The ability of an adaptive imaging procedure to enhance the inspection of unknown anisotropic materials is investigated. The method combines the Total Focusing Method (TFM) imaging with an optimization algorithm to improve quality and reliability of images of flaws. Two optimization algorithms are considered to maximize the detection amplitude: a customized gradient ascent (local optimization) and a particle swarm (global optimization). We use a Kernel-Ridge surrogate model to speed up the computation times of TFM images, in order to achieve Sobol sensitivity analysis and a statistical evaluation of the procedure robustness. The optimization procedure is first evaluated with simulated echoes, and then with experimental ones acquired from several welding samples, highlighting various homogeneous or inhomogeneous anisotropies and different geometries. We experimentally show that the procedure is able to produce high quality images in complex welds by varying up to a dozen of unknown parameters.