Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear 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.

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

At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

Banks, H. T.↗
NASA NTRS2009

Direct Multiple Shooting Optimization with Variable Problem Parameters

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

Whitley, Ryan J.↗
DOE OSTI2015

A time-parallel method for the solution of PDE-constrained optimization problems

We study a time-parallel approach to solving quadratic optimization problems with linear time-dependent partial differential equation (PDE) constraints. These problems arise in formulations of optimal control, optimal design and inverse problems that are governed by parabolic PDE models. They may also arise as subproblems in algorithms for the solution of optimization problems with nonlinear time-dependent PDE constraints, e.g., in sequential quadratic programming methods. We apply a piecewise linear finite element discretization in space to the PDE constraint, followed by the Crank-Nicolson discretization in time. The objective function is discretized using finite elements in space and the trapezoidal rule in time. At this point in the discretization, auxiliary state variables are introduced at each discrete time interval, with the goal to enable: (i) a decoupling in time; and (ii) a fixed-point iteration to recover the solution of the discrete optimality system. The fixed-point iterative schemes can be used either as preconditioners for Krylov subspace methods or as smoothers for multigrid (in time) schemes. We present promising numerical results for both use cases.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Three-dimensional Finite Element Formulation and Scalable Domain Decomposition for High Fidelity Rotor Dynamic Analysis

This paper has two objectives. The first objective is to formulate a 3-dimensional Finite Element Model for the dynamic analysis of helicopter rotor blades. The second objective is to implement and analyze a dual-primal iterative substructuring based Krylov solver, that is parallel and scalable, for the solution of the 3-D FEM analysis. The numerical and parallel scalability of the solver is studied using two prototype problems - one for ideal hover (symmetric) and one for a transient forward flight (non-symmetric) - both carried out on up to 48 processors. In both hover and forward flight conditions, a perfect linear speed-up is observed, for a given problem size, up to the point of substructure optimality. Substructure optimality and the linear parallel speed-up range are both shown to depend on the problem size as well as on the selection of the coarse problem. With a larger problem size, linear speed-up is restored up to the new substructure optimality. The solver also scales with problem size - even though this conclusion is premature given the small prototype grids considered in this study.

Datta, Anubhav↗
DOE OSTI2024

Adaptive Power Flow Approximations With Second-Order Sensitivity Insights

The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these challenges, recent research has proposed adaptive power flow linearizations that aim to achieve accuracy over wide operating ranges. The accuracy of these approximations inherently depends on the curvature of the power flow equations within these ranges, which necessitates considering second-order sensitivities. In this paper, we leverage second-order sensitivities to both analyze and improve power flow approximations. We evaluate the curvature across broad operational ranges and subsequently utilize this information to inform the computation of various sample-based power flow approximation techniques. Additionally, we leverage second-order sensitivities to guide the development of rational approximations that yield linear constraints in optimization problems. In conclusion, this approach is extended to enhance accuracy beyond the limitations of linear functions across varied operational scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

WEC-Sim Modeling of Laminar Scientific's Patented Seesaw Wave Energy Converter: Preprint

Laminar Scientific's patented seesaw wave energy converter was modeled in WEC-Sim to predict performance. The device operates by utilizing ocean surface waves to rotate a truss in pitch about a pivot. The pivot is located at the top of two pylons, which are embedded in the seafloor. The seesaw has a float on either end, and the buoyancy forces from each float cause the system to rise or fall with passing waves. Device performance relies upon seesaw length and ocean wavelength creating an antiphase effect. The seesaw truss has an adjustable length intended to achieve this effect. The operation method enforces a narrow band of wavelengths which induce the largest rotational motion from the device. The hydrodynamic analysis of the device was performed using Capytaine, and the results confirmed that the device operates best in a narrow frequency band. Four float-to-float spacing cases and three pylon radii were examined. The hydrodynamic results indicate a match between the model and the physical expectations for the device, and that varying the pylon radii by 0.1-m increments for three instances creates minimal changes in hydrodynamic properties. Power matrices for three float spacing cases of the device were simulated with Joint North Sea Wave Project spectra waves and optimal power take-off damping in WEC-Sim. The maximum average power production for the 15-m spacing case was 14.1 kW with a 5.0-s peak wave period and 4-m significant wave heights. Plots of capture-width ratios indicated that the device performance was linear and confirmed that the device is optimal in a narrow frequency band. The maximum percentage of the available wave power produced by the 15-m device was approximately 16%. Simulations of the device in regular waves were used to produce plots of average power compared to a ratio of float spacing to wavelength. These plots indicate that the power production is maximized at a ratio of 0.5, and further confirm that the device has a narrow frequency response. The device was simulated at an example field location, where the device produced an annual average power rating of 1.6 kW given an average omnidirectional wave climate of 10.3 kW m-1 and an optimal, linearized power take-off model. While the maximum predicted device performance is reliant upon a narrow band of wave frequencies, the conducted analysis provides an opportunity to improve device design prior to prototyping and testing. Modifying the design to respond to a broader frequency range would improve device performance.

