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Advanced Statistical Methods in Spacecraft Flight Software Cost Estimation: Bayesian Regression and Nonlinear Principal Components Analysis to Support System Engineering in the Early Project Lifecycle

This paper provides an overview of the new features and model updates in the upcoming release of the NASA Analogy Software Cost Tool (ASCoT). ASCoT, hosted within the Online NASA Space Estimation Tools (ONSET) on the One NASA Cost Engineering (ONCE) Database, is a web-based tool that provides a suite of estimation tools to support early lifecycle NASA flight software cost analysis. In addition to the traditional parametric flight software costing method COCOMO II, ASCoT contains a Bayesian linear regression to predict total flight software development cost as a function of total spacecraft cost, as well as four analogic methods: k-Nearest Neighbors (kNN) and Clustering models to predict Effort (in work-months) and total source lines of code (SLOC). These methods are designed to work primarily with system-level inputs such as mission type (orbiter, lander, etc.), mission destination (Earth, Inner Planetary, etc.), and the number of instruments and deployables. Nonlinear principal components analysis (NLPCA) is performed to find the principal features of the data composed of both categorical and numerical variables and is necessary prior to defining our analogic methods. Sensitivity analyses and in- and out-of-sample model performance results are presented for the Bayesian CER and the analogic models.

Johnson, James K.

Method of Real-Time Principal-Component Analysis

Dominant-element-based gradient descent and dynamic initial learning rate (DOGEDYN) is a method of sequential principal-component analysis (PCA) that is well suited for such applications as data compression and extraction of features from sets of data. In comparison with a prior method of gradient-descent-based sequential PCA, this method offers a greater rate of learning convergence. Like the prior method, DOGEDYN can be implemented in software. However, the main advantage of DOGEDYN over the prior method lies in the facts that it requires less computation and can be implemented in simpler hardware. It should be possible to implement DOGEDYN in compact, low-power, very-large-scale integrated (VLSI) circuitry that could process data in real time.

Duong, Tuan

Quantitative determination of mineral types and abundances from reflectance spectra using principal components analysis

A procedure was developed for analyzing remote reflectance spectra, including multispectral images, that quantifies parameters such as types of mineral mixtures, the abundances of mixed minerals, and particle sizes. Principal components analysis reduced the spectral dimensionality and allowed testing the uniqueness and validity of spectral mixing models. By analyzing variations in the overall spectral reflectance curves, the type of spectral mixture was identified, mineral abundances quantified and the effects of particle size identified. The results demonstrate an advantage in classification accuracy over classical forms of analysis that ignore effects of particle-size or mineral-mixture systematics on spectra. The approach is applicable to remote sensing data of planetary surfaces for quantitative determinations of mineral abundances.

Smith, M. O.

Spatiotemporal Filtering Using Principal Component Analysis and Karhunen-Loeve Expansion Approaches for Regional GPS Network Analysis

Spatial filtering is an effective way to improve the precision of coordinate time series for regional GPS networks by reducing so-called common mode errors, thereby providing better resolution for detecting weak or transient deformation signals. The commonly used approach to regional filtering assumes that the common mode error is spatially uniform, which is a good approximation for networks of hundreds of kilometers extent, but breaks down as the spatial extent increases. A more rigorous approach should remove the assumption of spatially uniform distribution and let the data themselves reveal the spatial distribution of the common mode error. The principal component analysis (PCA) and the Karhunen-Loeve expansion (KLE) both decompose network time series into a set of temporally varying modes and their spatial responses. Therefore they provide a mathematical framework to perform spatiotemporal filtering.We apply the combination of PCA and KLE to daily station coordinate time series of the Southern California Integrated GPS Network (SCIGN) for the period 2000 to 2004. We demonstrate that spatially and temporally correlated common mode errors are the dominant error source in daily GPS solutions. The spatial characteristics of the common mode errors are close to uniform for all east, north, and vertical components, which implies a very long wavelength source for the common mode errors, compared to the spatial extent of the GPS network in southern California. Furthermore, the common mode errors exhibit temporally nonrandom patterns.

displacement

Modeling MTS pyrolysis and SiC deposition kinetics using principal component analysis and neural networks

