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Register a new userReduced-Order Modeling through Machine Learning Approaches for Brittle Fracture Applications
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Added by
Maruti Mudunuru
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms, each method incorporates different physics-based assumptions in order to reduce the computational complexity while maintaining the physics as much as possible. This work specifically focuses on using the ML approaches to model a 2D concrete sample under low strain rate pure tensile loading conditions with 20 preexisting cracks present. A high-fidelity finite element-discrete element model is used to both produce a training dataset of 150 simulations and an additional 35 simulations for validation. Results from the ML approaches are directly compared against the results from the high-fidelity model. Strengths and weaknesses of each approach are discussed and the most important conclusion is that a combination of physics-informed and data-driven features are necessary for emulating the physics of crack propagation, interaction and coalescence. All of the models presented here have runtimes that are orders of magnitude faster than the original high-fidelity model and pave the path for developing accurate reduced order models that could be used to inform larger length-scale models with important sub-scale physics that often cannot be accounted for due to computational cost.
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The goal of this paper is to assess the utility of Reduced-Order Models (ROMs) developed from 3D physics-based models for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations are performed based on Latin Hypercube Sampling (LHS) of model inputs drawn from uniform probability distributions. Key sensitive parameters are identified from these simulations, which are fracture zone permeability, well/skin factor, bottom hole pressure, and injection flow rate. The inputs for ROMs are based on these key sensitive parameters. The ROMs are then used to evaluate the influence of subsurface attributes on thermal power production curves. The resulting ROMs are compared with field-data and the detailed physics-based numerical simulations. We propose three different ROMs with different levels of model parsimony, each describing key and essential features of the power production curves. ROM-1 is able to accurately reproduce the power output of numerical simulations for low values of permeabilities and certain features of the field-scale data, and is relatively parsimonious. ROM-2 is a more complex model than ROM-1 but it accurately describes the field-data. At higher permeabilities, ROM-2 reproduces numerical results better than ROM-1, however, there is a considerable deviation at low fracture zone permeabilities. ROM-3 is developed by taking the best aspects of ROM-1 and ROM-2 and provides a middle ground for model parsimony. It is able to describe various features of numerical simulations and field-data. From the proposed workflow, we demonstrate that the proposed simple ROMs are able to capture various complex features of the power production curves of Fenton Hill HDR system. For typical EGS applications, ROM-2 and ROM-3 outperform ROM-1.
Subsurface applications including geothermal, geological carbon sequestration, oil and gas, etc., typically involve maximizing either the extraction of energy or the storage of fluids. Characterizing the subsurface is extremely complex due to heterogeneity and anisotropy. Due to this complexity, there are uncertainties in the subsurface parameters, which need to be estimated from multiple diverse as well as fragmented data streams. In this paper, we present a non-intrusive sequential inversion framework, for integrating data from geophysical and flow sources to constraint subsurface Discrete Fracture Networks (DFN). In this approach, we first estimate bounds on the statistics for the DFN fracture orientations using microseismic data. These bounds are estimated through a combination of a focal mechanism (physics-based approach) and clustering analysis (statistical approach) of seismic data. Then, the fracture lengths are constrained based on the flow data. The efficacy of this multi-physics based sequential inversion is demonstrated through a representative synthetic example.
This article proposes an open-source implementation of a phase-field model for brittle fracture using a recently developed finite element toolbox, Gridap in Julia. The present work exploits the advantages of both the phase-field model and Gridap toolbox for simulating fracture in brittle materials. On one hand, the use of the phase-field model, which is a continuum approach and uses a diffuse representation of sharp cracks, enables the proposed implementation to overcome such well-known drawbacks of the discrete approach for predicting complex crack paths as the need for re-meshing, enrichment of finite element shape functions and an explicit tracking of the crack surfaces. On the other hand, the use of Gridap makes the proposed implementation very compact and user-friendly that requires low memory usage, and provides a high degree of flexibility to the users in defining weak forms of partial differential equations. A test on a notched beam under symmetric three-point bending and a set of tests on a notched beam with three holes under asymmetric three-point bending is considered to demonstrate how the proposed Gridap based phase-field Julia code can be used to simulate fracture in brittle materials.
Failure in brittle materials led by the evolution of micro- to macro-cracks under repetitive or increasing loads is often catastrophic with no significant plasticity to advert the onset of fracture. Early failure detection with respective location are utterly important features in any practical application, both of which can be effectively addressed using artificial intelligence. In this paper, we develop a supervised machine learning (ML) framework to predict failure in an isothermal, linear elastic and isotropic phase-field model for damage and fatigue of brittle materials. Time-series data of the phase-field model is extracted from virtual sensing nodes at different locations of the geometry. A pattern recognition scheme is introduced to represent time-series data/sensor nodes responses as a pattern with a corresponding label, integrated with ML algorithms, used for damage classification with identified patterns. We perform an uncertainty analysis by superposing random noise to the time-series data to assess the robustness of the framework with noise-polluted data. Results indicate that the proposed framework is capable of predicting failure with acceptable accuracy even in the presence of high noise levels. The findings demonstrate satisfactory performance of the supervised ML framework, and the applicability of artificial intelligence and ML to a practical engineering problem, i.,e, data-driven failure prediction in brittle materials.
In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a $k$-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective modulii at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are $approx mathcal{O}(10^6)$ times faster compared to high-fidelity HOSS.
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