Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convex approximation”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Local convergence analysis of an inexact trust-region method for nonsmooth optimization

In Baraldi, we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. Furthermore, this algorithm has demonstrated excellent performance and scalability with problem size. In this paper, we enrich the convergence analysis for this algorithm, proving strong convergence of the iterates with guaranteed rates. In particular, we demonstrate that the trust-region algorithm recovers superlinear, even quadratic, convergence rates when using a second-order Taylor approximation of the smooth objective function term.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Measurements of local convective heat transfer coefficients on ice accretion shapes

The thin-skin heat rate technique was used to determine local convective heat transfer coefficients for four representative ice accretion shapes. The shapes represented three stages of glaze ice formation and one rime ice formation; the ice models had varying degrees of surface roughness. In general, convective heat transfer was higher in regions where the model's surfaces were convex and lower in regions where the surfaces were concave. The effect of roughness was different for the glaze and rime ice shapes. On the glaze ice shapes, roughness increased the maximum Nu by 80 percent, but the other Nu values were virtually unchanged. On the rime ice shape, the Nu numbers near the stagnation point were unchanged. The maximum Nu value increased by 45 percent, and the Nu number downstream of the peak increased by approximately 150 percent.

Arimilli, R. V.↗
NASA NTRS1992

Pressure distribution for the wing of the YAV-8B airplane; with and without pylons

Pressure distribution data have been obtained in flight at four span stations on the wing panel of the YAV-8B airplane. Data obtained for the supercritical profiled wing, with and without pylons installed, ranged from Mach 0.46 to 0.88. The altitude ranged from approximately 20,000 to 40,000 ft and the resultant Reynolds numbers varied from approximately 7.2 million to 28.7 million based on the mean aerodynamic chord. Pressure distribution data and flow visualization results show that the full-scale flight wing performance is compromised because the lower surface cusp region experiences flow separation for some important transonic flight conditions. This condition is aggravated when local shocks occur on the lower surface of the wing (mostly between 20 and 35 percent chord) when the pylons are installed for Mach 0.8 and above. There is evidence that convex fairings, which cover the pylon attachment flanges, cause these local shocks. Pressure coefficients significantly more negative than those for sonic flow also occur farther aft on the lower surface (near 60 percent chord) whether or not the pylons are installed for Mach numbers greater than or equal to 0.8. These negative pressure coefficient peaks and associated local shocks would be expected to cause increasing wave and separation drag at transonic Mach number increases.

Saltzman, Edwin J.↗
NASA NTRS2008

Jet Engine Fan Blade Containment Using an Alternate Geometry

With a goal of reducing jet engine weight, simulations of a fan blade containment system with an alternate geometry were tested and analyzed. A projectile simulating a fan blade was shot at two alternate geometry containment case configurations using a gas gun. The first configuration was a flat plate representing a standard case configuration. The second configuration was a flat plate with a radially convex curve section at the impact point. The curved surface was designed to force the blade to deform plastically, dissipating energy before the full impact of the blade is received by the plate. The curved case was able to tolerate a higher impact velocity before failure. The computational model was developed and correlated with the tests and a weight savings assessment was performed. For the particular test configuration used in this study the ballistic impact velocity of the curved plate was approximately 60 m/s (200 ft/s) greater than that of the flat plate. For the computational model to successfully duplicate the test, the very high strain rate behavior of the materials had to be incorporated.

Carney, K.S.↗
NASA NTRS1973

Feasibility test for a V-slit star mapper for pioneer spacecraft terminal navigation

A laboratory demonstration of the feasibility of using a V-slit star mapper to meet the sensitivity and accuracy of on-board navigational requirements for future Pioneer Missions to the outer planets was conducted by the Control and Sensors Laboratory of TRW. The breadboard was extremely simple in configuration, consisting of an end-on photomultiplier tube and a V-slit reticle located at the focal plane of the objective lens. In addition, a plano-convex lens was used between the reticle and the PMT in a Fabry-Perot configuration. The analytical effort indicated that the sensor should easily meet the requirements. The Pioneer SRA test set was examined to determine its basic accuracy and modify it where necessary to bring its accuracy into the 1-3 arc second range. The test results show that it is feasible to use this type of star mapper in the 10 arc second accuracy range. The test equipment accuracy (approximately 5 arc Sec) was sufficient to bound the sensor errors at less than 10 arc seconds.

