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NASA NTRS1995

Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis

Explicit expressions for terms of the stiffness and geometric stiffness matrices are derived for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation is based on Ritz analysis using simple polynomials, and leads to explicit expressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber directions, and panel shape. Integration with wing box analysis using either the equivalent plate approach or the finite element method, makes it possible to obtain sensitivities of panel buckling constraints with respect to wing planform shape or locations of internal ribs and spars. The analytic sensitivities are used to construct approximations of panel buckling constraints for integrated wing/panel design synthesis.

Livne, Eli↗

NASA NTRS1999

Sensitivity Analysis of ProSEDS (Propulsive Small Expendable Deployer System) Data Communication System

This paper discusses analytical approaches to evaluating performance of Spacecraft On-Board Computing systems, thereby ultimately achieving a reliable spacecraft data communications systems. The sensitivity analysis approach of memory system on the ProSEDS (Propulsive Small Expendable Deployer System) as a part of its data communication system will be investigated. Also, general issues and possible approaches to reliable Spacecraft On-Board Interconnection Network and Processor Array will be shown. The performance issues of a spacecraft on-board computing systems such as sensitivity, throughput, delay and reliability will be introduced and discussed.

Park, Nohpill↗

NASA NTRS1977

Benefit-cost evaluation of an intra-regional air service in the Bay area

Utilization of an iterative statistical model is presented to evaluate combinations of commuter airport sites and surface transportation facilities in confunction with service by a given commuter aircraft type in light of Bay Area regional growth alternatives and peak and off-peak regional travel patterns. The model evaluates such transportation options with respect to criteria of airline profitability, public acceptance, and public and private nonuser costs. It incorporates information modal split, peak and off-peak use of the air commuter fleet, terminal and airport cost, development costs and uses of land in proximity to the airport sites, regional population shifts, and induced zonal shifts in travel demand. The model is multimodal in its analytical capability, and performs exhaustive sensitivity analysis.

Haefner, L. E.↗

NASA NTRS1978

Executive summary: Benefit-cost evaluation of an intra-regional air service in the Bay Area and a technology assessment of transportation system investments

The benefits and costs that would result from an intra-regional air service operation in the San Francisco Bay area were determined by utilizing an iterative statistical decision model to evaluate combinations of commuter airport sites and surface transportation facilities in conjunction with service by a given commuter aircraft type in light of area regional growth alternatives and peak and off-peak regional travel patterns. The model evaluates such transportation option with respect to criteria of airline profitability, public acceptance, and public and private non-user costs. In so doing, it incorporates information on modal split, peak and off-peak use of the air commuter fleet, terminal and airport costs, development costs and uses of land in proximity to the airport sites, regional population shifts, and induced zonal shifts in travel demand. The model is multimodal in its analytic capability, and performs exhaustive sensitivity analysis.

Haefner, L. E.↗

NASA NTRS1988

Metal with anomalously low Ni and Ge concentrations in the Allan Hills A77081 winonaite

The Ge content of metal in the Allan Hills A77081 winonaite was determined by high-sensitivity electron microprobe analysis. By optimizing analytical conditions for Ge determination, a detection limit of about 75 ppm could be achieved. In A77081 some small kamacite grains contain less Ni and Ge and more Co than coarse-grained metal. These small grains are always associated with sulfide, raising the possibility that anomalous metal is related to eutectic melting. However, when published partition coefficients for Ni and Ge in the Fe-Ni-S system are used to model fractionation of these elements during eutectic melting, one finds that secondary metal should be enriched in Ni and depleted in Ge. Thus, the positive Ni-Ge correlation found in this study is the opposite of the expected trend. No explanation for this discrepancy has yet been found. Nonetheless, the existence of anomalous metal is an indication that A77081, and probably other winonaites as well, have undergone some fractionation. This supports the notion that the high-temperature history of winonaites is related to the formation of IAB iron meteorites, whose silicate inclusions are very similar to winonaites.

Kracher, Alfred↗

NASA NTRS1989

Results of an integrated structure/control law design sensitivity analysis

A design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations is discussed. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changes in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient than finite difference methods for the computation of the equivalent sensitivity information.