numerical modeling↗
DOE OSTI2017

Optimal current profile control for enhanced repeatability of L-mode and H-mode discharges in DIII-D

In this work, model-based control techniques are used to obtain target current profiles in low-confinement-mode (L-mode) as well as high-confinement-mode (H-mode) DIII-D discharges. The control problem is formulated as a trajectory optimization problem to search for a feasible path from the expected initial condition to the desired target. The result comprises a sequence of feedforward (open-loop) control requests and a corresponding state evolution from the initial condition to the desired target. On top of this optimal feedforward control sequence a feedback (closed-loop) controller based on a linearized model and optimal control design techniques is added to track the desired state evolution. Furthermore, the effectiveness of the control approach is demonstrated with experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Hanks, Brantley R.↗
NASA NTRS1973

On optimal modeling of systems.

A procedure for modeling a linear system by an optimal finite-dimensional approximation is developed on the basis of Sard's (1967) generalized spline. Error bounds are given, and the application of the procedure is illustrated by two presented examples. The procedure may be employed, not only in the modeling of conventional lumped-parameter and distributed-parameter continuous dynamical systems, but also in mathematical operations such as those involved in pattern recognition and picture enhancement problems.

De Figueiredo, R. J. P.↗
NASA NTRS1990

End-point controller design for an experimental two-link flexible manipulator using convex optimization

Recent results in linear controller design are used to design an end-point controller for an experimental two-link flexible manipulator. A nominal 14-state linear-quadratic-Gaussian (LQG) controller was augmented with a 528-tap finite-impulse-response (FIR) filter designed using convex optimization techniques. The resulting 278-state controller produced improved end-point trajectory tracking and disturbance rejection in simulation and experimentally in real time.

Oakley, Celia M.↗
NASA NTRS1989

Guidance and Control strategies for aerospace vehicles

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Hibey, J. L.↗
DOE OSTI2023

Mitigation-Aware Bidding Strategies in Electricity Markets

Market power exercise in the electricity markets distorts market prices and diminishes social welfare. Many markets have implemented market power mitigation processes to eliminate the impact of such behavior. The design of mitigation mechanisms has a direct influence on investors' profitability and thus mid-/long-term resource adequacy. In order to evaluate the effectiveness of the existing market power mitigation mechanisms, this paper proposes a mitigation-aware strategic bidding model and studies the bidding strategies of the market participants under current practice. The proposed bidding model has a bilevel structure with strategic participant's profit maximization problem in the upper level and the dispatch problem for market operators in the lower level. In particular, the consideration of potential offer mitigation is incorporated as upper-level constraints based on the conduct and impact tests. This bilevel problem is reduced to a single-level mixed-integer linear program using the KKT optimality conditions, duality theory, and linearization. Numerical results illustrate how a strategic player can exercise market power to achieve a higher profit even under the current market power mitigation process and we analyze the social impact that the market power exercise results.