Accurate chemical kinetics modeling is crucial for improving the efficiency of chemical processing and synthesis of ceramic matrix composites. Detailed kinetic models are computationally expensive due to the large number of transported chemical species, while the simplified physics-based models, such as single-step global mechanisms, are efficient but often overlook key chemical intermediates and pathways. Recent deep learning approaches promise accurate and cost-effective models. Yet, they require additional closures for the transported nonlinear latent variables, complicating integration with existing solvers. In this work, we develop a hybrid linear—nonlinear reduced model for silicon carbide deposition from methyltrichlorosilane precursor by combining principal component analysis (PCA) and autoencoder (AE) neural network (NN) approaches. PCA is used to identify a smaller set of linear transport variables, enabling direct reuse of conventional transport solvers. NNs then reconstruct the full chemical state from these reduced variables. We demonstrate the method on a chemical vapor deposition reactor—comprising a gas-phase pyrolysis plug flow reactor and a heterogeneous surface reactor—over a wide range of temperatures, pressures, and residence times. Our PCA–AE model achieves high accuracy with only five transported scalars, achieving an eightfold cost reduction compared to detailed mechanisms, in both a priori (using data from the test set only) and a posteriori (coupled with a differential equation solver). In conclusion, notable errors arise primarily near training domain boundaries and for long residence times, indicating the need for domain shift indicators and better long-horizon predictions in future reduced chemistry model development.

autoencoder neural networks

Principal Component Analysis of Arctic Solar Irradiance Spectra

During the FIRE (First ISCPP Regional Experiment) Arctic Cloud Experiment and coincident SHEBA (Surface Heat Budget of the Arctic Ocean) campaign, detailed moderate resolution solar spectral measurements were made to study the radiative energy budget of the coupled Arctic Ocean - Atmosphere system. The NASA Ames Solar Spectral Flux Radiometers (SSFRs) were deployed on the NASA ER-2 and at the SHEBA ice camp. Using the SSFRs we acquired continuous solar spectral irradiance (380-2200 nm) throughout the atmospheric column. Principal Component Analysis (PCA) was used to characterize the several tens of thousands of retrieved SSFR spectra and to determine the number of independent pieces of information that exist in the visible to near-infrared solar irradiance spectra. It was found in both the upwelling and downwelling cases that almost 100% of the spectral information (irradiance retrieved from 1820 wavelength channels) was contained in the first six extracted principal components. The majority of the variability in the Arctic downwelling solar irradiance spectra was explained by a few fundamental components including infrared absorption, scattering, water vapor and ozone. PCA analysis of the SSFR upwelling Arctic irradiance spectra successfully separated surface ice and snow reflection from overlying cloud into distinct components.

Rabbette, Maura

Forward and Inverse Models for Satellite Remote Sensors using Principal Component Analysis

Satellite remote sensors such as AIRS on Aqua, CrIS on S-NPP, NOAA20 and JPSS-2, IASI on Metop A, B, and C make millions of observations each day with thousands of spectral channels for each observation; this poses challenges for efficiently inversion of the inherently large dataset as needed to retrieve atmospheric and surface properties. This presentation will illustrate the use of Principal Component Analysis (PCA) to speed up radiative transfer forward model calculations and to stabilize the inversion algorithms. A Principal Component-based radiative transfer model (PCRTM) developed at NASA Langley Research Center can simulate top of atmosphere (TOA) radiance or reflectance spectra from 50 cm-1 to 50000 cm-1 (200 m to 0.20 m quickly and accurately. PCRTM demonstrated very high accuracy relative to reference line-by-line radiative transfer models and it saves orders of magnitude computational time. Examples of the PCRTM model developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, CPF, TEMPO, SBG, OMI, and SCIAMACHY will be presented. In addition to using the PCRTM as forward model, the NASA Langley developed inversion algorithm also uses PCA to compress the state vector into a compressed dimension to speed up and stabilize the inversion process. Examples of retrieved atmospheric temperature, water vapor, CO2, CO, CH4, N2O, and O3 profiles, cloud properties (optical depth, size, phase, and height), and surface properties (surface emissivity spectra and skin temperatures) will be presented. This algorithm is being transitioned to the NASA Sounder SIPS and NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC).

forward model

Data structure characterization of miltispectral data using principal component and principal factor analysis

Both principal component analysis (PCA) and principal factor analysis (PFA) were used to analyze an experimental multispectral data structure in terms of common and unique variance. Only the common variance of the multispectral data was associated with the principal factor, while higher-order principal components were associated with both common and unique variance. The unique variance was found to represent small spectral variations within each cover type as well as noise vectors, and was most abundant in the lower-order principal components. The lower-order principal components can be useful in research designed to discriminate minor physical variations within features, and to highlight localized change when using multitemporal-multispectral data. Conversely, PFA of the multispectral data provided an insight into a great potential for discriminating basic land-cover types by excluding the unique variance which was related to the noise and minor spectral variations.

