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NASA NTRS2020

Structural Model Tuning Tool: User's Reference Manual

This report presents an efficient approach for tuning finite element models to match the measured ground vibration test and static test data. Frequencies, mode shapes, total weight, location of the center of gravity, and static deformation computed from the finite element model are matched to the measured data. The model tuning procedure used in this work is based on solving an optimization problem in which the errors for the considered metrics, between the finite element prediction and the measured data, are minimized. Analytical sensitivity values of performance indices are computed using the NASTRAN-generated sensitivity values together with the in-house computer codes, which allow for faster computational time and the use of gradient-based optimizers. The method is applied to the Aerostructures Test Wing IV model. The study shows that the military standard and the National Aeronautics and Space Administration standard for comparing analytical and experimental modal data are all satisfied. The final finite element model correlates well with the test data. The flutter speed decreases by 8.91 percent after model tuning compared with the original Aerostructures Test Wing IV design.

Chan-gi Pak↗

NASA NTRS2017

High-Fidelity Multidisciplinary Design Optimization of Aircraft Configurations

To evaluate new airframe technologies we need design tools based on high-fidelity models that consider multidisciplinary interactions early in the design process. The overarching goal of this NRA is to develop tools that enable high-fidelity multidisciplinary design optimization of aircraft configurations, and to apply these tools to the design of high aspect ratio flexible wings. We develop a geometry engine that is capable of quickly generating conventional and unconventional aircraft configurations including the internal structure. This geometry engine features adjoint derivative computation for efficient gradient-based optimization. We also added overset capability to a computational fluid dynamics solver, complete with an adjoint implementation and semiautomatic mesh generation. We also developed an approach to constraining buffet and started the development of an approach for constraining utter. On the applications side, we developed a new common high-fidelity model for aeroelastic studies of high aspect ratio wings. We performed optimal design trade-o s between fuel burn and aircraft weight for metal, conventional composite, and carbon nanotube composite wings. We also assessed a continuous morphing trailing edge technology applied to high aspect ratio wings. This research resulted in the publication of 26 manuscripts so far, and the developed methodologies were used in two other NRAs. 1

Martins, Joaquim R. R. A.↗

DOE OSTI2021

Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Restricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter (β) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2019

Load Flow Analysis with Analytic Derivatives for Electric Aircraft Design Optimization

Many of the aircraft concepts of the future are exploring the use of hybrid-, turbo- or all-electric propulsion systems to improve performance and decrease environmental impacts. These aircraft concepts range from small rotorcraft for urban air mobility to conventional commercial transports to large blended wing body designs. Developing the conceptual design for these vehicles presents a challenge, however, as traditional aircraft design tools often were not developed to handle these unique propulsion system architectures. Previous studies on these vehicles have therefore relied on relatively simple models of the electrical transmission and distribution system. This paper presents the development of a hybrid AC-DC load flow (or power flow) analysis capability to enhance the conceptual design of these concept vehicles. Specifically, the desire was to create a load flow analysis capability within the OpenMDAO framework that is also being used to develop a set of compatible tools for rapid optimization of conceptual designs. This load flow analysis capability is unique in its flexible object-oriented structure and implementation of analytic derivatives to facilitate the use of solvers and gradient based optimization in the design process. The developed hybrid load flow analysis capability is first verified against a published 13-bus example then used to model the electrical distribution system for a turbo-electric tiltwing aircraft.

Load flow↗

DOE OSTI2023

MrHyDE v.1.0

SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE is designed to enable moving beyond forward simulation for multiscale applications which includes optimization, control, uncertainty quantification, and stochastic inversion. The framework provides interfaces to several packages within the Trilinos framework and leverages automatic differentiation to enable adjoint capabilities for large-scale, gradient-based optimization. MrHyDE provides automated multiscale capabilities through a subgrid model interface and multiscale Dirichlet-to-Neumann maps. For extreme-scale applications, MrHyDE provides in situ data-compression algorithms to reduce memory requirements while maintaining performance. MrHyDE is a general-purpose, computational framework for the solution of multiscale and multiphysics applications. It uses a combination of structure-preserving, physics-compatible discretizations, fully implicit methods, multi-resolution schemes, or fully explicit methods. 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.

