Search NASA⌕ Search

SEARCH · Search NASA

Results for “numerical 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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Shape optimization and CAD

Structural optimization has attracted the attention since the days of Galileo. Olhoff and Taylor have produced an excellent overview of the classical research within this field. However, the interest in structural optimization has increased greatly during the last decade due to the advent of reliable general numerical analysis methods and the computer power necessary to use them efficiently. This has created the possibility of developing general numerical systems for shape optimization. Several authors, eg., Esping; Braibant & Fleury; Bennet & Botkin; Botkin, Yang, and Bennet; and Stanton have published practical and successful applications of general optimization systems. Ding and Homlein have produced extensive overviews of available systems. Furthermore, a number of commercial optimization systems based on well-established finite element codes have been introduced. Systems like ANSYS, IDEAS, OASIS, and NISAOPT are widely known examples. In parallel to this development, the technology of computer aided design (CAD) has gained a large influence on the design process of mechanical engineering. The CAD technology has already lived through a rapid development driven by the drastically growing capabilities of digital computers. However, the systems of today are still considered as being only the first generation of a long row of computer integrated manufacturing (CIM) systems. These systems to come will offer an integrated environment for design, analysis, and fabrication of products of almost any character. Thus, the CAD system could be regarded as simply a database for geometrical information equipped with a number of tools with the purpose of helping the user in the design process. Among these tools are facilities for structural analysis and optimization as well as present standard CAD features like drawing, modeling, and visualization tools. The state of the art of structural optimization is that a large amount of mathematical and mechanical techniques are available for the solution of single problems. By implementing collections of the available techniques into general software systems, operational environments for structural optimization have been created. The forthcoming years must bring solutions to the problem of integrating such systems into more general design environments. The result of this work should be CAD systems for rational design in which structural optimization is one important design tool among many others.

Rasmussen, John↗
NASA NTRS2015

Numerical Simulations of Thermographic Responses in Composites

Numerical simulations of thermographic responses in composite materials have been a useful for evaluating and optimizing thermographic analysis techniques. Numerical solutions are particularly beneficial for thermographic techniques, since the fabrication of specimens with realistic flaws is difficult. Simulations are presented with different ply layups that incorporated the anisotropic thermal properties that exist in each ply. The results are compared to analytical series solutions and thermal measurements on composites with flat bottom holes and delaminations.

Winfree, William P.↗
NASA NTRS2022

Wind-Optimal Lateral Trajectories for a Multirotor Aircraft in Urban Air Mobility

The primary motivation for this paper is to quantify the operational benefits (energy consumption and flight duration) of flying wind-optimal lateral trajectories for short flights (less than 60 miles) anticipated in the urban environment. The optimal control model presented includes a wind model for quantifying the effect of wind on the lateral trajectory. The optimal control problem is numerically solved using the direct collocation method. Energy consumption and flight duration flying wind-optimal lateral trajectories are compared with corresponding values obtained flying great-circle paths between the same origin and destination pairs to determine the operational benefits of wind-optimal routing for short flights. The flight duration results for different scenarios are validated using a simulation tool designed and developed at NASA for exploring advanced air traffic management concepts. This research study suggests that for short flights in an urban environment, operational benefits of the wind-optimal lateral trajectories over the corresponding great-circle trajectories in terms of energy consumption and flight duration per flight are dependent on: i) wind field’s spatial variability, ii) wind magnitude, iii) the direction of route relative to the wind field, and iv) cruise segment length. The operational benefits observed in realistic flyable wind scenarios are less than 2.5%; these could be translated to an equivalent of a maximum of 2 min of cruise flight duration savings in the urban air mobility environment. As expected, headwinds and tailwinds along the flight route most significantly impact energy consumption and flight duration.

Wind-Optimal Trajectory, Lateral Path, Urban Air M↗
NASA NTRS1990

Numerical evaluation of the performance of active noise control systems

This paper presents a generalized numerical technique for evaluating the optimal performance of active noise controllers. In this technique, the indirect BEM numerical procedures are used to derive the active noise controllers for optimal control of enclosed harmonic sound fields where the strength of the noise sources or the description of the enclosure boundary may not be known. The performance prediction for a single-input single-output system is presented, together with the analysis of the stability and observability of an active noise-control system employing detectors. The numerical procedures presented can be used for the design of both the physical configuration and the electronic components of the optimal active noise controller.

