Stochastic Reconstruction Algorithm Research Articles

Development of stochastically reconstructed 3D porous media micromodels using additive manufacturing: numerical and experimental validation

We propose an integrated methodology for the design and fabrication of 3D micromodels that are suitable for the pore-scale study of transport processes in macroporous materials. The micromodels, that bear the pore-scale characteristics of sandstone, such as porosity, mean pore size, etc, are designed following a stochastic reconstruction algorithm that allows for fine-tuning the porosity and the correlation length of the spatial distribution of the solid material. We then construct a series of 3D micromodels at very fine resolution (i.e. 16μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$16\\,\\upmu $$\\end{document}m) using a state-of-the-art 3D printing infrastructure, specifically a ProJet MJP3600 3D printer, that utilizes the Material Jetting technology. Within the technical constraints of the 3D printer resolution, the fabricated micromodels represent scaled-up replicas of natural sandstones, that are suitable for the study of the scaling between the permeability, the porosity and the mean pore size. The REV- and pore-scale characteristics of the resulting physical micromodels are recovered using a combination of X-ray micro-CT and microfluidic studies. The experimental results are then compared with single-phase flow simulations at pore-scale and geostatistic models in order to determine the effects of the design parameters on the intrinsic permeability and the spatial correlation of the velocity profile. Our numerical and experimental measurements reveal an excellent match between the properties of the designed and fabricated 3D domains, thus demonstrating the robustness of the proposed methodology for the construction of 3D micromodels with fine-tuned and well-controlled pore-scale characteristics. Furthermore, a pore-scale numerical study over a wider range of 3D digital domain realizations reveals a very good match of the measured permeabilities with the predictions of the Kozeny–Carman formulation based on a single control parameter, k0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_0$$\\end{document}, that is found to have a practically constant value for porosities ϕ≥0.2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi \\ge 0.2$$\\end{document}. This, in turn, enables us to customize the sample size to meet REV constraints, including enlarging pore morphology while considering the Reynolds number. It is also found that at lower porosities there is a significant increase in the fraction of the non-percolating pores, thus leading to different k0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_0$$\\end{document}, as the porosity approaches a numerically determined critical porosity value, ϕc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi _c$$\\end{document}, where the domain is no longer percolating.

Stochastic reconstruction and performance prediction of cathode microstructures based on deep learning

The effective properties of lithium-ion battery (LIB) cathode are determined by both the volume fractions of constituents and the morphological features of microstructure. However, it is difficult to establish an accurate quantitative relationship between the macroscopic effective properties and microstructural features. Deep learning techniques, due to their exceptional nonlinear fitting capabilities, have been widely applied in various complex fields. Our study presents a generation scheme of numerous three-dimensional (3D) digital microstructures of cathode, using a deep convolutional neural network (CNN)-based stochastic reconstruction algorithm combining with the scanning electron microscope (SEM) images. The reconstructed samples are substituted with the corresponding finite element (FE) models, and the effective mechanical and electrochemical properties are assessed through the FE-based homogenization theory. Finally, the generated cathode samples and their effective properties are used to train the 3D CNN for performance prediction. This study demonstrates that the deep learning approaches can accurately and rapidly reconstruct the microstructure of cathode and predict their effective properties. Furthermore, the established framework can be extended to other heterogeneous materials.

Adaptive phase-retrieval stochastic reconstruction with correlation functions: Three-dimensional images from two-dimensional cuts.

