Data-constrained Modeling Research Articles

Quantitative Determination of Partial Voxel Compositions with X-ray CT Image-Based Data-Constrained Modelling

X-ray CT imaging is an important three-dimensional non-destructive testing technique, which has been widely applied in various fields. However, segmenting image voxels as discrete material compositions may lose information below the voxel size. In this study, six samples with known volume fractions of compositions were imaged using laboratory micro-CT. Optical microscopic images of the samples reveal numerous small particles of compositions smaller than the CT voxel size within the samples. By employing the equivalent energy method to determine the X-ray beam energy for sample imaging experiments, data-constrained modelling (DCM) was used to obtain the volume fractions of different compositions in the samples for each voxel. The results demonstrated that DCM effectively captured information about compositions occupying CT voxels partially. The computed volume fractions of compositions using DCM closely matched the known values. The results of DCM and four automatic threshold segmentation algorithms were compared and analyzed. The results showed that DCM has obvious advantages in processing those samples containing a large number of particles smaller than the CT voxel size. This work is the first quantitative evaluation of DCM for laboratory CT image processing, which provides a new idea for multi-scale structure characterization of materials based on laboratory CT.

Magnetic fields and electric currents around the dayside magnetopause as inferred from data-constrained modeling

Magnetic fields and electric currents around the dayside magnetopause as inferred from data-constrained modeling

Data-constrained modeling of terrestrial gross primary production over the Tibetan Plateau for 2003–2019

The gross primary productivity (GPP) of terrestrial ecosystem is the largest carbon flux between atmosphere and land surface. However, accurately simulating ecosystem GPP remains a great challenge for most land surface models (LSMs) due to the biased leaf area index (LAI) simulated by the models. In this study, we use remotely sensed LAI dataset for the period 2003–2019 to drive the Farquhar model and simulate the spatial-temporal changes of GPP for the alpine ecosystem over Tibetan Plateau. The annual GPP over the Tibetan Plateau is estimated to be 540.8 ± 27.3 Tg C yr−1, which is consistent with the benchmark datasets derived from flux tower measurements and remote sensing estimations. The GPP for the past two decades has been increasing at a rate of 2.6 Tg C yr−2. The canopy greening featured by increasing LAI contributed to 27.2 % of the increasing trend in GPP, while the direct impacts from warming and wetting climate contributed to 65.2 % of GPP changes. The contribution from the direct impact of elevated atmosphere CO2 concentration is only 6.7 %. In this study we show that constraining Farquhar model with remotely sensed LAI datasets could provide reliable simulation of GPP. Given the great challenge in modeling LAI and the considerable overestimation of LAI in current LSMs, our results highlight the importance of improving LAI modeling in LSMs and the necessity of constraining LAI when tuning the parameters for photosynthesis module.

New formation and fate of Isoprene SOA markers revealed by field data-constrained modeling

Particulate 2-methyltetrols (2-MT) and 2-methylglyceric acid (2-MG) are typically used to indicate the abundance of isoprene-derived secondary organic aerosols (SOA). However, their formation and fate are not fully understood. In this study, we showed that particulate 2-MT and 2-MG collected at multiple monitoring sites under a wide range of atmospheric and emission conditions, with concentrations spanning six orders of magnitudes, are well reproduced with an expanded isoprene-SOA scheme implemented into the Community Multiscale Air Quality (CMAQ) model. The scheme considers their three-phase (gas-aqueous-organic phase) partitioning, formation from acid-driven multiphase reactions, and degradation by OH radicals in the gas and aqueous phases. The model results reveal that a non-aqueous formation pathway or direct biogenic emission is needed to supplement the commonly assumed acid-driven multiphase reaction process to explain the observed 2-MT concentrations. This missing pathway contributes to 20–40% of 2-MT in areas with aerosol pH<2 and more than 70% under less acidic conditions (pH~2–5), such as those encountered in the western US and China. The typical summertime gas-phase photochemical lifetimes of 2-MT and 2-MG are estimated to be 4–6 and 20–30 h, respectively, and their aqueous lifetimes are approximately 20–40 h. Our simulations show that predicted 2-MT is mainly influenced by its aqueous phase loss to OH, but 2-MG is more sensitive to gas phase OH loss due to the preferential partitioning of the two tracers in the aqueous and gas phases, respectively.

Model certainty in cellular network-driven processes with missing data.

