Adaptive Radial Basis Function Methods for Data Approximation
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Torchinsky, Jason Louis [Sandia National Laborator↗
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Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions
The time-dependent, 3D incompressible Navier-Stokes equations in (1) boundary layers, the semiinfinite domain, and (2) mixing layers or wakes, the fully infinite domain, are respectively solved by two numerical methods which employ rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions. These functions are then combined with one, for method (1), and two, for method (2), slowly decaying 'extra functions' for each wave vector. Each extra function can exactly represent the solution's irrotational component at large distances. The two methods have been applied to extensive direct-numerical simulation of transition and turbulence.
Spalart, Philippe R.↗
A six degree of freedom, plume-fuel optimal trajectory planner for spacecraft proximity operations using an A* node search
Spacecraft proximity operations are complicated by the fact that exhaust plume impingement from the reaction control jets of space vehicles can cause structural damage, contamination of sensitive arrays and instruments, or attitude misalignment during docking. The occurrence and effect of jet plume impingement can be reduced by planning approach trajectories with plume effects considered. An A* node search is used to find plume-fuel optimal trajectories through a discretized six dimensional attitude-translation space. A plume cost function which approximates jet plume isopressure envelopes is presented. The function is then applied to find relative costs for predictable 'trajectory altering' firings and unpredictable 'deadbanding' firings. Trajectory altering firings are calculated by running the spacecraft jet selection algorithm and summing the cost contribution from each jet fired. A 'deadbanding effects' function is defined and integrated to determine the potential for deadbanding impingement along candidate trajectories. Plume costs are weighed against fuel costs in finding the optimal solution. A* convergence speed is improved by solving approach trajectory problems in reverse time. Results are obtained on a high fidelity space shuttle/space station simulation. Trajectory following is accomplished by a six degree of freedom autopilot. Trajectories planned with, and without, plume costs are compared in terms of force applied to the target structure.
Jackson, Mark Charles↗
Challenges of Sustaining the International Space Station Through 2020 and Beyond: Reassessing Confidence Targets for System Availability
The International Space Station (ISS) was originally designed to operate until 2015 with a plan for deorbiting the ISS in 2016. Currently, the international partnership has agreed to extend the operations until 2020 and discussions are underway to extend the life even further to 2028. Each partner is responsible for the sustaining engineering, sparing, and maintenance of their own segments. National Aeronautics and Space Administration's (NASA's) challenge is to purchase the needed number of spares to maintain the functional availability of the ISS systems necessary for the United States On-Orbit Segment s contribution. This presentation introduces an analytical approach to assessing uncertainty in ISS hardware necessary to extend the life of the vehicle. Some key areas for consideration are: establishing what confidence targets are required to ensure science can be continuously carried out on the ISS, defining what confidence targets are reasonable to ensure vehicle survivability, considering what is required to determine if the confidence targets are too high, and whether sufficient number of spares are purchased. The results of the analysis will provide a methodological basis for reassessing vehicle subsystem confidence targets. This analysis compares the probability of existing spares exceeding the total expected unit demand of the Orbital Replacement Unit (ORU) in functional hierarchies approximating the vehicle subsystems. In cases where the functional hierarchies' availability does not meet subsystem confidence targets, the analysis will further identify which ORUs may require additional spares to extend the life of the ISS. The resulting probability is dependent upon hardware reliability estimates. However, the ISS hardware fleet carries considerable epistemic uncertainty which must be factored into the development and execution of sparing risk postures. In addition, it is also recognized that uncertainty in the assessment is due to disconnects between modeled functions and actual subsystem operations. Perhaps most importantly, it is acknowledged that conservative confidence targets per subsystem are currently accepted. This presentation will also discuss how subsystem confidence targets may be relaxed based on calculating the level of uncertainty for each corresponding ORU-function. The presentation will conclude with the various strengths and limitations for implementing the analytical approach in sustaining the ISS through end of life; 2020 and beyond.