Gates, R. F.↗
NASA NTRS2011

The Hyperspectral Thermal Emission Spectrometer (HyTES): Preliminary Results

The Hyperspectral Thermal Emission Spectrometer (HyTES) is being developed as part of the risk reduction activities associated with the Hyperspectral Infrared Imager (HyspIRI). HyspIRI is one of the Tier 2 Decadal Survey Missions. HyTES will provide information on how to place the filters on the HyspIRI Thermal Infrared Instrument (TIR) as well as provide antecedent science data. The pushbroom design has 512 spatial pixels over a 50-degree field of view and 256 spectral channels between 7.5 micrometers to 12 micrometers. HyTES includes many key enabling state-of-the-art technologies including a high performance convex diffraction grating, a quantum well infrared photodetector (QWIP) focal plane array, and a compact Dyson-inspired optical design. The Dyson optical design allows for a very compact and optically fast system (F/1.6). It also minimizes cooling requirements due to the fact it has a single monolithic prism-like grating design which allows baffling for stray light suppression. The monolithic configuration eases mechanical tolerancing requirements which are a concern since the complete optical assembly is operated at cryogenic temperatures ((is) approximately 100K). The QWIP allows for optimum spatial and spectral uniformity and provides adequate responsivity or D-star to allow 200mK noise equivalent temperature difference (NEDT) operation across the LWIR passband. Assembly of the system is nearly complete. After completion, alignment results will be presented which show low keystone and smile distortion. This is required to minimize spatial-spectral mixing between adjacent spectral channels and spatial positions. Predictions show the system will have adequate signal to noise for laboratory calibration targets.

Moon Mineralogical Mapper (M3).↗
NASA NTRS1981

On the velocity distribution of ion jets during substorm recovery

The velocity distribution of earthward jetting ions that are observed principally during substorm recovery by satellites at approximately 15-35 earth radii in the magnetotail is quantitatively compared with two different theoretical models - the 'adiabatic deformation' of an initially flowing Maxwellian moving into higher magnetic field strength (model A) and the field-aligned electrostatic acceleration of an initially nonflowing isotropic Maxwellian including adiabatic deformation effects (model B). The assumption is made that the ions are protons or, more generally, that they consist of only one species. It is found that both models can explain the often observed concave-convex shape of isodensity contours of the distribution function.

Birn, J.↗
NASA NTRS2000

Far Ultraviolet Imaging from the Image Spacecraft: Wideband FUV Imaging - 2

The Far Ultraviolet Wideband Imaging Camera (WIC) complements the magnetospheric images taken by the IMAGE satellite instruments with simultaneous global maps of the terrestrial aurora. Thus, a primary requirement of WIC is to image the total intensity of the aurora in wavelength regions most representative of the aurora] source and least contaminated by dayglow, have sufficient field of view to cover the entire polar region from spacecraft apogee and have resolution that is Sufficient to resolve auroras on a scale of 1 to 2 latitude degrees, The instrument is sensitive in the spectral region from 140- 190 nm. The WIC is mounted on the rotating, IMAGE spacecraft viewing radially outward and has a field of view of 17 deg in the direction parallel to the spacecraft spin axis. Its field of view is 30 deg in the direction perpendicular to the spin axis, although only a 17 deg x 17 deg image of the Earth is recorded. The optics was an all-reflective, inverted Cassegrain Burch camera using concentric optics with a small convex primary and a large concave secondary mirror. The mirrors were coated by a special multi-layer coating, which has low reflectivity in the visible and near UV region, The detector consists of a MCP-Intensified CCD. The MCP is curved to accommodate the focal surface of the concentric optics. Tile phosphor of the image intensifier is deposited on a concave fiberoptic window, which is then Coupled to the CCD with a fiberoptic taper. The camera head operates in a fast frame transfer mode with the CCD being read approximately 30 full frames (512 by 256 pixel) per second with an exposure time of 0.033 s. The image motion (file to the satellite spin is minimal during such a short exposure. Each image is electronically distortion corrected using the look up table scheme. An offset is added to each memory address that is proportional to the image shift due to satellite rotation, and the charge signal is digitally summed in memory. On orbit, approximately 300 frames will be added to produce one WIC image in memory. The advantage of the electronic motion compensation and distortion correction is that it is extremely flexible, permitting several kinds of corrections including motions parallel and perpendicular to the predicted axis of rotation. File instrument was calibrated by applying ultraviolet light through a vacuum monochromator and measuring the absolute responsivity of the instrument. To obtain the data for the distortion look up table the camera was turned through various angles and the input angles corresponding to a pixel matrix were recorded. It was found that the spectral response peaked at 150 nm and fell off in either direction. The equivalent aperture of the camera, including mirror reflectivities and effective photocathode quantum efficiency, is about 0.04 sq cm. Thus, a 100 Rayleigh LBH aurora is expected to produce 23 equivalent counts per pixel per 10 s exposure at the peak of instrument response.