Mathematical models are often used to explore network-driven cellular processes from a systems perspective. However, a dearth of quantitative data suitable for model calibration leads to models with parameter unidentifiability and questionable predictive power. Here we introduce a combined Bayesian and Machine Learning Measurement Model approach to explore how quantitative and non-quantitative data constrain models of apoptosis execution within a missing data context. We find model prediction accuracy and certainty strongly depend on rigorous data-driven formulations of the measurement, and the size and make-up of the datasets. For instance, two orders of magnitude more ordinal (e.g., immunoblot) data are necessary to achieve accuracy comparable to quantitative (e.g., fluorescence) data for calibration of an apoptosis execution model. Notably, ordinal and nominal (e.g., cell fate observations) non-quantitative data synergize to reduce model uncertainty and improve accuracy. Finally, we demonstrate the potential of a data-driven Measurement Model approach to identify model features that could lead to informative experimental measurements and improve model predictive power.

Quantitative 3D Characterization for Kinetics of Corrosion Initiation and Propagation in Additively Manufactured Austenitic Stainless Steel.

In situ X-ray computed tomography (X-ray CT) is used to investigate the effects of characteristic microstructural features on the pitting initiation and propagation in austenitic stainless steel specimens prepared with laser powder bed fusion (LPBF) additive manufacturing. In situ X-ray CT in probing the mechanism and kinetics of localized corrosion is demonstrated by immersing two LPBF specimens with different porosities in an aggressive ferric chloride solution for the evaluation of corrosion. X-ray CT images are acquired from the specimens after every 8hours of immersion over an extended period of time (216hours). Corrosion pit growth is then quantitatively analyzed with a data-constrained modeling method. The pitting growth mechanism of LPBF stainless steel is found to be different from that of conventional stainless steels. More specifically, the mechanism of corrosion pit initiation is closely correlated with the original lack of fusion porosity (LOF) distribution on the surface of the specimens and preferential pit propagation through the LOF pores inside the specimens. Pit growth kinetics are derived from pit volume changes determined through 3D data analysis. The pit growth kinetics in LPBF specimens are found to vary in the initial pit formation, competitive pit propagation, and the dominant pit growth stages.

Data-Constrained Modelling with multi-energy X-ray computed microtomography to evaluate the porosity of plasma sprayed ceramic coatings

Atmospheric plasma spray (APS) deposited ceramic coatings of zirconium boride (ZrB2) and hydroxyapatite (HAp) were inspected using Data-Constrained Modelling (DCM) of X-ray Micro-Computed Tomography (X-ray μ-CT) datasets to evaluate coating porosity. The DCM approach was used to quantify the porosity and void distributions in the coatings. The results from the 3D analysis were compared to 2D porosity and void distributions determined from the image analysis method. The 3D porosity determined from the ZrB2-1 model, 24.7%, agreed well with the 2D porosity estimation of 22.1 ± 2.6%. Additionally, the 3D porosity determined from the HAp-1 model, 22.8%, was marginally greater than the estimated 2D porosity, 19.8 ± 2.1%. However, a comparison of the 2D and 3D void distributions revealed that a 2D assessment poorly predicted the 3D microstructure of coatings and cannot be used to infer properties that depend strongly on the 3D void network. The DCM method has the ability to include the effect of fine-structure details over the 3D scan volume and hence incorporated micropores and cracks that are typically overlooked during traditional porosity inspections. Furthermore, the 3D analysis demonstrated the deficiencies in typical CT segmentation methods applied to data with a moderate CT resolution size, which was 5.4 μm. The superior DCM approach enabled the quantification of pores below the CT resolution limit that would not have been accurately modelled using typical CT segmentation methods.

Multi-energy X-ray CT and data-constrained modeling of shale 3D microstructure

Abstract Three Longmaxi Formation shale samples from different well depths were analyzed for their total organic carbon (TOC) content and mineral phases. Synchrotron-based multi-energy X-ray computed tomography (CT) slices have been acquired for these samples. Deviations of the sample center away from the harmonic trajectory during X-ray CT imaging were corrected to improve the accuracy of CT reconstructed tomographic slices. The three-dimensional (3D) distribution of porosity and mineral in the samples was derived using the data-constrained modeling (DCM) method. The equivalent spherical diameters of connected pore-organics clusters and the connection probabilities were calculated to evaluate the spatial agglomeration and the spatial correlation of pore-organics in the samples. Numerical results showed that the distribution of the connected regions size and the connection probabilities of pore-organics for three samples have similar characteristics. The connection probabilities versus the distance follow exponential law. The connection probability appeared to be positively correlated to the number of pore-organics connected clusters when the distance between the voxels is shorter than 10 μm. Comparing samples from the three well depths, both the numbers of connected regions and connection probabilities of the samples from a deeper well are higher. The approach would be applicable for structural characterization of other similar materials.

