A structural merit function for aerodynamic decelerators
Structural merit function for aerodynamic decelerators
Anderson, M. S.↗
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A New Merit Function for Evaluating the Flaw Tolerance of Composite Laminates: Arbitrary Size Holes and Center Cracks - Part 2
In a previous paper, a new merit function for determining the strength performance of flawed composite laminates was presented. This previous analysis was restricted to circular hole flaws that were large enough that failure could be predicted using the laminate stress concentration factor. In this paper, the merit function is expanded to include the flaw cases of an arbitrary size circular hole or center crack. Failure prediction for these cases is determined using the point stress criterion. An example application of the merit function is included for a wide range of graphite/epoxy laminates.
Martin, Mikulas M., Jr.↗
A New Merit Function for Evaluating the Flaw Tolerance of Composite Laminates: Arbitrary Size Holes and Center Cracks - Part 2
In a previous paper, a new merit function for determining the strength performance of flawed composite laminates was presented. This previous analysis was restricted to circular hole flaws that were large enough that failure could be predicted using the laminate stress concentration factor. In this paper, the merit function is expanded to include the flaw cases of an arbitrary size circular hole or a center crack. Failure prediction for these cases is determined using the point stress criterion. An example application of the merit function is included for a wide range of graphite/epoxy laminates.
Mikulas, Martin M., Jr.↗
A New Merit Function for Evaluating the Flaw Tolerance of Composite Laminates: Arbitrary Size Holes and Center Cracks - Pt. 2
In a previous paper, a new merit function for determining the strength performance of flawed composite laminates was presented. This previous analysis was restricted to circular hole flaws that were large enough that failure could be predicted using the laminate stress concentration factor. In this paper, the merit function is expanded to include the flaw cases of an arbitrary size circular hole or a center crack. Failure prediction for these cases is determined using the point stress criterion. An example application of the merit function is included for a wide range of graphite/epoxy laminates.
Mikulas, Martin M., Jr.↗
A new merit function for evaluating the flaw tolerance of composite laminates
Advanced composite materials are providing notable savings in numerous aerospace and non-aerospace applications by virtue of their uniquely high strength-to-density ratio and high stiffness-to-density ratio. However, their full potential for high performance has yet to be achieved because of the low tolerance of the 'brittle' material to impact, holes, flaws, and localized discontinuities due to relatively low toughness. In the present paper a new and simple merit function is proposed for maximizing the strength performance of flawed composite laminate for different design requirement. This new merit function takes into account the flaw tolerance of a composite laminated as well as its stiffness. After development of the new merit function, an example is presented of its application to a practical laminate family.
Mikulas, Martin M., Jr.↗
Emissions Merit Function for Evaluating Multifunctional Catalyst Beds
With emission control regulations getting stricter, multi-functional catalyst systems are increasingly important for low-temperature operation. We investigate a wide range of multi-component catalyst systems, as physical mixtures and in multi-bed configurations, while varying the ratios of hydrocarbon traps (HCT), passive NOx adsorbers (PNAs), and diesel oxidation catalysts (DOC). Using industrially guided protocols, we measured the ability of these complex catalyst systems to reduce emissions during a 40 °C/min temperature ramp to simulate cold-start conditions. Using a temperature boundary condition of 250 °C, the average conversion was calculated for each regulated pollutant: CO, NOx, and total hydrocarbons (THC). An emissions merit function was developed to evaluate the effectiveness of each system relative to the relevant emission standards and expected engine exhaust concentrations. This merit function identified that a 1:1:4 ratio of PNA:HCT:DOC was the most effective emissions reduction configuration and had similar reactivity as a physical mixture or as a PNA→HCT→DOC multi-bed reactor.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Optimizing X-Ray Optical Prescriptions for Wide-Field Applications
X-ray telescopes with spatial resolution optimized over the field of view (FOV) are of special interest for missions, such as WFXT, focused on moderately deep and deep surveys of the x-ray sky, and for solar x-ray observations. Here we report on the present status of an on-going study of the properties of Wolter I and polynominal grazing incidence designs with a view to gain a deeper insight into their properties and simply the design process. With these goals in mind, we present some results in the complementary topics of (1) properties of Wolter I x-ray optics and polynominal x-ray optic ray tracing. Of crucial importance for the design of wide-field x-ray optics is the optimization criteria. Here we have adopted the minimization of a merit function, M, which measures the spatial resolution averaged over the FOV: M= ((integral of d phi) between the limits of 0 and 2 pi) (integral of d theta theta w(theta) sigma square (theta,phi) between the limits of 0 and theta(sub FOV)) (integral of d phi between the limits of 0 and phi/4) (Integral of d theta theta w(theta) between the limits of 0 and theta(sub FOV) where w(theta(sub 1) is a weighting function and Merit function: sigma-square (theta, phi) = summation of (x,y,z) [ -<(x,y,z)> (exp 2)] is the spatial variance for a point source on the sky at polar and azimuthal off-axis angles (theta,phi).