Precise characterization of three-dimensional (3D) heterogeneous media is indispensable in finding the relationships between structure and macroscopic physical properties (permeability, conductivity, and others). The most widely used experimental methods (electronic and optical microscopy) provide high-resolution bidimensional images of the samples of interest. However, 3D material inner microstructure registration is needed to apply numerous modeling tools. Numerous research areas search for cheap and robust methods to obtain the full 3D information about the structure of the studied sample from its 2D cuts. In this work, we develop an adaptive phase-retrieval stochastic reconstruction algorithm that can create 3D replicas from 2D original images, APR. The APR is free of artifacts characteristic of previously proposed phase-retrieval techniques. While based on a two-point S_{2} correlation function, any correlation function or other morphological metrics can be accounted for during the reconstruction, thus, paving the way to the hybridization of different reconstruction techniques. In this work, we use two-point probability and surface-surface functions for optimization. To test APR, we performed reconstructions for three binary porous media samples of different genesis: sandstone, carbonate, and ceramic. Based on computed permeability and connectivity (C_{2} and L_{2} correlation functions), we have shown that the proposed technique in terms of accuracy is comparable to the classic simulated annealing-based reconstruction method but is computationally very effective. Our findings open the possibility of utilizing APR to produce fast or crude replicas further polished by other reconstruction techniques such as simulated annealing or process-based methods. Improving the quality of reconstructions based on phase retrieval by adding additional metrics into the reconstruction procedure is possible for future work.

Stochastic 3D Carbon Cloth GDL Reconstruction and Transport Prediction

This paper presents the 3D carbon cloth gas diffusion layer (GDL) to predict transport behaviors of anisotropic structure properties. A statistical characterization and stochastic reconstruction method is established to construct the 3D micro-structure using the data from the true materials. Statistics of the many microstructure characteristics, such as porosity, pore size distribution, and shape of the void, are all quantified by image-based characterization. Furthermore, the stochastic reconstruction algorithm is proposed to generate random and anisotropic 3D microstructure models. The proposed method is demonstrated by some classical simulation prediction and to give the evaluation of the transport properties. Various reconstructed GDLs are also generated to demonstrate the capability of the proposed method. In the end, the adapted structure properties are offered to optimize the carbon cloth GDLs.

Lattice Boltzmann simulation of oxygen diffusion and electrochemical reaction inside catalyst layer of PEM fuel cells

An in-depth understanding of pore-scale transport process and electrode reaction kinetics is critical to ease the sluggish oxygen reduction reaction of proton exchange membrane fuel cells. In this study, the effects of catalyst layer microstructure on the oxygen diffusion and electrochemical reaction consumption are analyzed, based on the developed 3D single-phase lattice Boltzmann model and optimized stochastic reconstruction algorithm. The results suggest that increasing the ionomer content and platinum loading are beneficial to increasing the active sites, while the oxygen transport along the thickness direction becomes more difficult due to the narrowed pores, so the platinum particles in the back region have less participation in the reaction, which causes the significant catalyst waste and limits the further cost reduction and improvement of power density. Improving the carbon particle diameter ensures the enlarged pores and more effective Pt particles covered by ionomer, thus enhances the oxygen supply and electrochemical reaction rate.

Stochastic 3D microstructure reconstruction and mechanical modeling of anisotropic battery separators

This paper presents a 3D microstructure model to predict mechanical behaviors of the anisotropic battery separator. A statistical characterization and stochastic reconstruction method is established to enable 3D microstructure modeling based on 2D microscopic images. Statistics of the key microstructure characteristics, such as porosity and the shape of the voids, are quantified by image-based characterization. Furthermore, a stochastic reconstruction algorithm is proposed to generate random but statistically equivalent 3D microstructure models for mechanical property analysis and uncertainty quantification. The proposed method is demonstrated on a commercial separator. Uniaxial tensile simulations are conducted with Finite Element Analysis (FEA) and the results are validated by experimental data. The 3D microstructure model captures anisotropic properties of the separator, and gives insights about the microstructure features under tensile load.