Physical conditions and frictional properties in the source region of a slow-slip event

Recent geodetic studies have shown that slow-slip events can occur on subduction faults, including their shallow (<15 km depth) parts where tsunamis are also generated. Although observations of such events are now widespread, the physical conditions promoting shallow slow-slip events remain poorly understood. Here we use full waveform inversion of controlled-source seismic data from the central Hikurangi (New Zealand) subduction margin to constrain the physical conditions in a region hosting slow slip. We find that the subduction fault is characterized by compliant, overpressured and mechanically weak material. We identify sharp lateral variations in pore pressure, which reflect focused fluid flow along thrust faults and have a fundamental influence on the distribution of mechanical properties and frictional stability along the subduction fault. We then use high-resolution data-derived mechanical properties to underpin rate–state friction models of slow slip. These models show that shallow subduction fault rocks must be nearly velocity neutral to generate shallow frictional slow slip. Our results have implications for understanding fault-loading processes and slow transient fault slip along megathrust faults. A shallow slow-slip source region has laterally variable elastic properties and pore pressure, and near-velocity-neutral frictional properties, according to seismic imaging of part of the Hikurangi subduction margin and data-constrained modelling.

Microstructure evolution of chalcopyrite agglomerates during leaching – A synchrotron-based X-ray CT approach combined with a data-constrained modelling (DCM)

Agglomeration provides substantial advantages on heap leaching, such as creating a porous heap to improve low-permeability ore leaching efficiency, as well as building an environmentally friendly heap by reducing metal releases from waste rock and tailings. In this study, we employed synchrotron X-ray computed tomography (X-ray CT) combined with a data-constrained modelling (DCM) approach to investigate the properties and evolution of pore networks of chalcopyrite-dominant agglomerates during leaching. In particular, these agglomerates, with and without prior CaCl2 addition to produce binding reagent gypsum, were subjected to column leaching tests for a period of 37 days. The copper recovery is found to be highly dependent on interior structures of agglomerates: oxidative dissolution of sulphide minerals within agglomerates was considerably promoted by high CaCl2 addition, through more interior connected pore network structure, resulting in effective migration and diffusion of lixiviant solution. The leaching data clearly show that sufficient binding capacity is essential for the maintenance of agglomerate structure by improving its mechanical resistance. Synchrotron X-ray CT data reveals that the decomposition of agglomerate has a performance of dispersing sulphide grains within the agglomerate particle and improved intra-particle porosity. This study demonstrates that combined synchrotron X-ray CT and DCM approach is a powerful tool for understanding the characteristics and evolution of valuable minerals during leaching of agglomerates.

Enhanced fish production during a period of extreme global warmth

Marine ecosystem models predict a decline in fish production with anthropogenic ocean warming, but how fish production equilibrates to warming on longer timescales is unclear. We report a positive nonlinear correlation between ocean temperature and pelagic fish production during the extreme global warmth of the Early Paleogene Period (62-46 million years ago [Ma]). Using data-constrained modeling, we find that temperature-driven increases in trophic transfer efficiency (the fraction of production passed up trophic levels) and primary production can account for the observed increase in fish production, while changes in predator-prey interactions cannot. These data provide new insight into upper-trophic-level processes constrained from the geological record, suggesting that long-term warming may support more productive food webs in subtropical pelagic ecosystems.

Sandstone 3D compositional microstructure analysis with synchrotron-based multi-energy x-ray micro-CT

Three-dimensional (3D) characterization of materials microstructure is important in understanding their physical and chemical properties. In this paper, the compositional microstructure of a sandstone sample from Yaodian area of Yan’an in Erdors Basin is analyzed using synchrotron-based multi-energy x-ray micro-CT data. The x-ray CT data of the sample are acquired at beam energies 25 KeV, 35 KeV and 45 KeV. The strip artifact in the sinogram images are corrected with a least square fitting method. The corrected sinogram image data are reconstructed with the X-tract software, and the reconstructed images under different energy spectra are calibrated. Finally, the multi-energy least square segmentation method is used to characterize the 3D microstructure of sandstone sample with the Data-Constrained Modeling (DCM) software. The results show that the sample has 71.8% of quartz and albite which is displayed as blue, calcite (22.3%) is displayed as red, pyrite (0.6%) is displayed as yellow and porosity (5.3%) is displayed as white.

