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At least 19 records

Learning Model Structural Uncertainty with Gaussian Processes

The advent of commercially available quantum computers has marked the beginning of quantum computing as a reality. Both quantum gate and annealing computers have been released by major computer hardware companies. In this work, the D-Wave 2XTM quantum annealing computer housed at the NASA Advanced Systems computational facility is investigated to accelerate Machine Learning (ML) for image registration. NASA collects large amounts of images over the globe remotely using space-based monitoring. Images of a fixed areas of the land surface are taken over time. Due to the orbit of the sensors, the viewing angles deviate slightly, and it is necessary to align or register the images precisely to create image time series over the land surface. Unaligned images can lead to substantial analysis errors. These time-series are then used in modeling Earth Systems models such as hydrological, weather, and carbon monitoring models. In this work, we consider the Moderate Resolution Image Spectrometer (MODIS) data collected by the NASA's terra satellite. Artificial Neural Networks (ANNs) is a natural fit for ML modelling of images. Several successes have been reported using machine learning related to image processing. We investigate the use of ML to register MODIS images. ANNs are investigated in combination with a Restricted Boltzmann Machines (RBM) as an auto-encoder. We will present results showing the accuracy and efficiency of this approach.The D-Wave 2XTM quantum annealer samples the ground-state wave-function of a spin-Ising systems with quadratic interactions between qubits and a Chimera connectivity. The system sits in a ~15 mK thermal bath. One can think of the system as being placed in the ground state initially and subject to thermal excitations governed by Boltzmann statistics. If this is assumed true, one can use the statistics from the D-Wave 2XTM to train RBMs. Generating statistics for training Boltzmann machines is an NP-hard problem and constitutes the largest compute cost. We investigate the use of the D-Wave 2XTM to accelerate the training of the RBMs in our ANNs and report on the results.

Kouatchou, Jules↗

Uncertainty Modeling for Structural Control Analysis and Synthesis

The development of an accurate model of uncertainties for the control of structures that undergo a change in operational environment, based solely on modeling and experimentation in the original environment is studied. The application used throughout this work is the development of an on-orbit uncertainty model based on ground modeling and experimentation. A ground based uncertainty model consisting of mean errors and bounds on critical structural parameters is developed. The uncertainty model is created using multiple data sets to observe all relevant uncertainties in the system. The Discrete Extended Kalman Filter is used as an identification/parameter estimation method for each data set, in addition to providing a covariance matrix which aids in the development of the uncertainty model. Once ground based modal uncertainties have been developed, they are localized to specific degrees of freedom in the form of mass and stiffness uncertainties. Two techniques are presented: a matrix method which develops the mass and stiffness uncertainties in a mathematical manner; and a sensitivity method which assumes a form for the mass and stiffness uncertainties in macroelements and scaling factors. This form allows the derivation of mass and stiffness uncertainties in a more physical manner. The mass and stiffness uncertainties of the ground based system are then mapped onto the on-orbit system, and projected to create an analogous on-orbit uncertainty model in the form of mean errors and bounds on critical parameters. The Middeck Active Control Experiment is introduced as experimental verification for the localization and projection methods developed. In addition, closed loop results from on-orbit operations of the experiment verify the use of the uncertainty model for control analysis and synthesis in space.

Campbell, Mark E.↗

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.↗

Kinetic model development and Bayesian uncertainty quantification for the complete reduction of Fe-based oxygen carriers with CH 4 , CO, and H 2 for chemical looping combustion

In this work, three kinetic models are developed and calibrated for the complete multi-step reduction of an Fe-based oxygen carrier (OC) particle with CH 4 , CO, and H 2 , using data from thermogravimetric analysis. The complete reduction rate profiles exhibit complex dynamics whose trajectory is significantly different depending on the reducing gas. A Bayesian model building and parameter estimation framework is applied for simultaneous parameter and model structure uncertainty quantification. The final models show excellent agreement between model predictions and calibration data, as well as new data not used for calibration (for the reduction of the OC with CH 4 ). Parameter uncertainty is quantified by determining joint posterior distribution, and model structure uncertainty is addressed by incorporating Gaussian process stochastic functions (represented by Bayesian smoothing splines) into the kinetic models. The final kinetic models with discrepancy functions are readily employable in equation-oriented simulation and optimization platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Closed Form Solution for Minimum Norm Model-Validating Uncertainty

