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All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Application of Gaussian Mixture Regression for the Correction of Low Cost PM2.5 Monitoring Data in Accra, Ghana

Low-cost sensors (LCSs) for air quality monitoring have enormous potential to improve air quality data coverage in resource-limited parts of the world such as sub-Saharan Africa. LCSs, however, are affected by environment and source conditions. To establish high-quality data, LCSs must be collocated and calibrated with reference grade PM2.5 monitors. From March 2020, a low-cost PurpleAir PM2.5 monitor was collocated with a Met One Beta Attenuation Monitor 1020 in Accra, Ghana. While previous studies have shown that multiple linear regression (MLR) and random forest regression (RF) can improve accuracy and correlation between PurpleAir and reference data, MLR and RF yielded suboptimal improvement in the Accra collocation (R2 = 0.81 and R2 = 0.81, respectively). We present the first application of Gaussian mixture regression (GMR) to air quality data calibration and demonstrate improvement over traditional methods by increasing the collocated PM2.5 correlation and accuracy to R2 = 0.88 and MAE = 2.2 μg/cu. m. Gaussian mixture models (GMMs) are a probability density estimator and clustering method from which nonlinear regressions that tolerate missing inputs can be derived. We find that even when given missing inputs, GMR provides better correlation than MLR and RF performed with complete data. GMR also allows us to estimate calibration certainty. When evaluated, 95% confidence intervals agreed with reference PM2.5 data 96% of the time, suggesting that the model accurately assesses its own confidence. Additionally, clustering within the GMM is consistent with climate characteristics, providing confidence that the calibration approach can learn underlying relationships in data.

Sensors↗
NASA NTRS2010

Distributed Prognostic Health Management with Gaussian Process Regression

Distributed prognostics architecture design is an enabling step for efficient implementation of health management systems. A major challenge encountered in such design is formulation of optimal distributed prognostics algorithms. In this paper. we present a distributed GPR based prognostics algorithm whose target platform is a wireless sensor network. In addition to challenges encountered in a distributed implementation, a wireless network poses constraints on communication patterns, thereby making the problem more challenging. The prognostics application that was used to demonstrate our new algorithms is battery prognostics. In order to present trade-offs within different prognostic approaches, we present comparison with the distributed implementation of a particle filter based prognostics for the same battery data.

Saha, Sankalita↗
NASA NTRS2022

Gaussian Process Regression Method for Costing SmallSat Bus Capabilities

NASA is responding to the growing interest in, andcapabilities of, small satellites for science applications with an increasingnumber and frequency of Announcements of Opportunityfor small satellite space missions. Estimating the probabilitythat these mission concepts will fit within the small cost capsof these opportunities is largely driven by the probability thatone of the burgeoning number of small satellite providers will beable to meet the payload’s accommodation requirements withinthe budget for the spacecraft. JPL has collected a databasecontaining technical specifications and cost of commerciallyavailable Smallsat buses across various vendors. The primarypurpose of the database is for use in JPL’s Team X architecturestudies to inform cost estimates of a spacecraft bus which fitsthe customer’s technical requirements for their payload andmission. Customer needs are often unique and don’t alignperfectly with an off-the-shelf commercial spacecraft bus, whichmotivates the need to develop a cost model across the continuoustechnical parameter space.Al’s Bus Cost Distribution Estimator (ABCDE) uses Gaussianprocess regression (GPR) to predict commercial Smallsat spacecraftbus cost based on a subset of a customer’s technicalrequirements (payload mass, payload power, delta V, pointingcontrol, and downlink rate). GPR is implemented in ABCDE asa Bayesian method which fits an implied multivariate regressionon the technical parameters and uses kriging to intentionally“overfit” the residuals. Overfitting the residuals allows costestimates to collapse in uncertainty closer to the data pointswhile maintaining larger uncertainty intervals in regions of parameterspace with fewer data records. The data used to fit thismodel is sensitive and represents cost estimates for off-the-shelfcommercial buses. GPR simultaneously protects the sensitivityof the database and uses the sparse nature of the database toaccount for uncertainty in cost in a useful way. For a givenset of customer technical requirements, the tool provides a costestimate distribution, the percentiles of which can be interpretedas a confidence level of finding a commercial bus under a specifiedcost cap. ABCDE dramatically pushes the boundaries ofspacecraft cost estimation models due to its Bayesian methodology(accounting for the maximum uncertainty in the underlyingregression), the mathematically advanced kriging methodology,and the novelty of its application in Team X architecture tradestudies.

