Stochastic Simulation of Mudcrack Damage Formation in an Environmental Barrier Coating

The FEAMAC/CARES program, which integrates finite element analysis (FEA) with the MAC/GMC (Micromechanics Analysis Code with Generalized Method of Cells) and the CARES/Life (Ceramics Analysis and Reliability Evaluation of Structures / Life Prediction) programs, was used to simulate the formation of mudcracks during the cooling of a multilayered environmental barrier coating (EBC) deposited on a silicon carbide substrate. FEAMAC/CARES combines the MAC/GMC multiscale micromechanics analysis capability (primarily developed for composite materials) with the CARES/Life probabilistic multiaxial failure criteria (developed for brittle ceramic materials) and Abaqus (Dassault Systmes) FEA. In this report, elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio elements enabled the formation of crack boundaries, leading to development of mudcrack-patterned damage. Finite element models of a disk-shaped three-dimensional specimen and a twodimensional model of a through-the-thickness cross section subjected to progressive cooling from 1,300 C to an ambient temperature of 23 C were made. Mudcrack damage in the coating resulted from the buildup of residual tensile stresses between the individual material constituents because of thermal expansion mismatches between coating layers and the substrate. A two-parameter Weibull distribution characterized the coating layer stochastic strength response and allowed the effect of the Weibull modulus on the formation of damage and crack segmentation lengths to be studied. The spontaneous initiation of cracking and crack coalescence resulted in progressively smaller mudcrack cells as cooling progressed, consistent with a fractal-behaved fracture pattern. Other failure modes such as delamination, and possibly spallation, could also be reproduced. The physical basis assumed and the heuristic approach employed, which involves a simple stochastic cellular automaton methodology to approximate the crack growth process, are described. The results ultimately show that a selforganizing mudcrack formation can derive from a Weibull distribution that is used to describe the stochastic strength response of the bulk brittle ceramic material layers of an EBC

Multiscale spectral analysis of bathymetry on the flank of the Mid-Atlantic Ridge : modification of the seafloor by mass wasting and sedimentation

Author Posting. © American Geophysical Union, 1997. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 102, no. B7 (1997): 15447–15462, doi:10.1029/97JB00723.The results of a multiscale spectral analysis of bathymetric data on the flank of the Mid-Atlantic Ridge are described. Data were collected during two cruises using Hydrosweep multibeam (tens of kilometers to ∼0.2 km scale range) and Mesotech scanning pencil-beam sonar attached to remotely operated vehicle Jason (∼1 km to ∼0.5 m scale range). These data are augmented by visual data which enabled us to identify bathymetric profiles which are over unsedimented or thinly sedimented crust. Our analysis, therefore, is focused primarily on statistical characterization of basement morphology. Work is concentrated at two sites: site B on ∼24 Ma crust in an outside-corner setting, and site D on ∼3 Ma crust in an inside-corner setting. At site B we find that an anisotropic, band-limited fractal model (i.e., the “von Kármán” model proposed for abyssal hill morphology by Goff and Jordan [1988]) is not sufficient to describe the full range of scales observed in this study. Our observations differ from this model in two ways: (1) strike and cross-strike (dip) spectral properties converge for wavelengths smaller than ∼300 m, and (2) in both strike and dip directions the fractal dimension changes at ∼10 m wavelength, from ∼1.27 at larger scales to ∼1.0 at smaller scales. The convergence of strike and dip spectral properties appears to be associated with destruction of ridge-parallel fault scarps by mass wasting, which develops canyon-like incisions that cross scarps at high angles. The change in fractal dimension at ∼10 m scale appears to be related to a minimum spacing of significant slope breaks associated with scarps which are created by faulting and mass wasting. At site D, although there is no significant abyssal hill anisotropy, the spectral properties at all scales are consistent with the von Kármán model. The fractal dimension at this site (∼1.15) is less than at site B. This difference may be reflect different morphology related to crustal formation at inside-corner versus outside-corner position or, more likely, differences in the degree of mass wasting. The smoothing of seafloor morphology by sediments is evident in Hydrosweep periodograms where, relative to basement roughness, spectral power decreases progressively with decreasing wavelength.This work was supported under ONR grants N00014-94-1-0197 and N00014-96-1-0462 (J.A.G.) and N00014-90-J-1621 and N00014-94-1-0466 (B.E.T.)

