Search NASASearch

SEARCH · Search NASA

Results for “DISCRETE FUNCTION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Results and Analysis from Space Suit Joint Torque Testing

A space suit s mobility is critical to an astronaut s ability to perform work efficiently. As mobility increases, the astronaut can perform tasks for longer durations with less fatigue. The term mobility, with respect to space suits, is defined in terms of two key components: joint range of motion and joint torque. Individually these measures describe the path which in which a joint travels and the force required to move it through that path. Previous space suits mobility requirements were defined as the collective result of these two measures and verified by the completion of discrete functional tasks. While a valid way to impose mobility requirements, such a method does necessitate a solid understanding of the operational scenarios in which the final suit will be performing. Because the Constellation space suit system requirements are being finalized with a relatively immature concept of operations, the Space Suit Element team elected to define mobility in terms of its constituent parts to increase the likelihood that the future pressure garment will be mobile enough to enable a broad scope of undefined exploration activities. The range of motion requirements were defined by measuring the ranges of motion test subjects achieved while performing a series of joint maximizing tasks in a variety of flight and prototype space suits. The definition of joint torque requirements has proved more elusive. NASA evaluated several different approaches to the problem before deciding to generate requirements based on unmanned joint torque evaluations of six different space suit configurations being articulated through 16 separate joint movements. This paper discusses the experiment design, data analysis and results, and the process used to determine the final values for the Constellation pressure garment joint torque requirements.

Matty, Jennifer E.

Development of Carbon-Nanotube/Polymer Composites

A report presents a short discussion of one company's effort to develop composites of carbon nanotubes in epoxy and other polymer matrices. The focus of the discussion is on the desirability of chemically modifying carbon nanotubes to overcome their inherent chemical nonreactivity and thereby enable the formation of strong chemical bonds between nanotubes and epoxies (or other polymeric matrix materials or their monomeric precursors). The chemical modification is effected in a process in which discrete functional groups are covalently attached to the nanotube surfaces. The functionalization process was proposed by the company and demonstrated in practice for the first time during this development effort. The covalently attached functional groups are capable of reacting with the epoxy or other matrix resin to form covalent bonds. Furthermore, the company uses this process to chemically modify the nanotube surfaces, affording tunable adhesion to polymers and solubility in select solvents. Flat-sheet composites containing functionalized nanotubes demonstrate significantly improved mechanical, thermal, and electrical properties.

Reynolds, Thomas A.

Maximum-entropy probability distributions under Lp-norm constraints

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Dolinar, S.

Practical Probabilistic Programming

Recent advances in probabilistic programming languages (PPLs) have provided the capability for exact inference: computing a closed-form probability distribution for a given probabilistic program. In particular, the new language Roulette uses a language oriented programming (LOP) approach, wherein analysts build new programming languages on top of a set of primitives provided by Roulette, which then translates these structures into a weighted model counting problem which can be solved by automated reasoning tools. However, because Roulette provides few convenience features, developing these new languages is challenging even for expert users. We developed a standard library of common probability functions for Roulette with the goal of improved usability. This included approximation of continuous probability density functions using discrete probability mass functions. We demonstrated this approach by modeling a cosmic ray striking a RAM controller. We found that Roulette provides a powerful interface for highly expressive probabilistic programs to be generated. In collaboration with the NNSA Advanced Simulation and Computing program, which resulted in development of a tool called Circulette, we were able to model complex circuits expressed in Verilog using probabilistic programs with an expressivity not previously possible. Our research question that motivated the development of a Roulette standard library was to determine whether non-experts could use a PPL to model relevant problems regarding radiation effects on microelectronics. This standard library improved the expressivity of Roulette by implementing common probability density functions, mathematical operators on distributions, and support for empirical distributions. While Roulette is a powerful modeling language, the untyped, LOP approach makes error messages difficult to understand and requires expert aid. We recommend further research on Roulette, especially with its error messages, to enable improved usability. At the same time, this project demonstrated that for users familiar with Roulette and the LOP approach, Roulette provides powerful new capabilities that can be integrated with other Sandia modeling capabilities.

97 MATHEMATICS AND COMPUTING

Discrete regulation of transfer function of a circuit in experimental data automatic collection and processing systems

A device for discrete control of the circuit transfer function in automatic analog data processing systems is reported that coordinates the dynamic range of the vibration level change with the signal range of the processing device output. Experimental verification of the device demonstrates that its maximum control speed does not exceed 0.5 sec for a frequency nonuniformity of about 10%.

Lyubashevskiy, G. S.

Limit cycles resulting from quantization in digital control systems.

The existence of quantizer-induced limit cycles in digital control systems is a well-known phenomenon. This paper reports the results of an investigation into the discrete describing function technique which is applicable not only to the quantizer nonlinearity but also to any nonlinearity in an otherwise linear discrete system. First a general expression is developed for the discrete describing function that is applicable to any nonlinearity. The describing function is then obtained for the quantizer nonlinearity. Finally, the use of the discrete describing function is illustrated by an example of a digital control system.

Phillips, C. L.