SciDAC↗

NASA NTRS1993

Multidisciplinary Design Techniques Applied to Conceptual Aerospace Vehicle Design

Multidisciplinary design optimization (MDO) is an emerging discipline within aerospace engineering. Its goal is to bring structure and efficiency to the complex design process associated with advanced aerospace launch vehicles. Aerospace vehicles generally require input from a variety of traditional aerospace disciplines - aerodynamics, structures, performance, etc. As such, traditional optimization methods cannot always be applied. Several multidisciplinary techniques and methods were proposed as potentially applicable to this class of design problem. Among the candidate options are calculus-based (or gradient-based) optimization schemes and parametric schemes based on design of experiments theory. A brief overview of several applicable multidisciplinary design optimization methods is included. Methods from the calculus-based class and the parametric class are reviewed, but the research application reported focuses on methods from the parametric class. A vehicle of current interest was chosen as a test application for this research. The rocket-based combined-cycle (RBCC) single-stage-to-orbit (SSTO) launch vehicle combines elements of rocket and airbreathing propulsion in an attempt to produce an attractive option for launching medium sized payloads into low earth orbit. The RBCC SSTO presents a particularly difficult problem for traditional one-variable-at-a-time optimization methods because of the lack of an adequate experience base and the highly coupled nature of the design variables. MDO, however, with it's structured approach to design, is well suited to this problem. The result of the application of Taguchi methods, central composite designs, and response surface methods to the design optimization of the RBCC SSTO are presented. Attention is given to the aspect of Taguchi methods that attempts to locate a 'robust' design - that is, a design that is least sensitive to uncontrollable influences on the design. Near-optimum minimum dry weight solutions are determined for the vehicle. A summary and evaluation of the various parametric MDO methods employed in the research are included. Recommendations for additional research are provided.

Olds, John Robert↗

DOE OSTI2022

FLOW Estimation and Rose Superposition (FLOWERS): an integral approach to engineering wake models

Abstract. Annual energy production (AEP) is often the objective function in wind plant layout optimization studies. The conventional method to compute AEP for a wind farm is to first evaluate power production for each discrete wind direction and speed using either computational fluid dynamics simulations or engineering wake models. The AEP is then calculated by weighted-averaging (based on the wind rose at the wind farm site) the power produced across all wind directions and speeds. We propose a novel formulation for time-averaged wake velocity that incorporates an analytical integral of a wake deficit model across every wind direction. This approach computes the average flow field more efficiently, and layout optimization is an obvious application to exploit this benefit. The clear advantage of this new approach is that the layout optimization produces solutions with comparable AEP performance yet is completed 2 orders of magnitude faster. The analytical integral and the use of a Fourier expansion to express the wind speed and wind direction frequency create a relatively smooth solution space for the gradient-based optimizer to excel in comparison to the existing weighted-averaging power calculation.

17 WIND ENERGY↗

DOE OSTI2025

Deep Learning without Global Optimization by Random Fourier Neural Networks

Here we introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Observations on computational methodologies for use in large-scale, gradient-based, multidisciplinary design incorporating advanced CFD codes

How a combination of various computational methodologies could reduce the enormous computational costs envisioned in using advanced CFD codes in gradient based optimized multidisciplinary design (MdD) procedures is briefly outlined. Implications of these MdD requirements upon advanced CFD codes are somewhat different than those imposed by a single discipline design. A means for satisfying these MdD requirements for gradient information is presented which appear to permit: (1) some leeway in the CFD solution algorithms which can be used; (2) an extension to 3-D problems; and (3) straightforward use of other computational methodologies. Many of these observations have previously been discussed as possibilities for doing parts of the problem more efficiently; the contribution here is observing how they fit together in a mutually beneficial way.

