Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Adjoint methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗
NASA NTRS1997

An Efficient Multiblock Method for Aerodynamic Analysis and Design on Distributed Memory Systems

The work presented in this paper describes the application of a multiblock gridding strategy to the solution of aerodynamic design optimization problems involving complex configurations. The design process is parallelized using the MPI (Message Passing Interface) Standard such that it can be efficiently run on a variety of distributed memory systems ranging from traditional parallel computers to networks of workstations. Substantial improvements to the parallel performance of the baseline method are presented, with particular attention to their impact on the scalability of the program as a function of the mesh size. Drag minimization calculations at a fixed coefficient of lift are presented for a business jet configuration that includes the wing, body, pylon, aft-mounted nacelle, and vertical and horizontal tails. An aerodynamic design optimization is performed with both the Euler and Reynolds Averaged Navier-Stokes (RANS) equations governing the flow solution and the results are compared. These sample calculations establish the feasibility of efficient aerodynamic optimization of complete aircraft configurations using the RANS equations as the flow model. There still exists, however, the need for detailed studies of the importance of a true viscous adjoint method which holds the promise of tackling the minimization of not only the wave and induced components of drag, but also the viscous drag.

Reuther, James↗
DOE OSTI2021

Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman, Nucl. Fusion , vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlak et al. , Nucl. Fusion , vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul, Nucl. Fusion , vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al. , Nucl. Fusion , vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson, Phys. Fluids , vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau, Phys. Plasmas , vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

Physics↗
DOE OSTI2021

Progress on Optimizing Wind Farms and Rotor Designs Using Adjoints

Modern wind plants are increasingly tasked with multiple performance objectives. In addition to designing plants that maximize power output and minimize the levelized cost of energy (LCOE), the design and operation of wind plants is increasingly influenced by challenges regarding grid integration of variable generation renewables. This places a growing emphasis on making wind plants more controllable and predictable. WindSE is a Reynolds-averaged Navier-Stokes (RANS) model designed around analytical gradient and adjoint methods, with the ability to capture terrain-induced effects, as shown in Figure 1. The recent addition of an unsteady solver with an actuator line method (ALM) and ongoing work to enable massively parallel optimizations gives it a unique niche to explore coupled plant-level controls and design problems. This code is an open source python package built on the FEniCS framework that utilizes fast, parallel PETSc solvers to model fluid flow throughout wind-farm scale domains. Two recent studies performed using WindSE demonstrate the capability to optimize under a wide variety of flow conditions and objective functions. In the first, we present an optimization focused on modifying the layout of a wind farm with a fixed number of turbines for maximum total power output [1]. This study highlights the ability to quickly perform simulations using the steady Navier-Stokes solver combined with rotors represented as actuator disks while also stressing the importance of capturing terrain-induced effects. Gradient-based optimization using the RANS equations is viable due to the inclusion of efficiently computed adjoint derivatives. We interpret the physical results of the optimal layout and also discuss the computational cost of scaling to larger problems. In the second study, we present the capabilities of the unsteady Navier-Stokes solver, where rotor-blade profiles represented by actuator lines are optimized to enhance wake steering effects and overall power production [2]. We quantify the wind plant performance gains obtained from this type of simultaneous control co-design optimization as compared to optimizing the blade design and yaw independently. Figure 2 shows the differences between a baseline two-turbine system and an optimized system where we fine-tune the blade chord profile. Results and challenges from each study are quickly summarized and used to motivate the current development efforts within WindSE. Current and future work is focused on enabling higher-resolution studies with more degrees of freedom through parallelization of both the simulation and optimization algorithms. We present benchmarking results to show that WindSE performs well in both weak- and strong-scaling tests and further demonstrate that the optimizer obtains the same convergence rates in both shared- and distributed-memory environments. Using larger wind farms, we can study deep-array effects within an optimization context, allowing the use of objective functions that have been previously unstudied. As an example, we present ongoing work on a blockage metric which characterizes the loss of available kinetic energy due to wake effects from multiple upstream turbines.

adjoint optimization↗
DOE OSTI2017

Box tomography: localized imaging of remote targets buried in an unknown medium, a step forward for understanding key structures in the deep Earth

