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At least 289 records · Page 16

Adjusting Surfaces Of Large Antenna Reflectors

New approach more effective than traditional rms-surface-distortion approach. Optimization procedure for control of shape of reflector of large space antenna (LSA). Main feature is shape-controlling mathematical mechanism driven by need to satisfy explicit EM design requirements. Uses standard finite-element structural analysis, aperture-integration EM analysis, and constrained optimization techniques to predict set of actuator inputs that improves performance of antenna while minimizing applied control effort. Procedure applicable to wide variety of LSA concepts.

Padula, Sharon L.↗

Configuration-shape-size optimization of space structures by material redistribution

This project investigates the configuration-shape-size optimization (CSSO) of orbiting and planetary space structures. The project embodies three phases. In the first one the material-removal CSSO method introduced by Kikuchi and Bendsoe (KB) is further developed to gain understanding of finite element homogenization techniques as well as associated constrained optimization algorithms that must carry along a very large number (thousands) of design variables. In the CSSO-KB method an optimal structure is 'carved out' of a design domain initially filled with finite elements, by allowing perforations (microholes) to develop, grow and merge. The second phase involves 'materialization' of space structures from the void, thus reversing the carving process. The third phase involves analysis of these structures for construction and operational constraints, with emphasis in packaging and deployment. The present paper describes progress in selected areas of the first project phase and the start of the second one.

Vandenbelt, D. N.↗

SENTRA: A Modular Computational Graph Framework for Critical Mineral and Materials Supply Chains: Part I: Network Construction Latent-Quantity Estimation, and Temporal Graph Forecasting

Global supply chains for critical minerals and materials are complex, evolving networks of countries, products, production stages, and trade relationships. Existing analytical approaches are limited by fragmented data and static network representations that do not capture the dynamic production dependencies linking raw materials, intermediate products, and final goods across multiple countries. Trade and production statistics provide only a partial view of domestic production, inventories, and material flows, making it difficult to identify indirect sourcing pathways, hidden dependencies, and embedded foreign exposures. This paper introduces the Supply Chain Exposure Network Tracking and Risk Assessment (SENTRA) framework, a modular graph-based computational framework for constructing, analyzing, and forecasting dynamic supply chain networks. As the first paper in a three-part methodological series, it establishes the computational foundation of SENTRA by constructing a temporal attributed multi-relational graph whose nodes represent product–country pairs and whose edges encode observed trade and within-country value-chain relationships. Statistical estimation and constrained optimization recover latent production, final demand, and product input dependency coefficients while enforcing economic accounting constraints. Graph-derived exposure measures quantify direct, transshipment, value-chain, and multi-hop supply chain dependencies independently of the forecasting model. A temporal graph forecasting architecture based on a relational graph neural network then forecasts the evolution of the graph under mass-balance constraints with distribution-free conformal uncertainty quantification. Validation on the global aluminum supply chain shows that the learned graph representations recover economically meaningful supply chain structure, accurately forecast out-of-sample trade relationships, and produce well-calibrated prediction intervals. Subsequent papers apply this computational foundation to exposure assessment, disruption analysis, and scenario-based policy analysis, and extend the framework to multimaterial supply chain modeling and decision support.

36 MATERIALS SCIENCE↗

CONMIN: A FORTRAN program for constrained function minimization: User's manual

CONMIN is a FORTRAN program, in subroutine form, for the solution of linear or nonlinear constrained optimization problems. The basic optimization algorithm is the Method of Feasible Directions. The user must provide a main calling program and an external routine to evaluate the objective and constraint functions and to provide gradient information. If analytic gradients of the objective or constraint functions are not available, this information is calculated by finite difference. While the program is intended primarily for efficient solution of constrained problems, unconstrained function minimization problems may also be solved, and the conjugate direction method of Fletcher and Reeves is used for this purpose. This manual describes the use of CONMIN and defines all necessary parameters. Sufficient information is provided so that the program can be used without special knowledge of optimization techniques. Sample problems are included to help the user become familiar with CONMIN and to make the program operational.

