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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b , where A is an m by x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as 4x(sub 1) + 6x(sub 2) + 5x (sub 3) = 10, where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or a minimum norm solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.

Sen, Syamal K.↗
NASA NTRS2011

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b, where A is an m x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as an equation 4x(sub 1) + 6x(sub 2) + 5x(sub 3) = 10 , where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. It is assumed that at least one information, i.e. one equation is known to be correct and which will be our first equation. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The . error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.

Sen, Syamal K.↗
NASA NTRS1992

Recursive optimal pruning with applications to tree structured vector quantizers

A pruning algorithm of Chou et al. (1989) for designing optimal tree structures identifies only those codebooks which lie on the convex hull of the original codebook's operational distortion rate function. The authors introduce a modified version of the original algorithm, which identifies a large number of codebooks having minimum average distortion, under the constraint that, in each step, only modes having no descendents are removed from the tree. All codebooks generated by the original algorithm are also generated by this algorithm. The new algorithm generates a much larger number of codebooks in the middle- and low-rate regions. The additional codebooks permit operation near the codebook's operational distortion rate function without time sharing by choosing from the increased number of available bit rates. Despite the statistical mismatch which occurs when coding data outside the training sequence, these pruned codebooks retain their performance advantage over full search vector quantizers (VQs) for a large range of rates.

Kiang, Shei-Zein↗
NASA NTRS1998

Toward a More Robust Pruning Procedure for MLP Networks

Choosing a proper neural network architecture is a problem of great practical importance. Smaller models mean not only simpler designs but also lower variance for parameter estimation and network prediction. The widespread utilization of neural networks in modeling highlights an issue in human factors. The procedure of building neural models should find an appropriate level of model complexity in a more or less automatic fashion to make it less prone to human subjectivity. In this paper we present a Singular Value Decomposition based node elimination technique and enhanced implementation of the Optimal Brain Surgeon algorithm. Combining both methods creates a powerful pruning engine that can be used for tuning feedforward connectionist models. The performance of the proposed method is demonstrated by adjusting the structure of a multi-input multi-output model used to calibrate a six-component wind tunnel strain gage.

Stepniewski, Slawomir W.↗
NASA NTRS2003

Mining Distance Based Outliers in Near Linear Time with Randomization and a Simple Pruning Rule

Defining outliers by their distance to neighboring examples is a popular approach to finding unusual examples in a data set. Recently, much work has been conducted with the goal of finding fast algorithms for this task. We show that a simple nested loop algorithm that in the worst case is quadratic can give near linear time performance when the data is in random order and a simple pruning rule is used. We test our algorithm on real high-dimensional data sets with millions of examples and show that the near linear scaling holds over several orders of magnitude. Our average case analysis suggests that much of the efficiency is because the time to process non-outliers, which are the majority of examples, does not depend on the size of the data set.

Bay, Stephen D.↗
NASA NTRS2020

Search Tree Pruning for Progressive Neural Architecture Search

Our neural architecture search algorithm progressively searches a tree of neural network architectures. Child nodes are created by inserting new layers determined by a transition graph into a parent network up to a maximum depth and pruned when performance is worse than its parent. This increases efficiency but makes the algorithm greedy. Simpler networks are successfully found before more complex ones that can achieve benchmark performance similar to other top-performing networks.

Deanna Flynn↗
NASA NTRS1991

Surface reconstruction from scattered data through pruning of unstructured grids

This paper describes an algorithm for reconstructing a surface from a randomly digitized object. Scan data (treated as a cloud of points) is first tesselated out to its convex hull using Delaunay triangulation. The line-of-sight between each surface point and the scanning device is traversed, and any tetrahedra which are pierced by it are removed. The remaining tetrahedra form an approximate solid model of the scanned object. Due to the inherently limited resolution of any scan, this algorithm requires two additional procedures to produce a smooth, polyhedral surface: one process removes long, narrow tetrahedra which span indentations in the surface between digitized points; the other smooths sharp edges. The results for a moderately resolved sample body and a highly resolved aircraft are displayed.

