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NASA NTRS1990

Improved calculation of optimum design sensitivity

Optimum design parameter sensitivity analysis has become an important topic in recent years. The principal reasons for obtaining optimum design sensitivity information with respect to various problem parameters are (l) to predict revised optimum designs, associated with specified perturbations of the problem parameters, without re-optimizing the problem and, (2) to provide sensitivity information in multilevel optimization strategies. Methods for calculating these derivatives were proposed by several authors. The most important drawback in estimating parameter sensitivities by the current methods is that they do not allow for changes in the active constraint set. Changes in the active constraint set produce discontinuities in the optimum design sensitivities, and therefore, a correct formulation has to be cast in terms of directional derivatives. Optimum design parameter sensitivity analysis is addressed in terms of directional derivatives so as to include possible discontinuities and it also presents a method for estimating optimum design sensitivities using finite differences.

Sepulveda, Abdon E.↗

NASA NTRS2011

Electromagnetic Launch Vehicle Fairing and Acoustic Blanket Model of Received Power Using FEKO

Evaluating the impact of radio frequency transmission in vehicle fairings is important to sensitive spacecraft. This paper employees the Multilevel Fast Multipole Method (MLFMM) feature of a commercial electromagnetic tool to model the fairing electromagnetic environment in the presence of an internal transmitter. This work is an extension of the perfect electric conductor model that was used to represent the bare aluminum internal fairing cavity. This fairing model includes typical acoustic blanketing commonly used in vehicle fairings. Representative material models within FEKO were successfully used to simulate the test case.

Trout, Dawn H.↗

NASA NTRS2011

Electromagnetic Launch Vehicle Fairing and Acoustic Blanket Model of Received Power Using FEKO

Evaluating the impact of radio frequency transmission in vehicle fairings is important to electromagnetically sensitive spacecraft. This study employs the multilevel fast multipole method (MLFMM) from a commercial electromagnetic tool, FEKO, to model the fairing electromagnetic environment in the presence of an internal transmitter with improved accuracy over industry applied techniques. This fairing model includes material properties representative of acoustic blanketing commonly used in vehicles. Equivalent surface material models within FEKO were successfully applied to simulate the test case. Finally, a simplified model is presented using Nicholson Ross Weir derived blanket material properties. These properties are implemented with the coated metal option to reduce the model to one layer within the accuracy of the original three layer simulation.

Trout, Dawn H.↗

NASA NTRS2019

Multilevel Monte Carlo Estimation of Unbiased Expectation via Sample Reuse and the Low Variance Estimation of Asymptotic Rates

A new variant of the multilevel Monte Carlo estimator [5, 3, 9, 12] is presented for the estimation of expectation statistics that utilizes sample reuse in specified levels, explicitly removes approximation error bias associated with numerically computed output quantities of interest that have an asymptotic limit behavior, and permits a low variance estimate of the asymptotic rate of convergence to that limit. In addition, it is shown that this new multilevel Monte Carlo variant can yield a computational cost savings. A review of Monte Carlo and multilevel Monte Carlo estimators is presented that includes analysis of expected value, expected mean squared error, and the calculation of optimized multilevel sample size parameters. The multilevel Monte Carlo estimator produces estimates of expectation for numerically approximated output quantities of interest that are biased by approximation error. When the quantity of interest can be modeled as the asymptotic limit of numerically approximated output quantities of interest, it is theoretically possible to remove this approximation error bias in the multilevel Monte Carlo estimator. In actual implementations, however, this procedure is unreliable due to statistical variability and inaccuracy in estimating the needed asymptotic limit. Analysis and numerical experiment show that the proposed variant of the multilevel Monte Carlo method greatly reduces (in some cases eliminates) the statistical variability in this limit estimation.