Mollo, C. G.↗
DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗
NASA NTRS1995

Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme

Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.

Lee, Duck-Joo↗
NASA NTRS1996

A wavelet-optimized, very high order adaptive grid and order numerical method

Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis.

Jameson, Leland↗
NASA NTRS2000

Annual Research Briefs - 2000: Center for Turbulence Research

This report contains the 2000 annual progress reports of the postdoctoral Fellows and visiting scholars of the Center for Turbulence Research (CTR). It summarizes the research efforts undertaken under the core CTR program. Last year, CTR sponsored sixteen resident Postdoctoral Fellows, nine Research Associates, and two Senior Research Fellows, hosted seven short term visitors, and supported four doctoral students. The Research Associates are supported by the Departments of Defense and Energy. The reports in this volume are divided into five groups. The first group largely consists of the new areas of interest at CTR. It includes efficient algorithms for molecular dynamics, stability in protoplanetary disks, and experimental and numerical applications of evolutionary optimization algorithms for jet flow control. The next group of reports is in experimental, theoretical, and numerical modeling efforts in turbulent combustion. As more challenging computations are attempted, the need for additional theoretical and experimental studies in combustion has emerged. A pacing item for computation of nonpremixed combustion is the prediction of extinction and re-ignition phenomena, which is currently being addressed at CTR. The third group of reports is in the development of accurate and efficient numerical methods, which has always been an important part of CTR's work. This is the tool development part of the program which supports our high fidelity numerical simulations in such areas as turbulence in complex geometries, hypersonics, and acoustics. The final two groups of reports are concerned with LES and RANS prediction methods. There has been significant progress in wall modeling for LES of high Reynolds number turbulence and in validation of the v(exp 2) - f model for industrial applications.

Source record↗
NASA NTRS1989

Robust eigenstructure assignment by a projection method - Applications using multiple optimization criteria

A methodology for robust eigenstructure assignment for multivariable feedback systems is presented. The algorithm is based upon a pole placement technique using projections onto subspaces of admissible eigenvectors. New ideas are introduced to generate target (desired) sets of unitary eigenvectors and determine optimal feasible eigenvectors in a least-square sense. Useful connections are established between the pole-placement by independent modal space control and the method introduced in this paper. A multicriterion optimization algorithm is also presented, which takes efficient advantage of the present eigenstructure assignment method. These developments show significant improvement over an earlier version of this algorithm in both computational cost and accuracy. This optimization process appears to be numerically robust and suitable for high-dimensional multicriterion optimizations; it is especially attractive for computer-aided design of control systems.

Rew, D. W.↗
NASA NTRS1989

A least-squares finite element method for incompressible Navier-Stokes problem

Most finite element schemes for solving the Navier-Stokes equations can be categorized into the Galerkin mixed method and the penalty method. The mixed method leads to a saddle-point problem. In order to guarantee the existence of a solution, the combination of velocity and pressure interpolations requires satisfaction of the Ladyzhenskaya Babuska Brezzi (LBB) consistency condition which precludes the use of equal order interpolations and many seemingly natural pairs of velocity and pressure elements. In a previous paper a least-squares finite element method based on the first order velocity-pressure-vorticity formulation for the Stokes problem was proposed. This method leads to a minimization problem. The choice of combination of elements is thus not subject to the LBB condition. The numerical experiments exhibit the optimal rate of convergence for all variables with equal order interpolations. A theoretical error analysis supports the numerical results. In this paper the least-squares finite element method is extended to solving the incompressible Navier-Stokes problem.