Lutomski, Michael G.↗
Challenges of Sustaining the International Space Station through 2020 and Beyond: Including Epistemic Uncertainty in Reassessing Confidence Targets
This paper introduces an analytical approach, Probability and Confidence Trade-space (PACT), which can be used to assess uncertainty in International Space Station (ISS) hardware sparing necessary to extend the life of the vehicle. There are several key areas under consideration in this research. We investigate what sparing confidence targets may be reasonable to ensure vehicle survivability and for completion of science on the ISS. The results of the analysis will provide a methodological basis for reassessing vehicle subsystem confidence targets. An ongoing annual analysis currently compares the probability of existing spares exceeding the total expected unit demand of the Orbital Replacement Unit (ORU) in functional hierarchies approximating the vehicle subsystems. In cases where the functional hierarchies availability does not meet subsystem confidence targets, the current sparing analysis further identifies which ORUs may require additional spares to extend the life of the ISS. The resulting probability is dependent upon hardware reliability estimates. However, the ISS hardware fleet carries considerable epistemic uncertainty (uncertainty in the knowledge of the true hardware failure rate), which does not currently factor into the annual sparing analysis. The existing confidence targets may be conservative. This paper will also discuss how confidence targets may be relaxed based on the inclusion of epistemic uncertainty for each ORU. The paper will conclude with strengths and limitations for implementing the analytical approach in sustaining the ISS through end of life, 2020 and beyond.
Anderson, Leif↗
A42F-03: Small-Scale Variability in Tropical Tropopause Layer Humidity
Recent advances in statistical parameterizations of cirrus cloud processes for use in global models are highlighting the need for information about small-scale fluctuations in upper tropospheric humidity and the physical processes that control the humidity variability. To address these issues, we have analyzed high-resolution airborne water vapor measurements obtained in the Airborne Tropical TRopopause EXperiment (ATTREX) over the tropical Pacific between 14 and 20 km. Using accurate and precise 1-Hz water vapor measurements along approximately-level aircraft flight legs, we calculate structure functions spanning horizontal scales ranging from about 0.2 to 50 km, and we compare the water vapor variability in the lower (about 14 km) and upper (16-19 km) Tropical Tropopause Layer (TTL). We also compare the magnitudes and scales of variability inside TTL cirrus versus in clear-sky regions. The measurements show that in the upper TTL, water vapor concentration variance is stronger inside cirrus than in clear-sky regions. Using simulations of TTL cirrus formation, we show that small variability in clear-sky humidity is amplified by the strong sensitivity of ice nucleation rate to supersaturation, which results in highly-structured clouds that subsequently drive variability in the water vapor field. In the lower TTL, humidity variability is correlated with recent detrainment from deep convection. The structure functions indicate approximately power-law scaling with spectral slopes ranging from about minus 5 divided by 3, to minus 2.
water vapor↗
Approximating Density Probability Distribution Functions Across Cosmologies
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Huanqing Chen↗
On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws
A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods.
Huynh, H. T.↗
Meshfree Methods
Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2
Chen, Jiun-Shyan↗
Approximation of the dielectric properties of Maxwellian plasmas - Dispersion functions and physical constraints
The dielectric properties of Maxwellian plasmas are approximated using high Pade approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytical work and in accelerating large-scale numerical computations.
Robinson, P. A.↗
A compendium of human gene functions derived from evolutionary modelling
A comprehensive, computable representation of the functional repertoire of all macromolecules encoded within the human genome is a foundational resource for biology and biomedical research. The Gene Ontology Consortium has been working towards this goal by generating a structured body of information about gene functions, which now includes experimental findings reported in more than 175,000 publications for human genes and genes in experimentally tractable model organisms 1,2 . Here, we describe the results of a large, international effort to integrate all of these findings to create a representation of human gene functions that is as complete and accurate as possible. Specifically, we apply an expert-curated, explicit evolutionary modelling approach to all human protein-coding genes. This approach integrates available experimental information across families of related genes into models that reconstruct the gain and loss of functional characteristics over evolutionary time. The models and the resulting set of 68,667 integrated gene functions cover approximately 82% of human protein-coding genes. The functional repertoire reveals a marked preponderance of molecular regulatory functions, and the models provide insights into the evolutionary origins of human gene functions. We show that our set of descriptions of functions can improve the widely used genomic technique of Gene Ontology enrichment analysis. The experimental evidence for each functional characteristic is recorded, thereby enabling the scientific community to help review and improve the resource, which we have made publicly available.