Newman, P. A.↗

NASA NTRS2006

Static and Dynamic Model Update of an Inflatable/Rigidizable Torus Structure

The present work addresses the development of an experimental and computational procedure for validating finite element models. A torus structure, part of an inflatable/rigidizable Hexapod, is used to demonstrate the approach. Because of fabrication, materials, and geometric uncertainties, a statistical approach combined with optimization is used to modify key model parameters. Static test results are used to update stiffness parameters and dynamic test results are used to update the mass distribution. Updated parameters are computed using gradient and non-gradient based optimization algorithms. Results show significant improvements in model predictions after parameters are updated. Lessons learned in the areas of test procedures, modeling approaches, and uncertainties quantification are presented.

Horta, Lucas G.↗

NASA NTRS1995

Domain decomposition for aerodynamic and aeroacoustic analyses, and optimization

The overarching theme was the domain decomposition, which intended to improve the numerical solution technique for the partial differential equations at hand; in the present study, those that governed either the fluid flow, or the aeroacoustic wave propagation, or the sensitivity analysis for a gradient-based optimization. The role of the domain decomposition extended beyond the original impetus of discretizing geometrical complex regions or writing modular software for distributed-hardware computers. It induced function-space decompositions and operator decompositions that offered the valuable property of near independence of operator evaluation tasks. The objectives have gravitated about the extensions and implementations of either the previously developed or concurrently being developed methodologies: (1) aerodynamic sensitivity analysis with domain decomposition (SADD); (2) computational aeroacoustics of cavities; and (3) dynamic, multibody computational fluid dynamics using unstructured meshes.

Baysal, Oktay↗

NASA NTRS2004

Aerodynamic Shape Optimization Based on Free-form Deformation

This paper presents a free-form deformation technique suitable for aerodynamic shape optimization. Because the proposed technique is independent of grid topology, we can treat structured and unstructured computational fluid dynamics grids in the same manner. The proposed technique is an alternative shape parameterization technique to a trivariate volume technique. It retains the flexibility and freedom of trivariate volumes for CFD shape optimization, but it uses a bivariate surface representation. This reduces the number of design variables by an order of magnitude, and it provides much better control for surface shape changes. The proposed technique is simple, compact, and efficient. The analytical sensitivity derivatives are independent of the design variables and are easily computed for use in a gradient-based optimization. The paper includes the complete formulation and aerodynamics shape optimization results.

Samareh, Jamshid A.↗

DOE OSTI2023

Journey Over Destination: Differentiable Sensor Placement Enhances Generalization [Poster]

The challenge of reconstructing spatial fields that change over time from limited sensor data has been a focal point for many research studies. Various machine learning methods have been used in attempts to address this complex issue, including convolutional neural networks. All of the proposed methods share a common requirement that the user needs to manually determine the sensor positions. This requirement remains a limiting factor in the ongoing quest for efficient learning and accurate field reconstruction. This study aims to present a method that enables a model to optimize sensor positions via backpropagation, thereby facilitating the model’s exploration of the spatial domain and enhancing sensor positioning effectively. Indexing naturally incorporates discrete decisions. This operation is nondifferentiable which is a requirement for the application of gradient-based optimization methods. We showcased its effectiveness by training an attention-based neural network, which achieved top-tier performance on two separate datasets. To our knowledge, this represents the first fully end-to-end differentiable workflow for enhancing sensor placement within a neural network model.

58 GEOSCIENCES↗

NASA NTRS2001

Accuracy Assessment of Response Surface Approximations for Supersonic Turbine Design

There is a growing trend to employ CFD tools to supply the necessary information for design optimization of fluid dynamics components/systems. Such results are prone to uncertainties due to reasons including discretization. errors, incomplete convergence of computational procedures, and errors associated with physical models such as turbulence closures. Based on this type of information, gradient-based optimization algorithms often suffer from the noisy calculations, which can seriously compromise the outcome. Similar problems arise from the experimental measurements. Global optimization techniques, such as those based on the response surface (RS) concept are becoming popular in part because they can overcome some of these barriers. However, there are also fundamental issues related to such global optimization technique such as RS. For example, in high dimensional design spaces, typically only a small number of function evaluations are available due to computational and experimental costs. On the other hand, complex features of the design variables do not allow one to model the global characteristics of the design space with simple quadratic polynomials. Consequently a main challenge is to reduce the size of the region where we fit the RS, or make it more accurate in the regions where the optimum is likely to reside. Response Surface techniques using either polynomials or and Neural Network (NN) methods offer designers alternatives to conduct design optimization. The RS technique employs statistical and numerical techniques to establish the relationship between design variables and objective/constraint functions, typically using polynomials. In this study, we aim at addressing issues related to the following questions: (1) How to identify outliers associated with a given RS representation and improve the RS model via appropriate treatments? (2) How to focus on selected design data so that RS can give better performance in regions critical to design optimization? (3) How to combine NN and polynomial techniques for improving the accuracy of the RS model?

