On pressure modes in ice-induced vibrations using multivariate analysis

Pressures at the ice-structure interface during model-scale ice-structure interaction are often measured with tactile sensors. Resulting datasets usually include large volume of data along with some measurement error and noise; therefore, it is inherently hard to extract the hidden fluctuating pressures in the system. Identifying the deterministic pressure fluctuation in ice-induced vibrations is essential to understand this complex phenomenon better. In this paper, we discuss the use of two different multivariate analysis techniques to decompose an ensemble of measured pressure data into spatiotemporal modes that gives insights into pressure distributions in ice-induced vibrations. In particular, we use proper-orthogonal decomposition (POD) and inexact robust principal component analysis (IRPCA) in conjunction with measurements of intermittent crushing at different ice speeds. Both decompositions show that most of the energy is captured in a ten-dimensional space; however, the corresponding eigenvalues are different between the decompositions. While POD-based modes have low energy contributions at the first subspace dimensions, IRPCA-based modes have larger energy contributions. This result is consistent with the reconstruction of the time history of the pressure sum using first three empirical modes, where POD and IRPCA-based modes yield similar accuracy at the same subspace dimension. Although both methods successfully illustrate the dominant pressure modes that are active in the system, IRPCA method is found to be more effective than POD in terms of differentiating the contribution of each mode because of its ability to better separate low-rank and sparse components (measurement error and/or noise) in the dataset.