Austin, Alex↗
NASA NTRS2024

Low-Cost Sensor Performance Intercomparison, Correction Factor Development, and 2+ Years of Ambient PM2.5 Monitoring in Accra, Ghana

Particulate matter air pollution is a leading cause of global mortality, particularly in Asia and Africa. Addressing the high and wide-ranging air pollution levels requires ambient monitoring, but many low- and middle-income countries (LMICs) remain scarcely monitored. To address these data gaps, recent studies have utilized low-cost sensors. These sensors have varied performance, and little literature exists about sensor intercomparison in Africa. By colocating 2 QuantAQ Modulair-PM, 2 PurpleAir PA-II SD, and 16 Clarity Node-S Generation II monitors with a reference-grade Teledyne monitor in Accra, Ghana, we present the first intercomparisons of different brands of low-cost sensors in Africa, demonstrating that each type of low-cost sensor PM2.5 is strongly correlated with reference PM2.5, but biased high for ambient mixture of sources found in Accra. When compared to a reference monitor, the QuantAQ Modulair-PM has the lowest mean absolute error at 3.04 μg/m3, followed by PurpleAir PA-II (4.54 μg/m3) and Clarity Node-S (13.68 μg/m3). We also compare the usage of 4 statistical or machine learning models (Multiple Linear Regression, Random Forest, Gaussian Mixture Regression, and XGBoost) to correct low-cost sensors data, and find that XGBoost performs the best in testing (R2: 0.97, 0.94, 0.96; mean absolute error: 0.56, 0.80, and 0.68 μg/m3 for PurpleAir PA-II, Clarity Node-S, and Modulair-PM, respectively), but tree-based models do not perform well when correcting data outside the range of the colocation training. Therefore, we used Gaussian Mixture Regression to correct data from the network of 17 Clarity Node-S monitors deployed around Accra, Ghana, from 2018 to 2021. We find that the network daily average PM2.5 concentration in Accra is 23.4 μg/m3, which is 1.6 times the World Health Organization Daily PM2.5 guideline of 15 μg/m3. While this level is lower than those seen in some larger African cities (such as Kinshasa, Democratic Republic of the Congo), mitigation strategies should be developed soon to prevent further impairment to air quality as Accra, and Ghana as a whole, rapidly grow.

Humidity↗
NASA NTRSDate not supplied

Characterizing Spatiotemporal Uncertainty in Interpolated Meteorological Data

Interpolated meteorological data invariably contain errors. These errors have structure in time and space, particularly autocorrelation, which can cause the effects of errors to compound when model outputs are aggregated temporally or spatially. One way to account for this uncertainty is with a probabilistic model from which samples can be drawn that are coherent with respect to underlying spatial and temporal covariance structure. This work describes a probabilistic method for spatial interpolation of point-wise meteorological time series. Observational data from weather stations are generally sparse in space and dense in time (but sometimes missing). The method works by projecting time series onto orthogonal basis vectors and spatially interpolating each resulting component independently. Under suitable assumptions, and data transformations to better satisfy those assumptions, Gaussian process regression provides a complete description of the joint predictive distribution over a Gaussian random field. Spatiotemporally coherent realizations are generated as the sum of conditional (spatial) simulations of each orthogonal (temporal) component. Data-derived and generic orthogonal bases are considered. In addition to spatial interpolation, imputation of missing observational data is examined. The method is applied using near-surface air temperature over the Western United States and validated by comparing theoretical versus actual coverage of predictive distributions and analyzing the degree to which spatial and temporal covariance structure is reproduced. Computational considerations, relating to conditional simulation of random fields, are also addressed.

