Development and application of bivariate 2D-EMD for the analysis of instantaneous flow structures and cycle-to-cycle variations of in-cylinder flow

International audienceThe bivariate two dimensional empirical mode decomposition (Bivariate 2D-EMD) is extended to estimate the turbulent fluctuations and to identify cycle-to-cycle variations (CCV) of in-cylinder flow. The Bivariate 2D-EMD is an adaptive approach that is not restricted by statistical convergence criterion, hence it can be used for analyzing the nonlinear and non-stationary phenomena. The methodology is applied to a high-speed PIV dataset that measures the velocity field within the tumble symmetry plane of an optically accessible engine. The instantaneous velocity field is decomposed into a finite number of 2D spatial modes. Based on energy considerations, the in-cylinder flow large-scale organized motion is separated from turbulent fluctuations. This study is focused on the second half of the compression stroke. For most of the cycles, the maximum of turbulent fluctuations is located between 50 and 30 crank angle degrees before top dead center (TDC). In regards to the phase-averaged velocity field, the contribution of CCV to the fluctuating kinetic energy is approximately 55% near TDC

Two-Dimensional Compact Variational Mode Decomposition

Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis. This decomposition enables space–frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting, or curvature estimation. Our model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image recomposition. L1 and TV terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function, we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman–Bence–Osher-like threshold dynamics to handle efficiently the motion by mean curvature of the support function boundaries under the sparsity promoting terms. The versatility and effectiveness of our proposed model is demonstrated on a broad variety of example images from different modalities. These demonstrations include the decomposition of images into overlapping modes with smooth or sharp boundaries, segmentation of images of crystal grains, and inpainting of damaged image regions through artifact detection