Mende, S. B.↗
DOE OSTI2024

A quasi-meshfree method for constructing boundary-aware reproducing bases on geometrically complex domains using manifold geodesics

In many applications, physical domains are geometrically complex making it challenging to perform coarse-scale approximation. A defeaturing process is often used to simplify the domain in preparation for approximation and analysis at the coarse scale. In this paper, a methodology is presented for constructing a coarse-scale reproducing basis on geometrically complex domains given an initial fine-scale mesh of the fully featured domain. The initial fine-scale mesh can be of poor quality and extremely refined. The construction of the basis functions begins with a coarse-scale covering of the domain and generation of weighting functions with local support. Manifold geodesics are used to define distances within the local support for general applicability to non-convex domains. Conventional moving least squares is used to construct the coarse-scale reproducing basis. Applications in quasi-interpolation and linear elasticity are presented.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2002

The Delta(dot) B = O Constraint vs. Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. On the other hand, the MHD equations can be derived from basic principles in either conservative or non-conservative form. The non-conservative system has a better conditioned eigensystem. The Delta(dot)B = 0 constraint of the A4HD equations is only an initial condition constraint. One does not need the Delta(dot)B condition to close the MHD system. We formulate our new low dissipative high order scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the Delta(dot)B condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗
DOE OSTI2022

Resilient Operating Constraints for Power Distribution Systems under Setpoint Attacks

Integration and operation of distributed generation (DG) and energy storage (ES) in power distribution systems are enabled by communication networks and embedded sensor and control devices that increase the vulnerability of the systems to cyber-threats, broadening the attack surface and making adversary actions more unpredictable. This paper proposes a methodology that uses ellipsoidal approximations to quantify the potential damage caused by successful attacks that affect, directly or indirectly, the desired operation setpoints and may drive the power distribution operation to unsafe states by violating the limits of voltage or line flows. More specifically, a new methodology is introduced to find the optimal non-symmetric operating constraints that can be imposed to each DG and ES in order to guarantee that the power distribution system is resilient to any malicious setpoints. The proposed method takes as inputs the system topology, DG and ES capabilities, and load limits to solve a convex optimization problem formulated using linear matrix inequalities (LMIs) and the power flow equations. The proposed solution is agnostic to the attacker's action or load profile and it does not require any assumption about the location or means of the attack. The numerical results on a test distribution feeder with several DG and ES illustrate how the proposed resilient operating constraints guarantee the security of the power distribution system under setpoint attacks.

Giraldo, Jairo↗
DOE OSTI2020

Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation

This work explores the application of the recently developed Koopman operator approach for model identification and feedback control of a hydraulic fracturing process. Controlling fracture propagation and proppant transport with precision is a challenge due in large part to the difficulty of constructing approximate models that accurately capture the characteristic moving boundary and highly-coupled dynamics exhibited by the process. Koopman operator theory is particularly attractive here as it offers a way to explicitly construct linear representations for even highly nonlinear dynamics. The method is data-driven and relies on lifting the states to an infinite-dimensional space of functions called observables where the dynamics are governed by a linear Koopman operator. Here this work considers two problems: (a) fracture geometry control, and (b) proppant concentration control. In both cases, an approximate linear model of the corresponding dynamics is constructed and used to design a model predictive controller (MPC). The manuscript shows that in the case of highly nonlinear dynamics, as observed in the proppant concentration, use of canonical functions in the observable basis fails. In such cases, a priori system knowledge can be leveraged to choose the required basis. The numerical experiments demonstrate that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired target values maximizing the oil and gas productivity. Additionally, due to its linear structure, the Koopman models allow convex MPC formulations that avoid any issues associated with nonlinear optimization.

