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NASA NTRS2019

Uncertainties in the Geostationary Ocean Color Imager (GOCI) Remote Sensing Reflectance for Assessing Diurnal Variability of Biogeochemical Processes

Short-term (sub-diurnal) biological and biogeochemical processes cannot be fully captured by the current suite of polar-orbiting satellite ocean color sensors, as their temporal resolution is limited to potentially one clear image per day. Geostationary sensors, such as the Geostationary Ocean Color Imager (GOCI) from the Republic of Korea, allow the study of these short-term processes because their orbit permit the collection of multiple images throughout each day for any area within the sensor’s field of regard. Assessing the capability to detect sub-diurnal changes in in-water properties caused by physical and biogeochemical processes characteristic of open ocean and coastal ocean ecosystems, however, requires an understanding of the uncertainties introduced by the instrument and/or geophysical retrieval algorithms. This work presents a study of the uncertainties during the daytime period for an ocean region with characteristically low-productivity with the assumption that only small and undetectable changes occur in the in-water properties due to biogeochemical processes during the daytime period. The complete GOCI mission data were processed using NASA’s SeaDAS/l2gen package. The assumption of homogeneity of the study region was tested using three-day sequences and diurnal statistics. This assumption was found to hold based on the minimal diurnal and day-to-day variability in GOCI data products. Relative differences with respect to the midday value were calculated for each hourly observation of the day in order to investigate what time of the day the variability is greater. Also, the influence of the solar zenith angle in the retrieval of remote sensing reflectances and derived products was examined. Finally, we determined that the uncertainties in water-leaving “remote-sensing” reflectance (Rrs) for the 412, 443, 490, 555, 660 and 680 nm bands on GOCI are 8.05 × 10−4, 5.49 × 10−4, 4.48 × 10−4, 2.51 × 10−4, 8.83 × 10−5, and 1.36 × 10−4 sr−1, respectively, and 1.09 × 10−2 mg m−3 for the chlorophyll-a concentration (Chl-a), 2.09 × 10−3 m−1 for the absorption coefficient of chromophoric dissolved organic matter at 412 nm (ag (412)), and 3.7 mg m−3 for particulate organic carbon (POC). These Rrs values can be considered the threshold values for detectable changes of the in-water properties due to biological, physical or biogeochemical processes from GOCI.

Geostationary Ocean Color Imager (GOCI)↗

NASA NTRS2021

Development and Validation of an Empirical Ocean Color Algorithm with Uncertainties: A Case Study with the Particulate Backscattering Coefficient

We explored how algorithm (model) and in situ measurement (observation) uncertainties can effectively be incorporated into empirical ocean color model development and assessment. In this study we focused on methods for deriving the particulate backscattering coefficient at 555 nm, b(bp)(555)/(m). We developed a simple empirical algorithm for deriving b(bp)(555) as a function of a remote sensing reflectance line height (LH) metric. Model training was performed using a high-quality bio-optical dataset that contains coincident in situ measurements of the spectral remote sensing reflectances, R(rs)(λ)/(sr), and the spectral particulate backscattering coefficients, b(bp)(λ). The LH metric used is defined as the magnitude of Rrs(555) relative to a linear baseline drawn between R(rs)(490) and R(rs)(670). Using an independent validation dataset, we compared the skill of the LH-based model with two other models. We used contemporary validation metrics, including bias and mean absolute error (MAE), that were corrected for model and observation uncertainties. The results demonstrated that measurement uncertainties do indeed impact contemporary validation metrics such as mean bias and MAE. Zeta-scores and z-tests for overlapping confidence intervals were also explored as potential methods for assessing model skill.

ocean color↗

NASA NTRSDate not supplied

Applicability of a Framework for Estimating Performance and Associated Uncertainty for Modified Aircraft Configurations

