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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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

The algebra of supertraces for 2+1 super de Sitter gravity

The algebra of the observables for 2+1 super de Sitter gravity, for one genus of the spatial surface is calculated. The algebra turns out to be an infinite Lie algebra subject to non-linear constraints. The constraints are solved explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which is referred to as a 'central extension' of the quantum algebra SU(2)q.

Urrutia, L. F.↗
NASA NTRS2014

Compositional Solution Space Quantification for Probabilistic Software Analysis

Probabilistic software analysis aims at quantifying how likely a target event is to occur during program execution. Current approaches rely on symbolic execution to identify the conditions to reach the target event and try to quantify the fraction of the input domain satisfying these conditions. Precise quantification is usually limited to linear constraints, while only approximate solutions can be provided in general through statistical approaches. However, statistical approaches may fail to converge to an acceptable accuracy within a reasonable time. We present a compositional statistical approach for the efficient quantification of solution spaces for arbitrarily complex constraints over bounded floating-point domains. The approach leverages interval constraint propagation to improve the accuracy of the estimation by focusing the sampling on the regions of the input domain containing the sought solutions. Preliminary experiments show significant improvement on previous approaches both in results accuracy and analysis time.

Monte Carlo Methods↗
NASA NTRSDate not supplied

Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.

Non-Ordinary State-Based Peridynamics↗
DOE OSTI2023

A Sequential Quadratic Programming Algorithm for Nonsmooth Problems with Upper- \({\boldsymbol{\mathcal{C}^2}}\) Objective

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objective functions is proposed and analyzed. Upper- \({\boldsymbol{\mathcal{C}^2}}\) is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems e.g., recourse of stochastic programming and projection onto closed sets. The algorithm can be viewed as an extension of sequential quadratic programming (SQP) to nonsmooth problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objectives or a simplified bundle method. It is globally convergent with bounded algorithm parameters that are updated with a trust-region criterion. The algorithm handles general smooth constraints through linearization and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. In conclusion, the capabilities of the algorithm are demonstrated by solving both simple upper- \({\boldsymbol{\mathcal{C}^2}}\) problems and a real-world optimal power flow problem used in current power grid industry practices.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Accommodation of practical constraints by a linear programming jet select

An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.

Bergmann, E.↗
NASA NTRS1985

The Construction of Curves and Surfaces Using Numerical Optimization Techniques

Numerical optimization techniques are playing an increasing role in curve and surface construction. Often difficult problems in curve and surface construction, especially when some aspect of shape control is involved, can be phrased as a constrained optimization problem. Four such classes of problems are explored: parametric curve fitting with non-linear shape constraints; explicit surface fitting with linear shape constraints; surface fitting to scattered data giving rise to ill-posed problems; finally, variable knot problems. In each of these problems there is a nonlinear aspect: either the shape of the curve or surface is important for manufacturing or engineering reasons or the shape affects the convergence of numerical algorithms which use the curve or surface or the placement of knots affects the accuracy of the fits. In all cases the class of functions used is that of parametric spline curves and tensor or direct product spline surfaces. The reason for choosing this class is that splines provide flexible models that are easily evaluated and stored. Furthermore, the B-spline representation of splines leads to convenient expressions for shape control over regions.

Ferguson, D. R.↗
NASA NTRS1994

Magnetotail dynamics under isobaric constraints

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Birn, Joachim↗
NASA NTRS1985

A sequential linear optimization approach for controller design

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

Horta, L. G.↗
NASA NTRSDate not supplied

Gradient-Based Optimization of the Common Research Model Wing Subject to CFD-Based Gust and Flutter Constraints

The linearized frequency-domain method was recently implemented in the stabilized finite element solver in NASA’s FUN3D code. Previous work by the authors used this method for enforcing flutter constraints during gradient-based optimizations. More recently, the solver was expanded to account for continuous (also known as stochastic) gust responses. This paper expands on recent Common Research Model wing optimization work, which demonstrated gradient-based optimization with flutter and stochastic gust constraints, among others. While that work utilized FUN3D for static aeroelastic solutions but relied on doublet lattice aerodynamics for gust and flutter responses, the present work replaces these unsteady aerodynamic analyses with those of FUN3D’s linearized frequency-domain solver. With analytic derivatives available, gradient-based optimization is performed through the use of the OpenMDAO/MPhys libraries with over 700 shape, structural, and aerodynamic design variables and over 10 nonlinear constraints. Comparisons of analysis results and optimized designs are made between doublet lattice and linearized frequency-domain solutions.

aeroelasticity↗
DOE OSTI2024

Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends

Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, in this work, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τ d,R for rings of length N R blended with linear chains of length N l to scale as τ d,R ~ N$^2_R$N$^{3.4}_L$.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

Order reduction in linear state estimation under performance constraints

The design and analysis of minimal-order state estimators for possibly time-varying linear systems, under constraints on the maximal allowable mean-square error, are considered. A global lower bound on the optimal error is derived, along with a lower bound on the minimal estimator order, needed for meeting the performance constraint. The ideal reduced-order estimator which satisfies the lower bound is derived, along with conditions for its realizability. When the ideal estimator is not realizable, its structure forms a suboptimal estimator, which maintains, in some sense, a local optimality property and is called the pseudoideal estimator. The mean-square error of the pseudoideal estimator defines upper bounds on the optimal error and on the estimator order needed for meeting the performance constraint. The lower and the upper bounds on the order define a reduced search set for the design problem. When the distance between the ideal and the pseudoideal estimators is sufficiently small in a certain numerical sense, the pseudoideal estimator may be considered optimal for practical purposes.

