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NASA NTRS2006

A Deconvolution Approach for the Mapping of Acoustic Sources (DAMAS) Determined from Phased Microphone Arrays

Current processing of acoustic array data is burdened with considerable uncertainty. This study reports an original methodology that serves to demystify array results, reduce misinterpretation, and accurately quantify position and strength of acoustic sources. Traditional array results represent noise sources that are convolved with array beamform response functions, which depend on array geometry, size (with respect to source position and distributions), and frequency. The Deconvolution Approach for the Mapping of Acoustic Sources (DAMAS) method removes beamforming characteristics from output presentations. A unique linear system of equations accounts for reciprocal influence at different locations over the array survey region. It makes no assumption beyond the traditional processing assumption of statistically independent noise sources. The full rank equations are solved with a new robust iterative method. DAMAS is quantitatively validated using archival data from a variety of prior high-lift airframe component noise studies, including flap edge/cove, trailing edge, leading edge, slat, and calibration sources. Presentations are explicit and straightforward, as the noise radiated from a region of interest is determined by simply summing the mean-squared values over that region. DAMAS can fully replace existing array processing and presentations methodology in most applications. It appears to dramatically increase the value of arrays to the field of experimental acoustics.

Brooks, Thomas F.↗

NASA NTRS2019

Measurement of Cyanobacterial Bloom Magnitude Using Satellite Remote Sensing

Cyanobacterial harmful algal blooms (cyano HABs) are a serious environmental, water quality and public health issue worldwide because of their ability to form dense biomass and produce toxins. Models and algorithms have been developed to detect and quantify cyanoHABs biomass using remotely sensed data but not for quantifying bloom magnitude,information that would guide water quality management decisions. We propose a method to quantify seasonal and annual cyanoHAB magnitude in lakes and reservoirs. The magnitude is the spatio temporal mean of weekly or biweekly maximum cyanobacteria biomass for the season or year. CyanoHAB biomass is quantified using a standard reflectance spectral shape based algorithm that uses data from Medium Resolution Imaging Spectrometer (MERIS). We demonstrate the method to quantify annual and seasonal cyanoHAB magnitude in Florida and Ohio (USA) respectively during 2003-2011 and rank the lakes based on median magnitude over the study period. The new method can be applied to Sentinel-3 Ocean Land Color Imager (OLCI) data for assessment of cyanoHABs and the change over time, even with issues such as variable data acquisition frequency or sensor calibration uncertainties between satellites. CyanoHAB magnitude can support monitoring and management decision making for recreational and drinking water sources.

Sachidananda Mishra↗

NASA NTRS1991

An analysis of the least-squares problem for the DSN systematic pointing error model

A systematic pointing error model is used to calibrate antennas in the Deep Space Network. The least squares problem is described and analyzed along with the solution methods used to determine the model's parameters. Specifically studied are the rank degeneracy problems resulting from beam pointing error measurement sets that incorporate inadequate sky coverage. A least squares parameter subset selection method is described and its applicability to the systematic error modeling process is demonstrated on Voyager 2 measurement distribution.

Alvarez, L. S.↗

NASA NTRS2006

Precision of Sensitivity in the Design Optimization of Indeterminate Structures

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffener method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

Patnaik, Surya N.↗

NASA NTRS1983

Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms

The minimal polynomial and reduced rank extrapolation algorithms are two acceleration of convergence methods for sequences of vectors. In a recent survey these methods were tested and compared with the scalar, vector, topological epsilon algorithms, and were observed to be more efficient than the latter. It was also observed that the two methods have similar convergence properties. The convergence and stability properties of these methods are analyzed and the performance of the acceleration methods when applied to a class of vector sequences that includes those sequences obtained from systems of linear equations by using matrix iterative methods is discussed.

Sidi, A.↗

NASA NTRS1991

A class of least-squares filtering and identification algorithms with systolic array architectures

A unified approach is presented for deriving a large class of new and previously known time- and order-recursive least-squares algorithms with systolic array architectures, suitable for high-throughput-rate and VLSI implementations of space-time filtering and system identification problems. The geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix. This method utilizes and extends the concept of oblique projections, as used previously in the derivations of the least-squares lattice algorithms. Exponentially weighted least-squares criteria are considered for both sliding and growing memory.

Kalson, Seth Z.↗

NASA NTRS2016

Decision Analysis Methods Used to Make Appropriate Investments in Human Exploration Capabilities and Technologies