As improvements are made to the accuracy and reliability of modeling and simulation techniques, certification by analysis becomes a more attractive alternative compared to traditional aircraft flight testing. Certification by analysis is especially cost-effective when one considers modifications to a previously certified aircraft. However, it is important that the models and methods used are applicable and accurate throughout the intended use domain. A framework for estimating the performance and associated uncertainty was introduced in an earlier paper. The factors and limitations of this framework for estimating the performance and associated model form uncertainty are explored to determine the range of applicability of the framework, particularly with respect to model form, process and sensor noise, and quality of available flight test data. This paper focuses on the general limitations and applicability of the framework and not the applicability of the individual methods to a range of modified configurations, which requires a large number of modified configurations and is an area for future work. The effects of these factors on the performance and uncertainty results are demonstrated using NASA’s Generic Transport Model aircraft.

uncertainty quantification↗

NASA NTRS2022

Framework for Estimating Performance and Associated Uncertainty for Modified Aircraft Configurations

Flight testing has been the historical standard for determining aircraft airworthiness. However, increases in the cost of flight testing and the accuracy of inexpensive CFD encourage the adoption of certification by analysis to reduce or replace flight testing. A framework is introduced to predict the performance in the special case of a modification to an existing, previously certified aircraft. This framework uses a combination of existing flight tests or high fidelity data of the original aircraft as well as lower fidelity data from CFD or wind tunnel testing of the original and modified configurations to create 6-DOF flight dynamics models. Two methods are presented which generate an updated flight dynamics model and estimate the model form uncertainty for the modified aircraft configuration using knowledge of the original aircraft. This updated dynamics model and uncertainty estimate are then used to conduct non-deterministic simulations with wind turbulence included. The framework is applied to an example aircraft system to demonstrate the ability to predict the performance and associated model from the uncertainty of modified aircraft configurations.

uncertainty quantification↗

NASA NTRSDate not supplied

Application of Framework for Estimating Performance and Associated Uncertainty for Modified Aircraft Configurations Using NASA's X-57 Maxwell

A framework to estimate the performance and associated uncertainty of modified configurations of certified aircraft is applied to the X-57 Maxwell aircraft. In previous theoretical studies, the framework was shown to predict performance and uncertainty bounds accurately. The X-57 Maxwell is an experimental aircraft designed to demonstrate the benefits of distributed electric propulsion through a series of four incremental modifications to a Tecnam P2006T aircraft. The available models and data are first shown to be within the application domain of the framework. We then apply the framework to two X-57 Maxwell modifications. We compare the estimated performance and associated uncertainties against the airworthiness criteria. The results indicate that the framework is a promising tool for the certification by analysis workflow. We expect the framework to reduce and supplement the flight testing required to show compliance to airworthiness certification criteria for a modified configuration.

Uncertainty Quantification↗

NASA NTRSDate not supplied

Application of Framework for Estimating Performance and Associated Uncertainty for Modified Aircraft Configurations Using NASA's X-57 Maxwell

Uncertainty Quantification↗

NASA NTRSDate not supplied

Measurement Accuracy and Uncertainty Analysis of the X-59 Air Data Probe Calibration Test Entry One

The X-59 is being developed to demonstrate quiet sonic boom technology. Data was obtained via two test entries in the NASA Glenn Research Center’s 8- by 6-Foot Supersonic Wind Tunnel to calibrate the X-59’s nose air data probe. The first entry tested two theoretically identical probes with the intention of one of the probes becoming the primary X-59 nose air data probe flight hardware and the other becoming a backup. A measurement accuracy and uncertainty analysis was performed on data obtained from the first test entry. The analysis showed that the uncertainties in the probe pressures were nearly identical for the two probes, with an average difference of 2.51 x 10-5 for the non-dimensional total pressure and 2.88 x 10-5 for the non-dimensional static pressures. The analysis also showed that the uncertainty in the probe yaw and pitch angles were 0.00034° and 0.01416°, respectively. This gives confidence in the X-59’s flight air data system.

Air Data Probe↗

NASA NTRS2023

Measurement Accuracy and Uncertainty Analysis of the X-59 Air Data Probe Calibration Test Entry One

The X-59 is being developed to demonstrate quiet sonic boom technology. Data was obtained via two test entries in the NASA Glenn Research Center’s 8- by 6-Foot Supersonic Wind Tunnel to calibrate the X-59’s nose air data probe. The first entry tested two theoretically identical probes with the intention of one of the probes becoming the primary X-59 nose air data probe flight hardware and the other becoming a backup. A measurement accuracy and uncertainty analysis was performed on data obtained from the first test entry. The analysis showed that the uncertainties in the probe pressures were nearly identical for the two probes, with an average difference of 2.51 x 10 -5 for the non-dimensional total pressure and 2.88 x 10 -5 for the non-dimensional static pressures. The analysis also showed that the uncertainty in the probe yaw and pitch angles were 0.00034° and 0.01416°, respectively. This gives confidence in the X-59’s flight air data system.

