Frozen-State Hierarchical Annealing

There is significant interest in the synthesis of discrete-state random fields, particularly those possessing structure over a wide range of scales. However, given a model on some finest, pixellated scale, it is computationally very difficult to synthesize both large and small-scale structures, motivating research into hierarchical methods. This thesis proposes a frozen-state approach to hierarchical modelling, in which simulated annealing is performed on each scale, constrained by the state estimates at the parent scale. The approach leads significant advantages in both modelling flexibility and computational complexity. In particular, a complex structure can be realized with very simple, local, scale-dependent models, and by constraining the domain to be annealed at finer scales to only the uncertain portions of coarser scales, the approach leads to huge improvements in computational complexity. Results are shown for synthesis problems in porous media

Towards effective information content assessment: analytical derivation of information loss in the reconstruction of random fields with model uncertainty

Structures are abundant in both natural and human-made environments and usually studied in the form of images or scattering patterns. To characterize structures a huge variety of descriptors is available spanning from porosity to radial and correlation functions. In addition to morphological structural analysis, such descriptors are necessary for stochastic reconstructions, stationarity and representativity analysis. The most important characteristic of any such descriptor is its information content - or its ability to describe the structure at hand. For example, from crystallography it is well known that experimentally measurable $S_2$ correlation function lacks necessary information content to describe majority of structures. The information content of this function can be assessed using Monte-Carlo methods only for very small 2D images due to computational expenses. Some indirect quantitative approaches for this and other correlation function were also proposed. Yet, to date no methodology to obtain information content for arbitrary 2D or 3D image is available. In this work, we make a step toward developing a general framework to perform such computations analytically. We show, that one can assess the entropy of a perturbed random field and that stochastic perturbation of fields correlation function decreases its information content. In addition to analytical expression, we demonstrate that different regions of correlation function are in different extent informative and sensitive for perturbation. Proposed model bridges the gap between descriptor-based heterogeneous media reconstruction and information theory and opens way for computationally effective way to compute information content of any descriptor as applied to arbitrary structure.Comment: Keywords: correlation functions, structure characterization, structural descriptors, image analysis, information conten

Gas diffusion layer characterization and microstructural modeling in polymer electrolyte fuel cells

Polymer electrolyte fuel cells (PEFCs), as promising clean energy power sources, are potential substitutes not only for stationary power generation but also for mobile applications specifically in transportation due to their high power density and performance as well as lack of pollutants. PEFC vehicles are at the dawn of commercialization, but still, cost, performance, and durability of current PEFCs need to be further improved to facilitate vast market integration especially under high current density conditions. Pursuant to this goal, comprehensive multidisciplinary understanding of multiphase transport of mass, heat, and electricity in the PEFC constituents including the gas diffusion layer (GDL), as the centerpiece of this thesis, will help to make progress towards material optimization and subsequently fuel cell performance improvements. The GDL transport capability is determined by its effective transport properties which are strongly dependent on its morphological, microstructural, and physical characteristics. Therefore, accurate knowledge regarding the correlation between the GDL microstructure and its transport properties is essential for improving the performance and durability of PEFCs as well as for material optimization, fuel cell design, and prototyping in the area of fuel cell development and manufacturing. In this context, this thesis aims to develop a fast and cost-effective design tool for GDL microstructural modeling and transport properties simulation. Given the limitations of experimental, analytical, and tomographic techniques, stochastic microstructural model development to retrieve the heterogeneous GDL microstructure is a more reliable and flexible tool for GDL material design and prototyping assignments to reduce cost and time of the design cycle. Inspired by the randomness of the GDL porous media structure and its fabrication process, the GDL microstructure is virtually reconstructed as a collection of stochastic processes to provide a robust representation of the structure. The technique of stochastic microstructural reconstruction relies on statistical correlation functions which describe the probabilities of the porous media constituents’ distribution and aim to encompass all the details of the porous media. The obtained 3D digitized realizations of the stochastic model are then used as a domain for numerical computation of transport properties. In this thesis, a unique stochastic GDL microstructural modeling framework inspired by manufacturing information and characterization data is developed in which all GDL substrate and MPL components are resolved, and thoroughly validated with literature and measured data for a variety of MPL-coated GDLs. The effects of PTFE loading and liquid water saturation on the GDL substrate anisotropic transport properties for both gas and liquid phases are found to be highly coupled and are therefore simulated and analyzed jointly. Furthermore, a parametric study is conducted to investigate the effect of MPL pore morphology composition on the MPL and MPL-coated GDL transport properties. The validated stochastic design tool can be used as a fast and accurate framework for reconstructing GDL porous materials and understanding the correlation between the GDL morphology and transport properties. This paves the way for development of improved GDL materials with desired transport properties in modern PEFCs

Statistical Fusion of Scientific Images

A practical and important class of scientific images are the 2D/3D images obtained from porous materials such as concretes, bone, active carbon, and glass. These materials constitute an important class of heterogeneous media possessing complicated microstructure that is difficult to describe qualitatively. However, they are not totally random and there is a mixture of organization and randomness that makes them difficult to characterize and study. In order to study different properties of porous materials, 2D/3D high resolution samples are required. But obtaining high resolution samples usually requires cutting, polishing and exposure to air, all of which affect the properties of the sample. Moreover, 3D samples obtained by Magnetic Resonance Imaging (MRI) are very low resolution and noisy. Therefore, artificial samples of porous media are required to be generated through a porous media reconstruction process. The recent contributions in the reconstruction task are either only based on a prior model, learned from statistical features of real high resolution training data, and generating samples from that model, or based on a prior model and the measurements. The main objective of this thesis is to some up with a statistical data fusion framework by which different images of porous materials at different resolutions and modalities are combined in order to generate artificial samples of porous media with enhanced resolution. The current super-resolution, multi-resolution and registration methods in image processing fail to provide a general framework for the porous media reconstruction purpose since they are usually based on finding an estimate rather than a typical sample, and also based on having the images from the same scene -- the case which is not true for porous media images. The statistical fusion approach that we propose here is based on a Bayesian framework by which a prior model learned from high resolution samples are combined with a measurement model defined based on the low resolution, coarse-scale information, to come up with a posterior model. We define a measurement model, in the non-hierachical and hierarchical image modeling framework, which describes how the low resolution information is asserted in the posterior model. Then, we propose a posterior sampling approach by which 2D posterior samples of porous media are generated from the posterior model. A more general framework that we propose here is asserting other constraints rather than the measurement in the model and then propose a constrained sampling strategy based on simulated annealing to generate artificial samples

Frozen-State Hierarchical Annealing

Abstract. There is growing demand for methods to synthesize large im-ages of porous media. Binary porous media generally contain structures with a wide range of scales. This poses difficulties for generating accu-rate samples using statistical techniques such as simulated annealing. Hierarchical methods have previously been found quite effective for such problems. In this paper, a frozen-state approach to hierarchical anneal-ing is presented that offers over an order of magnitude reduction in com-putational complexity versus existing hierarchical techniques. Current limitations to this approach and areas of further research are discussed.