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Stability analysis of the discrete-data Large-Space-Telescope system

This paper considers the application of the discrete describing function to the stability analysis of the Large-Space Telescope (LST) system. An analytical model of the CMG gimbal friction is derived, which is then used to arrive at a closed-form analytical expression for the discrete describing function of the nonlinearity. The analysis is used for the study of the fine-pointing stability of the LST vehicle. Simulation results corroborate the conclusions from the analytical analysis.

Kuo, B. C.

Response of discrete linear systems to forcing functions with inequality constraints.

An analysis is made of the maximum response of discrete, linear mechanical systems to arbitrary forcing functions which lie within specified bounds. Primary attention is focused on the complete determination of the forcing function which will engender maximum displacement to any particular mass element of a multi-degree-of-freedom system. In general, the desired forcing function is found to be a bang-bang type function, i.e., a function which switches from the maximum to the minimum bound and vice-versa at certain instants of time. Examples of two-degree-of-freedom systems, with and without damping, are presented in detail. Conclusions are drawn concerning the effect of damping on the switching times and the general procedure for finding these times is discussed.

Michalopoulos, C. D.

Medial axis and local thickness computation using the Fast Sweeping Method

This report describes an efficient and robust voxel-based methodology for computing the medial axis, local thickness, and distance-to-skeleton of arbitrary three-dimensional geometries. It is assumed that the object can be represented by an exact or approximate signed distance function on a discrete grid. The gradient of such function is used to formulate a hyperbolic partial differential equation (PDE) that models the collapse of the position vector in space. By exploiting the causality property of the PDE, the Fast Sweeping Method is able to obtain the solution in a finite number of sweeps independent of the mesh resolution. The intersection of characteristic lines leads to the formation of shocks and a discrete bisector function is used to identify the medial axis. The same PDE approach is used to compute the local thickness inside the object and obtain the distance-to-skeleton field. Multiple examples are given in two and three dimensions along with a resolution study. The methodology has optimal complexity and yields subsecond computational times for geometries with over a million zones on a single core. The methodology is also capable of parallelization across shared and distributed memory architectures.

97 MATHEMATICS AND COMPUTING

The control and estimation of large space structures

A shape control or estimation problem for a large space structure can be modeled by a partial differential equation which represents changes in shape with respect to space and time, together with spatially discrete forcing functions or observations which represent the placement of actuators or sensors at discrete points along the structure. The use of Green's functions to convert boundary value problems into integral equations provides a convenient treatment of this mixture of continuous and discrete mathematics. Control and estimation algorithms are developed for the one-dimensional static beam to illustrate this technique.

Weeks, C.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Cai, Wei

Analysis of Transonic Unsteady Aerodynamic Environments using Unsteady Pressure Sensitive Paint for the Space Launch System Block 1 Cargo Launch Vehicle

Predicting launch vehicle unsteady aerodynamic loads due to buffet remains a significant challenge. Current practices for modeling buffet environments involve the development of buffet forcing functions using discrete unsteady pressure measurements acquired during wind-tunnel tests. These practices often result in significant uncertainty in buffet environments for coupled loads analyses due to the complex spatio-temporal nature of the unsteady pressure field and the challenge of its estimation using discrete sensors. Unsteady pressure sensitive paint, on the other hand, can provide unsteady pressure data at a comparatively high spatial density and may overcome the challenge of unsteady pressure field estimation with discrete sensors and lead to improvements in the development of buffet forcing functions. In this paper, comparisons of the fluctuating pressure field are made for the Space Launch System Block 1 cargo launch vehicle measured using unsteady pressure sensitive paint and pressure transducers.

buffet

Analysis of Transonic Unsteady Aerodynamic Environments using Unsteady Pressure Sensitive Paint for the Space Launch System Block 1 Cargo Launch Vehicle

Predicting launch vehicle unsteady aerodynamic loads due to buffet remains a significant challenge. Current practices for modeling buffet environments involve the development of buffet forcing functions using discrete unsteady pressure measurements acquired during wind-tunnel tests. These practices often result in significant uncertainty in buffet environments for coupled loads analyses due to the complex spatio-temporal nature of the unsteady pressure field and the challenge of its estimation using discrete sensors. Unsteady pressure sensitive paint, on the other hand, can provide unsteady pressure data at a comparatively high spatial density and may overcome the challenge of unsteady pressure field estimation with discrete sensors and lead to improvements in the development of buffet forcing functions. In this paper, comparisons of the fluctuating pressure field are made for the Space Launch System Block 1 cargo launch vehicle measured using unsteady pressure sensitive paint and pressure transducers.

buffet

A Tomographic Method for the Reconstruction of Local Probability Density Functions

A method of obtaining the probability density function (PDF) of local properties from path integrated measurements is described. The approach uses a discrete probability function (DPF) method to infer the PDF of the local extinction coefficient from measurements of the PDFs of the path integrated transmittance. The local PDFs obtained using the method are compared with those obtained from direct intrusive measurements in propylene/air and ethylene/air diffusion flames. The results of this comparison are good.

Sivathanu, Y. R.