Vanderplaats, G. N.↗

On Managing the Use of Surrogates in General Nonlinear Optimization and MDO

This paper is concerned with a trust region approximation management framework (AMF) for solving the nonlinear programming problem in general and multidisciplinary optimization problems in particular The intent of the AMF methodology is to facilitate the solution of optimization problems with high-fidelity models. While such models are designed to approximate the physical phenomena they describe to a high degree of accuracy, their use in a repetitive procedure, for example, iterations of an optimization or a search algorithm, make such use prohibitively expensive. An improvement in design with lower-fidelity, cheaper models, however, does not guarantee a corresponding improvement for the higher-fidelity problem. The AMF methodology proposed here is based on a class of multilevel methods for constrained optimization and is designed to manage the use of variable-fidelity approximations or models in a systematic way that assures convergence to critical points of the original high-fidelity problem.

Alexandrov, Natalia M.↗

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

Lewis, Robert Michael↗

Design of optimally normal minimum gain controllers by continuation method

A measure of the departure from normality is investigated for system robustness. An attractive feature of the normality index is its simplicity for pole placement designs. To allow a tradeoff between system robustness and control effort, a cost function consisting of the sum of a norm of weighted gain matrix and a normality index is minimized. First- and second-order necessary conditions for the constrained optimization problem are derived and solved by a Newton-Raphson algorithm imbedded into a one-parameter family of neighboring zero problems. The method presented allows the direct computation of optimal gains in terms of robustness and control effort for pole placement problems.

Lim, K. B.↗

Optimization of Variable-Depth Liner Configurations for Increased Broadband Noise Reduction

This paper employs three acoustic propagation codes to explore variable-depth liner configurations for the NASA Langley Grazing Flow Impedance Tube (GFIT). The initial study demonstrates that a variable impedance can acceptably be treated as a uniform impedance if the spatial extent over which this variable impedance occurs is less than one-third of a wavelength of the incident sound. A constrained optimization study is used to design a variable-depth liner and to select an optimization metric. It also provides insight regarding how much attenuation can be achieved with variable-depth liners. Another optimization study is used to design a liner with much finer chamber depth resolution for the Mach 0.0 and 0.3 test conditions. Two liners are designed based on spatial rearrangement of chambers from this liner to determine whether the order is critical. Propagation code predictions suggest this is not the case. Both liners are fabricated via additive manufacturing and tested in the GFIT for the Mach 0.0 condition. Predicted and measured attenuations compare favorably across the full frequency range. These results clearly suggest that the chambers can be arranged in any order, thus offering the potential for innovative liner designs to minimize depth and weight.

Jones, M. G.↗

Digital robust active control law synthesis for large order flexible structure using parameter optimization

A generic procedure for the parameter optimization of a digital control law for a large-order flexible flight vehicle or large space structure modeled as a sampled data system is presented. A linear quadratic Guassian type cost function was minimized, while satisfying a set of constraints on the steady-state rms values of selected design responses, using a constrained optimization technique to meet multiple design requirements. Analytical expressions for the gradients of the cost function and the design constraints on mean square responses with respect to the control law design variables are presented.

Mukhopadhyay, V.↗

Design of low-speed airfoils by numerical optimization

A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on a gradient algorithm coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full-potential equation. The analysis program is valid for both incompressible and compressible flow, thereby making optimum design of high-speed, shock-free airfoils possible. Results are presented for the following three constrained optimization problems at fixed angle of attack and Mach number: (1) adverse pressure-gradient minimization, (2) pitching-moment minimization; and (3) lift maximization. All three optimization problems were studied with various aerodynamic and geometric constraints.

Hicks, R. M.↗

A zonal computational procedure adapted to the optimization of two-dimensional thrust augmentor inlets

A viscous-inviscid interaction methodology based on a zonal description of the flowfield is developed as a mean of predicting the performance of two-dimensional thrust augmenting ejectors. An inviscid zone comprising the irrotational flow about the device is patched together with a viscous zone containing the turbulent mixing flow. The inviscid region is computed by a higher order panel method, while an integral method is used for the description of the viscous part. A non-linear, constrained optimization study is undertaken for the design of the inlet region. In this study, the viscous-inviscid analysis is complemented with a boundary layer calculation to account for flow separation from the walls of the inlet region. The thrust-based Reynolds number as well as the free stream velocity are shown to be important parameters in the design of a thrust augmentor inlet.

