Delamination shape reconstruction using Bayesian optimization and the best sparse spatial sampling

Laminated carbon fiber-reinforced plastics (CFRP), a widely-used composite material, plays a significant role in modern industries. Lamb waves have shown promise for detecting invisible damages like cracks and delamination due to its high damage sensitivity and low attenuation. In this study, a sparse optimal spatial sampling technique integrating Lamb waves and Bayesian optimization has been developed to identify and quantify the delamination in composite structures. The full wavefield analysis suffered from either large data size or long data-acquisition time. The Bayesian optimization offers a Bayesian framework through which the posterior distribution can show the following spatial location with the greatest likelihood to be sampled, and the delamination can be revealed with minimal scanning points. Since the RMS(root mean square) values of the sampling points located in the damaged area are higher than those in the pristine area, the RMS value of the collected signal is supposed to be the objective function for Bayesian optimization. First, a prior distribution is established using a gaussian process model with a few sampling points chosen randomly. A subsequent model update is performed with more sampling points being evaluated based on Bayesian inference. Then, a penalty weight is set to ensure the points in the damage zone have similar values. Thereby, more damage points can be evaluated rather than constrained in a small area. Finally, the delamination shape is sketched based on all known damage points using a convex-hull based contour reconstruction algorithm. The proposed technique has been validated based on numerical findings, and the anticipated result exhibits good congruence with the actual damage.