Elight path analysis and mission planning for Mariner Venus 67.
Trajectory design and mission planning for Mariner Venus 67 /Mariner 5/ space project, discussing perturbative forces, orbit determination and midcourse guidance
Gordon, H. J.↗
SEARCH · Engineering Papers
Results for “perturbation analysis”
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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A limiting analysis for edge effects in angle-ply laminates
A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.
Hsu, P. W.↗
Interpretation of ozone temperature correlations. II - Analysis of SBUV ozone data
In an effort to understand the behavior of ozone in the transition region, the terms in the perturbation continuity equation have been evaluated from solar backscattered ultraviolet ozone data, National Meteorological Center temperature data, and geostrophic winds derived from the temperature data at 2 mbar, winter 1978-1979. A linear parameterization is used to estimate the chemical source term. The perturbation ozone field calculated by integrating the net forcing evaluated from the data compares well with the measured perturbation ozone field. There are occasions during the winter when the sum of the dynamic terms is small due to cancellation, and the ozone and temperature perturbations are anticorrelated. The -1 correlation between the ozone and temperature perturbations does not necessarily imply that chemical forcing is dominant.
Douglass, A. R.↗
A Non-Intrusive Algorithm for Sensitivity Analysis of Chaotic Flow Simulations
We demonstrate a novel algorithm for computing the sensitivity of statistics in chaotic flow simulations to parameter perturbations. The algorithm is non-intrusive but requires exposing an interface. Based on the principle of shadowing in dynamical systems, this algorithm is designed to reduce the effect of the sampling error in computing sensitivity of statistics in chaotic simulations. We compare the effectiveness of this method to that of the conventional finite difference method.
Blonigan, Patrick J.↗
Phase Plane Analysis and Observed Frozen Orbit for the TOPEX/Poseidon Mission
The existence and stability of low eccentricity frozen orbits in a zonal geopotential perturbed by atmospheric drag, solar radiation pressure, and a continuous along-track thrust is studied. General expressions are derived for the steady state eccentricity and gravity- only phase plane trajectories. The TOPEX/Poseidon satellite has remained in a frozen orbit throughout its three year primary mission.
TOPEX/Poseidon↗
Galaxy bias in the era of LSST: perturbative bias expansions
Upcoming imaging surveys will allow for high signal-to-noise measurements of galaxy clustering at small scales. In this work, we present the results of the Rubin Observatory Legacy Survey of Space and Time (LSST) bias challenge, the goal of which is to compare the performance of different nonlinear galaxy bias models in the context of LSST Year 10 (Y10) data. Specifically, we compare two perturbative approaches, Lagrangian perturbation theory (LPT) and Eulerian perturbation theory (EPT) to two variants of Hybrid Effective Field Theory (HEFT), with our fiducial implementation of these models including terms up to second order in the bias expansion as well as nonlocal bias and deviations from Poissonian stochasticity. Here, we consider a variety of different simulated galaxy samples and test the performance of the bias models in a tomographic joint analysis of LSST-Y10-like galaxy clustering, galaxy-galaxy-lensing and cosmic shear. We find both HEFT methods as well as LPT and EPT combined with non-perturbative predictions for the matter power spectrum to yield unbiased constraints on cosmological parameters up to at least a maximal scale of k max = 0.4 Mpc -1 for all samples considered, even in the presence of assembly bias. While we find that we can reduce the complexity of the bias model for HEFT without compromising fit accuracy, this is not generally the case for the perturbative models. We find significant detections of non-Poissonian stochasticity in all cases considered, and our analysis shows evidence that small-scale galaxy clustering predominantly improves constraints on galaxy bias rather than cosmological parameters. These results therefore suggest that the systematic uncertainties associated with current nonlinear bias models are likely to be subdominant compared to other sources of error for tomographic analyses of upcoming photometric surveys, which bodes well for future galaxy clustering analyses using these high signal-to-noise data.
