Randomized Kaczmarz and Landweber algorithms for impact force identification on a composite panel

Randomized Kaczmarz and Landweber methods, utilized for impact force identification, are iterative algorithms with exponential convergence rates, independent of the number of equations in the system. The Randomized Kaczmarz is used to reconstruct the time history of the impact force while the Landweber method, typically used for solving sparse and large-sized problems, is employed to identify the impact location. In this study, the two complementary techniques are adopted to identify the impact force applied on a rectangular carbon-fibre epoxy honeycomb composite panel. Using Randomized Kaczmarz to reconstruct the impact forces yields less sensitivity to the signal length, resulting in a correlation coefficient of approximately 0.98 for signal lengths ranging from 10 to 20 ms. There is an optimal range for the number of iterations to solve the inverse problem, beyond which the change in errors will be small enough such that the reconstructed impact force is still valid. The lowest and highest error percentages of 3% and 18% are reported for various reconstructed impact forces. The Randomized Kaczmarz and Landweber methods are found to be more robust compared to traditional methods such as Tikhonov and TSVD. They indicate favorable features that include but are not limited to: high convergence rate, high accuracy and reliability, robustness against varying signal length, and, having an optimal range for the number of iterations.