A methodology in which structured uncertainty models are directly constructed from measurement data for use in robust control design of multivariable systems is proposed. The formulation allows a general linear fractional transformation uncertainty structure connections with respect to a given nominal model. Existence conditions are given, and under mild assumptions, a closed-form expression for the smallest norm structured uncertainty that validates the model is given. The uncertainty bound computation is simple and is formulated for both open and closed loop systems.

Lim, Kyong Been↗

Aeroservoelastic Uncertainty Model Identification from Flight Data

Uncertainty modeling is a critical element in the estimation of robust stability margins for stability boundary prediction and robust flight control system development. There has been a serious deficiency to date in aeroservoelastic data analysis with attention to uncertainty modeling. Uncertainty can be estimated from flight data using both parametric and nonparametric identification techniques. The model validation problem addressed in this paper is to identify aeroservoelastic models with associated uncertainty structures from a limited amount of controlled excitation inputs over an extensive flight envelope. The challenge to this problem is to update analytical models from flight data estimates while also deriving non-conservative uncertainty descriptions consistent with the flight data. Multisine control surface command inputs and control system feedbacks are used as signals in a wavelet-based modal parameter estimation procedure for model updates. Transfer function estimates are incorporated in a robust minimax estimation scheme to get input-output parameters and error bounds consistent with the data and model structure. Uncertainty estimates derived from the data in this manner provide an appropriate and relevant representation for model development and robust stability analysis. This model-plus-uncertainty identification procedure is applied to aeroservoelastic flight data from the NASA Dryden Flight Research Center F-18 Systems Research Aircraft.

Brenner, Martin J.↗

NASA Engineering and Safety Center Technical Bulletin No. 22-04: Uncertainty Quantification of Reduced Order Structural Dynamic Models

Uncertainty quantification (UQ) provides statistical bounds on prediction accuracy based on finite element model (FEM) uncertainty. An alternate method for UQ, called the Hybrid Parametric Variation (HPV) combines a parametric variation of the Hurty/Craig-Bampton (HCB) fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method. This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available.

Uncertainty Quantification↗

The Climate Response to Emissions Reductions Due to COVID-19: Initial Results From CovidMIP

Many nations responded to the COVID-19 pandemic by restricting travel and other activities during 2020, resulting in temporarily reduced emissions of CO 2 , other greenhouse gases and ozone and aerosol precursors. We perform a coordinated Intercomparison, CovidMIP, of Earth System model simulations to assess the impact on climate of these emissions reductions. Eleven models performed multiple initial-condition ensembles to produce over 280 simulations spanning both initial condition and model structural uncertainty. We find model consensus on reduced aerosol amounts (particularly over East Asia) and associated increases in surface shortwave radiation levels. However, any impact on near-surface temperature or rainfall during 2020-2024 is extremely small and is not detectable in this initial analysis. Regional analyses on a finer scale, and closer attention to extremes (especially linked to changes in atmospheric composition and air quality) are required to test the impact of COVID-19-related emission reductions on near-term climate.

54 ENVIRONMENTAL SCIENCES↗

The Climate Response to Emissions Reductions due to COVID-19: Initial Results from CovidMIP

Many nations responded to the COVID-19 pandemic by restricting travel and other activities during 2020, resulting in temporarily reduced emissions of CO2, other greenhouse gases and ozone and aerosol precursors. We present the initial results from a coordinated Intercomparison, CovidMIP, of Earth system model simulations which assess the impact on climate of these emissions reductions. Twelve models performed multiple initial-condition ensembles to produce over 300 simulations spanning both initial condition and model structural uncertainty. We find model consensus on reduced aerosol amounts (particularly over southern and eastern Asia) and associated increases in surface shortwave radiation levels. However, any impact on near-surface temperature or rainfall during 2020-2024 is extremely small and is not detectable in this initial analysis. Regional analyses on a finer scale, and closer attention to extremes (especially linked to changes in atmospheric composition and air quality) are required to test the impact of COVID- 19-related emission reductions on near-term climate.

