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Results for “Adjoint-based error estimation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Multi-fidelity thermal modeling of laser powder bed additive manufacturing

Laser powder bed fusion (LPBF) Additive manufacturing (AM) has attracted interest as an agile method of building production metal parts to reduce design-build-test cycle times for systems. However, predicting part performance is difficult due to inherent process variabilities. This makes qualification challenging. Computational process models have attempted to address some of these challenges, including mesoscale, full physics models and reduced fidelity conduction models. The goal of this work is credible multi-fidelity modeling of the LPBF process by investigating methods for estimating the error between models of two different fidelities. Two methods of error estimation are investigated, adjoint-based error estimation and Bayesian calibration. Adjoint-based error estimation is found to effectively bounding the error between the two models, but with very conservative bounds, making predictions highly uncertain. Bayesian parameter calibration applied to conduction model heat source parameters is found to effectively bound the observed error between the models for melt pool morphology quantities of interest. However, the calibrations do not effectively bound the error in heat distribution.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Variable-fidelity multipoint aerodynamic shape optimization with output-based adapted meshes

This work presents a method to control the discretization error in multipoint aerodynamic shape optimization using output-based adapted meshes. The meshes are adapted via adjoint-based error estimates, taking into account both the objective and constraint output errors. A multi-fidelity optimization framework is then developed by taking advantage of the variable fidelity offered by adaptive meshes. The objective functional and its sensitivity at each design point (operating condition) are first evaluated on the same initial coarse mesh, which is then subsequently adapted for each design point individually as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. As the shape approaches the optimal design, the mesh at each design point becomes finer, in regions necessary for that particular operating condition. The multi-fidelity framework is tightly coupled with the objective error estimation to ensure the optimization accuracy at each fidelity. Computational savings arise from a reduction of the mesh size when the design is far from optimal and avoiding an exhaustive search on low-fidelity meshes. The proposed method is demonstrated on multipoint drag minimization problems of a transonic airfoil with lift and area constraints. Improved accuracy and efficiency are shown compared to traditional fixed-fidelity optimization with a fixed computational mesh.

42 ENGINEERING↗
DOE OSTI2023

A unified hp-HDG framework for Friedrichs' PDE systems

Here, this work proposes a unified hp-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified hp-HDG formulations for abstract one-field and two-field structures and prove their well-posedness. In order to handle non-conforming interfaces we simply take advantage of HDG built-in mortar structures. With split-type mortars and the approximation space of trace, a numerical flux can be derived via Godunov approach and be naturally employed without any additional treatment. As a consequence, the proposed formulations are parameter-free. We perform several numerical experiments for time-independent and linear PDEs including elliptic, hyperbolic, and mixed-type to verify the proposed unified hp-formulations and demonstrate the effectiveness of hp-adaptation. Two adaptivity criteria are considered: one is based on a simple and fast error indicator, while the other is rigorous but more expensive using an adjoint-based error estimate. The numerical results show that these two approaches are comparable in terms of convergence rate even for problems with strong gradients, discontinuities, and singularities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Calibr8 v.1.0

Calibr8 provides an application to rapidly prototype and perform material model calibration for complex plasticity models using advanced adjoint or forward sensitivity analyses for execution on massively parallel machines. These techniques can be orders of magnitude faster than traditional finite difference approaches for material model calibration. The underlying technology used in Calibr8 is automatic differentiation, which allows for the rapid implementation and testing of new plasticity models within its framework. Additionally, Calibr8 can perform adjoint-based error estimation to approximate discretization errors for user-implemented plasticity models. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-10630 O

Granzow, BrianN.↗
DOE OSTI2023

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. Here, we show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

42 ENGINEERING↗
DOE OSTI2022

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US carbon dioxide (CO2) storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending pointwise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego County, Michigan, USA, as our case study. The input data consist of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs, and processing of seismic data. A static earth model (SEM) of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) was used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results of observations. Results were interpreted through a Bayesian framework. The focus of this paper is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained; it does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to noninvasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters to produce results optimally agreeing with available measurements and thus extend partial pointwise estimates to full tensor fields compatible with the physics of the site.

Engineering↗