A fraction function regularization model for the structural damage identification

The conventional model updating based on sensitivity analysis generally employs l 1 -norm regularizer to characterize the sparsity of the structural damage. However, the l 1 -norm regularizer inevitably excessively penalizes the larger components in the damage parameter, which certainly causes the extra estimation bias of the damage parameter and reduces the damage identification accuracy. A fraction function regularizer not only well characterizes the sparsity, but also overcomes the excessive penalty drawback of the l 1 -norm regularizer. Based on this, a fraction function regularization model is proposed to improve the damage identification accuracy. Numerical and experimental results illustrate that the damage identification accuracy of the proposed model is averagely improved 4.96% and 3.68% than that of the l 1 regularization one, the iteratively reweighted l 1 regularization one and the elastic net one, respectively.