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Results for “derivative free 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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

An Active Subspace Method for Accelerating Convergence in Delaunay-Based Optimization via Dimension Reduction

Delaunay-based derivative-free optimization, ∆DOGS, is an efficient and provably-convergent global optimization method for the problems which has computationally expensive objection function and the analytical expression for the objective function is not available. ∆-DOGS is a novel optimization scheme in the family of response surface methods (RSMs); however, it suffers from the curse of dimensionality since the computational cost increases dramatically as the number of design parameters increases. As a result, the number of design parameters in ∆-DOGS algorithm is relatively low (n.10). To avoid such problems, this paper proposes a combination of derivative-free optimization, seeking the global minimizer of an expensive and nonconvex objective function f(x) and active subspace method, detecting the directions of the most variability using evaluations of the gradient. The contribution of other directions to the objective function is bounded by a sufficiently small constant. This new algorithm iteratively applied Delaunay-based derivative-free optimization to seek the minimizer on the d-dimensional active subspace that has most function variation. Inverse mapping is needed to project data from active subspace to full-model for evaluating function values. This task is overcome by solving an inequality constrained problem that curves the response surface of the objective function. The test results show that this strategy is effective on a handful of optimization problems.

Bewley, Thomas R.↗
NASA NTRS2020

Tuning a variational autoencoder for data accountability problem in the Mars Science Laboratory ground data system

The Mars Curiosity rover is frequently sending back engineering and science data that goes through a pipeline of systems before reaching its final destination at the mission operations center making it prone to volume loss and data corruption. A ground data system analysis (GDSA) team is charged with the monitoring of this flow of information and the detection of anomalies in that data in order to request a re-transmission when necessary. This work presents ∆-MADS, a derivative-free optimization method applied for tuning the architecture and hyperparameters of a variational autoencoder trained to detect the data with missing patches in order to assist the GDSA team in their mission.

Lakhmiri, Dounia↗
NASA NTRSDate not supplied

Fixed- and Free-Mode Flutter Derivatives during Aeroelastic Optimization

Aeroelastic flutter design derivatives may be approximated by ignoring the sensitivity of the structural mode shapes. This “fixed-mode” derivative is less-expensive to compute than the exact “free-mode” derivative (which accommodates the mode shape dependency), but also may provide inaccurate sensitivities for optimization. This work formulates both fixed- and free-mode flutter derivatives, and demonstrates the conditions under which they are equivalent. Two different types of fixed-mode derivatives are also developed in this work. Using a cantilevered-plate demonstration problem with both shape and sizing design parameters, the accuracy of the free-mode derivative and the two fixed-mode derivatives, are all demonstrated via gradient-based optimization.

Bret K. Stanford↗
NASA NTRS2018

A Singular Value Decomposition Framework for Retrievals with Vertical Distribution Information from Greenhouse Gas Column Absorption Spectroscopy Measurements

We review the singular value decomposition (SVD) framework and use it for quantifying and discerning vertical information in greenhouse gas retrievals from column integrated absorption measurements. While the commonly used traditional Bayesian optimal estimation (OE) assumes a prior distribution in order to regularize the inversion problem, the SVD approach identifies principal components that can be retrieved from the measurement without explicitly specifying a prior mean and prior covariance matrix. We review the SVD method, explicitly recognize the use of an uninformative prior and show it to incur no bias from the choice of the prior. We also make the connection between the SVD method and the pseudo-inverse, which makes it more intuitive and easy to understand. We illustrate the use of the SVD method on an integrated path differential absorption CO2 lidar measurement model and verify our derivations and bias-free properties versus optimal estimation using numerical simulations. In contrast, traditional OE retrievals exhibit bias when the prior mean used in the retrieval differs from the true mean. Hence, the SVD method is particularly useful for situations in which knowledge of the prior mean and prior covariance of the true state (e.g., greenhouse gas profiles) is inadequate.

Ramanathan, Anand K.↗
NASA NTRS1997

Numerical Optimization Using Computer Experiments

Engineering design optimization often gives rise to problems in which expensive objective functions are minimized by derivative-free methods. We propose a method for solving such problems that synthesizes ideas from the numerical optimization and computer experiment literatures. Our approach relies on kriging known function values to construct a sequence of surrogate models of the objective function that are used to guide a grid search for a minimizer. Results from numerical experiments on a standard test problem are presented.