Chris D. Jones↗

Stochastic Control Synthesis of Systems with Structured Uncertainty

This paper presents a study on the design of robust controllers by using random variables to model structured uncertainty for both SISO and MIMO feedback systems. Once the parameter uncertainty is prescribed with probability density functions, its effects are propagated through the analysis leading to stochastic metrics for the system's output. Control designs that aim for satisfactory performances while guaranteeing robust closed loop stability are attained by solving constrained non-linear optimization problems in the frequency domain. This approach permits not only to quantify the probability of having unstable and unfavorable responses for a particular control design but also to search for controls while favoring the values of the parameters with higher chance of occurrence. In this manner, robust optimality is achieved while the characteristic conservatism of conventional robust control methods is eliminated. Examples that admit closed form expressions for the probabilistic metrics of the output are used to elucidate the nature of the problem at hand and validate the proposed formulations.

Padula, Sharon L.↗

Bayesian Spatial Models for Projecting Corn Yields

Climate change is predicted to impact corn yields. Previous studies analyzing these impacts differ in data and modeling approaches and, consequently, corn yield projections. We analyze the impacts of climate change on corn yields using two statistical models with different approaches for dealing with county-level effects. The first model, which is novel to modeling corn yields, uses a computationally efficient spatial basis function approach. We use a Bayesian framework to incorporate both parametric and climate model structural uncertainty. We find that the statistical models have similar predictive abilities, but the spatial basis function model is faster and hence potentially a useful tool for crop yield projections. We also explore how different gridded temperature datasets affect the statistical model fit and performance. Compared to the dataset with only weather station data, we find that the dataset composed of satellite and weather station data results in a model with a magnified relationship between temperature and corn yields. For all statistical models, we observe a relationship between temperature and corn yields that is broadly similar to previous studies. We use downscaled and bias-corrected CMIP5 climate model projections to obtain detrended corn yield projections for 2020–2049 and 2069–2098. In both periods, we project a decrease in the mean corn yield production, reinforcing the findings of other studies. However, the magnitude of the decrease and the associated uncertainties we obtain differ from previous studies.

54 ENVIRONMENTAL SCIENCES↗

On the formulation of a minimal uncertainty model for robust control with structured uncertainty

In the design and analysis of robust control systems for uncertain plants, representing the system transfer matrix in the form of what has come to be termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents a transfer function matrix M(s) of the nominal closed loop system, and the delta represents an uncertainty matrix acting on M(s). The nominal closed loop system M(s) results from closing the feedback control system, K(s), around a nominal plant interconnection structure P(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unsaturated uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, but for real parameter variations delta is a diagonal matrix of real elements. Conceptually, the M-delta structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the currently available literature addresses computational methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty, where the term minimal refers to the dimension of the delta matrix. Since having a minimally dimensioned delta matrix would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta would be useful. Hence, a method of obtaining the interconnection system P(s) is required. A generalized procedure for obtaining a minimal P-delta structure for systems with real parameter variations is presented. Using this model, the minimal M-delta model can then be easily obtained by closing the feedback loop. The procedure involves representing the system in a cascade-form state-space realization, determining the minimal uncertainty matrix, delta, and constructing the state-space representation of P(s). Three examples are presented to illustrate the procedure.

