser solution than the Bayesian lasso (BL). Therefore, this approach is extremely suitable for structural damage identification with sparse solutions in nature. Other advantages of using HS consist of the easy implementation of Gibbs sampling, effective convergence rate and hyper‐parameter tuning, good stability, and the ability to conduct the indeterminate inverse identification arising from insufficient mode order. The effectiveness and performance of the proposed approach are validated by numerical and experimental studies, considering the effects of measurement noise and a limited number of modal measurements with an insufficient number of mode orders and incomplete measurements.