Papila, Nilay↗

NASA NTRSDate not supplied

Advancement of the General Aviation Synthesis Program Using Python to Enable Optimization-Based Hybrid-Propulsion Aircraft Design

In support of the Electrified Powertrain Flight Demonstrator and Advanced Air Transport Technologies projects at NASA, a new tool has been developed at NASA’s Ames and Glenn Research Centers to enable coupled engine and airframe optimization and analysis. The new tool combines the engineering-level analysis methods and empirical models of the FORTRAN General Aviation Synthesis Program (GASP) with the Python-based OpenMDAO framework to provide a modular framework for efficient gradient-based optimization with the aim of incorporating new subsystem models for unconventional configurations. The tool has been verified against GASP analyses of several aircraft models and mission formulations. Preliminary efforts have been made to integrate pyCycle, a thermodynamic cycle analysis tool, to enable simultaneous optimization of hybrid propulsion system and vehicle parameters while taking full mission performance and constraints into account. This will improve current capabilities to assess impacts of electrified powertrain technologies on future aircraft designs.

Kenneth R. Lyons↗

NASA NTRSDate not supplied

Advancement of the General Aviation Synthesis Program Using Python to Enable Optimization-Based Hybrid-Propulsion Aircraft Design

In support of the Electrified Powertrain Flight Demonstrator and Advanced Air Transport Technologies projects at NASA, a new tool has been developed at NASA's Ames and Glenn Research Centers to enable coupled engine and airframe optimization and analysis. The new tool combines the engineering-level analysis methods and empirical models of the FORTRAN General Aviation Synthesis Program (GASP) with the Python-based OpenMDAO framework to provide a modular framework for efficient gradient-based optimization with the aim of incorporating new subsystem models for unconventional configurations. The tool has been verified against GASP analyses of several aircraft models and mission formulations. Preliminary efforts have been made to integrate pyCycle, a thermodynamic cycle analysis tool, to enable simultaneous optimization of hybrid propulsion system and vehicle parameters while taking full mission performance and constraints into account. This will improve current capabilities to assess impacts of electrified powertrain technologies on future aircraft designs.

Kenneth R Lyons↗

DOE OSTI2024

Differentiable Simulation of a Liquid Argon Time Projection Chamber

Liquid argon time projection chambers (LArTPCs) are widely used in particle detection for their tracking and calorimetric capabilities. The particle physics community actively builds and improves high-quality simulators for such detectors in order to develop physics analyses in a realistic setting. The ability of these simulators to mimic real, measured data is limited by the modeling of the physical detectors used for data collection. This modeling can be improved by performing dedicated calibration measurements. Conventional approaches calibrate individual detector parameters or processes one at a time. However, the impact of detector processes is entangled, making this a poor description of the underlying physics. We introduce a differentiable simulator that enables a gradient-based optimization, allowing for the first time a simultaneous calibration of all detector parameters. We describe the procedure of making a differentiable simulator, highlighting the challenges of retaining the physics quality of the standard, non-differentiable version while providing meaningful gradient information. We further discuss the advantages and drawbacks of using our differentiable simulator for calibration. Finally, we provide a starting point for extensions to our approach, including applications of the differentiable simulator to physics analysis pipelines.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

An error-in-constitutive equations strategy for topology optimization for frequency-domain dynamics

This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. In this work, we propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topology optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.

42 ENGINEERING↗