79 ASTRONOMY AND ASTROPHYSICS↗
Sensitivity of magnetic islands in permanent magnet stellarators using the gradient and Hessian methods
Stellarator plasmas are known to be very sensitive to perturbations in the magnetic field. The permanent magnet stellarator was in part developed as a solution to high machining tolerances placed on the shape properties of electromagnetic coils in traditional stellarators. However, as a consequence of this high sensitivity to the field structure, sensitivities of permanent magnet stellarator plasmas to perturbations of permanent magnet properties must necessarily be well-understood. The gradient and Hessian matrix methods have been previously demonstrated to be useful sensitivity analysis methods for modular coils. We apply these two methods to the study of island width sensitivities in both the MUSE and PM4STELL permanent magnet stellarator projects. These sensitivity methods were used to determine the relative impacts of permanent magnet parameter perturbations on island widths in the vacuum field approximation of both stellarator equilibria. The square of resonant magnetic field perturbation is used here as a proxy for island width. In particular, gradients of magnetizations of individual magnets were examined in MUSE, as well as gradients of magnet group displacements informed by device design. Three different forms of permanent magnet magnetization perturbations are investigated for MUSE, and the flux surface response to perturbations is demonstrated. The Hessian matrix method is applied to PM4STELL, illustrating the sensitivity of dominant island widths to displacements of toroidal wedge structures. These methods allow for selective direction of experimental resources toward regions of heightened sensitivity, while constraints on less impactful permanent magnet parameters can be relaxed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Loss Landscape Analysis for Reliable Quantized ML Models for Scientific Sensing
In this paper, we propose a method to perform empirical analysis of the loss landscape of machine learning (ML) models. The method is applied to two ML models for scientific sensing, which necessitates quantization to be deployed and are subject to noise and perturbations due to experimental conditions. Our method allows assessing the robustness of ML models to such effects as a function of quantization precision and under different regularization techniques -- two crucial concerns that remained underexplored so far. By investigating the interplay between performance, efficiency, and robustness by means of loss landscape analysis, we both established a strong correlation between gently-shaped landscapes and robustness to input and weight perturbations and observed other intriguing and non-obvious phenomena. Our method allows a systematic exploration of such trade-offs a priori, i.e., without training and testing multiple models, leading to more efficient development workflows. This work also highlights the importance of incorporating robustness into the Pareto optimization of ML models, enabling more reliable and adaptive scientific sensing systems.
Baldi, Tommaso [Pisa, Scuola Normale Superiore]↗
An efficient method to identify uncertainties of WRF-Solar variables in forecasting solar irradiance using a tangent linear sensitivity analysis
Uncertainty in predicting solar energy resources introduces major challenges in power system management and necessitates the development of reliable probabilistic solar forecasts. As the first part of the development of probabilistic forecasts based on the Weather Research and Forecasting model with solar extensions (WRF-Solar), this study presents a tangent linear approach to identify input variables responsible for the largest uncertainties in predicting surface solar irradiance and clouds. A tangent linear analysis is capable of efficiently investigating sensitivities of output variables with respect to various input variables of WRF-Solar because this approach avoids the computational burden of perturbing the initial conditions of individual input variables. We develop tangent linear models (TLMs) for six WRF-Solar physics packages that control the formation and dissipation of clouds and solar radiation, and we evaluate the validity of TLMs using a linearity test. The tangent linear sensitivity analysis is conducted under various scenarios based on satellite observations and model simulations to consider realistic input conditions. A simple method is used to quantify the impact of the uncertainty of input variables on the output variables from the TLMs. The results demonstrate that uncertainties in the output variables that are the focus of this study—including global horizontal irradiance, direct normal irradiance, cloud mixing ratio, cloud tendency, cloud fraction, and sensible and latent heat fluxes—are highly sensitive to uncertainties in 14 input variables. This study indicates that the tangent linear method can identify key variables of physics modules in WRF-Solar that can be stochastically perturbed to generate ensemble-based probabilistic forecasts.
