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At least 163 records · Page 9

Robustness analysis for real parametric uncertainty

Some key results in the literature in the area of robustness analysis for linear feedback systems with structured model uncertainty are reviewed. Some new results are given. Model uncertainty is described as a combination of real uncertain parameters and norm bounded unmodeled dynamics. Here the focus is on the case of parametric uncertainty. An elementary and unified derivation of the celebrated theorem of Kharitonov and the Edge Theorem is presented. Next, an algorithmic approach for robustness analysis in the cases of multilinear and polynomic parametric uncertainty (i.e., the closed loop characteristic polynomial depends multilinearly and polynomially respectively on the parameters) is given. The latter cases are most important from practical considerations. Some novel modifications in this algorithm which result in a procedure of polynomial time behavior in the number of uncertain parameters is outlined. Finally, it is shown how the more general problem of robustness analysis for combined parametric and dynamic (i.e., unmodeled dynamics) uncertainty can be reduced to the case of polynomic parametric uncertainty, and thus be solved by means of the algorithm.

Sideris, Athanasios↗

Methods for evaluating the predictive accuracy of structural dynamic models

Modeling uncertainty is defined in terms of the difference between predicted and measured eigenvalues and eigenvectors. Data compiled from 22 sets of analysis/test results was used to create statistical databases for large truss-type space structures and both pretest and posttest models of conventional satellite-type space structures. Modeling uncertainty is propagated through the model to produce intervals of uncertainty on frequency response functions, both amplitude and phase. This methodology was used successfully to evaluate the predictive accuracy of several structures, including the NASA CSI Evolutionary Structure tested at Langley Research Center. Test measurements for this structure were within + one-sigma intervals of predicted accuracy for the most part, demonstrating the validity of the methodology and computer code.

Hasselman, Timothy K.↗

Magnetized Winds of M-type Stars and Star–Planet Magnetic Interactions: Uncertainties and Modeling Strategy

M-type stars are the most common stars in the Universe. They are ideal hosts for the search of exoplanets in the habitable zone (HZ), as their small size and low temperature make the HZ much closer-in than their solar twins. Harboring very deep convective layers, they also usually exhibit very intense magnetic fields. Understanding their environment, in particular their coronal and wind properties, is thus very important, as they might be very different from what is observed in the solar system. The mass-loss rate of M-type stars is poorly known observationally, and recent attempts to estimate it for some of them (e.g., TRAPPIST-1 and Proxima Centauri) can vary by an order of magnitude. In this work, we revisit the stellar wind properties of M dwarfs in the light of the latest estimates of $\dot{M}$ through Lyα absorption at the astropause and slingshot prominences. We outline a modeling strategy to estimate the mass-loss rate, radiative loss, and wind speed, with uncertainties, based on an Alfvén-wave-driven stellar wind model. We find that it is very likely that several TRAPPIST-1 planets lie within the Alfvén surface, which implies that these planets experience star–planet magnetic interactions (SPMIs). We also find that SPMIs between Proxima Cen b and its host star could be the reason for recently observed radio emissions.

M stars↗

Backshell Radiative Heating and Shock Layer Kinetic Measurement in NASA’s Electric Arc Shock Tube Facility

A methodology for creating incident shocks with similarity to the backshell radiative heating environment on planetary probes is presented. Two test series were carried out in the Electric Arc Shock Tube (EAST) at NASA Ames to quantify the backshell environment for planned and executed missions entering the atmospheres of Mars and Titan. The comparison of measured radiance in the shock tube to predicted post shock radiation levels is used to quantify the uncertainty in the model. This model uncertainty may then be related back to the flight condition to assess the error in the flight heating prediction. Tests for Mars entry show the shock tube measurements to be bracketed between two kinetic models by 2-7%. This suggests an 8% error in predicting the measured heating cannot be attributed to radiation. Comparisons to planned Titan entry suggest a substantial overprediction of the backshell radiation, which suggests opportunity for future refinement of radiative heating models.

radiation↗

Probabilistic data fusion and physics-informed machine learning: A new paradigm for modeling under uncertainty, and its application to accelerating the discovery of new materials

In this report we summarize the work conducted by PI Perdikaris and his group under this Early Career project DE–SC0019116 during the period of 09/01/2018 – 08/31/2023. The central aim of the work was to introduce a new paradigm for scientific data analysis that can seamlessly synthesize rigorous mathematical modeling with data of variable fidelity (e.g., measurements at multiple scales/resolutions or predictions of variable fidelity models) and multiple modalities (e.g., images, time–series, or scattered measurements). The setting we are interested in involves complex systems that are partially observed and whose dynamical behavior could be hard to model or totally unknown. The inherent uncertainty associated with this setting necessitates a departure from the classical deterministic realm of modeling and scientific computation, and, consequently, our main building blocks can no longer be crisp deterministic numbers and governing laws, but instead we must operate with probabilistic models.