Baram, Yoram↗
NASA NTRS1992

Stacking sequence optimization of simply supported laminates with stability and strain constraints

An integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented. The design variables that define the stacking sequence of the laminate are ply-identity zero-one integers. The buckling constraint is linear in terms of the ply-identity design variables, but strains are nonlinear functions of these variables. A linear approximation is developed for the strain constraints so that the problem can be solved by sequential linearization using the branch and bound algorithm. Examples of graphite-epoxy plates under biaxial compression are presented. Optimum stacking sequences obtained using the linear approximation are compared with global optimum designs obtained using a genetic search procedure.

Nagendra, S.↗
DOE OSTI2025

Optimal Network Reconfiguration and Scheduling With Hardware-in-the-Loop Validation for Improved Microgrid Resilience

With the increased occurrence of various major extreme weather events, power outages and prompt power system restorations have recently drawn more attention to the resilience and recovery of power systems. From the perspective of a more resilient power delivery at the distribution grid, system restoration using network topology reconfiguration together with optimal scheduling of distributed energy resources are adopted in this paper. The proposed optimization model aims at minimizing the total load shedding cost and other operational costs, in which linearized topological constraints borrowed from graph theory and linearized DistFlow models are respectively used to maintain the radial network topology and power flow balance after system contingencies. To demonstrate the applicability of the proposed strategy, a real-world case study of a networked three-microgrid system in Adjuntas, Puerto Rico, is used with the consideration of different independent/interconnected microgrid scenarios, contingencies, and fairness settings. Furthermore, hardware-in-the-loop testing is conducted for the same three-microgrid network, where the closely matched results with the simulated ones have validated the effectiveness of the proposed restoration strategy, which is now ready to move one step forward towards field deployment. Finally, to test the proposed restoration strategy in a larger networked system, the modified IEEE-33 bus test distribution system is considered, and the results show a more resilient power delivery for critical loads under three and four line outages.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Substation-Level Grid Topology Optimization Using Bus Splitting

Operations of substation circuit breakers are important for maintenance needs and topology reconfiguration in power systems. Bus splitting is one type of topology change where the two bus bars at a substation can become electrically disconnected under certain actions of circuit breakers. Because these events involve detailed substation modeling, they are typically not considered in routine power system operation and control. In this paper, an improved substation-level topology optimization framework is developed by expanding traditional line switching decisions by breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bilinear terms in the resultant optimization problem to linear inequality constraints. Thus, a tractable mixed-integer linear program reformulation is attained that allows for efficient solutions in real-time operations. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the computational performance and economic benefits of the proposed topology optimization approach.

bus split↗
DOE OSTI2020

Incorporating physical constraints into Gaussian process surrogate models (LDRD Project Summary)

This report summarizes work done under the Laboratory Directed Research and Development (LDRD) project titled "Incorporating physical constraints into Gaussian process surrogate models?' In this project, we explored a variety of strategies for constraint implementations. We considered bound constraints, monotonicity and related convexity constraints, Gaussian processes which are constrained to satisfy linear operator constraints which represent physical laws expressed as partial differential equations, and intrinsic boundary condition constraints. We wrote three papers and are currently finishing two others. We developed initial software implementations for some approaches. This report summarizes the work done under this LDRD.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Optimization of composite box-beam structures including effects of subcomponent interactions

Minimum mass designs are obtained for a simple box beam structure subject to bending, torque and combined bending/torque load cases. These designs are obtained subject to point strain and linear buckling constraints. The present work differs from previous efforts in that special attention is payed to including the effects of subcomponent panel interaction in the optimal design process. Two different approaches are used to impose the buckling constraints. When the global approach is used, buckling constraints are imposed on the global structure via a linear eigenvalue analysis. This approach allows the subcomponent panels to interact in a realistic manner. The results obtained using this approach are compared to results obtained using a traditional, less expensive approach, called the local approach. When the local approach is used, in-plane loads are extracted from the global model and used to impose buckling constraints on each subcomponent panel individually. In the global cases, it is found that there can be significant interaction between skin, spar, and rib design variables. This coupling is weak or nonexistent in the local designs. It is determined that weight savings of up to 7% may be obtained by using the global approach instead of the local approach to design these structures. Several of the designs obtained using the linear buckling analysis are subjected to a geometrically nonlinear analysis. For the designs which were subjected to bending loads, the innermost rib panel begins to collapse at less than half the intended design load and in a mode different from that predicted by linear analysis. The discrepancy between the predicted linear and nonlinear responses is attributed to the effects of the nonlinear rib crushing load, and the parameter which controls this rib collapse failure mode is shown to be the rib thickness. The rib collapse failure mode may be avoided by increasing the rib thickness above the value obtained from the (linear analysis based) optimizer. It is concluded that it would be necessary to include geometric nonlinearities in the design optimization process if the true optimum in this case were to be found.

Ragon, Scott A.↗
NASA NTRS1978

Design and analysis of supersonic aircraft

Integrated system of computer programs, developed for design and analysis of supersonic configurations, uses linearized-theory methods to calculate surface pressures and uses supersonic area-rule concepts in combination with linearized theory to calculate aerodynamic force coefficients. Programs include constraints on linear theory methods to provide physical realism. Package proves useful for any type of supersonic configuration.

Coleman, J. L.↗