Determination of impact fragments from particle analysis via smoothed particle hydrodynamics and k-means clustering

Abstract

In this paper, particles produced by a high velocity impact were first analyzed numerically by using smooth particle hydrodynamics (SPH). Then, a method to cluster the particles into fragments dispersed in a space due to the impact was developed. High velocity impact simulations using SPH on different types of projectiles and target plates were conducted, and the predicted results including the residual velocity, hole diameter, and spall ring diameter in the target plate were verified by comparing them with the measured values reported in the reference. Subsequently, a method to determine the fragments from the particles resulting from the impact was developed. Instead of the individual particle location at a certain time, the trajectory of the particles in an arbitrary time interval was analyzed. This approach enabled clear identification of the similarities and differences among the particles belonging to each fragment. In order to calculate the number of fragments followed by grouping the particles into each fragment based on the trajectory similarity, a k-means algorithm together with a silhouette index was employed using a machine learning based clustering method. Therefore, the fragments can be determined from the grouped particles as well as the physical quantities such as the mass, velocity, and kinetic energy of each fragment, which can then be calculated. The fragment mass distribution obtained from the proposed method, in association with the characteristics of the debris particles, was validated through a comparison with the reported results in the reference within a 7% deviation. As a result, the quantitative characteristics of the fragments such as the count distributions, kinetic energy distributions, and lethal dispersion angles were predicted based on the proposed method. In conclusion, the threat of a high velocity impact on a certain structure can therefore be estimated effectively by combining high velocity impact analysis with a machine learning based clustering algorithm.