59 BASIC BIOLOGICAL SCIENCES↗
Development of Response Surface Models for Rapid Analysis & Multidisciplinary Optimization of Launch Vehicle Design Concepts
Multdisciplinary design optimization (MDO) is an important step in the design and evaluation of launch vehicles, since it has a significant impact on performance and lifecycle cost. The objective in MDO is to search the design space to determine the values of design parameters that optimize the performance characteristics subject to system constraints. Vehicle Analysis Branch (VAB) at NASA Langley Research Center has computerized analysis tools in many of the disciplines required for the design and analysis of launch vehicles. Vehicle performance characteristics can be determined by the use of these computerized analysis tools. The next step is to optimize the system performance characteristics subject to multidisciplinary constraints. However, most of the complex sizing and performance evaluation codes used for launch vehicle design are stand-alone tools, operated by disciplinary experts. They are, in general, difficult to integrate and use directly for MDO. An alternative has been to utilize response surface methodology (RSM) to obtain polynomial models that approximate the functional relationships between performance characteristics and design variables. These approximation models, called response surface models, are then used to integrate the disciplines using mathematical programming methods for efficient system level design analysis, MDO and fast sensitivity simulations. A second-order response surface model of the form given has been commonly used in RSM since in many cases it can provide an adequate approximation especially if the region of interest is sufficiently limited.
Unal, Resit↗
Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics
Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
Pratt, D. T.↗
Neural network-based control using Lyapunov functions
We have successfully demonstrated how the problem of stabilization of plants can be reduced to a problem of approximation of functions. Neural networks have been shown to have approximating and interpolating properties. This approach is good for linear and nonlinear plants. Software has been generated to demonstrate this approach.
Luxemburg, Leon A.↗
Characterizing the Aging of Alphasense NO2 Sensors in Long-term Field Deployments
Low-cost NO2 sensors have been widely deployed for atmospheric sampling. While their initial performance has been characterized, few studies have examined their long-term degradation. This study focused on the performance of Alphasense low-cost NO2 sensors (NO2-B42F and NO2-B43F) over 4 years (2016–2020). A total of 29 NO2 sensors from 10 batches were collocated 78 times at two sites with reference instruments. Raw signals from “functional” NO2 sensors correlated linearly with reference NO2 concentrations. After long-term deployment, sensor raw signals started to deviate from reference NO2 concentrations due to sensor aging, an accumulated effect after sensor unpacking. Several sensors eventually became “non-functional” as sensor raw signals showed no correlation with reference NO2 concentrations. Sensor aging and non-functionality may be primarily caused by expiration of the ozone (O3) scrubber built into these sensors so that sensors responded to both ambient NO2 and O3. The influence of O3 on sensor response is quantified through the permutation importance method. Most of the sensors are non-functional after approximately 200–400 days of deployment, and no sensor was functional after 400 days of deployment. This result agrees well with the estimated lifetime of the built-in ozone scrubbers considering the ambient ozone concentration in the Pittsburgh area where these sensors were deployed. To ensure reliable data quality in long-term field deployments, we recommend collocating NO2 sensors with reference instruments regularly after 200–400 days of deployment to identify and replace non-functional sensors in a timely manner.
NO2sensors↗
Ares I-X In-Flight Modal Identification
Operational modal analysis is a procedure that allows the extraction of modal parameters of a structure in its operating environment. It is based on the idealized premise that input to the structure is white noise. In some cases, when free decay responses are corrupted by unmeasured random disturbances, the response data can be processed into cross-correlation functions that approximate free decay responses. Modal parameters can be computed from these functions by time domain identification methods such as the Eigenvalue Realization Algorithm (ERA). The extracted modal parameters have the same characteristics as impulse response functions of the original system. Operational modal analysis is performed on Ares I-X in-flight data. Since the dynamic system is not stationary due to propellant mass loss, modal identification is only possible by analyzing the system as a series of linearized models over short periods of time via a sliding time-window of short time intervals. A time-domain zooming technique was also employed to enhance the modal parameter extraction. Results of this study demonstrate that free-decay time domain modal identification methods can be successfully employed for in-flight launch vehicle modal extraction.
Bartkowicz, Theodore J.↗
On the use of Pade approximants to represent unsteady aerodynamic loads for arbitrarily small motions of wings
The general behavior of unsteady airloads in the frequency domain is explained. Based on this, a systematic procedure is described whereby the airloads, produced by completely arbitrary, small, time-dependent motions of a thin lifting surface in an airstream, can be predicted. This scheme employs as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. Although these approximations have many uses, they are proving especially valuable in the design of automatic control systems intended to modify aeroelastic behavior.
Vepa, R.↗
Extended use of the Coulomb approximation - Mean powers of r, a sum rule, and improved transition integrals.
Mean powers of r, sum rule and improved transition integrals computed for effective quantum number range up to 8.5, using Coulomb approximation wave functions
WAVE FUNCTION↗