Trosset, Michael W.↗
NASA NTRS1993

Optimal open multistep discretization formulas for real-time simulation

The performance of digital real-time simulations is considered. A figure of merit is derived that quantifies a simulation's fidelity in terms of the time-domain discrepancy between its output and that of the plant it simulates, assuming that the plant is linearizable and asymptotically stable. This performance index is then used in deriving an easily automated procedure for calculating optimal values for free parameters in plant discretizations based on a generalized form of open linear multistep integration formulas. The theory is demonstrated in simulating the rigid-body dynamics of a fully articulated helicopter rotor blade system.

Moerder, Daniel D.↗
NASA NTRS1992

Fluid flow in a jet and the Ca XIX line profiles observed during solar flares

The present study considers two types of fluid models as methods for reproducing the blueshifts and line broadening observed in soft X-ray lines during the rise of solar flares. The fluid models representing the laminar flow of material in a jet and through a pipe were used to derive the velocity at each location in the flow. The optimal values for the free parameters in the jet model were within the ranges expected for solar flare conditions. The jet was much smaller than typical flare volumes estimated from spatial images, but the resulting densities were consistent with the upper limit of densities derived using density-sensitive line ratios. This supports previous reports of small filling factors and is interpreted as evidence for a chromospheric origin for the flow. Stability analysis indicates that, although the laminar jet can reproduce the observations, instabilities may cause the flow to become turbulent, and that this laminar treatment is not strictly valid.

Bornmann, P. L.↗
NASA NTRS1995

Utilization of [14C]phenylalanine derived from arylphorin or free amino acid in Manduca sexta pharate adults

The role of arylphorin as a storage protein was studied using 14C-arylphorin. 14C-arylphorin was produced optimally by incubating one-half fat body from Manduca sexta fifth instar larvae at 22 degrees C for 24 h, in 1 ml of medium containing amino acids at 25% of their physiological concentration with [U-14C]-phenylalanine (phe) provided initially without nonlabeled phenylalanine. Nonlabeled phe was provided after 1 h at 16% of its physiological concentration. The specific activity of 14C-arylphorin produced in vitro was 30 times greater than that generated in vivo. Injection of 14C-arylphorin into pharate adults was used to study the distribution of 14C-phe derived from this protein into 14CO2 and tissues for comparison with injection of free 14C-phe during the middle (days 6 to 12 pharate adult) and late (days 12 to 17 pharate adult) stages of adult development. Appearance of 14CO2 from 14C-arylphorin as compared to 14C-phenylalanine showed a slower time course during both the middle and late stages of development, in keeping with the time needed for degradation of the protein. In accord with faster phe turnover near the end of adult development, total 14CO2 production was greater and the retention of 14C in hemolymph and fat body was less compared to the middle stage of development regardless of whether 14C-arylphorin or 14C-phe was injected. In the middle stage of development, the appearance of 14C in the cuticle and head parts was greater, whereas incorporation into abdomen and thorax was less than during the late stage of development. Since the pattern of 14C distribution from 14C-arylphorin and 14C-phe was similar, one major function of arylphorin must be as a storage protein replenishing the supply of free amino acids used for synthesis of adult tissues. These results also suggest a limited contribution of M. sexta arylphorin to formation of the cuticle subsequent to day-6 pharate adult.

Non-NASA Center↗
NASA NTRS1984

The effect of parking orbit constraints on the optimization of ballistic planetary trajectories

The optimization of ballistic planetary trajectories is developed which includes constraints on departure parking orbit inclination and node. This problem is formulated to result in a minimum total Delta V where the entire constrained injection Delta V is included in the optimization. An additional Delta V is also defined to allow for possible optimization of parking orbit inclination when the launch vehicle orbit capability varies as a function of parking orbit inclination. The optimization problem is formulated using primer vector theory to derive partial derivatives of total Delta V with respect to possible free parameters. Minimization of total Delta V is accomplished using a quasi-Newton gradient search routine. The analysis is applied to an Eros rendezvous mission whose transfer trajectories are characterized by high values of launch asymptote declination during particular launch opportunities. Comparisons in performance are made between trajectories where parking orbit constraints are included in the optimization and trajectories where the constraints are not included.