97 MATHEMATICS AND COMPUTING↗

A critical verification of beam and shell models of wind turbine blades

Ever-increasing wind turbine size has challenged predictive capabilities on several fronts. Here, to address part of the blade structural modeling uncertainty, a systematic model fidelity comparison study was conducted on commonly used finite elements. pyNuMAD was utilized to create beam, shell, and solid models of a 100 m long blade undergoing large static deflections. The solid model avoided the use of layered-solid elements by resolving core and facesheet layers. An unprecedented model with 73.7 million elements revealed insights that have never been possible from prior experimental and numerical studies. As compared to the solid element model, the tip deflection from the shell and beam model was found to be about 2% and 4.3% too low, respectively. The twist from the beam model was found to be about 5.6% too high, while the twist from shell model was 24% too low, though improvement was demonstrated with mesh refinement. The beam model adhesive stresses were more accurate than the shell model. Out-of-plane stresses were of great significance near geometric and material discontinuities, and neither the shell nor beam model captured these effects well. Failure predictions from beam, shell, or layered-solid models are unlikely to be reliable at trailing edges, adhesives, ply-drops, spar-cap boundaries.

17 WIND ENERGY↗

Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD

Using forward matrix elements of local leading-twist operators, we present a determination of the isovector third Mellin moments ⟨𝑥 2 ⟩ of nucleon unpolarized, polarized, and transversity parton distribution functions. Two lattice QCD ensembles at the physical pion mass are used, which were generated using a tree-level Symanzik-improved gauge action and 2+1 flavor tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. Leveraging a wide set of operators, two extraction methods for the matrix elements, and the automatic inclusion of model uncertainties via bootstrapped model averages, we extract values of the third Mellin moments. Furthermore, this is the first direct calculation of these observables performed at the physical pion mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Regional quasigeoid determination in Northern Germany and comparison with GPS

For the northern part of the Federal Republic of Germany, new quasigeoid solutions were computed by least squares collocation and fast Fourier transformation (FFT) techniques using point and mean gravity data, a digital terrain model, and a global geopotential model. As severe accuracy limitations for precise regional quasigeoid determination come from global model uncertainties, different geopotential models were investigated by combining them with gravimetric data and comparing the quasigeoid heights with GPS and leveling. Optimum results were obtained by a global model tailored to gravity data in Europe. Collocation and FFT results based on this model agree well. The comparison with GPS and leveling yields rms discrepancies of + or - 2 cm over approximately 400 km range.

Denker, Heiner↗

The Advanced Modeling, Simulation and Analysis Capability Roadmap Vision for Engineering

This paper summarizes a subset of the Advanced Modeling Simulation and Analysis (AMSA) Capability Roadmap that was developed for NASA in 2005. The AMSA Capability Roadmap Team was chartered to "To identify what is needed to enhance NASA's capabilities to produce leading-edge exploration and science missions by improving engineering system development, operations, and science understanding through broad application of advanced modeling, simulation and analysis techniques." The AMSA roadmap stressed the need for integration, not just within the science, engineering and operations domains themselves, but also across these domains. Here we discuss the roadmap element pertaining to integration within the engineering domain, with a particular focus on implications for future observatory missions. The AMSA products supporting the system engineering function are mission information, bounds on information quality, and system validation guidance. The Engineering roadmap element contains 5 sub-elements: (1) Large-Scale Systems Models, (2) Anomalous Behavior Models, (3) advanced Uncertainty Models, (4) Virtual Testing Models, and (5) space-based Robotics Manufacture and Servicing Models.