Lee, Jae K.

Derivation of Boundary Manikins: A Principal Component Analysis

When designing any human-system interface, it is critical to provide realistic anthropometry to properly represent how a person fits within a given space. This study aimed to identify a minimum number of boundary manikins or representative models of subjects anthropometry from a target population, which would realistically represent the population. The boundary manikin anthropometry was derived using, Principal Component Analysis (PCA). PCA is a statistical approach to reduce a multi-dimensional dataset using eigenvectors and eigenvalues. The measurements used in the PCA were identified as those measurements critical for suit and cockpit design. The PCA yielded a total of 26 manikins per gender, as well as their anthropometry from the target population. Reduction techniques were implemented to reduce this number further with a final result of 20 female and 22 male subjects. The anthropometry of the boundary manikins was then be used to create 3D digital models (to be discussed in subsequent papers) intended for use by designers to test components of their space suit design, to verify that the requirements specified in the Human Systems Integration Requirements (HSIR) document are met. The end-goal is to allow for designers to generate suits which accommodate the diverse anthropometry of the user population.

Young, Karen

Effective use of principal component analysis with high resolution remote sensing data to delineate hydrothermal alteration and carbonate rocks

Methods of applying principal component (PC) analysis to high resolution remote sensing imagery were examined. Using Airborne Imaging Spectrometer (AIS) data, PC analysis was found to be useful for removing the effects of albedo and noise and for isolating the significant information on argillic alteration, zeolite, and carbonate minerals. An effective technique for using PC analysis using an input the first 16 AIS bands, 7 intermediate bands, and the last 16 AIS bands from the 32 flat field corrected bands between 2048 and 2337 nm. Most of the significant mineralogical information resided in the second PC. PC color composites and density sliced images provided a good mineralogical separation when applied to a AIS data set. Although computer intensive, the advantage of PC analysis is that it employs algorithms which already exist on most image processing systems.

Feldman, Sandra C.

Thermal Inspection of a Composite Fuselage Section Using a Fixed Eigenvector Principal Component Analysis Method

A composite fuselage aircraft forward section was inspected with flash thermography. The fuselage section is 24 feet long and approximately 8 feet in diameter. The structure is primarily configured with a composite sandwich structure of carbon fiber face sheets with a Nomex(Trademark) honeycomb core. The outer surface area was inspected. The thermal data consisted of 477 data sets totaling in size of over 227 Gigabytes. Principal component analysis (PCA) was used to process the data sets for substructure and defect detection. A fixed eigenvector approach using a global covariance matrix was used and compared to a varying eigenvector approach. The fixed eigenvector approach was demonstrated to be a practical analysis method for the detection and interpretation of various defects such as paint thickness variation, possible water intrusion damage, and delamination damage. In addition, inspection considerations are discussed including coordinate system layout, manipulation of the fuselage section, and the manual scanning technique used for full coverage.

Zalameda, Joseph N.

Martian Fretted Terrain Morphometry Interpreted Using Principal Components Analysis

Martian fretted terrain is an extensive area of complex topography characterized by smooth, flat-floor valleys and mesas separated by abrupt escarpments along the boundary of heavily cratered uplands. The Deuteronilus-Protonilus region of the fretted terrain between latitude 35 degrees N and 50 degrees N and between 305 degrees W and 350 degrees W longitude was selected for quantitative landform study with the use of principal components analysis (PCA). The morphometry of upland mesa remnants and debris aprons was digitized with respect to latitude, longitude, and distance from the cratered terrain boundary (CTB). The PCA demonstrates that there are definable spatial variations in morphology with respect to longitude and latitude which suggest that the degradation along the CTB proceeded toward the southwest. The PCA also showed that there are organized relationships within the fretted landforms irrespective of their location. Finally, PCA indicated that an orientation of the degraded mesas exists which may be controlled by structure.

Kochell, R. C.

