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NASA NTRS1992

Inference in infinite-dimensional inverse problems - Discretization and duality

Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.

Stark, Philip B.↗
NASA NTRS1988

Robustness with real parametric and structured complex uncertainty

The problem of robust stability and performance in feedback control systems with n real (possibly related) uncertain parameters and structured unmodeled dynamics (the latter taking the form of m complex blocks dynamic uncertainties) is considered. A robustness margin rm is defined with respect to such model uncertainty structure and an algorithm is developed to compute it. Robust stability and performance are characterized in terms of r sub m or the structured singular value mu. An iterative procedure using the above algorithm is given to compute tight bounds on k sub m and mu. These bounds are exact for the case m = 3 or less.

Pena, Ricardo S. Sanchez↗
NASA NTRSDate not supplied

SMOS Salinity Retrieved from New Seawater Dielectric Constant Models at L-band

The accuracy of the Sea Surface Salinity (SSS) retrieved from L-Band radiometer measurements is strongly dependent on the accuracy of the modelling of the dielectric constant. Two new parametrizations have recently been developed based on one hand on the Soil Moisture and Ocean Salinity (SMOS) satellite multi-angular brightness temperature measurements [1] (BV) and on the other hand on new laboratory measurements [3] (GW2020). These two approaches are fully independent. The brightness temperatures, Tb, simulated with the BV and GW2020 parametrizations are compared with each other and with the ones derived from dielectric constant models previously in use in the SMOS, Soil Moisture Active Passive (SMAP) and Aquarius SSS retrievals. Tb simulated with the BV and GW2020 parametrizations agree particularly well for most SSS and SST commonly observed over the open ocean and are found to be in closer agreement than with earlier parametrizations. Nevertheless, uncertainty remains at low SST where a ∼ 0.1 K relative difference between the two models is observed. A complete reprocessing of SMOS SSS (2010–2020) has been performed using the BV parametrization instead of the Klein and Swift (1977) model previously used in SMOS processing. When compared with Argo derived near surface salinity maps, clear improvements are observed in warm and cold regions. Remaining uncertainties in cold waters will be discussed relatively to the uncertainties in SMOS Tb linked to sea ice contamination and given the constraints given by the GW2020 laboratory measurements.

J. Boutin↗
NASA NTRS1998

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

Belcastro, Christine M.↗
NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗
NASA NTRSDate not supplied

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗
NASA NTRS1992

The energy-time uncertainty principle and the EPR paradox: Experiments involving correlated two-photon emission in parametric down-conversion

The energy-time uncertainty principle is on a different footing than the momentum position uncertainty principle: in contrast to position, time is a c-number parameter, and not an operator. As Aharonov and Bohm have pointed out, this leads to different interpretations of the two uncertainty principles. In particular, one must distinguish between an inner and an outer time in the definition of the spread in time, delta t. It is the inner time which enters the energy-time uncertainty principle. We have checked this by means of a correlated two-photon light source in which the individual energies of the two photons are broad in spectra, but in which their sum is sharp. In other words, the pair of photons is in an entangled state of energy. By passing one member of the photon pair through a filter with width delta E, it is observed that the other member's wave packet collapses upon coincidence detection to a duration delta t, such that delta E(delta t) is approximately equal to planks constant/2 pi, where this duration delta t is an inner time, in the sense of Aharonov and Bohm. We have measured delta t by means of a Michelson interferometer by monitoring the visibility of the fringes seen in coincidence detection. This is a nonlocal effect, in the sense that the two photons are far away from each other when the collapse occurs. We have excluded classical-wave explanations of this effect by means of triple coincidence measurements in conjunction with a beam splitter which follows the Michelson interferometer. Since Bell's inequalities are known to be violated, we believe that it is also incorrect to interpret this experimental outcome as if energy were a local hidden variable, i.e., as if each photon, viewed as a particle, possessed some definite but unknown energy before its detection.