Air Data Probe↗

NASA NTRSDate not supplied

Results of the NASA Prediction Uncertainty Reduction Tech Challenge

In January 2021 the Advanced Air Vehicles Program approved a new Tech Challenge (TC) to be run out of the Commercial Supersonic Technology (CST) Project. The objective of the TC was to bring uncertainties in the empirical noise modeling for civilian supersonic aircraft into the same range as that of conventional aircraft. The TC goal statement was to “Produce data and demonstrate tools that reduce the uncertainty in predicting Landing & Takeoff Noise levels of supersonic-relevant designs by 5 EPNdB and are ready for use in studies to inform FAA rule-making.” To make the required improvements in noise prediction methods for supersonic aircraft, NASA decided to validate and use high-fidelity numerical simulations to acquire the needed noise data on supersonic propulsion configurations. High-fidelity component designs were developed, such as a two-stage propulsor behind a supersonic inlet designed by General Electric Aviation and variable area exhaust systems using input from recent contracts with GE and Rolls Royce. A noise database was generated as a function of geometric and flow parameters, providing corrections to the empirical noise models and added new input variables to describe the complexities created by the supersonic-specific design features. Statistically, the new models were able to predict the acoustic impact of supersonic-specific features, the reduction in uncertainty being reduced from the baseline 7.8 EPNdB at the beginning of the TC to 2.0 EPNdB at the end.

noise prediction↗

NASA NTRS1970

Minimax control of a system with process uncertainty in substate space

The control of a single input-single output plant with parameter uncertainty was approached using a minimax technique. A linear time invariant controller results which requires only partial state feedback and is optimal in the sense that it minimizes a quadratic criterion involving tracking error, control, and parameter uncertainty. Bounded input-bounded output stability is guaranteed provided the transfer function has only left half plane zeros. If uncertainties are bounded, it is always possible to stabilize the system when sufficient control amplitude is available. The number of states required to generate the control is equal to the system order less the number of zeros.

Basuthakur, S.↗

NASA NTRS1972

Parameter uncertainties in control system design.

Development of a design method for including the effects of parameter uncertainties in the design of linear control systems. The approach taken to this problem may be classified as a special case of the stochastic control problem. Thus the formulation is based on the minimization of the expected value of a quadratic performance index defined in terms of the system state vector. The uncertainty in the value of the performance index is the result of the statistical nature of the system parameters rather than a random input signal. It is shown that the expected value of the performance index may be written as a sum of two terms under the assumption of first-order variations of the system state. The first of these terms expresses the nominal performance of the system when the system parameters assume their mean values. The second term represents the effect of the uncertainties on the expected value of the performance index, and is interpreted as an index of system sensitivity.

Palsson, T.↗

NASA NTRS1972

Incomplete state feedback for systems with parameter uncertainty and random disturbances

A unified design philosophy is presented for limited state feedback control problems with parameter uncertainty for both deterministic and stochastic problems. Two approaches are considered: linear compensator for the deterministic problem with parameter uncertainty, and for the single input-single output system with parameter uncertainty, a model on order equal to that of the system less the number of zeroes. The limitations of these approaches are discussed along with suggestions for further research.

Basuthakur, S.↗

NASA NTRS1978

Modeling and parameter uncertainties for aircraft flight control system design

As aircraft designs trend toward further applications of control-configured vehicle concepts, aircraft control systems increasingly rely on stability augmentation to obtain normal flying qualities and reasonable structural margins. Although the control system designer would choose to have a perfect dynamic description of the vehicle, he knows that a level of uncertainty of plant dynamics will exist. This paper gives typical values of plant uncertainties for some recent aircraft design and development programs. Histories of pertinent aerodynamic, inertial, and structural parameters from program initiation to aircraft certification are given. These data can be used as typical of future vehicles so that control system design concepts can be evaluated with due consideration to their sensitivity to uncertainties in plant dynamics.