The spectral relationships between NEA and the meteorites: An overview using principal components analysis

One of the primary reservoirs for meteorites is probably the planet-crossing Aten, Apollo, and Amor asteroids. Comparing the spectral characteristics of these two populations with each other and with the spectra of the main belt asteroids would provide insight into the dynamical processes that deliver meteorites to Earth. One method for obtaining an overview of general relationships in a large spectral data set is the statistical technique of principal components analysis. This technique quantifies general spectral similarities and reprojects the data in a plot of major axes of variation where distance is a measure of relative similarity. A major caveat should be kept in mind, however, spectra are sensitive to particle size and viewing geometry effects, and near Earth asteroids (NEA's) are probably significantly different from main belt asteroids in both these factors. The analysis was restricted to the spectral range of ECAS filters and included 116 meteorite spectra from the Gaffey (1976) survey and 417 asteroids from the Zellner et. al. (1985) survey of which 13 are planet-crossers. Although thirteen asteroids are not much of a sample on which to base conclusions, a few inferences can be drawn from this exercise. First, the NEA spectral characteristics are, on average, more consistent with the spectra of meteorites than are the main belt asteroids. Second, the S-type NEA's tend to be spectrally more similar to the ordinary chondrite meteorites than the main belt S-types. This suggests that the planet-crossing S-types do not represent the spectral range of the main belt S-type population and that the planet-crossing S-types are on average more like the ordinary chondrites than the main belt S-types. Third, the only direct asteroidal ordinary chondrite analog, the Q-type asteroid, 1862 Apollo, plots well within the field of the ordinary chondrite meteorites and represents the most common meteorite fall type. Finally, it is interesting that the planet-crossing asteroids occupy similar PCA space with the general trend of the meteorites while most of the main belt objects are offset from the meteorites in statistical space.

Britt, D. T.

Principal Components Analysis of Triaxial Vibration Data From Helicopter Transmissions

Research on the nature of the vibration data collected from helicopter transmissions during flight experiments has led to several crucial observations believed to be responsible for the high rates of false alarms and missed detections in aircraft vibration monitoring systems. This work focuses on one such finding, namely, the need to consider additional sources of information about system vibrations. In this light, helicopter transmission vibration data, collected using triaxial accelerometers, were explored in three different directions, analyzed for content, and then combined using Principal Components Analysis (PCA) to analyze changes in directionality. In this paper, the PCA transformation is applied to 176 test conditions/data sets collected from an OH58C helicopter to derive the overall experiment-wide covariance matrix and its principal eigenvectors. The experiment-wide eigenvectors. are then projected onto the individual test conditions to evaluate changes and similarities in their directionality based on the various experimental factors. The paper will present the foundations of the proposed approach, addressing the question of whether experiment-wide eigenvectors accurately model the vibration modes in individual test conditions. The results will further determine the value of using directionality and triaxial accelerometers for vibration monitoring and anomaly detection.

Tumer, Irem Y.

Using principal component analysis to distinguish different dynamic phases in superconducting vortex matter

Vortices in type-II superconductors driven over random disorder are known to exhibit a remarkable variety of distinct nonequilibrium dynamical phases that arise owing to the competition between vortex-vortex interactions, the quenched disorder, and the drive. These include pinned states, elastic flows, plastic or disordered flows, and dynamically reordered moving crystal or moving smectic states. The plastic flow phases can be particularly difficult to characterize since the flows are strongly disordered. Here, we perform principal component analysis (PCA) on the positions and velocities of vortex matter moving over random disorder for different disorder strengths and drives. We find that PCA can distinguish the known dynamic phases as well as or better than previous measures based on transport signatures or topological defect densities. In addition, PCA recognizes distinct plastic flow regimes, a slowly changing channel flow and a moving amorphous fluid flow, that do not produce distinct signatures in the standard measurements. In conclusion, our results suggest that this position and velocity-based PCA approach could be used to characterize dynamic phases in a broader class of systems that exhibit depinning and nonequilibrium phase transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Revisiting AVHRR Tropospheric Aerosol Trends Using Principal Component Analysis

