Experimental studies of wave-ice interactions – insights into data analysis methods and their applications to studying the wave-induced responses of ice cover
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Studies of wave-ice interactions include field and laboratory experiments, theoretical model developments, the implementation of these theoretical models in simulation tools, and the validation and calibration of these theoretical models. Laboratory experiments can provide measured data with reduced uncertainties in comparison with field experimental campaigns. In both theoretical and experimental studies, the major focus has been on the effect of ice cover on the evolution of waves, such as wave attenuation and changes in wavelength. Research on the responses of ice cover to waves is still limited. This study focuses on exploring and developing various data analysis methods that are suitable for laboratory experimental studies of wave-ice interactions and on investigating the ice cover responses to waves, such as how ice floes collide with each other and how an ice floe bends under wave actions. Several data analysis methods are introduced from other scientific communities and devised by synthesizing various data analysis techniques (including machine learning) together. For the first time, these methods, including robust principal component analysis (RPCA), the Kalman filter (Kalman), optimal hard thresholding (i.e., optimal truncated singular value decomposition), intersite phase clustering (ISPC), Prony's method, dynamic mode decomposition (DMD) and its variants, smooth orthogonal decomposition (SOD), bandpass filtering based on fast Fourier transform in the frequency domain (hereafter bp), Tikhonov regularization-based signal denoising (Tikhonov), makima interpolation, robust local regression (RLOESS), the polynomial fitting in conjunction with the Bayesian information criterion (B-poly), shape language modeling (SLM) and the smoothing spline (SMSP), are applied to wave-ice interaction laboratory experimental studies. Four methods are newly proposed: (1) the time-delay method in conjunction with principal component analysis (PCA) for estimating time derivatives (hereafter referred to as TDD); (2) RPCA together with optimal hard thresholding and signal element-wise multiplication for identifying ice-ice collisions; (3) the Kalman filter in combination with RLOESS and crossspectrum analysis for correlating the measurements of ice floes undergoing similar motions; and (4) the synthesis of ISPC, Prony's method, the genetic algorithm and cross-spectrum analysis with cross-validation concepts in machine learning for reducing the uncertainty in estimating the wavelength from measurements collected at closely spaced and equidistant sensors. These methods are employed to analyze the measurements collected from the HYDRALAB+ project entitled Loads on Structure and Waves in Ice (LS-WICE). The analysis suggests that ice-ice collisions are quasi-inelastic. Both the restitution coefficient, which represents the kinetic energy loss, and the collision duration, describing interfloe collision processes, appear to increase with the wave steepness. The examination of the measured data also indicates that waves cause neighboring ice floes to collide with each other. Another important finding is that ice-ice collisions account for a nonnegligible part of wave energy attenuation. Results show that TDD and TDD in conjunction with mirroring technique produce time derivative estimates that are comparable with those yielded by the other well-established numerical di erentiation methods. Analyses performed by using PCA (also known as proper orthogonal decomposition (POD)) and SOD reveal that weak nonlinearity exists in the flexural responses of ice floes induced by linear incoming waves. This finding is confirmed by extensive analysis conducted by applying Prony'smethod and Morlet wavelet time-frequency analysis. The weak nonlinearity originates from the higher-order harmonic embedded in the incident waves and most likely from frequent inter floe collisions as well. In this study, case studies demonstrate that the wavelengths estimated by the cross-validation approach match the estimated values from measurements taken by another type of sensors that are spaced with varying and large distances.