14 SOLAR ENERGY↗
Thermal perturbation of NMR properties in small polar and non-polar molecules
Water is an important constituent in an abundant number of chemical systems; however, its presence complicates the analysis of in situ 1 H MAS NMR investigations due to water’s ease of solidification and vaporization, the large changes in mobility, affinity for hydrogen bonding interactions, etc., that are reflected by dramatic changes in temperature-dependent chemical shielding. To understand the signatures of water and other small molecules in complex environments, in particular how water interacts with the other molecules, in this work the thermally-perturbed NMR properties of water are investigated in detail by in situ MAS NMR. Our results substantially extend the previously published temperature-dependent 1 H and 17 O chemical shifts, linewidths, and spin-lattice relaxation times over a much wider range of temperatures and with significantly enhanced thermal resolution. The following major results are obtained: Hydrogen bonding is clearly shown to weaken at elevated temperatures in both 1 H and 17 O spectra, showing an increase in chemical shielding. At low temperatures, tetrahedral domains of H-bonding networks are evidenced and the observation of solid ice is made under in situ MAS conditions. The 1 H chemical shift properties in other small polar and non-polar molecules have also been described over a range of temperatures, showing the dramatic effect hydrogen bonding perturbation. Gas phase species are described where chemical exchange between gas and liquid phases plays an important role on the observed NMR shifts. The results disclosed herein lay the foundation for a clearer interpretation of complex systems during the increasingly popular in situ NMR characterization at elevated temperatures and pressures for studying chemical systems containing water molecules.
17O NMR↗
Space-Split Algorithm for Sensitivity Analysis of Discrete Chaotic Systems With Multidimensional Unstable Manifolds
Accurate approximations of the change of a system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing the linear response of chaotic dynamical systems. In this paper, we propose an algorithm for sensitivity analysis of discrete chaos with an arbitrary number of positive Lyapunov exponents. We combine the concept of perturbation space-splitting, which regularizes Ruelle's original expression, together with measure-based parameterization of the expanding subspace. We use these tools to rigorously derive trajectory-following recursive relations that converge exponentially fast, and construct a memory-efficient Monte Carlo scheme for derivatives of the output statistics. Thanks to the regularization and lack of simplifying assumptions on the system's behavior, our method is immune to the common problems of other popular methods such as the exploding tangent solutions and unphysical shadowing directions. Here, we provide a ready-to-use algorithm, analyze its complexity, and demonstrate several numerical examples of sensitivity computation using physically-inspired low-dimensional systems.
97 MATHEMATICS AND COMPUTING↗
Bifurcation analysis of aircraft pitching motions near the stability boundary
Bifuraction theory is used to analyze the nonlinear dynamic stability characteristics of an aircraft subject to single degree of freedom pitching-motion perturbations about a large mean angle of attack. The requisite aerodynamic information in the equations of motion is represented in a form equivalent to the response to finite-amplitude pitching oscillations about the mean angle of attack. This information is deduced from the case of infinitesimal-amplitude oscillations. The bifurcation theory analysis reveals that when the mean angle of attack is increased beyond a critical value at which the aerodynamic damping vanishes, new solutions representing finite-amplitude periodic motions bifurcate from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solutions are stable (supercritical) or unstable (subcritical). For flat-plate airfoils flying at supersonic/hypersonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop.
Hui, W. H.↗
Dynamic analysis of a flexible spacecraft with rotating components. Volume 1: Analytical developments
Analytical procedures and digital computer code are presented for the dynamic analysis of a flexible spacecraft with rotating components. Topics, considered include: (1) nonlinear response in the time domain, and (2) linear response in the frequency domain. The spacecraft is assumed to consist of an assembly of connected rigid or flexible subassemblies. The total system is not restricted to a topological connection arrangement and may be acting under the influence of passive or active control systems and external environments. The analytics and associated digital code provide the user with the capability to establish spacecraft system nonlinear total response for specified initial conditions, linear perturbation response about a calculated or specified nominal motion, general frequency response and graphical display, and spacecraft system stability analysis.
Bodley, C. S.↗
Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming
In this report, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform controllability and boundedness assumptions for the problem data, we prove that the directional derivative of the optimal state and control at time $k$, $x^*_k$, and $u^*_k$, with respect to the reference signal at time $i$, $d_i$, will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length. The key technical step is to prove that a version of the convexification approach proposed by Verschueren et al. can be applied to the KKT conditions and results in a convex quadratic program with uniformly bounded data. In turn, Riccati techniques can be further employed to obtain the sensitivity result, borne from the observation that the directional derivatives are solutions of quadratic programs with structure similar to the KKT conditions themselves. We validate our findings with numerical experiments on a small nonlinear, nonconvex, dynamic program.