Chiao, Raymond Y.↗
NASA NTRS2019

Bayesian Inference and the Effects of Varying Uncertainty Models in Charring Ablator Calibration and Uncertainty Quantification Problems

The Mars Science Laboratory (MSL) vehicle utilized a heat shield constructed from NASA’s Phenolic-Impregnated Carbon Ablator (PICA) material to protect the main structure from the high enthalpy environment encountered during hypersonic atmospheric entry. During the vehicle’s descent through Martian atmosphere, multiple thermocouples embedded within the heat shield captured in-depth material temperature data that allow for studies to be conducted on current material response reconstruction tools. In the present work, material temperature data obtained from thermocouples within the MISP-4 plug (MEDLI (Mars Science Laboratory Entry, Descent, and Landing Instrument) Integrated Sensor Plug) are utilized in the calibration of Theoretical Ablative Composite for Open Testing (TACOT) model parameters in conjunction with NASA’s Porous material Analysis Toolbox (PATO) through Bayesian inference where uncertainty due to parametric, modeling, and experimental sources is simultaneously quantified. Prior to the study, a sensitivity analysis is performed through computation of the robust Sobol indices in an effort to study the relationship between input space and model response and to reduce the dimensionality of the statistical inverse problem. The Bayesian inference methodology necessitates an a-priori choice to be made for the uncertainty model for which numerous possibilities are available. Across most works, however, only basic additive or multiplicative models are utilized with pre-defined magnitudes of uncertainty based on a-priori knowledge or to-be-calibrated multipliers of static covariance matrix structures. The present effort explores the effects of informed uncertainty models, ones with temporal dependence that are simultaneously calibrated through Bayesian inference, on calibrated results for parameters that make up the uncertain input space.

Sensitivity Analysis↗
NASA NTRS1993

Neural control of magnetic suspension systems

The purpose of this research program is to design, build and test (in cooperation with NASA personnel from the NASA Langley Research Center) neural controllers for two different small air-gap magnetic suspension systems. The general objective of the program is to study neural network architectures for the purpose of control in an experimental setting and to demonstrate the feasibility of the concept. The specific objectives of the research program are: (1) to demonstrate through simulation and experimentation the feasibility of using neural controllers to stabilize a nonlinear magnetic suspension system; (2) to investigate through simulation and experimentation the performance of neural controllers designs under various types of parametric and nonparametric uncertainty; (3) to investigate through simulation and experimentation various types of neural architectures for real-time control with respect to performance and complexity; and (4) to benchmark in an experimental setting the performance of neural controllers against other types of existing linear and nonlinear compensator designs. To date, the first one-dimensional, small air-gap magnetic suspension system has been built, tested and delivered to the NASA Langley Research Center. The device is currently being stabilized with a digital linear phase-lead controller. The neural controller hardware is under construction. Two different neural network paradigms are under consideration, one based on hidden layer feedforward networks trained via back propagation and one based on using Gaussian radial basis functions trained by analytical methods related to stability conditions. Some advanced nonlinear control algorithms using feedback linearization and sliding mode control are in simulation studies.

Gray, W. Steven↗
NASA NTRS2005

Adaptive Control for Microgravity Vibration Isolation System

Most active vibration isolation systems that try to a provide quiescent acceleration environment for space science experiments have utilized linear design methods. In this paper, we address adaptive control augmentation of an existing classical controller that employs a high-gain acceleration feedback together with a low-gain position feedback to center the isolated platform. The control design feature includes parametric and dynamic uncertainties because the hardware of the isolation system is built as a payload-level isolator, and the acceleration Sensor exhibits a significant bias. A neural network is incorporated to adaptively compensate for the system uncertainties, and a high-pass filter is introduced to mitigate the effect of the measurement bias. Simulations show that the adaptive control improves the performance of the existing acceleration controller and keep the level of the isolated platform deviation to that of the existing control system.

Yang, Bong-Jun↗
NASA NTRS2019

Global Crop Production: Adaptation to Temperature Increase Is Possible by Maintaining the Current Growing Periods

Increasing temperature trends are expected to impact yields of major field crops by affecting various plant processes, such as phenology and growth. However, future projections, especially at the global scale, do not consider any agronomic adaptation in farming practices. We use an ensemble of seven Global Gridded Crop Models (GGCMs) contributing to the AgMIP-Gridded project to quantify the impacts and adaptation potential of field crops under increasing temperature. We study how uniform warming scenarios up to 6 K affect the productivity and growing period duration of five major crops. The design of the experiment aims at understanding adaptation measures targeted to temperature-driven impacts and therefore leaves out changes in any other climate variable. We find that, without adaptation the dominant effect of temperature increase is to shorten the growing period and to reduce yields and production, consistently across crops and regions. We then test the potential of two agronomic measures to contrast warming-induced yield reduction, assuming that (i) cultivars with adjusted phenology would be used to regain the reference growing period duration; (ii) rainfed systems would be converted to irrigated. Despite substantial uncertainties in model parametrization and little agreement in spatial patterns, at the global aggregation, model results are robust. We find that up to 3 K of temperature increase, production losses could be fully compensated by maintaining the original crop growing period. Irrigation would also compensate production losses, but would not reduce the temperature impacts. Across regions, the model ensemble estimates larger adaptation potentials from unchanged growing periods in continental and temperate regions, than in tropical and arid regions, where also irrigation has respectively little effects and availability.