Combination and application of machine learning and computational mechanics

With the steady development of computer science, machine learning and data science have made significant progress in recent decades. These techniques generally rely on a substantial amount of data samples to extract the abstract mapping hidden within the data. Hence, these technologies have gradually attracted the attention of researchers in the field of computational mechanics. Combining the recent studies of the authors and other researchers, this paper aims to interpret several forms of applications that integrate machine learning and data science with computational mechanics. In the first application, the core algorithm of the convolutional neural network is implemented to solve the linear elastic finite element problem. A standard finite element equation is transformed into an optimization problem in this method. The method is verified by a plane strain linear elastic finite element problem. The method demonstrates promising accuracy by comparing the results obtained by traditional finite element solver. However, some limitations of this method need to be addressed. First, though the optimization process can be accelerated by GPU, the efficiency of the proposed method is still lower than most mainstream numerical solvers. And, the framework of convolutional neural networks requires that the input layer data should be a constant matrix. This is a major challenge for solving nonlinear finite element equations whose stiffness matrices contain variables. These are the issues worth considerations in future studies. In the second application, a method is proposed to establish the implicit mapping between the effective mechanical property and the mesoscale structure of heterogeneous materials. Shale is employed in this paper as an example to illustrate the method. At the mesoscale, a shale sample is a complex heterogeneous composite that consists of multiple mineral constituents. The mechanical properties of each mineral constituent vary significantly, and mineral constituents are distributed in an utterly random manner within shale samples. Large quantities of shale samples are generated based on mesoscale scanning electron microscopy images using a stochastic reconstruction algorithm. Image processing techniques are employed to transform the shale sample images to finite element models. Finite element analysis is utilized to evaluate the effective mechanical properties of the shale samples. A convolutional neural network is trained based on the images of stochastic shale samples and their effective moduli. The trained network is validated to be able to predict the effective moduli of real shale samples accurately and efficiently. Not limited to shale, the proposed method can be further extended to predict effective mechanical properties of various heterogeneous materials. In the third application, the authors discuss a data-driven computational mechanics framework proposed by Kirchdoerfer and Ortiz. The most outstanding feature of the framework is that explicit material constitutive equations are no longer required. More specifically, experimental material response data are employed in the framework to replace constitutive equations. Combined with traditional compatibility and equilibrium equations, the framework is able to find the optimal stress-strain combination from a material response dataset to best fit the current element. With this framework, the errors and uncertainties induced by the empirical constitutive functions of traditional computational mechanics approaches can be avoided. The aforementioned applications are only the tip of an iceberg in the recent advancement of computational mechanics. Hence, researchers have reasons to believe that there would be more application scenarios that integrate data science and machine learning with computational mechanics in the future. Hopefully, computational mechanics methods with more robustness, efficiency, and fidelity will be developed.

Predicting the effective mechanical property of heterogeneous materials by image based modeling and deep learning

In contrast to the composition uniformity of homogeneous materials, heterogeneous materials are normally composed of two or more distinctive constituents. It is usually recognized that the effective material property of a heterogeneous material is related to the mechanical property and the distribution pattern of each forming constituent. However, to establish an explicit relationship between the macroscale mechanical property and the microstructure appears to be complicated. On the other hand, machine learning methods are broadly employed to excavate inherent rules and correlations based on a significant amount of data samples. Specifically, deep neural networks are established to deal with situations where input–output mappings are extensively complex. In this paper, a method is proposed to establish the implicit mapping between the effective mechanical property and the mesoscale structure of heterogeneous materials. Shale is employed in this paper as an example to illustrate the method. At the mesoscale, a shale sample is a complex heterogeneous composite that consists of multiple mineral constituents. The mechanical properties of each mineral constituent vary significantly, and mineral constituents are distributed in an utterly random manner within shale samples. Large quantities of shale samples are generated based on mesoscale scanning electron microscopy images using a stochastic reconstruction algorithm. Image processing techniques are employed to transform the shale sample images to finite element models. Finite element analysis is utilized to evaluate the effective mechanical properties of the shale samples. A convolutional neural network is trained based on the images of stochastic shale samples and their effective moduli. The trained network is validated to be able to predict the effective moduli of real shale samples accurately and efficiently. Not limited to shale, the proposed method can be further extended to predict effective mechanical properties of other heterogeneous materials.