Landscape inferred from gene expression data governs pluripotency in embryonic stem cells

Embryonic stem cells (ESCs) can differentiate into diverse cell types and have the ability of self-renewal. Therefore, the study of cell fate decisions on embryonic stem cells has far-reaching significance for regenerative medicine and other biomedical fields. Mathematical models have been used to study emryonic stem cell differentiation. However, the underlying mechanisms of cell differentiation and lineage reprogramming remain to be elucidated. Especially, how to integrate the computational models with quantitative experimental data is still challenging. In this work, we developed a data-constrained modelling approach, and established a model of mouse embryonic stem cells. We used the truncated moment equations (TME) method to quantify the potential landscape of the ESC network. We identified two attractors on the landscape, which represent the embryonic stem cell (ESC) state and differentiated cell (DC) state, respectively, and quantified high dimensional biological paths for differentiation and reprogramming process. Through identifying the optimal combinations of gene targets based on a landscape control strategy, we offered some predictions about the key regulatory factors that govern the differentiation and reprogramming in ESCs.

Nondestructive quantitative characterisation of material phases in metal additive manufacturing using multi-energy synchrotron X-rays microtomography

Metal additive manufacturing (MAM) has found emerging application in the aerospace, biomedical and defence industries. However, the lack of reproducibility and quality issues are regarded as the two main drawbacks to AM. Both of these aspects are affected by the distribution of defects (e.g. pores) in the AM part. Computed tomography (CT) allows the determination of defect sizes, shapes and locations, which are all important aspects for the mechanical properties of the final part. In this paper, data-constrained modelling (DCM) with multi-energy synchrotron X-rays is employed to characterise the distribution of defects in 316L stainless steel specimens manufactured with laser metal deposition (LMD). It is shown that DCM offers a more reliable method to the determination of defect levels when compared to traditional segmentation techniques through the calculation of multiple volume fractions inside a voxel, i.e. by providing sub-voxel information. The results indicate that the samples are dominated by a high number of small light constituents (including pores) that would not be detected under the voxel size in the majority of studies reported in the literature using conventional thresholding methods.

Microstructure evolution of low-grade chalcopyrite ores in chloride leaching - A synchrotron-based X-ray CT approach combined with a data-constrained modelling (DCM)

The dissolution of metal sulfides, especially chalcopyrite and the development of porosity in samples of two different low-grade ores during chloride leaching have been studied by synchrotron-based micro-CT. Quantitative analysis of the changes was achieved by using a data-constrained modelling (DCM) approach. The result indicated that void spaces developed from the surface gradually into the core of a sample, which increased from 0.08% to as much as 11.1% in the Chilean ore, and from 0.05% to 0.93% in the Mongolian ore. Combining the results of DCM modelling and CsCl distribution test, no pore structure stretching into the core of the samples was found. As a result, the leaching of metal sulfide mostly happened in the out rim of both samples, where the mineral is directly exposed to the solution. For the Chilean ore, the volume fraction of metal sulfide decreased from 4.45% to 4.06% in 17 h in the sample as a whole, and from 1.23% to 1.2% in the core. For the Mongolian ore, the volume fraction of metal sulfide decreased from 0.23% to 0.21% in the same time span. This study provides clear evidence that contact of the target mineral with leaching solution is the primary premise for metal dissolution to happen. It also demonstrates that the combination of synchrotron CT and DCM is a useful approach for mineral micro-structure analysis.

Microstructure-based multi-scale evaluation of fluid flow in an anthracite coal sample with partially-percolating voxels