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Wavelets and partial differential equations for image denoising

In this paper a wavelet based model for image de-noising is presented. Wavelet coefficients are modelled as waves that grow while dilating along scales. The model establishes a precise link between corresponding modulus maxima in the wavelet domain and then allows to predict wavelet coefficients at each scale from the first one. This property combined with the theoretical results about the characterization of singularities in the wavelet domain enables to discard noise. Significant structures of the image are well recovered while some annoying artifacts along image edges are reduced. Some experimental results show that the proposed approach outperforms the most recent and effective wavelet based denoising schemes

2D Phase Unwrapping via Graph Cuts

Phase imaging technologies such as interferometric synthetic aperture radar (InSAR), magnetic resonance imaging (MRI), or optical interferometry, are nowadays widespread and with an increasing usage. The so-called phase unwrapping, which consists in the in- ference of the absolute phase from the modulo-2π phase, is a critical step in many of their processing chains, yet still one of its most challenging problems. We introduce an en- ergy minimization based approach to 2D phase unwrapping. In this approach we address the problem by adopting a Bayesian point of view and a Markov random field (MRF) to model the phase. The maximum a posteriori estimation of the absolute phase gives rise to an integer optimization problem, for which we introduce a family of efficient algo- rithms based on existing graph cuts techniques. We term our approach and algorithms PUMA, for Phase Unwrapping MAx flow. As long as the prior potential of the MRF is convex, PUMA guarantees an exact global solution. In particular it solves exactly all the minimum L p norm (p ≥ 1) phase unwrapping problems, unifying in that sense, a set of existing independent algorithms. For non convex potentials we introduce a version of PUMA that, while yielding only approximate solutions, gives very useful phase unwrap- ping results. The main characteristic of the introduced solutions is the ability to blindly preserve discontinuities. Extending the previous versions of PUMA, we tackle denoising by exploiting a multi-precision idea, which allows us to use the same rationale both for phase unwrapping and denoising. Finally, the last presented version of PUMA uses a frequency diversity concept to unwrap phase images having large phase rates. A representative set of experiences illustrates the performance of PUMA

Multi-resolution Active Models for Image Segmentation

Image segmentation refers to the process of subdividing an image into a set of non-overlapping regions. Image segmentation is a critical and essential step to almost all higher level image processing and pattern recognition approaches, where a good segmentation relieves higher level applications from considering irrelevant and noise data in the image. Image segmentation is also considered as the most challenging image processing step due to several reasons including spatial discontinuity of the region of interest and the absence of a universally accepted criteria for image segmentation. Among the huge number of segmentation approaches, active contour models or simply snakes receive a great attention in the literature. Where the contour/boundary of the region of interest is defined as the set of pixels at which the active contour reaches its equilibrium state. In general, two forces control the movement of the snake inside the image, internal force that prevents the snake from stretching and bending and external force that pulls the snake towards the desired object boundaries. One main limitation of active contour models is their sensitivity to image noise. Specifically, noise sensitivity leads the active contour to fail to properly converge, getting caught on spurious image features, preventing the iterative solver from taking large steps towards the final contour. Additionally, active contour initialization forms another type of limitation. Where, especially in noisy images, the active contour needs to be initialized relatively close to the object of interest, otherwise the active contour will be pulled by other non-real/spurious image features. This dissertation, aiming to improve the active model-based segmentation, introduces two models for building up the external force of the active contour. The first model builds up a scale-based-weighted gradient map from all resolutions of the undecimated wavelet transform, with preference given to coarse gradients over fine gradients. The undecimated wavelet transform, due to its near shift-invariance and the absence of down-sampling properties, produces well-localized gradient maps at all resolutions of the transform. Hence, the proposed final weighted gradient map is able to better drive the snake towards its final equilibrium state. Unlike other multiscale active contour algorithms that define a snake at each level of the hierarchy, our model defines a single snake with the external force field is simultaneously built based on gradient maps from all scales. The second model proposes the incorporation of the directional information, revealed by the dual tree complex wavelet transform (DT CWT), into the external force field of the active contour. At each resolution of the transform, a steerable set of convolution kernels is created and used for external force generation. In the proposed model, the size and the orientation of the kernels depend on the scale of the DT CWT and the local orientation statistics of each pixel. Experimental results using nature, synthetic and Optical Coherent Tomography (OCT) images reflect the superiority of the proposed models over the classical and the state-of-the-art models