Detection of spatially sparse damage using impulse response sensitivity and LASSO regularization

This paper presents an impulse response sensitivity approach enhanced with a least absolute shrinkage and selection operator regularization in order to detect spatially sparse (localized) damage. The analytical expression for impulse response sensitivity was derived using Vetter calculus. The proposed algorithm exploits the fact that when damage is sparse, an l(1)-norm regularization is more suitable than the common least squares (l(2)-norm) minimization. The proposed methodology is successfully applied in the context of a simulated 21 degree of freedom non-uniform shear beam with noise-contaminated measurements, limited modal parameters and limited sensor locations. Single input-single output and single input-two output cases are investigated.