We discuss an application of tomographic methods to the imaging of localized geological structures buried inside the Earth, where neither seismic sources nor receivers are necessarily present. We call this ‘box tomography’. The essential difference between box-tomography and standard tomographic methods is that the numerical modelling (i.e. the ray tracing in traveltime tomography and the wave propagation in waveform tomography or full waveform inversion) is completely confined within the small box-region imaged. Thus, box tomography is a lot more efficient than global tomography (i.e. where we invert for the velocity in the larger volume that encompasses all the sources and receivers), for imaging localized objects. The principal difficulty in the box tomography problem comes from the medium outside the box-region imaged, that masks the target structure. In the data recorded at the surface, the information carried by the waves about the target structure is mixed with that about the surrounding medium. The main focus of this paper is to evaluate how well box tomography can extract useful information to produce accurate images of remote buried objects, especially in the difficult situation where the velocity distribution above the target structure is not known a priori. We implemented traveltime box tomography, where first arrival times are inverted using ray theory, and, waveform box tomography or full waveform box inversion, where seismograms are inverted using either scattering integrals or adjoint methods. Whatever the method employed, we found that, in the simple situation where the velocity structure is known around the target region, box-tomography is faster and more accurate than global tomography. Most importantly, through examples and simple analysis, we show that box-tomography can produce accurate images of localized structures even though the velocity distribution is not a priori known around the box-region imaged. In the last section of this paper, we evaluate the usage of box-tomography for imaging geological structures in the deep Earth. We performed 2-D synthetic experiments in a fluid planet and we argue that box tomography can be employed for refining our current global tomographic models within arbitrary regions inside the Earth. This has important implications for understanding the composition and dynamics of the Earth’s interior.

Masson, Yder↗
DOE OSTI2025

Differentiable lagrangian shock hydrodynamics with application to stable shock acceleration of density interfaces

We develop a gradient based optimization approach for the equations of compressible, Lagrangian hydrodynamics and demonstrate how it can be employed to automatically uncover strategies to control hydrodynamic instabilities arising from shock acceleration of density interfaces. Strategies for controlling the Richtmyer-Meshkov instability (RMI) are of great benefit for inertial confinement fusion (ICF) where shock interactions with many small imperfections in the density interface lead to instabilities which rapidly grow over time. These instabilities lead to mixing which, in the case of laser driven ICF, quenches the runaway fusion process ruining the potential for positive energy return. Here, we demonstrate that control of these instabilities can be achieved by optimization of initial conditions with ( > 100) parameters. Optimizing over a large parameter space like this is not possible with gradient-free optimization strategies. This requires computation of the gradient of the outputs of a numerical solution to the equations of Lagrangian hydrodynamics with respect to the inputs. We show that the efficient computation of these gradients is made possible via a judicious application of (i) adjoint methods, the exact formal representation of sensitivities involving partial differential equations, and (ii) automatic differentiation (AD), the algorithmic calculation of derivatives of functions. Careful regularization of multiple operators including artificial viscosity and timestep control is required. We perform design optimization of > 100 parameter energy field driving the Richtmyer Meshkov instability showing significant suppression while simultaneously enhancing the acceleration of the interface relative to a nominal baseline case.

Hydrophysics↗
DOE OSTI2023

Training material models using gradient descent algorithms

High temperature design requires accurate constitutive models to describe material inelastic deformation and failure behavior. Oftentimes, calibrating accurate models devolves into the problem of fitting the model parameters against experimental test data. Here, we present the pyopmat package, an open source framework for calibrating constitutive models against experiment data subjected to various loading conditions using machine learning techniques. The package calculates the exact gradient of the model response with respect to the parameters using a combination of automatic differentiation and the adjoint method. Given this exact gradient, we compare the performance of several gradient-based optimization techniques in fitting realistic constitutive models against data. Here, we demonstrate the efficiency and accuracy of our package through example problems using both synthetic data, generated using known parameter sets, under monotonic and cyclic loading conditions and also with an example applying the techniques developed here to actual high temperature creep-fatigue test data.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Tunable phononic bandgap materials designed via topology optimization

Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

42 ENGINEERING↗
DOE OSTI2018

Symmetric spectrum current drive due to finite radial drift effects

We report the drift surfaces of minority heated ions differ from flux surfaces due to finite poloidal gyroradius effects. As the minority poloidal gyroradius approaches radial scale lengths in the plasma, the difference between drift and flux surfaces can modify the heating and lead to a symmetric spectrum minority counter-current being driven. In response, a corresponding overall net co-current of comparable size is driven. This beneficial symmetric spectrum current drive in a tokamak is due to the parallel velocity asymmetry in the drift departure from a flux surface. As this new source of driven current is a side effect of minority heating it comes without any additional economic cost to reactor power balance. The symmetric spectrum current driven for near Maxwellian minorities is evaluated by an adjoint method and found to be modest. However, minority heating typically results in strong non-Maxwellian features on minority distributions so it may be possible to drive a significantly larger co-current. A related evaluation is performed for alpha particles in a deuterium minority heated plasma with a tritium majority. The low density of the alphas tends to keep this driven symmetric spectrum current small, but at very high heating levels a significant co-current might be driven. Other mechanisms to drive co-current with a symmetric spectrum are discussed and estimated, including asymmetric electron drag and focusing of the applied minority heating radio frequency fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared with unoptimised configurations. Although stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratios and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared with solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface, three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

CFD-based design optimization of ducted hydrokinetic turbines

Abstract Hydrokinetic turbines extract kinetic energy from moving water to generate renewable electricity, thus contributing to sustainable energy production and reducing reliance on fossil fuels. It has been hypothesized that a duct can accelerate and condition the fluid flow passing the turbine blades, improving the overall energy extraction efficiency. However, no substantial evidence has been provided so far for hydrokinetic turbines. To investigate this problem, we perform a CFD-based optimization study with a blade-resolved Reynolds-averaged Navier–Stokes (RANS) solver to explore the design of a ducted hydrokinetic turbine that maximizes the efficiency of energy extraction. A gradient-based optimization approach is utilized to effectively deal with the high-dimensional design space of the blade and duct geometry, with gradients being calculated through the adjoint method. The final design is re-evaluated through higher-fidelity unsteady RANS (URANS) simulations. Our optimized ducted turbine achieves an efficiency of about 54% over a range of operating conditions, higher than the typical 46% efficiency of unducted turbines.

13 HYDRO ENERGY↗
DOE OSTI2026

Optimized Tandem Catalyst Patterning for CO 2 Reduction Flow Reactors

Tandem catalysis involves two or more catalysts arranged in proximity within a single reaction vessel, with the aim of synergistically aligning the catalysts’ reaction pathways to maximize overall system performance. This study presents a proof of concept showing the integration of continuum transport modeling with design optimization in a simplified two-dimensional flow reactor setup for electrochemical CO 2 reduction. Ag catalysts provide the CO 2 ⟶ CO reaction capability, and Cu catalysts provide the CO ⟶ high-value products reaction capability. Given a set of input parameters, the optimization algorithm uses adjoint methods to modify the Ag/Cu surface patterning in order to maximize the current density toward high-value products, such as ethylene. The optimized designs yield significant performance enhancement especially at more negative applied voltages (i.e., stronger surface reactions) and for larger numbers of patterning sections. For an applied voltage of −1.7 V vs. SHE, the 12-section optimized design increases the current density toward ethylene by up to 65% compared to the unoptimized 2-section design. For the optimized cases, observed differences in the production and consumption of CO (the key intermediate species) and minimized zones of low CO reactant surface concentration on Cu sections explain the improved reactor performance.

CO2 reduction↗
DOE OSTI2020

Quandary

Quandary numerically simulates and optimizes the time-evolution of open quantum systems. The underlying dynamics are modelled by Lindblad's master equation, a linear ordinary differential equation (ODE) describing quantum systems interacting with the environment. Quandary solves this ODE numerically by applying a time-stepping integration scheme, and utilizes a gradient-based optimization approach to determine optimal control pulses that drive the quantum system to a desired target state. Two optimization objectives are considered: (a) Unitary gate optimization that finds controls to realize a unitary gate transformation, and (b) optimal reset that aims to drive the quantum system to the ground states. Gradient-based optimization schemes utilizing Petsc's Tao optimization package are applied to generate control pulses that minimize the respective measure. To evaluate the gradient of the objective function, the discrete adjoint method is used while leveraging techniques from Algorithmic Differentiation to produce exact and consistent gradients. To mitigate excessive execution run times, the software can be build together with the XBraid software library which provides a parallelization strategy to distribute the time-evolution of the underlying dynamics onto multiple processor.

