Browsing by Subject "Inverse analysis"

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Forward and inverse modeling of granular flows using differentiable graph neural network simulator
(2024-05) Choi, Yongjin; Kumar, Krishna (Engineering geologist); Mrinal Sen; Berkin Dortdivanlioglu; Ellen M Rathje
Granular flows such as landslides can cause extensive damage to infrastructure and pose significant hazards. Accurate forward and inverse modeling granular flows are critical for developing effective risk mitigation strategies and designs. However, conventional high-fidelity forward simulators, like the material point method (MPM), or discrete element method (DEM), are computationally intensive, which limits their ability to efficiently solve inverse problems like parameter optimization or optimal design. Additionally, their non-differentiable nature makes gradient-based optimization methods, known for their efficiency in high-dimensional problems, inapplicable. While machine learning-based surrogate models offer computational efficiency and differentiability, they often struggle to generalize beyond their training data due to their reliance on low-dimensional input-output mappings that fail to capture the complete physics of granular flows. This study introduces a differentiable graph neural network simulator (GNS) as a generalizable surrogate model for high-fidelity simulators to accelerate forward simulation for granular flows. Graphs represent the state of dynamically changing granular flows and their interactions. By learning the interaction law that governs the granular flow behavior, GNS is generalizable to predict granular flow dynamics not seen during training. It also shows great computation efficiency compared to the high-fidelity model (CB-Geo MPM) by showing up to 2000x speed up. We then propose a novel approach for solving inverse problems by combining differentiable GNS with gradient-based optimization leveraging reverse mode automatic differentiation (AD) of GNNs. The AD-GNS solves various inverse problems in granular flows. Besides the forward and inverse modeling of granular flows, this study addresses a machine learning approach to predicting pore water pressure response in liquefiable sands under cyclic loading. The pore pressure response in liquefiable sands is largely affected by the history of the cyclic shear stress. When the amplitude of cyclic shear stress is lower than the previous peak amplitude, excess pore pressure does not increase—an effect known as shielding. Many advanced constitutive models do not accurately capture this shielding effect observed in cyclic simple shear tests. We develop a data-driven machine learning model based on the long short-term memory (LSTM) neural network to capture the liquefaction response of soils under cyclic loading. We train the LSTM model on the data from 12 laboratory cyclic simple shear tests performed on Nevada sand samples with varying relative densities and subjected to different cyclic simple shear loading conditions. The model inputs include the soil's relative density and previous stress history to predict the pore water pressure response. The LSTM model successfully replicated the pore pressure response for three cyclic simple shear test cases, accounting for the shielding and density effects.
Multiphase soil-water interaction in granular media
(2023-08-07) Wang, Qiuyu, 1995-; Kumar, Krishna (Engineering geologist); Rathje, Ellen M.; Zornberg, Jorge G.; Gilbert, Robert B.; Prodanović, Maša
The study of soil-water interaction has been a fundamental and longstanding issue in the field of geotechnical engineering. It plays a critical role by affecting the shear strength, compressibility, permeability, and volumetric changes in soils, thereby influencing the design and safety of structures like dams, embankments, and foundations. Investigation into soil-water interaction typically employs experimental techniques and continuum mechanics-based models, such as Finite Element and Finite Difference Methods. However, these traditional methods face challenges in dealing with the heterogeneity and nonlinearity of the soil, complicated boundary conditions, and transient or non-equilibrium processes. Therefore, the development of more realistic models to better capture soil-water interaction remains crucial. This dissertation focuses on the development and application of advanced numerical algorithms utilizing the lattice Boltzmann Method (LBM) and Discrete Element Method (DEM) across three primary areas of study. These include 1) The investigation of water retention behavior and the source of hysteresis by multiphase LBM; 2) The evaluation of submarine landslides through modeling granular column collapse by coupling LBM with DEM; and 3) The reverse analysis of fluid flow in complex granular media by integrating automatic differentiation (AD) with LBM. First, we focus on the investigation of water retention behavior in granular soils, leveraging both Computed Tomography (CT) experiments and the multiphase lattice Boltzmann Method (LBM). We conduct a CT experiment on Hamburg sand to acquire its water retention curve, then apply LBM simulations based on the CT-derived grain skeleton. These simulations successfully capture hysteresis and other pore-scale behaviors seen in the experimental data. Our LBM analysis reveals how variations in the spatial distribution and morphology of gas clusters between drainage and imbibition processes underpin hysteresis. Next, we turn our attention to submarine landslides, which despite their low slope angles, transport vast amounts of sediment across continental shelves, potentially causing significant infrastructural damage and loss of life. We use a two-dimensional coupled lattice Boltzmann and discrete element (LBM-DEM) method to understand how the initial volume of sediment affects the run-out characteristics of these landslides. Our approach allows for pore-scale resolution of fluid flow, aiding in understanding the grain-scale mechanisms behind these complex phenomena. Lastly, we introduce an effective method for inverse analysis of fluid flow problems. Our goal is to accurately determine boundary conditions and characterize the physical properties of granular media, such as permeability, and fluid components, like viscosity. By combining the lattice Boltzmann Method (LBM) with Automatic Differentiation (AD), facilitated by the GPU-capable Taichi programming language, we can backpropagate through the entire LBM simulation. This approach provides accurate estimates of boundary conditions, helping to derive macro-scale permeability and fluid viscosity for complex flow paths in porous media. The method offers significant advantages in prediction accuracy and computational efficiency, making it a potent tool for a wide range of applications.
Optimization, design and performance analysis of light trapping structures in thin film solar cells
(2013-08) Hajimirza, Shima; Howell, John R.
Solar cells are at the frontier of renewable energy technologies. Photovoltaic energy is clean, reusable, can be used anywhere in our solar system and can be very well integrated with power distribution grids and advanced technological systems. Thin film solar cells are a class of solar cells that offer low material cost, efficient fabrication process and compatibility with advanced electronics. However, as of now, the conversion efficiency of thin film solar cells is inferior to that of thick crystalline cells. Research efforts to improve the performance bottlenecks of thin film solar cells are highly motivated. A class of techniques towards this goal is called light trapping methods, which aims at improving the spectral absorptivity of a thin film cell by using surface texturing. The precise mathematical and physical characterization of these techniques is very challenging. This dissertation proposes a numerical and computational framework to optimize, design, and fabricate efficient light trapping structures in thin film solar cells, as well as methods to verify the fabricated designs. The numerical framework is based on the important "inverse optimization" technique, which is very is widely applicable to engineering design problems. An overview of the state-of-the-art thin film technology and light trapping techniques is presented in this thesis. The inverse problem is described in details with numerous examples in engineering applications, and is then applied to light trapping optimization. The proposed designs are studied for sensitivity analysis and fabrication error, as other aspects of the proposed computational framework. At the end, reports of fabrication, measurement and verification of some of the proposed designs are presented.