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Results for “gradient-based shape optimization”

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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24 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Minimum feature size control in level set topology optimization via density fields

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0-1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

42 ENGINEERING↗
DOE OSTI2026

Multipoint Aerostructural Optimization of Wind Turbine Rotors Using a Coupled Blade‐Resolved Aerostructural Solver

Physics‐based design optimization workflows thread the needle between computational cost limitations and simulation complexity, often compromising between modeling detail and the range of operating design conditions. Multipoint aerostructural optimization of wind turbine rotors has so far been confined to low‐fidelity analyses or to high‐fidelity studies with simplified structural models, leaving the most complex design trade‐offs unexplored. We close this gap by performing the first tightly coupled gradient‐based multipoint aerostructural rotor optimization using 3D aerodynamic and structural solvers with discrete coupled adjoints. The optimizer simultaneously varies blade planform, airfoil shapes, and structural thickness through more than 270 design variables, minimizing a weighted combination of rotor mass and power across multiple wind speeds. Applied to a modified DTU 10‐MW benchmark under conservative structural and aerodynamic constraints, our multipoint optimization reduces rotor mass by up to 36% and increases power by 12%–15% across the main operating conditions; biasing the objective toward power yields power gains up to 18% and a 17% mass reduction. For a nominal wind distribution, 3‐point rotor designs accounting for low RPM and high thrust conditions capture dominant trade‐offs and outperform single‐point designs. Adding two off‐design points changes individual‐condition power by less than 3% but leaves the weighted average within 0.5%, and the mass‐power bias has a stronger effect on the final design than the operating‐point weighting itself. Our framework extends naturally to richer load cases and site‐specific wind distributions, providing a basis for high‐fidelity multipoint design earlier in industrial workflows.

17 WIND ENERGY↗
DOE OSTI2021

An adjoint method for determining the sensitivity of island size to magnetic field variations

An adjoint method to calculate the gradient of island width in stellarators is presented and applied to a set of magnetic field configurations. The underlying method for calculation of the island width is that of Cary & Hanson ( Phys. Fluids B, vol. 3, issue 4, 1991, pp. 1006–1014) (with a minor modification), and requires that the residue of the island centre be small. Therefore, the gradient of the residue is calculated in addition. Both the island width and the gradient calculations are verified using an analytical magnetic field configuration introduced by Reiman & Greenside ( Comput. Phys. Commun. , vol. 43, issue 1, 1986, pp. 157–167). The method is also applied to the calculation of the shape gradient of the width of a magnetic island in a National Compact Stellarator Experiment (NCSX) vacuum configuration with respect to positions on a coil. A gradient-based optimization is applied to a magnetic field configuration studied by Hanson & Cary ( Phys. Fluids , vol. 27, issue 4, 1984, pp. 767–769) to minimize stochasticity by adding perturbations to a pair of helical coils. Although only vacuum magnetic fields and an analytical magnetic field model are considered in this work, the adjoint calculation of the island width gradient could also be applied to a magnetohydrodynamic (MHD) equilibrium if the derivative of the magnetic field, with respect to the equilibrium parameters, is known. Using the island width gradient calculation presented here, more general gradient-based optimization methods can be applied to design stellarators with small magnetic islands. Moreover, the sensitivity of the island size may itself be optimized to ensure that coil tolerances, with respect to island size, are kept as high as possible.

Physics↗
DOE OSTI2023

Pragmatic Uncertainty Quantification and Propagation in Inverse Estimation of Structural Dynamics Parameters given Material Property Uncertainties and Limited Sensor Data

In this report we demonstrate some relatively simple and inexpensive methods to effectively account for various sources of epistemic lack-of-knowledge type uncertainty in inverse problems. The demonstration problem involves inverse estimation of six parameters of a bolted joint that attaches a kettlebell shaped object to a thick plate. The parameters are efficiently inverted in a modal-based model calibration using gradient-based optimization. Two material properties of the kettlebell are treated as uncertain to within given epistemic uncertainty bounds. We apply and test interval and sparse-sample probabilistic approaches to account for uncertainty in the estimated parameters (and various scalar functionals of the parameters as generic quantities of interest, QOIs) due to uncertainties in the material properties. We also investigate the error effects of limited numbers of vibration sensors (accelerometers) on the kettlebell and plate, and therefore abbreviated excitation/response information in the parameter inversions. We propose and demonstrate a Leave-K-Sensors-Out “cross-prediction” UQ approach to estimate related uncertainties on the parameters and QOI functionals. We indicate how uncertainties from material properties and limited sensors are treated in a combined manner. The economical combined UQ approach involves just three to five samples (i.e. three to five inverse simulations), with no added complication or error/uncertainty from use of surrogate models for affordability. Finally, we describe a related economical UQ approach for handling potential parameter solution non-uniqueness and numerical optimization related precision uncertainties in the estimated parameter values. Indicated further research is identified.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Efficient Distributed Optimization of Wind Farms Using Proximal Primal-Dual Algorithms: Preprint

This paper presents a distributed approach to perform real-time optimization of large wind farms. Wind turbines in a wind farm typically operate individually to maximize their own performance regardless of the impact of aerodynamic interactions on neighboring turbines. This paper optimizes the overall power produced by a wind farm by formulating and solving a nonconvex optimization problem where the yaw angles are optimized to allow some turbines to operate in misaligned conditions and shape the aerodynamic interactions in a favorable way. The solution of the nonconvex smooth problem is tackled using a proximal primal-dual gradient method, which provably identifies a first-order stationary solution in a global sublinear manner. By adding auxiliary optimization variables for every pair of turbines that are coupled aerodynamically and properly adding consensus constraints into the underlying problem, a distributed algorithm with turbine-to-turbine message passing is obtained; this allows for turbines to be optimized in parallel using local information rather than information from the whole wind farm. This algorithm is computationally light, as it involves closed-form updates. This approach is demonstrated on a large wind farm with 60 turbines. The results indicate that similar performance can be achieved as with finite-difference gradient-based optimization at a fraction of the computational time and thus approach real-time control/optimization.

17 WIND ENERGY↗
DOE OSTI2019

Efficient Distributed Optimization of Wind Farms Using Proximal Primal-Dual Algorithms

This paper presents a distributed approach to performing real-time optimization of large wind farms. Wind turbines in a wind farm typically operate individually to maximize their own performance regardless of the impact of aerodynamic interactions on neighboring turbines. This paper optimizes the overall power produced by a wind farm by formulating and solving a nonconvex optimization problem where the yaw angles are optimized to allow some turbines to operate in misaligned conditions and shape the aerodynamic interactions in a favorable way. The solution of the nonconvex smooth problem is tackled using a proximal primal-dual gradient method, which provably identifies a first-order stationary solution in a global sublinear manner. By adding auxiliary optimization variables for every pair of turbines that are coupled aerodynamically, and properly adding consensus constraints into the underlying problem, a distributed algorithm with turbine-to-turbine message passing is obtained; this allows for turbines to be optimized in parallel using local information rather than information from the whole wind farm. This algorithm is computationally light, as it involves closed-form updates. This approach is demonstrated on a large wind farm with 60 turbines. The results indicate that similar performance can be achieved as with finite-difference gradient-based optimization at a fraction of the computational time and thus approaching real-time control/optimization.

17 WIND ENERGY↗