Barth, Timothy↗

NASA NTRS1994

Buckling and vibration analysis of laminated panels using VICONOPT

The analysis aspects of the 23,000-line FORTRAN program VIPASA with constraints and optimization (VICONOPT) are described. Overall stiffness matrices assembled from the earlier exact vibration and instability of plate assemblies including shear and anisotropy (VIPASA) flat plate stiffnesses are optionally coupled by Langrangian multipliers to find critical buckling loads, or natural frequencies of undamped vibration, of prismatic assemblies of anisotropic flat plates with arbitrarily located point supports or simple transverse supporting frames. The longitudunal continuity of typical wing and fuselage panels is closely approximated because the solutions are for the infinitely long structure obtained by repeating a bay and its supports longitudinally. Any longitudinally invariant in-plane plate stresses are permitted, and very rapid solutions are guaranteed by numerous refinements, including multilevel substructuring and a method for repetitive cross sections that is exact for regular polygons used to represent cylinders. Modal displacements and stresses in or between plies of laminated plates are calculated and plotted, with values being recovered at all nodes of substructures. Comparison with usual approximate finite-element methods confirms that, for comparably converged solutions, VICONOPT is typically between 100 and 10(exp 4) times faster.

Kennedy, David↗

NASA NTRS1974

Design guidelines for advanced LSI microcircuit packaging using thick film multilayer technology

Ceramic multilayer circuitry results from the sequential build-up of two or more layers of pre-determined conductive interconnections separated by dielectric layers and fired at an elevated temperature to form a solidly fused structure. The resultant ceramic interconnect matrix is used as a base to mount active and passive devices and provide the necessary electrical interconnection to accomplish the desired electrical circuit. Many methods are known for developing multilevel conductor mechanisms such as multilayer printed circuits, welded wire matrices, flexible copper tape conductors, and thin and thick-film ceramic multilayers. Each method can be considered as a specialized field with each possessing its own particular set of benefits and problems. This design guide restricts itself to the art of design, fabrication and assembly of ceramic multilayer circuitry and the reliability of the end product.

Peckinpaugh, C. J.↗

NASA NTRS1984

Aerospace engineering design by systematic decomposition and multilevel optimization

This paper describes a method for systematic analysis and optimization of large engineering systems, e.g., aircraft, by decomposition of a large task into a set of smaller, self-contained subtasks that can be solved concurrently. The subtasks may be arranged in many hierarchical levels with the assembled system at the top level. Analyses are carried out in each subtask using inputs received from other subtasks, and are followed by optimizations carried out from the bottom up. Each optimization at the lower levels is augmented by analysis of its sensitivity to the inputs received from other subtasks to account for the couplings among the subtasks in a formal manner. The analysis and optimization operations alternate iteratively until they converge to a system design whose performance is maximized with all constraints satisfied. The method, which is still under development, is tentatively validated by test cases in structural applications and an aircraft configuration optimization. It is pointed out that the method is intended to be compatible with the typical engineering organization and the modern technology of distributed computing.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1989

Multilevel filtering elliptic preconditioners

A class of preconditioners is presented for elliptic problems built on ideas borrowed from the digital filtering theory and implemented on a multilevel grid structure. They are designed to be both rapidly convergent and highly parallelizable. The digital filtering viewpoint allows the use of filter design techniques for constructing elliptic preconditioners and also provides an alternative framework for understanding several other recently proposed multilevel preconditioners. Numerical results are presented to assess the convergence behavior of the new methods and to compare them with other preconditioners of multilevel type, including the usual multigrid method as preconditioner, the hierarchical basis method and a recent method proposed by Bramble-Pasciak-Xu.

Kuo, C. C. Jay↗

NASA NTRS1990

Direct handling of equality constraints in multilevel optimization

In recent years there have been several hierarchic multilevel optimization algorithms proposed and implemented in design studies. Equality constraints are often imposed between levels in these multilevel optimizations to maintain system and subsystem variable continuity. Equality constraints of this nature will be referred to as coupling equality constraints. In many implementation studies these coupling equality constraints have been handled indirectly. This indirect handling has been accomplished using the coupling equality constraints' explicit functional relations to eliminate design variables (generally at the subsystem level), with the resulting optimization taking place in a reduced design space. In one multilevel optimization study where the coupling equality constraints were handled directly, the researchers encountered numerical difficulties which prevented their multilevel optimization from reaching the same minimum found in conventional single level solutions. The researchers did not explain the exact nature of the numerical difficulties other than to associate them with the direct handling of the coupling equality constraints. The coupling equality constraints are handled directly, by employing the Generalized Reduced Gradient (GRG) method as the optimizer within a multilevel linear decomposition scheme based on the Sobieski hierarchic algorithm. Two engineering design examples are solved using this approach. The results show that the direct handling of coupling equality constraints in a multilevel optimization does not introduce any problems when the GRG method is employed as the internal optimizer. The optimums achieved are comparable to those achieved in single level solutions and in multilevel studies where the equality constraints have been handled indirectly.