Sauer, C. G., Jr.↗
NASA NTRS2000

Interference Lattice-based Loop Nest Tilings for Stencil Computations

A common method for improving performance of stencil operations on structured multi-dimensional discretization grids is loop tiling. Tile shapes and sizes are usually determined heuristically, based on the size of the primary data cache. We provide a lower bound on the numbers of cache misses that must be incurred by any tiling, and a close achievable bound using a particular tiling based on the grid interference lattice. The latter tiling is used to derive highly efficient loop orderings. The total number of cache misses of a code is the sum of (necessary) cold misses and misses caused by elements being dropped from the cache between successive loads (replacement misses). Maximizing temporal locality is equivalent to minimizing replacement misses. Temporal locality of loop nests implementing stencil operations is optimized by tilings that avoid data conflicts. We divide the loop nest iteration space into conflict-free tiles, derived from the cache miss equation. The tiling involves the definition of the grid interference lattice an equivalence class of grid points whose images in main memory map to the same location in the cache-and the construction of a special basis for the lattice. Conflicts only occur on the boundaries of the tiles, unless the tiles are too thin. We show that the surface area of the tiles is bounded for grids of any dimensionality, and for caches of any associativity, provided the eccentricity of the fundamental parallelepiped (the tile spanned by the basis) of the lattice is bounded. Eccentricity is determined by two factors, aspect ratio and skewness. The aspect ratio of the parallelepiped can be bounded by appropriate array padding. The skewness can be bounded by the choice of a proper basis. Combining these two strategies ensures that pathologically thin tiles are avoided. They do not, however, minimize replacement misses per se. The reason is that tile visitation order influences the number of data conflicts on the tile boundaries. If two adjacent tiles are visited successively, there will be no replacement misses on the shared boundary. The iteration space may be covered with pencils larger than the size of the cache while avoiding data conflicts if the pencils are traversed by a scanning-face method. Replacement misses are incurred only on the boundaries of the pencils, and the number of misses is minimized by maximizing the volume of the scanning face, not the volume of the tile. We present an algorithm for constructing the most efficient scanning face for a given grid and stencil operator. In two dimensions it is based on a continued fraction algorithm. In three dimensions it follows Voronoi's successive minima algorithm. We show experimental results of using the scanning face, and compare with canonical loop orderings.

VanderWijngaart, Rob F.↗
NASA NTRS2013

A Next Generation Air Monitor: Combining Orion and ISS Requirements for a Common Major Constituent Analyzer

The Major Constituent Analyzer (MCA) is a mass spectrometer-based instrument designed to provide critical monitoring of six major atmospheric constituents; nitrogen, oxygen, hydrogen, carbon dioxide, methane, and water vapor on-board the International Space Station. The analyzer has been an integral part of the Environmental Control and Life Support System (ECLSS) since the station went on-line. The Orion Air Monitor (OAM) was derived from the MCA and heavily optimized for reduced mass, lower power, faster water vapor response, and maintenance-free operation. The resulting OAM is approximately the size of the analyzer portion of the MCA, orbital-replacement unit 02 (ORU 02), while incorporating the functions of three other modules: Data Processing and Communication (ORU 01), Verification Gas Assembly (ORU 08), and Low Voltage Power Supply (ORU 04). The overlap in MCA and OAM requirements makes it possible to derive a common Air Monitor design that spans both applications while minimally impacting the weight and power limits imposed by the Multipurpose Crew Vehicle (MPCV). Benefits to ISS include the retirement of ORUs 01, 04, and 08, reducing up-mass and eliminating EEE parts obsolescence issues through the extended ISS mission phases. Benefits to MPCV and future deployed habitats under the Constellation program include greater interchangeability across ECLSS subsystems. This paper discusses the results of the requirements development study, where a superset of ISS and Orion air monitoring requirements were distilled; evaluated against increases in OAM functionality, mass, and power; and traded-off where possible using simple operating mode modifications. A system architecture and preliminary design addressing the common requirements will be presented.