Maksymiuk, C. M.↗
NASA NTRS1993

Pruning the Lyman alpha forest of Q1331+170

A multitude of absorption lines seen shortward of QSO Ly-alpha emission, that cannot be traced to heavy element absorption systems, are assumed to be Ly-alpha lines arising in intervening clouds. Studies of these Ly-alpha clouds, typically done at 1 A or lower resolution, have shown N(H1) approximately equal to 10(exp 13) - 10(exp 17) sq cm and b approximately equal to 35 km/s. Sargent et al 1980, on the basis of a flat pair velocity correlation function (PVCF), argued that these clouds are intergalactic. But Crotts 1989 showed that the strong Ly-alpha lines are spatially clustered. High resolution studies of Webb 1987 and Rauch et al 1992 also report some evidence for weak clustering, but overall such high resolution studies have been rare. A study of the Ly-alpha forest of Q1331 + 170 over x(sub abs) = 1.60 - 2.19 based on 18 km/s resolution data at S/N approximately equal to 15, with metal-line deblending incorporated.

Kulkarni, Varsha P.↗
NASA NTRS1997

Locating Geometric Primitives by Pruning the Parameter Space

This paper examines the extraction of geometric primitives from two- and three-dimensional image data. The geometric primitives are represented by parametric manifolds in the image space, such as circles, planes, and cylinders.

geometric primitives image data parameter space im↗
NASA NTRS1997

Pointer Adaptation and Pruning of Min-Max Fuzzy Inference and Estimation

A new technique for adaptation of fuzzy membership functions in a fuzzy inference system is proposed. The pointer technique relies upon the isolation of the specific membership functions that contributed to the final decision, followed by the updating of these functions' parameters using steepset descent.

Fuzzy↗
NASA NTRS1992

Purposive discovery of operations

The Generate, Prune & Prove (GPP) methodology for discovering definitions of mathematical operators is introduced. GPP is a task within the IL exploration discovery system. We developed GPP for use in the discovery of mathematical operators with a wider class of representations than was possible with the previous methods by Lenat and by Shen. GPP utilizes the purpose for which an operator is created to prune the possible definitions. The relevant search spaces are immense and there exists insufficient information for a complete evaluation of the purpose constraint, so it is necessary to perform a partial evaluation of the purpose (i.e., pruning) constraint. The constraint is first transformed so that it is operational with respect to the partial information, and then it is applied to examples in order to test the generated candidates for an operator's definition. In the GPP process, once a candidate definition survives this empirical prune, it is passed on to a theorem prover for formal verification. We describe the application of this methodology to the (re)discovery of the definition of multiplication for Conway numbers, a discovery which is difficult for human mathematicians. We successfully model this discovery process utilizing information which was reasonably available at the time of Conway's original discovery. As part of this discovery process, we reduce the size of the search space from a computationally intractable size to 3468 elements.

Sims, Michael H.↗
NASA NTRS1979

Development of an Accelerated Test Design for Predicting the Service Life of the Solar Array at Mead, Nebraska

Potential long-term degradation modes for the two types of modules in the Mead array were determined and judgments were made as to those environmental stresses and combinations of stresses which accelerate the degradation of the power output. Hierarchical trees representing the severity of effects of stresses (test conditions) on eleven individual degradation modes were constructed and were pruned of tests judged to be nonessential. Composites of those trees were developed so that there is now one pruned tree covering eight degradation modes, another covering two degradation modes, and a third covering one degradation mode. These three composite trees form the basis for selection of test conditions in the final test plan which is now being prepared.

Gaines, G. B.↗
NASA NTRS2001

Greenhouse tomato limited cluster production systems: crop management practices affect yield

Limited-cluster production systems may be a useful strategy to increase crop production and profitability for the greenhouse tomato (Lycopersicon esculentum Mill). In this study, using an ebb-and-flood hydroponics system, we modified plant architecture and spacing and determined the effects on fruit yield and harvest index at two light levels. Single-cluster plants pruned to allow two leaves above the cluster had 25% higher fruit yields than did plants pruned directly above the cluster; this was due to an increase in fruit weight, not fruit number. Both fruit yield and harvest index were greater for all single-cluster plants at the higher light level because of increases in both fruit weight and fruit number. Fruit yield for two-cluster plants was 30% to 40% higher than for single-cluster plants, and there was little difference in the dates or length of the harvest period. Fruit yield for three-cluster plants was not significantly different from that of two-cluster plants; moreover, the harvest period was delayed by 5 days. Plant density (5.5, 7.4, 9.2 plants/m2) affected fruit yield/plant, but not fruit yield/unit area. Given the higher costs for materials and labor associated with higher plant densities, a two-cluster crop at 5.5 plants/m2 with two leaves above the cluster was the best of the production system strategies tested.