Zang, Thomas↗

Evaluating Model Performance of an Ensemble-based Chemical Data Assimilation System During INTEX-B Field Mission

We present a global chemical data assimilation system using a global atmosphere model, the Community Atmosphere Model (CAM3) with simplified chemistry and the Data Assimilation Research Testbed (DART) assimilation package. DART is a community software facility for assimilation studies using the ensemble Kalman filter approach. Here, we apply the assimilation system to constrain global tropospheric carbon monoxide (CO) by assimilating meteorological observations of temperature and horizontal wind velocity and satellite CO retrievals from the Measurement of Pollution in the Troposphere (MOPITT) satellite instrument. We verify the system performance using independent CO observations taken on board the NSFINCAR C-130 and NASA DC-8 aircrafts during the April 2006 part of the Intercontinental Chemical Transport Experiment (INTEX-B). Our evaluations show that MOPITT data assimilation provides significant improvements in terms of capturing the observed CO variability relative to no MOPITT assimilation (i.e. the correlation improves from 0.62 to 0.71, significant at 99% confidence). The assimilation provides evidence of median CO loading of about 150 ppbv at 700 hPa over the NE Pacific during April 2006. This is marginally higher than the modeled CO with no MOPITT assimilation (-140 ppbv). Our ensemble-based estimates of model uncertainty also show model overprediction over the source region (i.e. China) and underprediction over the NE Pacific, suggesting model errors that cannot be readily explained by emissions alone. These results have important implications for improving regional chemical forecasts and for inverse modeling of CO sources and further demonstrate the utility of the assimilation system in comparing non-coincident measurements, e.g. comparing satellite retrievals of CO with in-situ aircraft measurements. The work described above also brought to light several short-comings of the data assimilation approach for CO profiles. Because of the limited vertical resolution of the measurement, the retrievals at different altitudes are correlated which can lead to problems with numerical error and overall efficiency. This has resulted in a manuscript that is about to be submitted to JGR:

Arellano, A. F., Jr.↗

PACE Technical Report Series, Volume 6: Data Product Requirements and Error Budgets Consensus Document

This chapter summarizes ocean color science data product requirements for the Plankton, Aerosol, Cloud,ocean Ecosystem (PACE) mission's Ocean Color Instrument (OCI) and observatory. NASA HQ delivered Level-1 science data product requirements to the PACE Project, which encompass data products to be produced and their associated uncertainties. These products and uncertainties ultimately determine the spectral nature of OCI and the performance requirements assigned to OCI and the observatory. This chapter ultimately serves to provide context for the remainder of this volume, which describes tools developed that allocate these uncertainties into their components, including allowable OCI systematic and random uncertainties, observatory geo location uncertainties, and geophysical model uncertainties.

Cetinic, Ivona↗

Spectral Correlation in MODIS Water-Leaving Reflectance Retrieval Uncertainty

Spectral remote sensing reflectance, Rrs(λ) (sr−1), is the fundamental quantity used to derive a host of bio-optical and biogeochemical properties of the water column from satellite ocean color measurements. Estimation of uncertainty in those derived geophysical products is therefore dependent on knowledge of the uncertainty in satellite-retrieved R rs . Furthermore, since the associated algorithms require R rs at multiple spectral bands, the spectral (i.e., band-to-band)error covariance in R rs is needed to accurately estimate the uncertainty in those derived properties. This study establishes a derivative-based approach for propagating instrument random noise, instrument systematic uncertainty, and forward model uncertainty into R rs as retrieved using NASA’s multiple-scattering epsilon (MSEPS) atmospheric correction algorithm, to generate pixel-level error covariance in R rs . The approach is applied to measurements from Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite and verified using Monte Carlo (MC) analysis. We also make use of this full spectral error covariance in R rs to calculate uncertainty in phytoplankton pigment chlorophyll-a concentration (chl a , mg/m 3 ) and diffuse attenuation coefficient of downwelling irradiance at 490 nm (K d (490), m -1 ). Accounting for the error covariance in R rs generally reduces the estimated relative uncertainty in chl a by ∼1-2% (absolute value) in waters with chl a < 0.25 mg/m 3 where the color index (CI) algorithm is used. The reduction is ∼5-10% in waters with chl a > 0.35 mg/m 3 where the blue-green ratio (OCX) algorithm is used. Such reduction can be higher than 30% in some regions. For K d (490), the reduction by error covariance is generally ∼2%, but can be higher than 20% in some regions. The error covariance in R rs is further verified through forward-calculating chl a from MODIS-retrieved and in situ R rs and comparing estimated uncertainty with observed differences. An 8-day global composite of propagated uncertainty shows that the goal of 35% uncertainty in chl a can be achieved over deep ocean waters (chl a ≤ 0.1 mg/m3). While the derivative-based approach generates reasonable error covariance in R rs some assumptions should be updated as our knowledge improves. These include the inter-band error correlation in top-of-atmosphere reflectance, and uncertainties in the calibration of MODIS 869 nm band, in ancillary data, and in the in situ data used for system vicarious calibration.