42 ENGINEERING↗
NASA NTRS1986

A study of the microstructure of a rapidly solidified nickel-base superalloy modified with boron

The microstructures of melt-spun superalloy ribbons with variable boron levels have been studied by transmission electron microscopy. The base alloy was of approximate composition Ni-11% Cr-5%Mo-5%Al-4%Ti with boron levels of 0.06, 0.12, and 0.60 percent (all by weight). Thirty micron thick ribbons display an equiaxed chill zone near the wheel contact side which develops into primary dendrite arms in the ribbon center. Secondary dendrite arms are observed near the ribbon free surface. In the higher boron bearing alloys, boride precipitates are observed along grain boundaries. A concerted effort has been made to elucidate true grain shapes by the use of bright field/dark field microscopy. In the low boron alloy, grain shapes are often convex, and grain faces are flat. Boundary faces frequently have large curvature, and grain shapes form concave polygons in the higher boron level alloys. It is proposed that just after solidification, in all of the alloys studied, grain shapes were initially concave and boundaries were wavy. Boundary straightening is presumed to occur on cooling in the low boron alloy. Boundary migration is precluded in the higher boron alloys by fast precipitation of borides at internal interfaces.

Speck, J. S.↗
DOE OSTI2020

Data-driven learning of nonlocal physics from high-fidelity synthetic data

A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. Here, we extract nonlocal models from data, circumventing these challenges and providing data-driven justification for the resulting model form. Extracting data-driven surrogates is a major challenge for machine learning (ML) approaches, due to nonlinearities and lack of convexity — it is particularly challenging to extract surrogates which are provably well-posed and numerically stable. Our scheme not only yields a convex optimization problem, but also allows extraction of nonlocal models whose kernels may be partially negative while maintaining well-posedness even in small-data regimes. To achieve this, based on established nonlocal theory, we embed in our algorithm sufficient conditions on the non-positive part of the kernel that guarantee well-posedness of the learnt operator. These conditions are imposed as inequality constraints to meet the requisite conditions of the nonlocal theory. We demonstrate this workflow for a range of applications, including reproduction of manufactured nonlocal kernels; numerical homogenization of Darcy flow associated with a heterogeneous periodic microstructure; nonlocal approximation to high-order local transport phenomena; and approximation of globally supported fractional diffusion operators by truncated kernels.

42 ENGINEERING↗
DOE OSTI2021

Second-order invariant domain preserving approximation of the compressible Navier–Stokes equations

Here, we present a fully discrete approximation technique for the compressible Navier–Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time step is the standard hyperbolic CFL condition, i.e. τ ≲ O ( h ) / V where V is some reference velocity scale and h the typical meshsize.

42 ENGINEERING↗
DOE OSTI2022

Diffraction and thermal effect of a Bessel-Gaussian laser for Ag nanoparticle deposition

Nanoparticles are known to sinter at much lower temperatures than the corresponding bulk or micro size particles. A laser-assisted sintering process is considered in this study to sinter Ag nanoparticles by dispensing Ag paste onto an indium tin oxide-coated Si substrate. The Gaussian beam of a CO 2 laser source is propagated through axicon and biconvex lenses, and the resulting hollow beam is focused on the Ag paste with a hollow parabolic mirror. A Bessel-Gaussian irradiance distribution is obtained at the focal plane of the parabolic mirror due to the interference of the hollow laser cone. The Fresnel diffraction approximation is considered to determine the phasor of the laser and an analytical approach is implemented to calculate the irradiance distribution of the Bessel-Gaussian beam. This irradiance distribution is utilized as a heat source in a heat conduction model and the temperature distribution is analyzed for thin Ag films formed during the laser sintering of Ag nanoparticles. An analytical expression is obtained for the temperature distribution by solving the heat conduction equation using Fourier transform for finite media. The widths of the deposited Ag lines are predicted from the temperature profiles and the model predictions compare well with the experimental results. The isotherms are found to be geometrically noncongruent with convex and concave tips depending on the locally maximum and minimum irradiances of the Bessel-Gaussian beam, respectively. The convex and concave tips, however, appear in the same isotherm for sufficiently high substrate speed relative to the laser beam.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

A high-order explicit Runge-Kutta approximation technique for the shallow water equations

Here, we introduce a high-order space–time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP), well-balanced with respect to rest states, and employs a novel explicit Runge–Kutta (ERK) introduced in Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366–A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

97 MATHEMATICS AND COMPUTING↗