Rickard, W. W.↗

NASA NTRS1980

Effects of aerodynamic heating and TPS thermal performance uncertainties on the Shuttle Orbiter

A procedure for estimating uncertainties in the aerodynamic-heating and thermal protection system (TPS) thermal-performance methodologies developed for the Shuttle Orbiter is presented. This procedure is used in predicting uncertainty bands around expected or nominal TPS thermal responses for the Orbiter during entry. Individual flowfield and TPS parameters that make major contributions to these uncertainty bands are identified and, by statistical considerations, combined in a manner suitable for making engineering estimates of the TPS thermal confidence intervals and temperature margins relative to design limits. Thus, for a fixed TPS design, entry trajectories for future Orbiter missions can be shaped subject to both the thermal-margin and confidence-interval requirements. This procedure is illustrated by assessing the thermal margins offered by selected areas of the existing Orbiter TPS design for an entry trajectory typifying early flight test missions.

Goodrich, W. D.↗

NASA NTRS1982

The development of aerodynamic uncertainties for the Space Shuttle Orbiter

The methodology involved in developing the ability to reproduce aerodynamic results between various wind tunnel tests and to determine uncertainties due to differences between preflight aerodynamic predictions and flight results derived from analysis of past aircraft programs is presented. The uncertainties were developed for pitching moment, lateral-directional stability, rudder power, and aileron power, and were formulated to yield aerodynamic uncertainties for an orbital, manned first flight. The compressed development schedule required the aerodynamics results from wind tunnel tests be equipped with tolerances, which accounted for reasonable changes in the vehicle configuration. A worst case scenario was decided on, with the results that every prediction included the widest possible aerodynamic margins. Repeatibility was emphasized between wind tunnel model tests, and was achieved with an accuracy of 0.006 with inclusion of Reynolds effects.

Young, J. C.↗

NASA NTRS1982

A new design approach to achieve a minimum impulse limit cycle in the presence of significant measurement uncertainties

A new design was developed for the Space Shuttle Transition Phase Digital Autopilot to reduce the impact of large measurement uncertainties in the rate signal during attitude control. The signal source, which was dictated by early computer constraints, is characterized by large quantization, noise, bias, and transport lag which produce a measurement uncertainty larger than the minimum impulse rate change. To ensure convergence to a minimum impulse limit cycle, the design employed bias and transport lag compensation and a switching logic with hysteresis, rate deadzone, and 'walking' switching line. The design background, the rate measurement uncertainties, and the design solution are documented.

Martin, M. W.↗

NASA NTRS1982

The development and application of aerodynamic uncertainties in the design of the entry trajectory and flight control system of the Space Shuttle Orbiter

In connection with the decision to conduct with the Shuttle an orbital, manned mission on its first launch, certain problems arose related to mission safety, which had to be provided without the benefit of either a graduated flight test program or an initial unmanned flight concept. In an attempt to overcome these problems, the philosophy was adopted to provide a reasonable estimate of maximum possible errors in the preflight predicted aerodynamics. The flight control system (FCS) was to be certified on the basis of the estimated errors prior to STS-1. A set of 'worst case' aerodynamic uncertainties, defined as variations, was developed. As part of the first flight certification, variations, combined with other system uncertainties, were used to 'stress' the FCS through a multitude of simulations. Attention is given to an Orbiter description, the entry mission, the correlation of aerodynamic uncertainties, the application of aerodynamic variation in FCS and trajectory design, and the flight test results.

Gamble, J. D.↗

NASA NTRS1983

Uncertainty methodology for in-flight thrust determination

A methodology is proposed for the evaluation of uncertainty in the in-flight determination of aircraft thrust, which provides error traceability to a national standards laboratory, and is independent of the procedure used to calculate or measure thrust in flight, thereby yielding a consistent means for the evaluation of measurement capabilities. Attention is given to the factors of measurement error, precision, bias, uncertainty, error estimation and classification, error propagation, ground testing, and the related problems of model bias error, model precision error, and the uncertainty limit.

Adams, G. R.↗