Ocean color↗

Lessons Learned from the AIRS Pre-Flight Radiometric Calibration

The Atmospheric Infrared Sounder (AIRS) instrument flies on the NASA Aqua satellite and measures the upwelling hyperspectral earth radiance in the spectral range of 3.7-15.4 micron with a nominal ground resolution at nadir of 13.5 km. The AIRS spectra are achieved using a temperature controlled grating spectrometer and HgCdTe infrared linear arrays providing 2378 channels with a nominal spectral resolution of approximately 1200. The AIRS pre-flight tests that impact the radiometric calibration include a full system radiometric response (linearity), polarization response, and response vs scan angle (RVS). We re-derive the AIRS instrument radiometric calibration coefficients from the pre-flight polarization measurements, the response vs scan (RVS) angle tests as well as the linearity tests, and a recent lunar roll test that allowed the AIRS to view the moon. The data and method for deriving the coefficients is discussed in detail and the resulting values compared amongst the different tests. Finally, we examine the residual errors in the reconstruction of the external calibrator blackbody radiances and the efficacy of a new radiometric uncertainty model. Results show the radiometric calibration of AIRS to be excellent and the radiometric uncertainty model does a reasonable job of characterizing the errors.

Sounder↗

Quantification of model error via an interval model with nonparametric error bound

The quantification of model uncertainty is becoming increasingly important as robust control is an important tool for control system design and analysis. This paper presents an algorithm that effectively characterizes the model uncertainty in terms of parametric and nonparametric uncertainties. The algorithm utilizes the frequency domain model error which is estimated from the spectra of output error and input data. The parametric uncertainty is represented as an interval transfer function while the nonparametric uncertainty is bounded by a designed error bound transfer function. Both discrete and continuous systems are discussed in this paper. The algorithm is applied to the Mini-Mast example, and the detail analysis is given.

Lew, Jiann-Shiun↗

Gradient-informed Hamiltonian Monte Carlo for multicomponent CALPHAD model optimization and uncertainty quantification

CALPHAD model parameter optimization is inherently challenging due to non-smooth objective functions, high-dimensional parameter spaces, and the need for uncertainty quantification (UQ). Traditional weighted nonlinear least squares approaches are computationally efficient but local, whereas black-box global optimizers and ensemble Markov Chain Monte Carlo (MCMC) methods provide broader exploration at substantial computational cost. The objective of this work is to combine the global exploration capability of gradient-informed Hamiltonian Monte Carlo – specifically the No-U-Turn Sampler (NUTS) – with local deterministic refinement using BFGS to efficiently optimize multicomponent CALPHAD models with minimal manual intervention. Analytic gradients are computed via the Jansson derivative framework. The methodology is demonstrated on the Cr—Fe binary system and extended to the Cr—Fe—Ni ternary system with 32 degrees of freedom. For Cr—Fe, NUTS achieves comparable or superior optimality relative to ensemble MCMC while requiring over an order-of-magnitude fewer likelihood evaluations. Parameter uncertainties are quantified through NUTS sampling and propagated to thermodynamic observables using local expansion, demonstrating a novel modular approach that combines binary and ternary parameter subsets without requiring global relaxation. These results establish gradient-informed exploration as a scalable strategy for multicomponent CALPHAD optimization and provide a practical route towards efficient higher-order database development with quantified uncertainty.