Conor T Doherty↗
NASA NTRS2021

Hot planets around cool stars – two short-period mini-Neptunes transiting the late K-dwarf TOI-1260

We present the discovery and characterization of two sub-Neptunes in close orbits, as well as a tentative outer planet of a similar size, orbiting TOI-1260 – a low metallicity K6 V dwarf star. Photometry from Transiting Exoplanet Survey Satellite(TESS) yields radii of R(b) = 2.33 ± 0.10 and R(c) = 2.82 ± 0.15 Rꚛ, and periods of 3.13 and 7.49 d for TOI-1260 b and TOI-1260 c, respectively. We combined the TESS data with a series of ground-based follow-up observations to characterize the planetary system. From HARPS-N high-precision radial velocities we obtain M(b) = 8.6(+1.4,−1.5) and M(c) = 11.8(+3.4,−3.2) Mꚛ. The star is moderately active with a complex activity pattern, which necessitated the use of Gaussian process regression for both the light-curve detrending and the radial velocity modelling, in the latter case guided by suitable activity indicators. We successfully disentangle the stellar-induced signal from the planetary signals, underlining the importance and usefulness of the Gaussian process approach. We test the system’s stability against atmospheric photoevaporation and find that the TOI-1260 planets are classic examples of the structure and composition ambiguity typical for the 2–3 Rꚛ range.

I Y Georgieva↗
NASA NTRS2012

Can Selforganizing Maps Accurately Predict Photometric Redshifts?

We present an unsupervised machine-learning approach that can be employed for estimating photometric redshifts. The proposed method is based on a vector quantization called the self-organizing-map (SOM) approach. A variety of photometrically derived input values were utilized from the Sloan Digital Sky Survey's main galaxy sample, luminous red galaxy, and quasar samples, along with the PHAT0 data set from the Photo-z Accuracy Testing project. Regression results obtained with this new approach were evaluated in terms of root-mean-square error (RMSE) to estimate the accuracy of the photometric redshift estimates. The results demonstrate competitive RMSE and outlier percentages when compared with several other popular approaches, such as artificial neural networks and Gaussian process regression. SOM RMSE results (using delta(z) = z(sub phot) - z(sub spec)) are 0.023 for the main galaxy sample, 0.027 for the luminous red galaxy sample, 0.418 for quasars, and 0.022 for PHAT0 synthetic data. The results demonstrate that there are nonunique solutions for estimating SOM RMSEs. Further research is needed in order to find more robust estimation techniques using SOMs, but the results herein are a positive indication of their capabilities when compared with other well-known methods

Way, Michael J.↗
NASA NTRS2025

Gaussian Process for Flight Delay Prediction: Learning a Stochastic Process

This paper presents a machine-learning approach to predict flight delays. Whereas neural networks are extensively studied for predictive capabilities, they involve non-intuitive design and extensive analysis, particularly in training and optimization processes. Instead, the proposed framework employs Gaussian Processes as a supervised learning technique for flight delay prediction. This data-driven approach trains the model using prior information, specifically the mean and covariance tied to existing data. The proposed Gaussian Process Regression (GPR) model employs the day of flight as a pivotal feature for delay forecasting. We analyze flights from various routes and gauge the accuracy of the presented learning technique by comparing the predicted delays with the actual ones. Given the inherent challenges in precisely forecasting delays, we predict the delays with a 95 % confidence interval. Also, an error propagation analysis in the prediction horizon is carried out to determine the optimal time frame for prediction. The proposed method for flight delay prediction is important as airlines can strategize flight operations and issue timely advisories.

stochastic↗
NASA NTRS2009

Evaluating Algorithm Performance Metrics Tailored for Prognostics

Prognostics has taken a center stage in Condition Based Maintenance (CBM) where it is desired to estimate Remaining Useful Life (RUL) of the system so that remedial measures may be taken in advance to avoid catastrophic events or unwanted downtimes. Validation of such predictions is an important but difficult proposition and a lack of appropriate evaluation methods renders prognostics meaningless. Evaluation methods currently used in the research community are not standardized and in many cases do not sufficiently assess key performance aspects expected out of a prognostics algorithm. In this paper we introduce several new evaluation metrics tailored for prognostics and show that they can effectively evaluate various algorithms as compared to other conventional metrics. Specifically four algorithms namely; Relevance Vector Machine (RVM), Gaussian Process Regression (GPR), Artificial Neural Network (ANN), and Polynomial Regression (PR) are compared. These algorithms vary in complexity and their ability to manage uncertainty around predicted estimates. Results show that the new metrics rank these algorithms in different manner and depending on the requirements and constraints suitable metrics may be chosen. Beyond these results, these metrics offer ideas about how metrics suitable to prognostics may be designed so that the evaluation procedure can be standardized. 1