Lund, T. S.↗

Computationally Efficient Decompositions of Oblique Projection Matrices

Oblique projection matrices arise in problems in weighted least squares, signal processing, and optimization. While these matrices can be potentially very large, their low-rank structure can be exploited for efficient computation. Here, we propose fast and scalable algorithms for computing their eigendecomposition and singular value decomposition (SVD). Numerical experiments that compare our proposed approaches to existing methods, including randomized SVD, are presented. In addition, we test their accuracy on linear systems from equality constrained optimization problems.

97 MATHEMATICS AND COMPUTING↗

A data-driven peridynamic continuum model for upscaling molecular dynamics

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials’ behavior, we propose a learning framework to extract, from MD data, an optimal Linear Peridynamic Solid (LPS) model as a surrogate for MD displacements. To maximize the accuracy of the learnt model we allow the peridynamic influence function to be partially negative, while preserving the well-posedness of the resulting model. To achieve this, we provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions and develop a constrained optimization algorithm that minimizes the equation residual while enforcing such solvability conditions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our two-dimensional tests show the robustness of the proposed algorithm on validation data sets that include thermal noise, different domain shapes and external loadings, and discretizations substantially different from the ones used for training.

homogenization↗

On optimal infinite impulse response edge detection filters

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Sarkar, Sudeep↗

One Stomatal Model to Rule Them All? Toward Improved Representation of Carbon and Water Exchange in Global Models

Abstract Stomatal conductance schemes that optimize with respect to photosynthetic and hydraulic functions have been proposed to address biases in land‐surface model (LSM) simulations during drought. However, systematic evaluations of both optimality‐based and alternative empirical formulations for coupling carbon and water fluxes are lacking. Here, we embed 12 empirical and optimization approaches within a LSM framework. We use theoretical model experiments to explore parameter identifiability and understand how model behaviors differ in response to abiotic changes. We also evaluate the models against leaf‐level observations of gas‐exchange and hydraulic variables, from xeric to wet forest/woody species spanning a mean annual precipitation range of 361–3,286 mm yr −1 . We find that models differ in how easily parameterized they are, due to: (a) poorly constrained optimality criteria (i.e., resulting in multiple solutions), (b) low influence parameters, (c) sensitivities to environmental drivers. In both the idealized experiments and compared to observations, sensitivities to variability in environmental drivers do not agree among models. Marked differences arise in sensitivities to soil moisture (soil water potential) and vapor pressure deficit. For example, stomatal closure rates at high vapor pressure deficit range between −45% and +70% of those observed. Although over half the new generation of stomatal schemes perform to a similar standard compared to observations of leaf‐gas exchange, two models do so through large biases in simulated leaf water potential (up to 11 MPa). Our results provide guidance for LSM development, by highlighting key areas in need for additional experimentation and theory, and by constraining currently viable stomatal hypotheses.

54 ENVIRONMENTAL SCIENCES↗

Investigation of Optimal Control Allocation for Gust Load Alleviation in Flight Control

Advances in sensors and avionics computation power suggest real-time structural load measurements could be used in flight control systems for improved safety and performance. A conventional transport flight control system determines the moments necessary to meet the pilot's command, while rejecting disturbances and maintaining stability of the aircraft. Control allocation is the problem of converting these desired moments into control effector commands. In this paper, a framework is proposed to incorporate real-time structural load feedback and structural load constraints in the control allocator. Constrained optimal control allocation can be used to achieve desired moments without exceeding specified limits on monitored load points. Minimization of structural loads by the control allocator is used to alleviate gust loads. The framework to incorporate structural loads in the flight control system and an optimal control allocation algorithm will be described and then demonstrated on a nonlinear simulation of a generic transport aircraft with flight dynamics and static structural loads.

Frost, Susan A.↗

Level-Set Topology Optimization with Aeroelastic Constraints

Level-set topology optimization is used to design a wing considering skin buckling under static aeroelastic trim loading, as well as dynamic aeroelastic stability (flutter). The level-set function is defined over the entire 3D volume of a transport aircraft wing box. Therefore, the approach is not limited by any predefined structure and can explore novel configurations. The Sequential Linear Programming (SLP) level-set method is used to solve the constrained optimization problems. The proposed method is demonstrated using three problems with mass, linear buckling and flutter objective and/or constraints. A constraint aggregation method is used to handle multiple buckling constraints in the wing skins. A continuous flutter constraint formulation is used to handle difficulties arising from discontinuities in the design space caused by a switching of the critical flutter mode.

Dunning, Peter D.↗

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.

Hughes, Steven P.↗