Irrigation↗
NASA NTRSDate not supplied

Informing the Space Launch System Booster Separation Initial CFD Run Matrix with Observed Parametric Sensitivity

It currently requires significant computational cost to simulate the flow physics of the booster separation event on the Space Launch System. This comes from the large parametric space in which the event occurs, as pre-separation flight conditions and separated booster core-relative trajectories can vary. Functionally removing the risk of core-booster collision mandates careful assessment of the fluid dynamics in terms of several trajectory parameters. However, simulating the entire trajectory envelope is computationally intractable given the high parametric dimension. In order to reduce the uncertainty in the resulting low-parametric-resolution aerodynamic booster separation database, a data-driven approach was developed to select which breakpoints should be studied by simulations and experiments and which should be relegated to a regression-based interpolation procedure. This technique works by simulating cases where the flow physics are most sensitive to changes in the parameters and leaving the less parametrically sensitive regions for interpolation. The result is a booster separation run matrix whose computational cost is comparable to that of previous database generations but has lower interpolation errors.

SLS↗
NASA NTRSDate not supplied

Informing the Space Launch System Booster Separation Initial CFD Run Matrix with Observed Parametric Sensitivity

It currently requires significant computational cost to simulate the flow physics of the booster separation event on the Space Launch System. This comes from the large parametric space in which the event occurs, as pre-separation flight conditions and separated booster core-relative trajectories can vary. Functionally removing the risk of core-booster collision mandates careful assessment of the fluid dynamics in terms of several trajectory parameters. However, simulating the entire trajectory envelope is computationally intractable given the high parametric dimension. In order to reduce the uncertainty in the resulting low-parametric-resolution aerodynamic booster separation database, a data-driven approach was developed to select which breakpoints should be studied by simulations and experiments and which should be relegated to a regression-based interpolation procedure. This technique works by simulating cases where the flow physics are most sensitive to changes in the parameters and leaving the less parametrically sensitive regions for interpolation. The result is a booster separation run matrix whose computational cost is comparable to that of previous database generations but has lower interpolation errors.

SLS↗
NASA NTRS2014

Output Feedback M-MRAC Backstepping With Aerospace Applications

The paper presents a certainty equivalence output feedback backstepping adaptive control design method for the systems of any relative degree with unmatched uncertainties without over-parametrization. It uses a fast prediction model to estimate the unknown parameters, which is independent of the control design. It is shown that the system's input and output tracking errors can be systematically decreased by the proper choice of the design parameters. The approach is applied to aerospace control problems and tested in numerical simulations.

Output feedback adaptive control↗
NASA NTRS2017

Assimilation of MODIS Dark Target and Deep Blue Observations in the Dust Aerosol Component of NMMB-MONARCH version 1.0

A data assimilation capability has been built for the NMMB-MONARCH chemical weather prediction system, with a focus on mineral dust, a prominent type of aerosol. An ensemble-based Kalman filter technique (namely the local ensemble transform Kalman filter - LETKF) has been utilized to optimally combine model background and satellite retrievals. Our implementation of the ensemble is based on known uncertainties in the physical parametrizations of the dust emission scheme. Experiments showed that MODIS AOD retrievals using the Dark Target algorithm can help NMMB-MONARCH to better characterize atmospheric dust. This is particularly true for the analysis of the dust outflow in the Sahel region and over the African Atlantic coast. The assimilation of MODIS AOD retrievals based on the Deep Blue algorithm has a further positive impact in the analysis downwind from the strongest dust sources of the Sahara and in the Arabian Peninsula. An analysis-initialized forecast performs better (lower forecast error and higher correlation with observations) than a standard forecast, with the exception of underestimating dust in the long-range Atlantic transport and degradation of the temporal evolution of dust in some regions after day 1. Particularly relevant is the improved forecast over the Sahara throughout the forecast range thanks to the assimilation of Deep Blue retrievals over areas not easily covered by other observational datasets.The present study on mineral dust is a first step towards data assimilation with a complete aerosol prediction system that includes multiple aerosol species.

atmospheric dust↗