Accelerating the Bayesian inference of inverse problems by using data-driven compressive sensing method based on proper orthogonal decomposition

Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.

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Low-Dimensional Representations of Inflow Turbulence and Wind Turbine Response Using Proper Orthogonal Decomposition

Journal of Solar Energy Engineering ◽

10.1115/1.2037108 ◽

2005 ◽

Vol 127 (4) ◽

pp. 553-562 ◽

Cited By ~ 18

Author(s):

Korn Saranyasoontorn ◽

Lance Manuel

Keyword(s):

Wind Turbine ◽

Proper Orthogonal Decomposition ◽

Low Frequency ◽

Orthogonal Decomposition ◽

Response Variance ◽

Spectral Models ◽

Inflow Turbulence ◽

Using Data ◽

Low Dimensional ◽

Proper Orthogonal

A demonstration of the use of Proper Orthogonal Decomposition (POD) is presented for the identification of energetic modes that characterize the spatial random field describing the inflow turbulence experienced by a wind turbine. POD techniques are efficient because a limited number of such modes can often describe the preferred turbulence spatial patterns and they can be empirically developed using data from spatial arrays of sensed input/excitation. In this study, for demonstration purposes, rather than use field data, POD modes are derived by employing the covariance matrix estimated from simulations of the spatial inflow turbulence field based on standard spectral models. The efficiency of the method in deriving reduced-order representations of the along-wind turbulence field is investigated by studying the rate of convergence (to total energy in the turbulence field) that results from the use of different numbers of POD modes, and by comparing the frequency content of reconstructed fields derived from the modes. The National Wind Technology Center’s Advanced Research Turbine (ART) is employed in the examples presented, where both inflow turbulence and turbine response are studied with low-order representations based on a limited number of inflow POD modes. Results suggest that a small number of energetic modes can recover the low-frequency energy in the inflow turbulence field as well as in the turbine response measures studied. At higher frequencies, a larger number of modes are required to accurately describe the inflow turbulence. Blade turbine response variance and extremes, however, can be approximated by a comparably smaller number of modes due to diminished influence of higher frequencies.

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The Rapid Data-Driven Prediction Method of Coupled Fluid–Thermal–Structure for Hypersonic Vehicles

Aerospace ◽

10.3390/aerospace8090265 ◽

2021 ◽

Vol 8 (9) ◽

pp. 265

Author(s):

Jing Liu ◽

Meng Wang ◽

Shu Li

Keyword(s):

Radial Basis Function ◽

Proper Orthogonal Decomposition ◽

Basis Function ◽

Thermal Structure ◽

Prediction Method ◽

Orthogonal Decomposition ◽

Data Driven ◽

Good Efficiency ◽

Radial Basis ◽

Proper Orthogonal

This work demonstrates the use of Latin Hypercube Sampling and Proper Orthogonal Decomposition in combination with a Radial Basis Function model to perform on vehicle prediction coupled fluid–thermal–structure. We regarded the Mach number, flight altitude and angle of attack as input parameters and established a rapid prediction model. The basic process of numerical simulation of the hypersonic vehicle coupled fluid–thermal–structure was studied to obtain the database of pressure coefficient, heat flux, structural temperature and structural stress as the sample data to train this prediction method. The prediction error was analyzed. The prediction results showed that the data-driven method proposed in this paper based on proper orthogonal decomposition and radial basis function could be used for predicting vehicle coupled fluid–thermal–structure with good efficiency.

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