36 MATERIALS SCIENCE↗

Modeling the Uncertainties of Solar System Ephemerides for Robust Gravitational-wave Searches with Pular-timing Arrays

The regularity of pulsar emissions becomes apparent once we reference the pulses’ times of arrivals to the inertial rest frame of the solar system. It follows that errors in the determination of Earthʼs position with respect to the solar system barycenter can appear as a time-correlated bias in pulsar-timing residual time series, affecting the searches for low-frequency gravitational waves performed with pulsar-timing arrays. Indeed, recent array data sets yield different gravitational-wave background upper limits and detection statistics when analyzed with different solar system ephemerides. Crucially, the ephemerides do not generally provide usable error representations. In this article, we describe the motivation, construction, and application of a physical model of solar system ephemeris uncertainties, which focuses on the degrees of freedom (Jupiterʼs orbital elements) most relevant to gravitational-wave searches with pulsar-timing arrays. This model, BAYESEPHEM, was used to derive ephemeris-robust results in NANOGravʼs 11 yr stochastic-background search, and it provides a foundation for future searches by NANOGrav and other consortia. The analysis and simulations reported here suggest that ephemeris modeling reduces the gravitational-wave sensitivity of the 11 yr data set and that this degeneracy will vanish with improved ephemerides and with pulsar-timing data sets that extend well beyond a single Jovian orbital period.

M Vallisneri↗

Integrated Modeling Activities for the James Webb Space Telescope (JWST): Structural-Thermal-Optical Analysis

This is a continuation of a series of papers on modeling activities for JWST. The structural-thermal- optical, often referred to as "STOP", analysis process is used to predict the effect of thermal distortion on optical performance. The benchmark STOP analysis for JWST assesses the effect of an observatory slew on wavefront error. The paper begins an overview of multi-disciplinary engineering analysis, or integrated modeling, which is a critical element of the JWST mission. The STOP analysis process is then described. This process consists of the following steps: thermal analysis, structural analysis, and optical analysis. Temperatures predicted using geometric and thermal math models are mapped to the structural finite element model in order to predict thermally-induced deformations. Motions and deformations at optical surfaces are input to optical models and optical performance is predicted using either an optical ray trace or WFE estimation techniques based on prior ray traces or first order optics. Following the discussion of the analysis process, results based on models representing the design at the time of the System Requirements Review. In addition to baseline performance predictions, sensitivity studies are performed to assess modeling uncertainties. Of particular interest is the sensitivity of optical performance to uncertainties in temperature predictions and variations in metal properties. The paper concludes with a discussion of modeling uncertainty as it pertains to STOP analysis.

Johnston, John D.↗

Yes, No, Maybe So: Human Factors Considerations for Fostering Calibrated Trust in Foundation Models Under Uncertainty

High-stakes analytical environments require analysts to evaluate evidence and generate conclusions to inform critical decisions often under conditions of uncertainty. Probabilistic decision-making based on incomplete or inaccurate information can reduce productivity, compromise national interests, and endanger public safety. Researchers are developing expert systems built on foundation models (FMs) to support analysts’ decision-making processes by enabling human-artificial intelligence (AI) teaming, in part through the quantification and expression of uncertainty information. As FMs continue to mature, it is imperative to correspondingly consider analysts’ needs for appropriately interpreting and using uncertainty information. However, prior research indicates that it remains unclear how analysts engage with FM-generated uncertainty information and the extent to which these interactions influence trust in, and reliance on, expert systems. We plan to review the state of the science and conduct an exploratory, qualitative study to (a) understand how properly communicated uncertainty can foster calibrated trust and appropriate reliance and (b) identify approaches for effectively conveying FM-generated uncertainty information during analytical workflows. We will administer semi-structured interviews with analysts from a specific high-stakes analytical environment to collect their current experiences with job-related uncertainty and their impressions when viewing FM-generated uncertainty information. During the interview protocol, participants will be presented with several different FM outputs and invited to discuss their thoughts and beliefs about the uncertainty information displayed. Participants may provide insights into how trust and reliance may be influenced by uncertainty. The results of this study will help us to better understand how analysts currently interpret and use uncertainty information. Our findings may inform human factors recommendations for effectively conveying uncertainty information to foster calibrated trust in, and appropriate reliance on, expert systems. Interaction designers and FM developers can use this knowledge to enhance human-AI teaming and ensure the responsible deployment of FM-based expert systems in analytical workflows.

97 MATHEMATICS AND COMPUTING↗