Jiang, Bonan↗
DOE OSTI2024

Enhancement of disposal efficiency for deep geological repositories based on three design factors - Decay heat optimization, increased thermal limit of the buffer and double-layer concept

This study investigates the enhancement of disposal efficiency for deep geological repositories (DGRs) based on three design factors: decay heat optimization, increased thermal limit of the buffer, and double-layer concept using coupled thermo-hydro-mechanical (THM) numerical simulations. Decay heat optimization is achieved by iteratively emplacing spent nuclear fuels having the maximum and minimum decay heat in a canister. Disposal areas can be reduced by 20 % to 40 % compared to the current reference disposal system in Korea (KRS+) in accordance with the combinations of the three design factors, alleviating challenges in site selection for the DGR. This study additionally identifies an optimal layer spacing of 500 m for the double-layer concept in the viewpoint of the buffer temperature, where thermal interaction between the upper and lower layers nearly disappears. However, determining the ultimate disposal and layer spacing requires engineering judgement, considering not only the thermal performance of the DGR but also various factors such as cost and difficulties of the construction and rock mass stability. DGRs designed with an increased thermal limit of the buffer poses a greater probability of rock mass failure around disposal tunnels and deposition holes due to elevated thermal stresses. Densely arranged heat sources for the DGRs with enhanced disposal efficiency lead to larger temperature increase even at the far-field scale, raising a possibility of thermally driven fracture shear activation with associated hydraulic, mechanical, and seismic changes.

58 GEOSCIENCES↗
NASA NTRS1975

Deterministic optimal maneuver strategy for multi-target missions

This paper presents an optimal strategy for making impulsive correction to a multi-target trajectory by a single maneuver. The concept of an optimal maneuver time is introduced. The choice of suitable weighting functions is explored to enable one to properly translate the subjective desire of mission success into an objective cost function whose minimization yields the optimal strategy. It is shown that a number of strategies previously formulated are derivable from one general expression. A number of other interesting properties of the optimal strategy are described. Numerical results are presented for a typical two-target mission. It is shown that the strategy formulated is optimal. For some perturbations, there exists an optimal maneuver time different from the time of initiation of the perturbation. That is, the physical properties of the trajectory can be exploited to select the optimal time of making a corrective maneuver.

Dwivedi, N. P.↗
NASA NTRS1971

Applications of generalized inverses to estimation in dynamic systems.

Generalized matrix inverses are used to obtain an estimation procedure for estimation of the state vector of a dynamic system. This sequential procedure is studied analytically with respect to the choice of an arbitrary vector. The covariance matrix of the estimator is determined and compared to the optimal Kalman type procedure. A numerical example illustrates the procedure and compares it to the optimal one.

Prochaska, B. J.↗
NASA NTRS1993

Robust Neighboring Optimal Guidance for the Advanced Launch System

In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system.

Hull, David G.↗
NASA NTRS2008

Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing

In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.

Guidance↗
NASA NTRSDate not supplied

An Initial Assessment of Variable Depth Liner Optimization for Ducted Proprotor Applications

The rise of the Urban Air Mobility market has spurred the design of a new generation of novel aircraft. To aid industry and researchers interested in these types of aircraft, the Revolutionary Vertical Lift Technology project at NASA has developed a fleet of reference vehicles for system studies. A new six-passenger reference vehicle has recently been added to the research portfolio that has ducted proprotors for propulsors. The ducts present an opportunity to apply acoustic treatment to the interior of the duct that could target both tonal and broadband noise, representative of the sound produced by this type of propulsor. In this paper, design methodologies are presented to design a variable depth liner for this application. An optimizer is used to design multiple liners with variable chamber depths. Experimental results from normal impedance testing are compared to numerical predictions using the optimizer model and a finite element model. Results show that an optimizer can be used to design an acoustic liner with favorable performance for a broad range of frequencies, which could be appropriate for a ducted proprotor application.

Matthew B Galles↗
DOE OSTI2026

Locally purified maximally mixed states at scale: Entanglement pruning and symmetries

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. Here, in this work we perform a comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue, we analyze two numerical tools, one analytic method, and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Further, away from the maximally mixed state, our simulations highlight how the truncation threshold smoothly interpolate, as a function of depolarization, between established matrix product results and our new results. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network’s fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that are accessible on near-term quantum devices.

Gangapuram, Amit Jamadagni [Oak Ridge National Lab↗