Systematic investigation of data analysis methods in wave-ice interaction problem
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Wave climate and extent of ice cover in the Arctic ocean have changed significantly in recent decades. Concomitantly, interest in studying wave-ice interaction has rapidly increased in the last two decades. Laboratory-scale experiments present a fundamental approach to understand the detailed processes involved in wave-ice interaction and to validate theoretical models. One key parameter that describes how waves evolve under ice cover is the spatial attenuation coefficient. To estimate this parameter from laboratory measurements, wave amplitudes at different positions along the wave propagation direction should be estimated. In addition to wave amplitudes, it is also critical to confirm that the period of incoming waves agree with a preset wave period since this parameter is involved in evaluating wave dispersion relation. In this study, we systematically explore various measurement (signal) processing techniques to extract wave parameters such as wave amplitudes and periods. The contamination of wave measurements with noise and wave reflection in addition to the sometimes use of low-sampling frequency and the possible lack of stationarity in the measurement require dedicated care when selecting the suitable analysis method. In this study, we investigate several methods including: Bandpass filtering in frequency domain (bp), Tikhonov regularization (Tikhonov), two MATLAB built-in functions, fir1 and smooth (Smooth), Fast Fourier Transform (FFT), Peak Analysis (Peak), Dynamic Mode Decomposition (DMD), Genetic Algorithm (Genetic) and Prony’s method (Prony). By using experimental measurements (from Qualisys systems, ultrasound and pressure sensors) and synthetic signals, we show that bp gives equivalent filtering results as fir1 (difference expressed by normalized root mean squared error less than 3.5%). Moreover, Tikhonov and Smooth produces similar smoothing of signal. Additionally, we find that Prony, DMD and FFT in combination with interpolation quantify incoming wave period accurately (normalized error less than 2.5%). As for wave amplitudes, FFT combined with interpolation, Genetic, a variant of DMD, Hilbert transform and its combination with interpolation and Peak combined with interpolation results in similar estimates with respect to FFT (normalized error less than 3%).