Saxena, Abhinav↗
NASA NTRS2011

Prognostics of Power MOSFET

This paper demonstrates how to apply prognostics to power MOSFETs (metal oxide field effect transistor). The methodology uses thermal cycling to age devices and Gaussian process regression to perform prognostics. The approach is validated with experiments on 100V power MOSFETs. The failure mechanism for the stress conditions is determined to be die-attachment degradation. Change in ON-state resistance is used as a precursor of failure due to its dependence on junction temperature. The experimental data is augmented with a finite element analysis simulation that is based on a two-transistor model. The simulation assists in the interpretation of the degradation phenomena and SOA (safe operation area) change.

Celaya, Jose Ramon↗
NASA NTRS2011

Prognostics of Power Mosfets Under Thermal Stress Accelerated Aging Using Data-Driven and Model-Based Methodologies

An approach for predicting remaining useful life of power MOSFETs (metal oxide field effect transistor) devices has been developed. Power MOSFETs are semiconductor switching devices that are instrumental in electronics equipment such as those used in operation and control of modern aircraft and spacecraft. The MOSFETs examined here were aged under thermal overstress in a controlled experiment and continuous performance degradation data were collected from the accelerated aging experiment. Dieattach degradation was determined to be the primary failure mode. The collected run-to-failure data were analyzed and it was revealed that ON-state resistance increased as die-attach degraded under high thermal stresses. Results from finite element simulation analysis support the observations from the experimental data. Data-driven and model based prognostics algorithms were investigated where ON-state resistance was used as the primary precursor of failure feature. A Gaussian process regression algorithm was explored as an example for a data-driven technique and an extended Kalman filter and a particle filter were used as examples for model-based techniques. Both methods were able to provide valid results. Prognostic performance metrics were employed to evaluate and compare the algorithms.

Electrolytic capacitors↗
NASA NTRSDate not supplied

Uncertainty Propagation in Pre-Flight Prediction of Unmanned Aerial Vehicle Separation Violation

Current forecasts on the future of aeronautics suggest an in- creasing number of unmanned aerial vehicles entering the low- altitude airspace in the next decades (FAA, 2018; Kopardekar et al., 2016). Small vehicles for package delivery as well as larger vehicles for urban air mobility will change the airspace drastically, increasing density of operations both in time, i.e. high number of take-off and landings per unit time, and in space, operating in dense urban environment. This scenario poses challenges to the current approach to air traffic control, and large efforts from academia, industry and regulatory bodies are dedicated to the development of new traffic management strategies that leverage higher computing and simulating capabilities available today. In this paper, we propose a simple look-ahead approach to predict potential minimum separation violations at the strategic level, that is before vehicles start flying, depending on the predefined 4D trajectories and uncertainty affecting the wind acting along those routes. The wind field is extracted from the NOAA North America Mesoscale Forecast System and interpolated using Gaussian process regression, while uncertainty affecting the expected cruise airspeed is propagated through error intervals. The approach allows the prediction of aircraft separation as a function of time, highlighting potential safety violations that would go undetected if uncertainty affecting the expected 4D trajectories is not considered. The paper will also discuss issues related to accuracy and scalability of the approach to multiple vehicle operations.

Trajectory Prediction↗
NASA NTRSDate not supplied

Probability of Obstacle Collision for UAVs in Presence of Wind

For incorporation of unmanned aerial vehicles into the National Airspace, ensuring safety of the airspace including the vehicles, people, and property on the ground is of utmost importance. One of the safety-critical factors for unmanned aviation flights is the risk of deviating from a planned trajectory resulting in a variety of hazards, including potential loss of separation between vehicle and obstacles or unexpected battery energy consumption. Off-nominal conditions introduced by component failures, degraded controllability and environmental disturbances such as wind gusts can lead to unacceptable unexpected deviations from the flight trajectory. It is essential to accurately model such effects on the flight trajectory while computing safety thresholds such as minimum separation from surrounding obstacles, available battery resource to complete the mission or determining delay in the expected time of arrival of flights. In this paper, a tool is presented based on Gaussian Process Regression for wind representation over a pre-defined trajectory for fast, yet approximated, in-time evaluation of possible trajectory deviations caused by wind gusts. The deviation in the planned trajectory caused by wind is further simulated utilizing a 6 degrees-of-freedom (DOF) UAV trajectory simulator comprising of a rotorcraft lumped-mass model with LQRI controller. Both steady-state wind and wind gust effects are investigated. The probability of collision with obstacle is computed and demonstrated on real flight data from experimental flights of an octocopter at NASA Langley Research Center in the presence of simulated obstacles and wind conditions. Effect of varying wind conditions and varying UAV airspeed is further demonstrated on experimental flights in the presence of wind measured by ground based weather service stations. The proposed approach would eventually benefit timely mitigation of current and future safety-critical events in autonomous systems by enabling risk-informed decision making.