The advanced very high resolution radiometer (AVHRR) satellite instruments provide a nearly 25 year continuous record of global aerosol properties over the ocean. It offers valuable insights into the long-term change in global aerosol loading. However, the AVHRR data record is heavily influenced by two volcanic eruptions, El Chichon on March 1982 and Mount Pinatubo on June 1991. The gradual decay of volcanic aerosols may last years after the eruption, which potentially masks the estimation of aerosol trends in the lower troposphere, especially those of anthropogenic origin. In this study, we show that a principal component analysis approach effectively captures the bulk of the spatial and temporal variability of volcanic aerosols into a single mode. The spatial pattern and time series of this mode provide a good match to the global distribution and decay of volcanic aerosols. We further reconstruct the data set by removing the volcanic aerosol component and reestimate the global and regional aerosol trends. Globally, the reconstructed data set reveals an increase of aerosol optical depth from 1985 to 1990 and decreasing trend from 1994 to 2006. Regionally, in the 1980s, positive trends are observed over the North Atlantic and North Arabian Sea, while negative tendencies are present off the West African coast and North Pacific. During the 1994 to 2006 period, the Gulf of Mexico, North Atlantic close to Europe, and North Africa exhibit negative trends, while the coastal regions of East and South Asia, the Sahel region, and South America show positive trends.

volcanoes

Model-Independent Time-Delay Interferometry Based on Principal Component Analysis

With a laser interferometric gravitational-wave detector in separate free flying spacecraft, the only way to achieve detection is to mitigate the dominant noise arising from the frequency fluctuations of the lasers via postprocessing. The noise can be effectively filtered out on the ground through a specific technique called time-delay interferometry (TDI), which relies on the measurements of time-delays between spacecraft and careful modeling of how laser noise enters the interferometric data. Recently, this technique has been recast into a matrix-based formalism by several authors, offering a different perspective on TDI, particularly by relating it to principal component analysis (PCA). In this work, we demonstrate that we can cancel laser frequency noise by directly applying PCA to a set of shifted data samples, without any prior knowledge of the relationship between single-link measurements and noise, nor time-delays. We show that this fully data-driven algorithm achieves a gravitational-wave sensitivity similar to classic TDI.

Quentin Baghi

Applicability of Spectral Decomposition by Varimax-Rotated, Principal Component Analysis to the Surface Biology and Geology (SBG) VNIR Mission Concept

Cyanobacterial and Harmful Algal Blooms (CyanoHABs) are a growing concern in coastal and inland waters. But, spectral interference from multiple constituents in optically complex waters can hamper application of remote sensing using traditional image processing methods. The Kent State University (KSU) spectral decomposition method can be applied to multispectral and hyperspectral remote sensing images (e.g. HICO and the NASA Glenn HSI2) to partition and identify signals related to cyanobacteria, algae, pigment degradation products and suspended sediment in each pixel. Fundamental to the use of remote sensing data is the ability to extract independent signals from correlated hyperspectral VNIR data cubes. The Kent State University varimax-rotated, principal component analysis method (VPCA) is important to integrate into the SBG VNIR mission concept because it provides greater specificity, a software-based SNR boost relative to hardware performance, and can assist with Cal/Val, Modeling and Applications. We present examples of the hyperspectral application of the KSU VPCA method with relevance to SBG. The information extracted by VPCA can be validated spectrally or spatially with laboratory and/or in situ sensors, which capture spatial or time series of information at discrete points within remote sensing images. Comparisons show hyperspectral sensors extract more components than multispectral ones, but more independent information can be extracted from multispectral sensors by VPCA than traditional band ratio approaches. The spectral decomposition method is capable of enhancing the signal to noise ratio (SNR) of the NASA Glenn, second-generation hyperspectral imager by a factor of 7x to 20x, with a spectral reproducibility of ±3%. The spectral decomposition method, when compared against existing remote sensing monitoring methods exhibits both greater specificity and a lower detection limit. The method has been validated with multispectral images in Lake Erie to quantify the Microcystis CyanoHAB and from the Indian River Lagoon, Florida to quantify the Brown Tide resulting from A. lagunesnsis. Field operations in the Western Basin of Lake Erie were conducted using a bbe Fluoroprobe to collect vertical profiles and horizontal tows along a transect from the Toledo to the Detroit Lighthouse during coincident satellite overpasses. Extraction of pixel values from the MODIS Aqua sensor yields agreement between in situ field and lab-based measures of cyanobacterial, cryptophyte, diatoms and green algae, suspended sediment and pigment degradation products with R2>0.8.

hyperspectral