Elsner, R. F.↗
HD 53975: An O-type spectroscopic binary with a large mass ratio
We present radial velocities and line profiles of the O-type star HD 53975, which we find to be a spectroscopic binary with a period of 6.0173 days. Although there are no obvious signatures of the secondary in the line profiles, we have used the merit function of Shafter et al. (1980) to show that a secondary component is present in lines found in B-type spectra. We have compared the observed merit functions with merit functions for model profiles constructed assuming a main-sequence secondary, and this comparison consistently indicates a companion with a mass ratio of q = M(sub 2)/M(sub 1) = 0.23 +/- 0.04 and a magnitude difference Delta m = 3.3 +/- 0.4. We present a tomographic reconstruction of the spectrum of the secondary for these parameters. We suggest that other large mass ratio binaries may be found among the O stars when observed with high-resolution and high signal-to-noise ratio spectroscopy.
Gies, D. R.↗
Catalyst design to direct high-octane gasoline fuel properties for improved engine efficiency
The paraffin-to-olefin (P/O) ratio in gasoline fuel is a critical metric affecting fuel properties and engine efficiency. In the conversion of dimethyl ether (DME) to high-octane hydrocarbons over BEA zeolite catalysts, the P/O ratio can be controlled through catalyst design. Here, we report bimetallic catalysts that balance the net hydrogenation and dehydrogenation activity during DME homologation. The Cu-Zn/BEA catalyst exhibited greater relative dehydrogenation activity attributed to higher ionic site density, resulting in a lower P/O ratio (6.6) versus the benchmark Cu/BEA (9.4). The Cu-Ni/BEA catalyst exhibited increased hydrogenation due to reduced Ni species, resulting in a higher P/O ratio (19). The product fuel properties were estimated with an efficiency merit function and compared against finished gasolines and a typical alkylate blendstock. Merit values for the hydrocarbon product from all three BEA catalysts exceeded those of the comparison fuels (0–5.3), with the product from Cu-Zn/BEA exhibiting the highest merit value (9.7).
Catalyst design↗
Modeling approaches for addressing unrelaxable bound constraints with unconstrained optimization methods
We explore novel approaches for solving nonlinear optimization problems with unrelaxable bound constraints, which must be satisfied before the objective function can be evaluated. Our method reformulates the unrelaxable bound-constrained problem as an unconstrained optimization problem that is amenable to existing unconstrained optimization methods. The reformulation relies on a domain warping to form a merit function; the choice of the warping determines the level of exactness with which the unconstrained problem can be used to find solutions to the bound-constrained problem, as well as key properties of the unconstrained formulation such as smoothness. We develop theory when the domain warping is a multioutput sigmoidal warping, and we explore the practical elements of applying unconstrained optimization methods to the formulation. Here, we develop an algorithm that exploits the structure of the sigmoidal warping to guarantee that unconstrained optimization algorithms applied to the merit function will find a stationary point to the desired tolerance.
97 MATHEMATICS AND COMPUTING↗
Impact of shorter wavelengths on optical quality for laws
This study explores parametrically as a function of wavelength the degrading effects of several common optical aberrations (defocus, astigmatism, wavefronttilts, etc.), using the heterodyne mixing efficiency factor as the merit function. A 60 cm diameter aperture beam expander with an expansion ratio of 15:1 and a primary mirror focal ratio of f/2 was designed for the study. An HDOS copyrighted analysis program determined the value of merit function for various optical misalignments. With sensitivities provided by the analysis, preliminary error budget and tolerance allocations were made for potential optical wavefront errors and boresight errors during laser shot transit time. These were compared with the baseline 1.5 m CO2 laws and the optical fabrication state of the art (SOA) as characterized by the Hubble Space Telescope. Reducing wavelength and changing optical design resulted in optical quality tolerances within the SOA both at 2 and 1 micrometer. However, advanced sensing and control devices would be necessary to be tightened by a factory of 1.8 for a 2 micrometer system and by 3.6 for a 1 micrometer system relative to the baseline CO2 LAWS. Available SOA components could be used for operation at 2 micrometers but operation at 1 micrometer does not appear feasible.
Wissinger, Alan B.↗
Impact of shorter wavelengths on optical quality for laws
This study explores parametrically as a function of wavelength the degrading effects of several common optical aberrations (defocus, astigmatism, wavefront tilts, etc.), using the heterodyne mixing efficiency factor as the merit function. A 60 cm diameter aperture beam expander with an expansion ratio of 15:1 and a primary mirror focal ratio of f/2 was designed for the study. An HDOS copyrighted analysis program determined the value of merit function for various optical misalignments. With sensitivities provided by the analysis, preliminary error budget and tolerance allocations were made for potential optical wavefront errors and boresight errors during laser shot transit time. These were compared with the baseline l.5 m CO2 LAWS and the optical fabrication state of the art (SOA) as characterized by the Hubble Space Telescope. Reducing wavelength and changing optical design resulted in optical quality tolerances within the SOA both at 2 and 1 micrometers. However, advanced sensing and control devices would be necessary to maintain on-orbit alignment. Optical tolerance for maintaining boresight stability would have to be tightened by a factor of 1.8 for a 2 micrometers system and by 3.6 for a 1 micrometers system relative to the baseline CO2 LAWS. Available SOA components could be used for operation at 2 micrometers but operation at 1 micrometers does not appear feasible.