Portia Banerjee↗
NASA NTRSDate not supplied

Uncertainty Estimates for Fitting Zernike Polynomials to Discrete Data

Zernike polynomials are a widely used metric in modern optical analysis. They conveniently represent surfaces as a series of weighted terms corresponding to various optical aberrations. Ideally, each term is independent of others in the series, but Zernike polynomials lose this property when working with sets of discrete data. This gives rise to uncertainty in each polynomial’s actual contribution and affects metrology and simulation estimates of their relative weights. Several factors influencing these estimates are the number and arrangement of sample locations, the method for calculating the weights, and the total number of Zernike terms used in the calculation. Discussed is the uncertainty associated with linear regression using random sampling. Other topics reviewed are complex Zernike polynomials and vector spaces of functions.

Zernike Polynomials↗
NASA NTRS2021

The M-dwarf Ultraviolet Spectroscopic Sample. I. Determining Stellar Parameters for Field Stars

Accurate stellar properties are essential for precise stellar astrophysics and exoplanetary science. In the M-dwarf regime, much effort has gone into defining empirical relations that can use readily accessible observables to assess physical stellar properties. Often, these relations for the quantity of interest are cast as a nonlinear function of available data; in Bayesian modeling, however, the reverse is needed. In this article, we introduce a new Bayesian framework to self-consistently and simultaneously apply multiple empirical calibrations to fully characterize the mass, luminosity, radius, and effective temperature of a field age M-dwarf. This framework includes a new M-dwarf mass–radius relation with a scatter of 3.1% at fixed mass. We further introduce the M-dwarf Ultraviolet Spectroscopic Sample (MUSS), and apply our methodology to provide consistent stellar parameters for these nearby low-mass stars, selected as having available spectroscopic data in the ultraviolet. These targets are of interest largely as either exoplanet hosts or benchmarks in multiwavelength stellar activity. We use the field MUSS stars to define a low-mass main sequence in the solar neighborhood through Gaussian Process (GP) regression. These results enable us to empirically measure a feature in the GP derivative at M ⊙ that indicates where the MUSS transitions from fully to partly convective interiors.

J. Sebastian Pineda↗
NASA NTRS2007

Estimating Dust and Water Ice Content of the Martian Atmosphere From THEMIS Data

Researchers at JPL and Arizona State University conducted a comparative study of three candidate algorithms for estimating components of the Martian atmosphere, using raw (uncalibrated) data collected by the Thermal Emission Imaging System (THEMIS). THEMIS is an instrument onboard the Mars Odyssey spacecraft that acquires image data in five visible and nine infrared (IR) wavelength bands. The algorithms under study used data collected from eight of the nine IR bands to estimate the dust and water ice content of the atmosphere. Such an algorithm could be used in onboard data processing to trigger other algorithms that search for features of scientific interest and to reduce the volume of data transmitted to Earth. The algorithms studied were based on regression models. In the study, the optical depths estimated by these algorithms were compared with optical depths estimated in ground-based processing using fully calibrated data from both THEMIS and the Thermal Emission Spectrometer (TES). TES is an instrument onboard the Mars Global Surveyor spacecraft that also observes the planet at infrared wavelengths, but at a lower spatial resolution than THEMIS does. Of the algorithms studied, the one that performed best was based on a Gaussian Support Vector Machine regression model. The test results indicated that this algorithm, operating on the raw data, had error rates that were within the uncertainty associated with the estimates obtained by the groundbased analysis of the fully calibrated data. This level of fidelity demonstrates that these algorithms are sufficiently accurate for use in an onboard setting.

Bandfield, Joshua↗