Burchfield, David E.↗
NASA NTRS2000

Optimal Wonderful Life Utility Functions in Multi-Agent Systems

The mathematics of Collective Intelligence (COINs) is concerned with the design of multi-agent systems so as to optimize an overall global utility function when those systems lack centralized communication and control. Typically in COINs each agent runs a distinct Reinforcement Learning (RL) algorithm, so that much of the design problem reduces to how best to initialize/update each agent's private utility function, as far as the ensuing value of the global utility is concerned. Traditional team game solutions to this problem assign to each agent the global utility as its private utility function. In previous work we used the COIN framework to derive the alternative Wonderful Life Utility (WLU), and experimentally established that having the agents use it induces global utility performance up to orders of magnitude superior to that induced by use of the team game utility. The WLU has a free parameter (the clamping parameter) which we simply set to zero in that previous work. Here we derive the optimal value of the clamping parameter, and demonstrate experimentally that using that optimal value can result in significantly improved performance over that of clamping to zero, over and above the improvement beyond traditional approaches.

Wolpert, David H.↗
NASA NTRSDate not supplied

Progress on Inverse Estimation Technique of Non-Linear Pitch Damping Coefficient Curves Using Free-Flight CFD Generated Trajectories

Characterization of entry vehicle pitch damping coefficient curves is crucial to ensure appropriate re-entry and overall mission success. The pitch damping coefficient (C_(m_q )+C_(m_α ̇ )) is used to encapsulate the oscillatory growth or decay of a body during a trajectory. The inverse estimation technique utilizes an existing Free-Flight CFD (FF-CFD) dataset and wraps a reconstruction algorithm in an optimizer. The reconstruction integrates the planar equations of motion derived by Schoenenberger, Queen [1] using Python’s scipy.integrate.solve_ivp. The optimizer’s objective function is the normalized 𝐿2 residual of the angle of attack peaks between the reconstructed trajectory and the original data produced with FF-CFD. Inclusion of the peak times in this residual calculation allows for simultaneous optimization of the pitch moment coefficient, C_(m_α ). This residual equation is shown below in Eq. 1. The optimizer scipy.optimize.minimize was used with the gradient-based Powell method for the analysis presented, however the differential evolution method was investigated as means of comparison, and was found to produce marginally lower residual values with prohibitively longer run times. Further, the pitch damping curve is found by fitting a cubic interpolation function to a set of (α, (C_(m_q )+C_(m_α ̇ ))) control points, where the α points are held constant and the (C_(m_q )+C_(m_α ̇ )) values are the optimized parameters. The pitch moment curve uses a linear interpolation between the minimum and maximum α in the dataset. FF-CFD generated trajectories using the Dragonfly capsule geometry with the Genesis ballistic range model parameters were simulated and used for this analysis. These FF-CFD trajectories simulate planar motion, as restricted by the reconstructing the equations of motion, of three different cases: 1-DoF (free-to-pitch), 2-DoF (free-to-pitch and heave), and 3-DoF (free-to-pitch, heave, and decelerate). Pitch damping coefficient curves generated using this inverse estimation curve technique with FF-CFD 1-DoF Dragonfly data are found in Fig. 1. Preliminary results reconstructing ballistic range shots using these FF-CFD derived predictions of the pitch damping curve (Fig. 1) are shown in Fig. 2. It should be noted that the ballistic range shot used a Genesis model whereas the FF-CFD data used a Dragonfly geometry, however these geometries are similar.

entry↗
NASA NTRS1992

Membrane triangles with corner drilling freedoms. II - The ANDES element

This is the second article in a three-part series on the construction of 3-node, 9-dof membrane elements with normal-to-its-plane rotational freedoms (the so-called drilling freedoms) using parametrized variational principles. In this part, one such element is derived within the context of the assumed natural deviatoric strain (ANDES) formulation. The higher-order strains are obtained by constructing three parallel-to-sides pure-bending modes from which natural strains are obtained at the corner points and interpolated over the element. To attain rank sufficiency, an additional higher-order 'torsional' mode, corresponding to equal hierarchical rotations at each corner with all other motions precluded, is incorporated. The resulting formulation has five free parameters. When these parameters are optimized against pure bending by energy balance methods, the resulting element is found to coalesce with the optimal EFF element derived in Part I. Numerical integration as a strain filtering device is found to play a key role in this achievement.