Renaud, John E.↗

NASA NTRS2020

Bayesian Statistical Models for Community Annoyance Survey Data

This paper demonstrates the use of two Bayesian statistical models to analyze single-event sonic boom exposure and human annoyance data from community response surveys. Each model is fit to data from a NASA pilot study.Unlike many community noise surveys, this study used a panel sample to collect multiple observations per participant instead of a single observation. Thus, a multilevel (also known as hierarchical or mixed-effects) model is used to account for the within-subject correlation in the panel sample data. This paper describes a multilevel logistic regression model and a multilevel ordinal regression model. The paper also proposes a method for calculating a summary dose-response curve from the multilevel models that represents the population. The two models’ summary dose-response curves are visually similar. However, their estimates differ when calculating the noise dose at a fixed percent highly annoyed.

Musical instruments↗

NASA NTRS1977

The application of LANDSAT-1 imagery for monitoring strip mines in the new river watershed in northeast Tennessee, part 2

The author has identified the following significant results. LANDSAT imagery and supplementary aircraft photography of the New River drainage basin were subjected to a multilevel analysis using conventional photointerpretation methods, densitometric techniques, multispectral analysis, and statistical tests to determine the accuracy of LANDSAT-1 imagery for measuring strip mines of common size. The LANDSAT areas were compared with low altitude measurements. The average accuracy over all the mined land sample areas mapped from LANDSAT-1 was 90%. The discrimination of strip mine subcategories is somewhat limited on LANDSAT imagery. A mine site, whether active or inactive, can be inferred by lack of vegetation, by shape, or image texture. Mine ponds are difficult or impossible to detect because of their small size and turbidity. Unless bordered and contrasted with vegetation, haulage roads are impossible to delineate. Preparation plants and refuge areas are not detectable. Density slicing of LANDSAT band 7 proved most useful in the detection of reclamation progress within the mined areas. For most state requirements for year-round monitoring of surface mined land, LANDSAT is of limited value. However, for periodic updating of regional surface maps, LANDSAT may provide sufficient accuracies for some users.

Shahrokhi, F.↗

NASA NTRS1982

Method for sequentially processing a multi-level interconnect circuit in a vacuum chamber

The processing of wafer devices to form multilevel interconnects for microelectronic circuits is described. The method is directed to performing the sequential steps of etching the via, removing the photo resist pattern, back sputtering the entire wafer surface and depositing the next layer of interconnect material under common vacuum conditions without exposure to atmospheric conditions. Apparatus for performing the method includes a vacuum system having a vacuum chamber in which wafers are processed on rotating turntables. The vacuum chamber is provided with an RF sputtering system and a DC magnetron sputtering system. A gas inlet is provided in the chamber for the introduction of various gases to the vacuum chamber and the creation of various gas plasma during the sputtering steps.

Routh, D. E.↗

NASA NTRS1992

Non-LTE radiative transfer with lambda-acceleration - Convergence properties using exact full and diagonal lambda-operators

We investigate the convergence properties of Lambda-acceleration methods for non-LTE radiative transfer problems in planar and spherical geometry. Matrix elements of the 'exact' A-operator are used to accelerate convergence to a solution in which both the radiative transfer and atomic rate equations are simultaneously satisfied. Convergence properties of two-level and multilevel atomic systems are investigated for methods using: (1) the complete Lambda-operator, and (2) the diagonal of the Lambda-operator. We find that the convergence properties for the method utilizing the complete Lambda-operator are significantly better than those of the diagonal Lambda-operator method, often reducing the number of iterations needed for convergence by a factor of between two and seven. However, the overall computational time required for large scale calculations - that is, those with many atomic levels and spatial zones - is typically a factor of a few larger for the complete Lambda-operator method, suggesting that the approach should be best applied to problems in which convergence is especially difficult.