NASA is transforming human spaceflight. The Agency is shifting from an exploration-based program with human activities in low Earth orbit (LEO) and targeted robotic missions in deep space to a more sustainable and integrated pioneering approach. Through pioneering, NASA seeks to address national goals to develop the capacity for people to work, learn, operate, live, and thrive safely beyond Earth for extended periods of time. However, pioneering space involves daunting technical challenges of transportation, maintaining health, and enabling crew productivity for long durations in remote, hostile, and alien environments. Prudent investments in capability and technology developments, based on mission need, are critical for enabling a campaign of human exploration missions. There are a wide variety of capabilities and technologies that could enable these missions, so it is a major challenge for NASA's Human Exploration and Operations Mission Directorate (HEOMD) to make knowledgeable portfolio decisions. It is critical for this pioneering initiative that these investment decisions are informed with a prioritization process that is robust and defensible. It is NASA's role to invest in targeted technologies and capabilities that would enable exploration missions even though specific requirements have not been identified. To inform these investments decisions, NASA's HEOMD has supported a variety of analysis activities that prioritize capabilities and technologies. These activities are often based on input from subject matter experts within the NASA community who understand the technical challenges of enabling human exploration missions. This paper will review a variety of processes and methods that NASA has used to prioritize and rank capabilities and technologies applicable to human space exploration. The paper will show the similarities in the various processes and showcase instances were customer specified priorities force modifications to the process. Specifically, this paper will describe the processes that the NASA Langley Research Center (LaRC) Technology Assessment and Integration Team (TAIT) has used for several years and how those processes have been customized to meet customer needs while staying robust and defensible. This paper will show how HEOMD uses these analyses results to assist with making informed portfolio investment decisions. The paper will also highlight which human exploration capabilities and technologies typically rank high regardless of the specific design reference mission. The paper will conclude by describing future capability and technology ranking activities that will continue o leverage subject matter experts (SME) input while also incorporating more model-based analysis.

Williams-Byrd, Julie↗

NASA NTRSDate not supplied

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

We demonstrate for state dynamics governed by the continuity equation and related hyperbolic partial differential equations that significant, spurious variance loss occurs during covariance propagation by traditional methods used in data assimilation, even at full rank. This inaccurate variance evolution is caused not by numerical dissipation, but rather by a discontinuous change in the continuum covariance dynamics as correlation lengths tend to zero.

Shay Gilpin↗

NASA NTRS2008

Improved Linear Algebra Methods for Redshift Computation from Limited Spectrum Data - II

Given photometric broadband measurements of a galaxy, Gaussian processes may be used with a training set to solve the regression problem of approximating the redshift of this galaxy. However, in practice solving the traditional Gaussian processes equation is too slow and requires too much memory. We employed several methods to avoid this difficulty using algebraic manipulation and low-rank approximation, and were able to quickly approximate the redshifts in our testing data within 17 percent of the known true values using limited computational resources. The accuracy of one method, the V Formulation, is comparable to the accuracy of the best methods currently used for this problem.

Foster, Leslie↗

NASA NTRS2012

Sensitivity Analysis for Atmospheric Infrared Sounder (AIRS) CO2 Retrieval

The Atmospheric Infrared Sounder (AIRS) is a thermal infrared sensor able to retrieve the daily atmospheric state globally for clear as well as partially cloudy field-of-views. The AIRS spectrometer has 2378 channels sensing from 15.4 micrometers to 3.7 micrometers, of which a small subset in the 15 micrometers region has been selected, to date, for CO2 retrieval. To improve upon the current retrieval method, we extended the retrieval calculations to include a prior estimate component and developed a channel ranking system to optimize the channels and number of channels used. The channel ranking system uses a mathematical formalism to rapidly process and assess the retrieval potential of large numbers of channels. Implementing this system, we identifed a larger optimized subset of AIRS channels that can decrease retrieval errors and minimize the overall sensitivity to other iridescent contributors, such as water vapor, ozone, and atmospheric temperature. This methodology selects channels globally by accounting for the latitudinal, longitudinal, and seasonal dependencies of the subset. The new methodology increases accuracy in AIRS CO2 as well as other retrievals and enables the extension of retrieved CO2 vertical profiles to altitudes ranging from the lower troposphere to upper stratosphere. The extended retrieval method for CO2 vertical profile estimation using a maximum-likelihood estimation method. We use model data to demonstrate the beneficial impact of the extended retrieval method using the new channel ranking system on CO2 retrieval.

sensitivity analysis↗

NASA NTRS1984

Analysis of hourglass instabilities and control in underintegrated finite element methods

Belytschko et al. (1981, 1984) has developed stabilization methods for the treatment of underintegrated FEM problems; these methods involve the computation of an underintegrated stiffness matrix, which is rank-deficient, and the addition of a stabilization matrix which effectively eliminates the spurious modes. An attempt is presently made to give this a priori stabilization method a mathematical means of support. Attention is also given to an a posteriority stabilization method for hourglass control, in which an approximate solution of the underintegrated system is obtained and then subjected to a special projection in order to eliminate the hourglass modes. A proof is obtained for the convergence of this stabilized underintegrated approximation to the exact solution of a model problem at almost the same rate (as the mesh is refined) as the fully integrated solutions.

Jacquotte, O.-P.↗

NASA NTRS1992

Upper bounds for convergence rates of vector extrapolation methods on linear systems with initial iterations

The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.

Sidi, Avram↗

NASA NTRSDate not supplied

Porosity Area Fraction Analysis of Bonded Borosilicate Specimens From in-Situ Optical Imagery

Image segmentation methods are routinely used to analyze data derived in nondestructive testing scenarios. A typical problem in this area is to estimate porosity from X-ray Computed Tomography (CT) inspections. This investigation aims to understand the effectiveness of open-source image segmentation methods for porosity estimation from optical images in the context of strength analysis of bonded materials and provides a benchmark of performance against a standard commercial software package. The rank ordering of the specimens by porosity area fraction is consistent across both methods.