Non-NASA Center↗
NASA NTRS2005

New high performance algorithmic solution for diagnosis problem

In this paper we address the problem of generating the minimal diagnosis from the conflicts. This problem can be formulated as the well-known Hitting Set Problem. Our approach starts by mapping the Hitting Set problem into the Integer Programming Problem that enables us, for the first time, a priori determination of the lower and upper bounds on the size for the solution. Based on these bounds, we introduce a new concept of solution window for the problem. We also propose a new branch-and-bound technique that not only is faster than the current techniques in terms of number of operations (by exploiting the structure of the problem) but also, using the concept of window, allows a massive reduction (pruning) in the number of branches. Furthermore, as the branch-and-bound proceeds, the solution window is dynamically updated and narrowed to enable further pruning.

diagnosis problems↗
NASA NTRS2014

Statistical Symbolic Execution with Informed Sampling

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

Reliability↗
NASA NTRS2015

An Active Learning Framework for Hyperspectral Image Classification Using Hierarchical Segmentation

Augmenting spectral data with spatial information for image classification has recently gained significant attention, as classification accuracy can often be improved by extracting spatial information from neighboring pixels. In this paper, we propose a new framework in which active learning (AL) and hierarchical segmentation (HSeg) are combined for spectral-spatial classification of hyperspectral images. The spatial information is extracted from a best segmentation obtained by pruning the HSeg tree using a new supervised strategy. The best segmentation is updated at each iteration of the AL process, thus taking advantage of informative labeled samples provided by the user. The proposed strategy incorporates spatial information in two ways: 1) concatenating the extracted spatial features and the original spectral features into a stacked vector and 2) extending the training set using a self-learning-based semi-supervised learning (SSL) approach. Finally, the two strategies are combined within an AL framework. The proposed framework is validated with two benchmark hyperspectral datasets. Higher classification accuracies are obtained by the proposed framework with respect to five other state-of-the-art spectral-spatial classification approaches. Moreover, the effectiveness of the proposed pruning strategy is also demonstrated relative to the approaches based on a fixed segmentation.

classification↗
NASA NTRS2014

Improving Coverage of Test Cases Generated by Symbolic PathFinder for Programs with Loops

Symbolic execution is a program analysis technique that is used for many purposes, one of which is test-case generation. For loop-free programs, this generates a test-set that achieves path coverage. Program loops, however, imply exponential growth of the number of paths in the best case and non-termination in the worst case. In practice, the number of loop unwindings needs to be bounded for analysis. We consider symbolic execution in the context of the tool Symbolic Pathfinder. This tool extends the model-checker Java Pathfinder and relies on its bounded state-space exploration for termination. We present an implementation of k-bounded loop unwinding, which increases the amount of user-control over the symbolic execution of loops. Bounded unwinding can be viewed as a naive way to prune paths through loops. When using symbolic execution for test-case generation, naively pruning paths is likely at the cost of coverage. In order to improve coverage of branches within a loop body, we present a technique that semi-automatically concretizes variables used in a loop. The basic technique is limited and we therefore present annotations to manually steer symbolic execution towards certain branches, as well as ideas on how the technique can be extended to be more widely applicable.

Programs With Loops↗
NASA NTRS2017

Semi-analytic preliminary design of low-thrust missions

Using generalized logarithmic spirals to approximate low-thrust trajectories, a new strategy for the design of low-thrust gravity-assist transfers has been developed. Each transfer leg is defined by a semi-analytic model, and its solution is equivalent to a hybrid Lambert’s problem. The method is suitable for approximating both flyby and rendezvous transfer legs. A branch and prune algorithm is used to generate a collection of initial guesses for further optimization. The analytic nature of the low-thrust model simplifies the pruning step, since dynamical and operational constraints (like maximum thrust or total v) can be imposed easily. The solutions obtained with the global search algorithm can be post-processed, filtered, and ranked according to various criteria. This is where the versatility of the method resides, because changing the selection criteria does not require a new search. Selected candidates are then optimized further, in order to generate actual low-thrust orbits. Two mission design examples are presented: an asteroid deflection mission using a kinetic impactor, and a rendezvous mission to Jupiter. These examples are used to analyze the convergence of the optimization stage, in particular how far from the optimal solution the initial guesses are.

Park, Ryan S.↗