Understanding fluid flow behavior in coal is of great significance for coal-bed methane exploration. X-ray CT and image segmentation have been widely used to extract pore network and generate flow field grids for flow simulation in coal samples. However, these techniques have fundamental limitations for the multi-scale characterization of coal samples, where the sub-voxel scale details could not be resolved for millimeter scale macroscopic samples. This makes it difficult to simulate the multi-scale flow behavior of fluid transport in coal sample with varying pore scales. The primary challenge is to make connection between simulation results of different scales. In the present work, multi-scale fluid flow in an anthracite coal sample was simulated by incorporating the data-constrained modeling (DCM), molecular dynamics (MD) method and partially-percolating lattice Boltzmann method (PP-LBM). In this multi-scale simulation method, three-dimensional (3D) flow field containing multi-scale structural information of the coal sample was generated by combining DCM with multi-energy synchrotron radiation CT. Multi-scale fluid flow was simulated by PP-LBM. In PP-LBM, an effective percolation fraction parameter which represents the effective volume fraction of the fluid that contributed to the flow for the voxel was used as a bridge to connect the fluid flow pattern of sub-voxel scales and voxel scales. The effective percolation fraction of a voxel versus its porosity was derived by MD simulations at the sub-voxel size level. The 3D distribution of fluid speed in the coal sample and its permeability were obtained by this multi-scale method. The numerical results are consistent with published laboratory measurements. Our proposed approach incorporated multi-scale effects and offered a more realistic fluid transport simulation method for a coal sample with varying pore size scales from the microscopic to macroscopic level. The method would be applicable for fluid transport simulations for other multi-scale porous materials.

A scale-consistent method for imaging porosity and micrite in dual-porosity carbonate rocks

Unlike many other clastic rocks, relating velocity and permeability to porosity for micrite-bearing carbonate rocks has been largely unsuccessful. Recent studies have shown that additional parameters, most notably the distribution and/or proportion of micrite, can be used to parameterize the velocity and permeability behavior. However, there is currently no scale-consistent, 3D methodology for differentiating macroporosity and microporosity from the total porosity measured on bench-top laboratory equipment. Previous studies estimated microporosity and micrite content by combining total porosity measurements conducted on whole 50 mm cores with measurements of phase volumes on 1 mm digital rocks (i.e., scale-inconsistent). As a step forward from those, we imaged dual-porosity carbonate rocks using X-ray microcomputed tomography and then leveraged a recently developed, optimization-based technique, called data-constrained modeling, to map the macroporosity and microporosity distribution of our samples. We evaluate the volumetric proportions of macropores, micropores, and coarse-grained calcite as a function of micrite content — with their respective uncertainties — all measured on the same digital rock and with the same method. Finally, we determine how measurements of the volumetric phase proportions could be extended using standard effective medium models to predict reservoir physical properties. The sensitivity of these models to the proportion of micrite and microporosity within the micrite is evidence that the nonuniqueness among permeability, velocity, and porosity that is commonly observed of micrite-bearing carbonate rocks can be explained by a variation of micrite content and microporosity at a similar porosity.

Visualizing the impact of mechanical strain and the environment on pipeline coatings from a three dimensional perspective

The effects of organic coating’s structural characteristics such as the void structure on pipeline coating degradation under combined mechanical and environmental effects have been studied using the data-constrained modelling (DCM) technique with multi-energy X-ray computed tomography (X-ray CT), in conjunction with three dimensions (3D) finite element analysis (FEA) modelling that provides a qualitative interpretation of the DCM microstructure data in terms of the concentration of stress at heterogeneous interfaces within coatings. It has been found using the DCM technique that unstrained coating films are heterogeneous in nature, showing characteristic features similar to the D-type and I-type coating regions espoused in the historical literature. For strained coating films, the interfaces of heterogeneities were seen to provide preferential sites to form voids by mechanical straining. Moreover, the void network was also found at the interfaces of the inorganic fillers and the organic polymers. These have been corroborated by simulation carried out using the FEA modelling, with a 3D model indicating the role of fillers in the formation of a tortuous void network in a heterogeneous coating subjected to both mechanical straining and corrosive environment.

Data-Constrained Modelling of Material Microstructures and Properties

Data-Constrained Modelling of Material Microstructures and Properties

Quantitative Analysis of 3D Reconstruction Parameters of Multi-Materialsin Soft Clay

The results of the three-dimensional reconstruction of soil were derived from the X-ray absorption coefficient of the material itself. However, the absorption coefficient is not a fixed value, and is related to densities, chemical molecular weight, and the weight percentages of chemical components. How to accurately obtain the density of one component is a vital issue in multi-materials. In this study, the influence of the physical parameters of each component in the data-constrained modeling (DCM) of the microstructure of soft clay was investigated. The results showed that density changes were more prominent. A reasonable multi-component density was calculated, and the density of organic matter had a significant effect on the volume percentage of three-dimensional soft clay. In the clay mineral montmorillonite, the density significantly affected the volume percentage data, which directly limited the accuracy of the material distribution analysis. Based on this, other physical parameters of each component in the data constraint model could be further explored. Based on the density value of the simple material, a reasonable multi-materials density was calculated, which provides a quantitative method for the evolution analysis of soil structure.