Porosity area fraction↗

NASA NTRSDate not supplied

Porosity Area Fraction Analysis of Bonded Borosilicate Specimens From in-Situ Optical Imagery

Porosity area fraction↗

NASA NTRS2016

Influence of Population Variation of Physiological Parameters in Computational Models of Space Physiology

The earliest manifestations of Visual Impairment and Intracranial Pressure (VIIP) syndrome become evident after months of spaceflight and include a variety of ophthalmic changes, including posterior globe flattening and distension of the optic nerve sheath. Prevailing evidence links the occurrence of VIIP to the cephalic fluid shift induced by microgravity and the subsequent pressure changes around the optic nerve and eye. Deducing the etiology of VIIP is challenging due to the wide range of physiological parameters that may be influenced by spaceflight and are required to address a realistic spectrum of physiological responses. Here, we report on the application of an efficient approach to interrogating physiological parameter space through computational modeling. Specifically, we assess the influence of uncertainty in input parameters for two models of VIIP syndrome: a lumped-parameter model (LPM) of the cardiovascular and central nervous systems, and a finite-element model (FEM) of the posterior eye, optic nerve head (ONH) and optic nerve sheath. Methods: To investigate the parameter space in each model, we employed Latin hypercube sampling partial rank correlation coefficient (LHSPRCC) strategies. LHS techniques outperform Monte Carlo approaches by enforcing efficient sampling across the entire range of all parameters. The PRCC method estimates the sensitivity of model outputs to these parameters while adjusting for the linear effects of all other inputs. The LPM analysis addressed uncertainties in 42 physiological parameters, such as initial compartmental volume and nominal compartment percentage of total cardiac output in the supine state, while the FEM evaluated the effects on biomechanical strain from uncertainties in 23 material and pressure parameters for the ocular anatomy. Results and Conclusion: The LPM analysis identified several key factors including high sensitivity to the initial fluid distribution. The FEM study found that intraocular pressure and intracranial pressure had dominant impact on the peak strains in the ONH and retro-laminar optic nerve, respectively; optic nerve and lamina cribrosa stiffness were also important. This investigation illustrates the ability of LHSPRCC to identify the most influential physiological parameters, which must therefore be well-characterized to produce the most accurate numerical results.

biomechanics↗

NASA NTRS2020

Pterodactyl: Trade Study for an Integrated Control System Design of a Mechanically Deployable Entry Vehicle

This paper presents the trade study method used to evaluate and downselect from a set of guidance and control (G&C) system designs for a mechanically Deployable Entry Vehicle (DEV). The Pterodactyl project was prompted by the challenge to develop an effective G&C system for a vehicle without a backshell, which is the case for DEVs. For the DEV, the project assumed a specific aeroshell geometry pertaining to an Adaptable, Deployable Entry and Placement Technology (ADEPT) vehicle, which was successfully developed by NASA’s Space Technology Mission Directorate (STMD) prior to this study. The Pterodactyl project designed three different entry G&C systems for precision targeting. This paper details the Figures of Merit (FOMs) and metrics used during the course of the project’s G&C system assessment. The relative importance of the FOMs was determined from the Analytic Hierarchy Process (AHP), which was used to develop weights that were combined with quantitative design metrics and engineering judgement to rank the G&C systems against one another. This systematic method takes into consideration the project’s input while simultaneously reducing unintentional judgement bias and ultimately was used to select a single G&C design for the project to pursue in the next design phase.

Alunni, Antonella I.↗

NASA NTRS2020

Pterodactyl: Trade Study for an Integrated Control System Design of a Mechanically Deployed Entry Vehicle

This paper presents a trade study method used to evaluate and down-select from a set of guidance and control (G&C) system designs for a mechanically deployable entry vehicle (DEV). The Pterodactyl project, funded by NASA's Space Technology Mission Directorate (STMD), was prompted by the challenge to develop an effective G&C system for a vehicle without a backshell, which is the case for DEVs. For the DEV, the project assumed a specific aeroshell geometry pertaining to an Adaptable, Deployable, Entry Placement Technology (ADEPT) vehicle, which was successfully developed by STMD prior to this study. The Pterodactyl project designed three different G&C systems for the vehicle's precise entry, which this paper briefly discusses. This paper details the Figures of Merit (FOMs) and metrics used during the course of the project's G&C system assessment. Each G&C configuration was traded against the three FOMs categories: G&C system performance, affordability and life cycle costs, and safety and mission success. The relative importance of the FOMs was determined from the Analytical Hierarchy Process (AHP), which was used to develop weights that were combined with quantitative design metrics and engineering judgement to rank the G&C systems against one another. This systematic method takes into consideration the project's input while simultaneously reducing unintentional judgement bias and ultimately was used to select a single G&C design for the project to continue pursuing in the next prototyping and testing phase.

Alunni, Antonella I.↗

NASA NTRS1981

On Hybrid and mixed finite element methods

Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.

Pian, T. H. H.↗