97 MATHEMATICS AND COMPUTING↗
Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
We investigate the phase diagram of a bilayer Kitaev honeycomb model with Ising interlayer interactions, deriving effective models via perturbation theory and performing Majorana mean-field theory calculations. We show that a diverse array of magnetic and topological phase transitions occur, depending on the direction of the interlayer Ising interaction and the relative sign of Kitaev interactions. When two layers have the same sign of the Kitaev interaction, a first-order transition from a Kitaev spin liquid to a magnetically ordered state takes place. The magnetic order points along the Ising axis and it is (anti)ferromagnetic for (anti)ferromagnetic Kitaev interactions. However, when two layers have opposite signs of the Kitaev interaction, we observe a notable weakening of magnetic ordering tendencies and the Kitaev spin liquid survives up to a remarkably larger interlayer exchange. Our mean-field analysis suggests the emergence of an intermediate gapped ℤ 2 spin-liquid state, which eventually becomes unstable upon vison condensation. The confined phase is described by a highly frustrated 120° compass model. We furthermore use perturbation theory to study the model with the Ising axis pointing along the $\hat{z}$ axis or lying in the 𝑥𝑦 plane. In both cases, our analysis reveals the formation of one-dimensional Ising chains, which remain decoupled in perturbation theory, resulting in a subextensive ground-state degeneracy. Our results highlight the interplay between topological order and magnetic ordering tendencies in bilayer quantum spin liquids.
Kitaev model↗
Steady and Unsteady Simulations of Transonic Truss-BracedWing Aircraft for Flight Dynamic Stability Analysis
This paper presents steady and unsteady simulations of the Mach 0.8 and Mach 0.745Transonic Truss-Braced Wing (TTBW) aircrafts using the high-fidelity CFD solver FUN3D for the flight dynamic stability analysis. The steady-state stability derivatives with respect to the angle of attack, angle of sideslip, and airspeed are calculated with perturbations in the angle of attack, angle of sideslip, and Mach number, respectively. A series of unsteady CFD simulations conducted for the TTBW aircrafts in pitch oscillation at various reduced frequencies. The dynamic stability derivatives are estimated using a frequency domain estimation method. The results are then compared to the results obtained from the VSPAERO stability analysis.
CFD↗
Techniques for the analysis of geodynamic effects using laser data
A technique is described by which laser measurements may be used in an explicit definition of geodetic parameters at the one-meter level of resolution. Observations made by a tracking station at the Goddard Space Flight Center of the Beacon Explorer C satellite are analyzed with this technique to yield highly precise measures of perturbations in the satellite's inclination, including the effect of earth and ocean tides and variations in the station's latitude due to polar motion. The tracking configuration is described, and the basic technique is outlined (analysis of six-hour observations with a weighted least squares orbit determination method). Techniques for analyzing orbital errors and inclination perturbations are described, and it is shown that quarter-day spans of laser data can be employed to monitor the inclination of the satellite to the order of 0.01 arcseconds precision over a period of 17 months.
Dunn, P. J.↗
Kinematic Characteristics of the Posture Corrective Responses After 6 Hours Exposure to Support Withdrawal Environment
Posture disorders are an inevitable consequence of exposure to microgravity . However, the role of different sensorimotor and sensory factors on postural function at different stages of the exposure to microgravity still remains unknown. The results obtained in a 6 hr dry immersion (DI) study where chest pushes served as a pre- and post-immersion perturbation, and DI was used as an analog of microgravity suggest that in addition to vestibular contributions, postural control may be related to a reduction of support loading and consequent decline of the tone of anti-gravitational muscles. Analysis of postural video data in response to chest pushes obtained before and after DI indicate that the structure of corrective responses was modified so that postural perturbations from threshold to moderate pushes showed a significant rise in the amplitude of ankle and knee angular displacement. With push intensity near the submaximal level, equilibrium was maintained by the elimination of excessive degrees of freedom; as manifested by the restriction of the hip joints mobility when coupled with a reduction of the knee and ankle displacement. These results suggest that DI increases the sensitivity of the posture control system by making posture control more rigid reflecting a change of the weight bearing receptors.
Sayenko D.↗