Wissinger, Alan B.↗
Using Approximations to Accelerate Engineering Design Optimization
Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.
Torczon, Virginia↗
Report of the subpanel on resampling functions
The state of the art and anticipated requirements for resampling in applications of remote sensing are examined. It is noted that the wide range of potential applications and expanded needs for resampling versatility in new imaging sensors leads to a concern for creating standardized test data sets and ground training sites. Several research areas are defined including the development of (1) a theory for defining an input psf of an instrument such that upon resampling of the processed data into the desired output grid the radiometric and geometric properties are a best estimate of the true upwelling radiances; (2) algorithms for estimating missing data or for ignoring missing data; (3) optimal resampling functions; (4) standard data sets; and (5) merit functions for assessing resampling techniques.
Source record↗
OSA Spotlight Summary: Designing Miniature X-ray Optics for the SmallSat Lunar Science Mission Concept CubeX
The scientific demand for extended field X-Ray remote sensing for mapping of planetary bodies has produced the CubeSat X-ray Telescope (CubeX) lunar mission concept. Orbiting the Moon at 6,000 km for 1 year sometime during the mid-decade solar maximum, the primary objectives of CubeX are to map lunar surface elemental abundances and to assess feasibility of x-ray pulsar timing navigation. CubeX’s Miniature X-ray Optics (MiXO) design builds on heritage of existing X-ray imaging designs using new electroformed NiCo alloy replication (ENR) to create shells of 1 mm thickness. MiXO will provide 1 arcmin resolution X-Ray imaging for an extended instantaneous field of view, at various energy range sensitivities. Based on the classic Wolter-Type I design (using a paraboloid/hyperboloid grazing mirror pair), mirror parameters were expanded to allow both shell length and focal-plane offsets to vary independently. The design was optimized with a merit function that factored together four sub-merits: PSF sharpness (measured as half-power diameter), consistency across the field, minimized scattering, and maximized effective area. Monte Carlo analysis was used to predict final performance, including surface scatter effects. The demonstrated configurations include a compact 34 shell design with a diameter of 105 mm more efficient at higher energies, and a larger 130 mm/24 shell version with a larger overall effective area at lower energies. The compact design carries more expensive fabrication and assembly cost (with more shells) as well as a more challenging alignment (with denser packing). Both have overall resolution <1’ up to 26’ off-axis and <1.5’ up to 33’ off-axis, whereas a conventional design’s image quality degrades quickly beyond 15’ off-axis. This opens up new possibilities for future SmallSat missions that could use two different configurations for wide energy ranges or midsized instruments using multiple identical modules for larger collecting area.
x-ray↗
A parallel trajectory optimization tool for aerospace plane guidance
A parallel trajectory optimization algorithm is being developed. One possible mission is to provide real-time, on-line guidance for the National Aerospace Plane. The algorithm solves a discrete-time problem via the augmented Lagrangian nonlinear programming algorithm. The algorithm exploits the dynamic programming structure of the problem to achieve parallelism in calculating cost functions, gradients, constraints, Jacobians, Hessian approximations, search directions, and merit functions. Special additions to the augmented Lagrangian algorithm achieve robust convergence, achieve (almost) superlinear local convergence, and deal with constraint curvature efficiency. The algorithm can handle control and state inequality constraints such as angle-of-attack and dynamic pressure constraints. Portions of the algorithm have been tested. The nonlinear programming core algorithm performs well on a variety of static test problems and on an orbit transfer problem. The parallel search direction algorithm can reduce wall clock time by a factor of 10 for this part of the computation task.
Psiaki, Mark L.↗
An adaptive stochastic sequential quadratic programming with differentiable exact augmented lagrangians
In this study, we consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and simplify an old SQP method Lucidi developed for solving deterministic problems, which serves as the skeleton of our stochastic algorithm. Based on the simplified deterministic algorithm, we then propose a non-adaptive SQP for dealing with stochastic objective, where the gradient and Hessian are replaced by stochastic estimates but the stepsizes are deterministic and prespecified. Finally, we incorporate a recent stochastic line search procedure Paquette and Scheinberg into the non-adaptive stochastic SQP to adaptively select the random stepsizes, which leads to an adaptive stochastic SQP. The global "almost sure" convergence for both non-adaptive and adaptive SQP methods is established. Numerical experiments on nonlinear problems in CUTEst test set demonstrate the superiority of the adaptive algorithm.
97 MATHEMATICS AND COMPUTING↗