Macfarlane, J. J.↗

NASA NTRS1984

An improved computational approach for multilevel optimum design

A penalty-function algorithm employing Newton's method with approximate second derivatives (Haftka and Starnes, 1980) is developed for two-level hierarchical design optimization problems. The difficulties posed by discontinuous behavior in typical multilevel problems are explained and illustrated for the case of a three-bar truss; the algorithm is formulated; and its advantages are demonstrated in the problem of a portal framework having three beams (described by six cross-section parameters), subjected to two loading conditions, and to be constructed in six different materials for comparison. The final design parameters are listed in a table.

Haftka, R. T.↗

NASA NTRS1987

Experiments in encoding multilevel images as quadtrees

Image storage requirements for several encoding methods are investigated and the use of quadtrees with multigray level or multicolor images are explored. The results of encoding a variety of images having up to 256 gray levels using three schemes (full raster, runlength and quadtree) are presented. Although there is considerable literature on the use of quadtrees to store and manipulate binary images, their application to multilevel images is relatively undeveloped. The potential advantage of quadtree encoding is that an entire area with a uniform gray level may be encoded as a unit. A pointerless quadtree encoding scheme is described. Data are presented on the size of the quadtree required to encode selected images and on the relative storage requirements of the three encoding schemes. A segmentation scheme based on the statistical variation of gray levels within a quadtree quadrant is described. This parametric scheme may be used to control the storage required by an encoded image and to preprocess a scene for feature identification. Several sets of black and white and pseudocolor images obtained by varying the segmentation parameter are shown.

Lansing, Donald L.↗

DOE OSTI2026

Two-Level System Spectroscopy from Correlated Multilevel Relaxation in Superconducting Qubits

Transmon qubits are a cornerstone of modern superconducting quantum computing platforms. Temporal fluctuations of energy relaxation in these qubits are widely attributed to microscopic two-level systems (TLSs) in device dielectrics and interfaces, yet isolating individual defects typically relies on tuning the qubit or the TLS into resonance. We demonstrate a novel spectroscopy method for fixed-frequency transmons based on multilevel relaxation: repeated preparation of the second excited state and simultaneous $T_1$ extraction of the first and second excited states reveals characteristic correlations in the decay rates of adjacent transitions. From these correlations we identify one or more dominant TLSs and reconstruct their frequency drift over time. Remarkably, we find that TLSs detuned by $\gtrsim 100\,\mathrm{MHz}$ from the qubit transition can still significantly influence relaxation. The proposed method provides a powerful tool for TLS spectroscopy without the need to tune the transmon frequency, either via a flux-tunable inductor or AC-Stark shifts.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗

NASA NTRS1976

A lateral boundary formulation for multi-level prediction models

A method is proposed for treating the lateral boundaries of a limited-area weather prediction model. The method involves the relaxation of the interior flow in the vicinity of the boundary to the external fully prescribed flow. Analytical and numerical results obtained with a linearized multilevel model confirm the effectiveness of this computationally effective method. The method is shown to give an adequate representation of outgoing gravity waves with and without an ambient shear flow and to allow the substantially undistorted transmission of geostrophically balanced flow out of the interior of the limited domain.

Davies, H. C.↗

NASA NTRS1976

Laser induced fluorescence applied to turbulent reacting flows

The saturated fluorescence method makes use of the great simplifications which occur when under conditions of intense radiation the excitation process becomes saturated. A description is presented of the saturated fluorescence method, taking into account rate equations and saturation, radiative transfer, the two-level system, a multilevel system, and measurements under saturation conditions. The detectability limits of the method are investigated. Fluorescence trapping is found to place an upper limit on the number density of the fluorescing species that can be measured without signal loss. Turbulence places time and spatial constraints on the measurements, but otherwise poses no difficulties. Saturated laser induced fluorescence spectroscopy appears to be a most promising method for measuring species concentrations in flames.

Daily, J. W.↗