Wind data extrapolation and stochastic field statistics estimation via compressive sampling and low rank matrix recovery methods

• Published in: Mechanical systems and signal processing Vol. 162; p. 107975
• Main Authors: Pasparakis, George D., dos Santos, Ketson R.M., Kougioumtzoglou, Ioannis A., Beer, Michael
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01.01.2022; Elsevier BV
• Subjects: Compressive sampling; Computing costs; Design optimization; Domains; Environment models; Extrapolation; Low-rank matrix; Methodology; Missing data; Power spectral density; Reconstruction; Sampling; Sparse representations; Stochastic field; Time measurement; Wavelengths; Wind data; Wind turbines; Low-rank matrix; Sparse representations; Wind data; Stochastic field; Compressive sampling
• DOI: 10.1016/j.ymssp.2021.107975
• ISSN: 0888-3270

•A compressive sampling approach for wind data reconstruction and extrapolation.•L1-norm minimization is used in conjunction with an adaptive basis scheme.•Higher-dimensional problems are addressed by nuclear norm minimization.•The approach can be integrated with structural system analysis and design schemes. A methodology based on compressive sampling is developed for incomplete wind time-histories reconstruction and extrapolation in a single spatial dimension, as well as for related stochastic field statistics estimation. This relies on l1-norm minimization in conjunction with an adaptive basis re-weighting scheme. Indicatively, the proposed methodology can be employed for monitoring of wind turbine systems, where the objective relates to either reconstructing incomplete time-histories measured at specific points along the height of a turbine tower, or to extrapolating to other locations in the vertical dimension where sensors and measurement records are not available. Further, the methodology can be used potentially for environmental hazard modeling within the context of performance-based design optimization of structural systems. Unfortunately, a straightforward implementation of the aforementioned approach to account for two spatial dimensions is hindered by significant, even prohibitive in some cases, computational cost. In this regard, to address computational challenges associated with higher-dimensional domains, a methodology based on low rank matrices and nuclear norm minimization is developed next for wind field extrapolation in two spatial dimensions. The efficacy of the proposed methodologies is demonstrated by considering various numerical examples. These refer to reconstruction of wind time-histories with missing data compatible with a joint wavenumber-frequency power spectral density, as well as to extrapolation to various locations in the spatial domain.