Petersson, NilsA.↗
DOE OSTI2023

DPFEHM: a differentiable subsurface physics simulator

The Earth’s subsurface is a key resource that provides energy via fossil fuels and geothermal sources, stores drinking water, and is used in the fight against climate change via carbon sequestration. Simulating the physical processes that occur in the Earth’s subsurface with computers enables better use of this resource. DPFEHM is a Julia package that includes computer models with a focus on the Earth’s subsurface, especially fluid flow, which is critical for the aforementioned applications. DPFEHM is able to solve the groundwater flow equations (single phase flow), Richards equation (air/water), the advection-dispersion equation, and the 2d wave equation. One of the key features of DPFEHM is that it supports automatic differentiation, so it can be integrated into machine learning workflows using frameworks such as Flux or PyTorch. The automatic differentiation capabilities give it the same performance as adjoint methods.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Cohesive phase-field fracture and a PDE constrained optimization approach to fracture inverse problems

In recent years there has been a proliferation of modeling techniques for forward predictions of crack propagation in brittle materials, including: phase-field/gradient damage models, peridynamics, cohesive-zone models, and G/XFEM enrichment techniques. However, progress on the corresponding inverse problems has been relatively lacking. Taking advantage of key features of existing modeling approaches, we propose a parabolic regularization of Barenblatt cohesive models which borrows extensively from previous phase-field and gradient damage formulations. An efficient explicit time integration strategy for this type of nonlocal fracture model is then proposed and justified. In addition, we present a C++ computational framework for computing in- put parameter sensitivities efficiently for explicit dynamic problems using the adjoint method. This capability allows for solving inverse problems involving crack propagation to answer interesting engineering questions such as: 1) what is the optimal design topology and material placement for a heterogeneous structure to maximize fracture resistance, 2) what loads must have been applied to a structure for it to have failed in an observed way, 3) what are the existing cracks in a structure given various experimental observations, etc. In this work, we focus on the first of these engineering questions and demonstrate a capability to automatically and efficiently compute optimal designs intended to minimize crack propagation in structures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Adjoint-based sensitivity analysis of localized ignition in a non-premixed hydrogen-air mixing layer

A space-time discrete-adjoint method recently developed for high-fidelity compressible turbulence simulations is extended to chemically-reacting mixtures for the purpose of measuring sensitivity of localized ignition in a non-premixed hydrogen-air mixing layer. The ignition source is modeled as a source in the energy equation, which introduces several parameters that need to be chosen with care. Because ignition is inherently discontinuous in parameter space (i.e., it succeeds or fails after some period), the resulting gradients in modeling parameters are ill-defined near its threshold. To this end, a cost functional is designed to provide short-time sensitivity in concert with an indicator function that informs whether or not successful ignition has occurred. The corresponding sensitivity is used in a line-search algorithm to identify a point on the ignition boundary in high-dimensional parameter space (7 dimensional in our 7-parameter demonstration). This is used to quantify the relative importance of parameters on ignition.

Capecelatro, Jesse↗
DOE OSTI2018

Symmetric spectrum current drive due to finite radial drift effects

The drift surfaces of minority heated ions differ from flux surfaces due to finite poloidal gyroradius effects. As the minority poloidal gyroradius approaches radial scale lengths in the plasma the difference between drift and flux surfaces can modify the heating and lead to a symmetric spectrum minority counter-current being driven. In response, a corresponding overall net co-current of comparable size is driven. This beneficial symmetric spectrum current drive in a tokamak is due to the parallel velocity asymmetry in the drift departure from a flux surface. As this new source of driven current is a side effect of minority heating it comes without any additional economic cost to reactor power balance. The symmetric spectrum current driven for near Maxwellian minorities is evaluated by an adjoint method and found to be modest. However, minority heating typically results in strong non-Maxwellian features on minority distributions so it may be possible to drive significantly larger co-current. A related evaluation is performed for alpha particles in a deuterium minority heated plasma with a tritium majority. The low density of the alphas tends to keep this driven symmetric spectrum current small, but at very high heating levels a significant co-current might be driven. Other mechanisms to drive co-current with a symmetric spectrum are discussed and estimated, including asymmetric electron drag and focusing of the applied minority heating radio frequency fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