A New Extended Structural Parameter Set for Stochastic Molecular Reconstruction: Application to Asphaltenes

The modeling of complex hydrocarbon mixtures is a current issue. The presently available analytical techniques are insufficient alone to fully characterize the molecular details of heavy oil fractions to the level for new development of a molecular-level kinetic model. Stochastic reconstruction (SR) methods which build a set of molecules that mimic the properties of complex mixtures by using partial analytical data help to overcome this drawback. Although the classical SR algorithm produces reasonable molecule sets for light and medium fractions, performance degrades for heavier fractions. The main reason for this is the lack of structural parameters needed to define the variations in side-chain and ring configurations. As an extension, a novel structural parameter set including specific parameters for ring and chain configurations was implemented to the SR algorithm. In addition to this, in order to ensure an extensive structural connection between the generated molecules and the experimental data, the 1...

Evaluation of a stochastic reconstruction algorithm for use in Compton camera imaging and beam range verification from secondary gamma emission during proton therapy

In this paper, we study the feasibility of using the stochastic origin ensemble (SOE) algorithm for reconstructing images of secondary gammas emitted during proton radiotherapy from data measured with a three-stage Compton camera. The purpose of this study was to evaluate the quality of the images of the gamma rays emitted during proton irradiation produced using the SOE algorithm and to measure how well the images reproduce the distal falloff of the beam. For our evaluation, we performed a Monte Carlo simulation of an ideal three-stage Compton camera positioned above and orthogonal to a proton pencil beam irradiating a tissue phantom. Scattering of beam protons with nuclei in the phantom produces secondary gamma rays, which are detected by the Compton camera and used as input to the SOE algorithm. We studied the SOE reconstructed images as a function of the number of iterations, the voxel probability parameter, and the number of detected gammas used by the SOE algorithm. We quantitatively evaluated the capabilities of the SOE algorithm by calculating and comparing the normalized mean square error (NMSE) of SOE reconstructed images. We also studied the ability of the SOE reconstructed images to predict the distal falloff of the secondary gamma production in the irradiated tissue. Our results show that the images produced with the SOE algorithm converge in ∼10 000 iterations, with little improvement to the image NMSE for iterations above this number. We found that the statistical noise of the images is inversely proportional to the ratio of the number of gammas detected to the SOE voxel probability parameter value. In our study, the SOE predicted distal falloff of the reconstructed images agrees with the Monte Carlo calculated distal falloff of the gamma emission profile in the phantom to within ±0.6 mm for the positions of maximum emission (100%) and 90%, 50% and 20% distal falloff of the gamma emission profile. We conclude that the SOE algorithm is an effective method for reconstructing images of a proton pencil beam from the data collected by an ideal Compton camera and that these images accurately model the distal falloff of secondary gamma emission during proton irradiation.

SU‐E‐T‐349: Evaluating a Stochastic Reconstruction Algorithm for Compton Camera Based Prompt Gamma Imaging during Proton Therapy

Purpose: Prompt gamma photons emitted during proton radiotherapy may provide a method to measure dose delivery and range. The utility of this method depends on how well the gammas can be detected and reconstructed. The purpose of this study is to demonstrate the feasibility of the stochastic origin ensemble (SOE) algorithm for reconstructing images of the origins of prompt gammas emitted during proton therapy and to introduce a metric for quantifying the accuracy of this image. Methods: Using Geant4 we simulated a Compton camera detecting prompt gamma emission from proton irradiated tissue phantoms. The information recorded by the simulated detector is used as the input to the SOE reconstruction algorithm, which iteratively determines the likely gamma emission origin. We introduce a metric to quantify the accuracy of the reconstruction and use the metric to provide a quantitative analysis of the SOE reconstructions. Results: We show both qualitatively and quantitatively that the SOE algorithm can reconstruct images which accurately predict the origins of prompt gammas emitted during proton therapy. We also show that the distal falloff of gamma production based on the reconstructed image agrees with the distal falloff in Monte Carlo calculated gamma origin distribution to within 1 mm for both the 50% and 20% regions. Conclusions: The SOE algorithm was able to reconstruct usable images of prompt gamma emission during proton irradiation. We believe these results justify further investigation of this technique for in‐vivo prompt gamma imaging.This work was supported by Award Number R21CA137362 from the National Cancer Institute.