Gilbert, Michael G.↗

NASA NTRS1975

Space shuttle SRM plume expansion sensitivity analysis

The exhaust plumes of the space shuttle solid rocket motors can have a significant effect on the base pressure and base drag of the shuttle vehicle. A parametric analysis was conducted to assess the sensitivity of the initial plume expansion angle of analytical solid rocket motor flow fields to various analytical input parameters and operating conditions. The results of the analysis are presented and conclusions reached regarding the sensitivity of the initial plume expansion angle to each parameter investigated. Operating conditions parametrically varied were chamber pressure, nozzle inlet angle, nozzle throat radius of curvature ratio and propellant particle loading. Empirical particle parameters investigated were mean size, local drag coefficient and local heat transfer coefficient. Sensitivity of the initial plume expansion angle to gas thermochemistry model and local drag coefficient model assumptions were determined.

Smith, S. D.↗

NASA NTRS1976

Definition study for photovoltaic residential prototype system

A site evaluation was performed to assess the relative merits of different regions of the country in terms of the suitability for experimental photovoltaic powered residences. Eight sites were selected based on evaluation criteria which included population, photovoltaic systems performance and the cost of electrical energy. A parametric sensitivity analysis was performed for four selected site locations. Analytical models were developed for four different power system implementation approaches. Using the model which represents a direct (or float) charge system implementation the performance sensitivity to the following parameter variations is reported: (1) solar roof slope angle; (2) ratio of the number of series cells in the solar array to the number of series cells in the lead-acid battery; and (3) battery size. For a Cleveland site location, a system with no on site energy storage and with a maximum power tracking inverter which feeds back excess power to the utility was shown to have 19 percent greater net system output than the second place system. The experiment test plan is described. The load control and data acquisition system and the data display panel for the residence are discussed.

Shepard, N. F.↗

DOE OSTI2026

Control Parameter Sensitivity Study for Inverter-Based-Resource Dominated Grids: A Small Signal Stability Approach and Framework

The growing adoption of renewable energy is driving the prevalence of inverter-based resources (IBRs) within power grids. Future power grids will integrate both grid-following IBRs (GFM-IBRs) and grid-forming IBRs (GFL-IBRs) alongside synchronous generators. Therefore, it is crucial to perform stability studies that account for all components and especially control interactions related to IBRs. Extensive research has performed to study the IBR-related stability, however, the sensitivity study of IBRs' control parameters on system stability has not been adequately studied yet, especially from a systematic way. Therefore, this paper conducts a small signal stability analysis for a generic grid with multiple types of resources and develops an analytical framework for assessing the sensitivity of control parameters affecting stability margins. To achieve that, the non-autonomous reduced-order non-linear dynamic model is developed for a generic power system with multiple synchronous generator-based resources (SGBRs), GFM-IBRs, and GFL-IBRs. Based on the analytic model, a systematic framework for parametric sensitivity on systems' asymptotic stability is developed. A parameter sensitivity analysis based on eigenvalue methods is proposed. The impact of the droop controllers of GFM-IBRs, PQ-dispatch and the PLL controller of GFL-IBR on the system asymptotic stability is discussed. This sensitivity study is aiming to provide deep insights on control parameters' impact on system stability, and gives direction for parameter tuning in case of instability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1995

Implementation of a multiblock sensitivity analysis method in numerical aerodynamic shape optimization

A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.

Lacasse, James M.↗

DOE OSTI2020

Data-Driven Preemptive Voltage Monitoring and Control Using Probabilistic Voltage Sensitivities

Increased penetration levels of distributed variable renewable generation can cause random voltage fluctuations and violations at multiple nodes. Traditional methods of voltage control typically involve reactionary responses of capacitor banks, tap changers, and recently even smart inverters. But because of the lack of foresight in voltage violations, these controls are ineffective to completely mitigate the issue. Therefore, new methods of predicting voltage violations subject to random power injection changes in the distribution network are needed, which can be used to guide optimal and dynamic methods of voltage control. This work lays the foundation for such preemptive voltage monitoring and control by proposing an analytical and sensor data-driven voltage sensitivity analysis method. Driven by stochastic data and forecasts, the method can be used to develop probabilistic voltage sensitivities and consequently to predict system nodes with high likelihood of voltage limit violations. The effectiveness of this method is tested on IEEE 69-node distribution system integrated with distributed solar. The results demonstrate the proposed method's ability to successfully predict nodes with high probability of voltage violations for a specific time-series simulation. The results also demonstrate the ability to guide timely power injection control actions to mitigate future voltage violations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1983

