Laboratory study of wave-induced ice-ice collisions using robust principal component analysis and sensor fusion

Abstract

Wave-induced ice-floe collisions contribute to the attenuation of surface gravity waves, but the nature of the interfloe collisions is not well understood. Two parameters, the restitution coefficient and the collision duration, are associated and considered important to describe interfloe interactions. The restitution coefficient and collision duration are also important for numerical modeling of wave-ice-structure interactions. Despite the importance of these two parameters, measurements to quantify their values are still limited. In the present study, experimental data on saline ice collected during the HYDRALAB+ project: Loads on Structure and Waves in Ice (LS-WICE) are analyzed to investigate the dynamics of ice floes during collisions and to enhance the understanding of wave-induced ice-ice collisions. We propose a new methodology based on robust principal component analysis (RPCA) to accurately identify collision duration. This methodology is robust, highly accurate, and not sensitive to noise in the signal, and the results are not influenced by the motion of ice floes due to surface convergence related to wave motion. Sensor fusion and state estimations based on Kalman filtering are used as means to quality-assure the velocity estimates that are used in quantifying the restitution coefficients. Analysis of the LS-WISE dataset shows that the collision duration is short compared to the wave period (5 % ∼ 16%) and rises with wave steepness, which is consistent with earlier studies. The velocity estimated with Kalman filtering agrees well with other numerical differentiators (normalized root-mean-squared error less than 1.9%). The estimated restitution coefficients range from 0.1 to 0.22 and increase with wave steepness. This result is consistent with previous experimental studies in which the restitution coefficients vary between 0 and 0.3, implying that wave-induced ice-ice collisions are inelastic and that a substantial portion of the kinematic energy of ice floes is lost, hence contributing to wave damping. The underlying governing mechanisms that drive the ice floes to collide with each other are also investigated, and the results illustrate the significance of the bending of the ice floes on our findings. Additionally, contribution of wave-induced ice-ice collision to wave attenuation is estimated by using LS-WICE datasets and found to account for approximately 25% of the total wave energy loss.