Felippa, Carlos A.↗
NASA NTRS2012

Resolution Enhancement of MODIS-Derived Water Indices for Studying Persistent Flooding

Monitoring coastal marshes for persistent flooding and salinity stress is a high priority issue in Louisiana. Remote sensing can identify environmental variables that can be indicators of marsh habitat conditions, and offer timely and relatively accurate information for aiding wetland vegetation management. Monitoring activity accuracy is often limited by mixed pixels which occur when areas represented by the pixel encompasses more than one cover type. Mixtures of marsh grasses and open water in 250m Moderate Resolution Imaging Spectroradiometer (MODIS) data can impede flood area estimation. Flood mapping of such mixtures requires finer spatial resolution data to better represent the cover type composition within 250m MODIS pixel. Fusion of MODIS and Landsat can improve both spectral and temporal resolution of time series products to resolve rapid changes from forcing mechanisms like hurricane winds and storm surge. For this study, using a method for estimating sub-pixel values from a MODIS time series of a Normalized Difference Water Index (NDWI), using temporal weighting, was implemented to map persistent flooding in Louisiana coastal marshes. Ordinarily NDWI computed from daily 250m MODIS pixels represents a mixture of fragmented marshes and water. Here, sub-pixel NDWI values were derived for MODIS data using Landsat 30-m data. Each MODIS pixel was disaggregated into a mixture of the eight cover types according to the classified image pixels falling inside the MODIS pixel. The Landsat pixel means for each cover type inside a MODIS pixel were computed for the Landsat data preceding the MODIS image in time and for the Landsat data succeeding the MODIS image. The Landsat data were then weighted exponentially according to closeness in date to the MODIS data. The reconstructed MODIS data were produced by summing the product of fractional cover type with estimated NDWI values within each cover type. A new daily time series was produced using both the reconstructed 250-m MODIS, with enhanced features, and the approximated daily 30-m high-resolution image based on Landsat data. The algorithm was developed and tested over the Calcasieu-Sabine Basin, which was heavily inundated by storm surge from Hurricane Ike to study the extent and duration of flooding following the storm. Time series for 2000-2009, covering flooding events by Hurricane Rita in 2005 and Hurricane Ike in 2008, were derived. High resolution images were formed for all days in 2008 between the first cloud free Landsat scene and the last cloud-free Landsat scene. To refine and validate flooding maps, each time series was compared to Louisiana Coastwide Reference Monitoring System (CRMS) station water levels adjusted to marsh to optimize thresholds for MODIS-derived time series of NDWI. Seasonal fluctuations were adjusted by subtracting ten year average NDWI for marshes, excluding the hurricane events. Results from different NDWI indices and a combination of indices were compared. Flooding persistence that was mapped with higher-resolution data showed some improvement over the original MODIS time series estimates. The advantage of this novel technique is that improved mapping of extent and duration of inundation can be provided.

Underwood, L. W.↗
NASA NTRS1981

Optimal damper location in the vibration control of large space structures

The problem of finding the optimal location of active dampers for the vibration control of space structures is investigated. The optimal location is where maximum damping can be introduced to a particular vibration mode. To this end, classical root locus techniques are used to study the effect on eigenvalues of placing a damper on an undamped structure. An efficient formulation is derived which avoids the solution of the damped eigenvalue problem. Based on the observation of the results for a free-free beam model, a Minimum Constrained Frequency Criterion (MCFC) for locating the optimal damper location is proposed.

Wang, B. P.↗
NASA NTRS1992

Membrane triangles with corner drilling freedoms. III - Implementation and performance evaluation

This paper completes a three-part series on the formulation of 3-node, 9-dof membrane triangles with corner drilling freedoms based on parametrized variational principles. The first four sections cover element implementation details including determination of optimal parameters and treatment of distributed loads. Then three elements of this type, labeled ALL, FF and EFF-ANDES, are tested on standard plane stress problems. ALL represents numerically integrated versions of Allman's 1988 triangle; FF is based on the free formulation triangle presented by Bergan and Felippa in 1985; and EFF-ANDES represent two different formulations of the optimal triangle derived in Parts I and II. The numerical studies indicate that the ALL, FF and EFF-ANDES elements are comparable in accuracy for elements of unitary aspect ratios. The ALL elements are found to stiffen rapidly in inplane bending for high aspect ratios, whereas the FF and EFF elements maintain accuracy. The EFF and ANDES implementations have a moderate edge in formation speed over the FF.

Felippa, Carlos A.↗