Experimental modal analysis

Experimental modal analysis is extremely important with regard to verification of analytical models, identification of vibration and acoustic problems, and structural modification and sensitivity analysis. With the expanding access of the testing environment to computational power, the complexity of existing approaches, as well as the development of new approaches, to the estimation of modal parameters has grown tremendously. Currently, the state of the art in experimental modal analysis involves methods that can be grouped in four categories: forced normal mode excitation method, frequency response function method, damped complex exponential function method, and mathematical input-output model methods. The theoretical basis of each of these general approaches, with appropriate references, is reviewed briefly.

Allemang, R. J.↗

NASA NTRS1984

A rotor optimization using regression analysis

The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

Giansante, N.↗

NASA NTRS1994

Analytic Sensitivities for Shape Optimization in Equivalent Plate Structural Wing Models

Equivalent plate modeling techniques based on Ritz analysis with simple polynomials prove to be efficient tools for structural modeling of wings in the preliminary design stage. Accuracy problems are encountered, however, when these models are used to obtain finite difference behavior sensitivities with respect to planform shape. The accuracy problems are associated with the poor numerical conditioning of static and eigenvalue equations. As higher-order polynomials are being used to Improve the analysis itself, the more sensitive is the finite difference derivative to the step size used. This article describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for stiffness and mass matrix elements without the need to perform numerical integration. This formulation leads naturally to analytic expressions for the derivatives of displacements, stresses, and natural frequencies with respect to shape design variables. This article examines the accuracy of finite difference derivatives compared with the analytic derivatives, and shows that In some cases it is impossible to obtain any information of value by finite differences. Analytic sensitivities, in this case, are still sufficiently accurate for design optimization.

Livne, Eli↗

NASA NTRS1975

Low gravity synthesis of polymers with controlled molecular configuration

Heterogeneous chemical systems have been studied for the synthesis of isotactic polypropylene in order to establish baseline parameters for the reaction process and to develop sensitive and accurate methods of analysis. These parameters and analytical methods may be used to make a comparison between the polypropylene obtained at one g with that of zero g (gravity). Baseline reaction parameters have been established for the slurry (liquid monomer in heptane/solid catalyst) polymerization of propylene to yield high purity, 98% isotactic polypropylene. Kinetic data for the slurry reaction showed that a sufficient quantity of polymer for complete characterization can be produced in a reaction time of 5 min; this time is compatible with that available on a sounding rocket for a zero-g simulation experiment. The preformed (activated) catalyst was found to be more reproducible in its activity than the in situ formed catalyst.

Heimbuch, A. H.↗

DOE OSTI2021

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I: Flux and Eigenvalue Solutions

Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Furthermore, original analytic expressions are established to quantify the discrepancy between the ψ k (E) and ψ α (E) flux amplitudes, respective solutions of the multiplication factor k, or the exponential time-evolution frequency α eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition α=0. Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239 Pu, the 6.67-eV resonance of 238 U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1990

Design sensitivity derivatives for isoparametric elements by analytical and semi-analytical approaches

This paper presents an analytical approach for incorporating design sensitivity calculations directly into the finite element analysis. The formulation depends on the implicit differentiation approach and requires few additional calculations to obtain the design sensitivity derivatives. In order to evaluate this approach, it is compared with the semi-analytical approach which is based on commonly used finite difference formulations. Both approaches are implemented to calculate the design sensitivities for continuum and structural isoparametric elements. To demonstrate the accuracy and robustness of the developed analytical approach compared to the semi-analytical approach, some test cases using different structural and continuum element types are presented.

Zumwalt, Kenneth W.↗

NASA NTRS1991

Aerodynamic sensitivity analysis methods for the compressible Euler equations

This study presents a mathematical formulation developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible 2D Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. The finite difference approach and the quasi-analytical approach are used to determine the aerodynamic sensitivity coefficients. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flowfield solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.

Baysal, Oktay↗