Wu, Yiqian↗
NASA NTRS2008

MACOS Version 3.31

Version 3.31 of Modeling and Analysis for Controlled Optical Systems (MACOS) has been released. MACOS is an easy-to-use computer program for modeling and analyzing the behaviors of a variety of optical systems, including systems that have large, segmented apertures and are aligned with the technology of wavefront sensing and control. Two previous versions were described in "Improved Software for Modeling Controlled Optical Systems" (NPO-19841) NASA Tech Briefs, Vol. 21, No. 12 (December 1997), page 42 and "Optics Program Modified for Multithreaded Parallel Computing" (NPO-40572) NASA Tech Briefs, Vol. 30, No. 1 (January 2006) page 13a. The present version incorporates the following enhancements over prior versions: a) A powerful system-optimization facility includes algorithms for linear, nonlinear, unconstrained, and constrained optimization of optical systems under a variety of settings. b) There is now enhanced capability to perturb optical components individually and on subsystem levels, and to optimize system performance by adjusting selected individual components as well as subsystems. c) Capabilities for modeling a variety of new optical aperture types have been added. d) Effects of multilayer thin-film coats on optical surfaces can now be taken into account when tracing polarized rays. e) Major software-engineering work was performed to make MACOS more reliable, flexible, and manageable for purposes of maintenance and further development.

Redding, David↗
DOE OSTI2019

Novel refractive index sensor based on fiber bragg grating in nano-bore optical fiber

In this paper, we propose a novel refractive index sensor with large dynamic range based on fiber Bragg grating in the nano-bore optical fiber. The spectral responses of grating on the filling index in the bore with different bore diameters and index ranges are numerically studied by the finite element method and coupled mode theory based transmission matrix method. It is found that the Bragg wavelength of grating is sensitive to the filling index in the bore. The influences of bore diameter on the wavelength sensitivity, resolution and dynamic range of the index sensor are analyzed. There exists a trade off between the linear dynamic range and sensitivity of index when the bore diameter varies. The optimized wavelength sensitivity and resolution of filling index are 53.6923 nm/index unit and 9.3123 × 10{sup −6} index under a linear index range of 1.0–1.4 using 2 µm bore diameter. The optimized linear dynamic range of index is 1.0–1.48 with wavelength sensitivity of 13.3056 nm/index unit and resolution of 3.7578 × 10{sup −5} index using 1 µm bore diameter. Our proposed index sensor has the technical advantages of simple all-fiber structure, large index range, and potential capability to synchronously detect index, temperature and strain.

36 MATERIALS SCIENCE↗
DOE OSTI2017

The impacts of oceanic deep temperature perturbations in the North Atlantic on decadal climate variability and predictability

Decadal climate predictability in the North Atlantic is largely related to ocean low frequency variability, whose sensitivity to initial conditions is not very well understood. Recently, three-dimensional oceanic temperature anomalies optimally perturbing the North Atlantic Mean Temperature (NAMT) have been computed via an optimization procedure using a linear adjoint to a realistic ocean general circulation model. The spatial pattern of the identified perturbations, localized in the North Atlantic, has the largest magnitude between 1000 and 4000 m depth. In the present study, the impacts of these perturbations on NAMT, on the Atlantic meridional overturning circulation (AMOC), and on climate in general are investigated in a global coupled model that uses the same ocean model as was used to compute the three-dimensional optimal perturbations. In the coupled model, these perturbations induce AMOC and NAMT anomalies peaking after 5 and 10 years, respectively, generally consistent with the ocean-only linear predictions. To further understand their impact, their magnitude was varied in a broad range. For initial perturbations with a magnitude comparable to the internal variability of the coupled model, the model response exhibits a strong signature in sea surface temperature and precipitation over North America and the Sahel region. The existence and impacts of these ocean perturbations have important implications for decadal prediction: they can be seen either as a source of predictability or uncertainty, depending on whether the current observing system can detect them or not. In fact, comparing the magnitude of the imposed perturbations with the uncertainty of available ocean observations such as Argo data or ocean state estimates suggests that only the largest perturbations used in this study could be detectable. This highlights the importance for decadal climate prediction of accurate ocean density initialisation in the North Atlantic at intermediate and greater depths.

54 ENVIRONMENTAL SCIENCES↗