Tomographic damage imaging based on inverse acoustic wave propagation using k-space method with adjoint method

A novel damage imaging of engineering structures and materials methodology using the k-space method with adjoint method is proposed in this paper. The proposed methodology consists of two parts: the wave propagation solution algorithms for elastic solids in k-space and adjoint method-based optimization algorithms for damage imaging. One major advantage of the proposed method is the superior computational efficiency compared to the classical finite element method-based wave propagation and gradient-based optimization algorithms. The k-space formulation for wave propagation in 2D and 3D solids are discussed first. Adjoint method and a modified conjugate gradient method is presented for the inverse problem of damage imaging. Following this, parametric studies for measurement duration, number of sensors, noise effect, and computational efficiency are discussed in detail. Next, demonstration examples for concrete structures with and without reinforcement are presented. Several conclusions and future work are given based on the proposed method.