Belcastro, Christine M.↗

Impact of Lateral Flow on Surface Water and Energy Budgets over the Southern Great Plains – A Modeling Study

As we see the horizontal grid spacing decrease, treatment of hydrologic processes in land surface models, such as the lateral flow of surface and subsurface flow, need to be explicitly represented. Unlike previous studies that mainly focused on the mountainous regions, in this study the offline WRF-Hydro model is employed to study the impact of lateral flow on soil moisture and energy fluxes over the relatively flat southern Great Plains (SGP). The vast amount of measurements over the SGP provide an unique opportunity to assess the model behavior. In addition, newly developed land surface properties and input forcing are ingested into the model, in an attempt to reduce uncertainties associated with the initial and boundary forcing and help to identify model deficiencies. Our results show that the more realistic inputs (parameters, soil types, forcing) lead to larger underestimation of latent heat flux and dry bias, indicating the existence of model structural uncertainty (embedded errors) in WRF-Hydro that need to be characterized to inform future model development efforts. Including lateral flow processes partly mitigates the model deficiencies in representing hydrologic processes and alleviates the dry bias. In particular, both surface and subsurface lateral flow increase soil moisture mainly over the lower elevations, except that subsurface flow also affects soil moisture over steeper terrains. Additional simulations are performed to assess the effect of routing resolution on model results. When LSM resolution is high, noticeable differences in soil moisture are produced between different routing resolutions especially over steep terrain. Whereas when LSM resolution is coarse, differences between routing resolutions become negligible, especially over flat terrain.

54 ENVIRONMENTAL SCIENCES↗

Development of a multi-layer canopy model for E3SM Land Model with support for heterogeneous computing

The vertical structure of vegetation canopies creates micro-climates. However, the land components of most Earth System Models, including the Energy Exascale Earth System Model (E3SM), typically neglect vertical canopy structure by using a single layer big-leaf representation to simulate water, CO 2 , and energy exchanges between the land and the atmosphere. In this study, we developed a Multi-Layer Canopy Model for the E3SM Land Model to resolve the micro-climate created by vegetation canopies. The model developed in this study re-implements the CLM-ml_v1 to support heterogeneous computing architectures consisting of CPUs and GPUs and includes three additional optimization-based stomatal conductance models. The use of Portable, Extensible Toolkit for Scientific Computation provides a speedup of 25–50 times on a GPU relative to a CPU. The numerical implementation of the model was verified against CLM-ml_v1 for a month-long simulation using data from the Ameriflux US-University of Michigan Biological Station site. Model structural uncertainty was explored by performing control simulations for five stomatal conductance models that exclude and include the control of plant hydrodynamics (PHD) on photosynthesis. The bias in simulated sensible and latent heat fluxes was lower when PHD was accounted for in the model. Additionally, six idealized simulations were performed to study the impact of three environmental variables (i.e. air temperature, atmospheric CO 2 , and soil moisture) on canopy processes (i.e. net CO 2 assimilation, leaf temperature, and leaf water potential). Increasing air temperature reduced net CO 2 assimilation and increased air temperature. Net CO 2 assimilation increased at higher atmospheric CO 2 , while decreasing soil moisture resulted in lower leaf water potential.

54 ENVIRONMENTAL SCIENCES↗

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↗

Reducing uncertainty of high-latitude ecosystem models through identification of key parameters

Abstract Climate change is having significant impacts on Earth’s ecosystems and carbon budgets, and in the Arctic may drive a shift from an historic carbon sink to a source. Large uncertainties in terrestrial biosphere models (TBMs) used to forecast Arctic changes demonstrate the challenges of determining the timing and extent of this possible switch. This spread in model predictions can limit the ability of TBMs to guide management and policy decisions. One of the most influential sources of model uncertainty is model parameterization. Parameter uncertainty results in part from a mismatch between available data in databases and model needs. We identify that mismatch for three TBMs, DVM-DOS-TEM, SIPNET and ED2, and four databases with information on Arctic and boreal above- and belowground traits that may be applied to model parametrization. However, focusing solely on such data gaps can introduce biases towards simple models and ignores structural model uncertainty, another main source for model uncertainty. Therefore, we develop a causal loop diagram (CLD) of the Arctic and boreal ecosystem that includes unquantified, and thus unmodeled, processes. We map model parameters to processes in the CLD and assess parameter vulnerability via the internal network structure. One important substructure, feed forward loops (FFLs), describe processes that are linked both directly and indirectly. When the model parameters are data-informed, these indirect processes might be implicitly included in the model, but if not, they have the potential to introduce significant model uncertainty. We find that the parameters describing the impact of local temperature on microbial activity are associated with a particularly high number of FFLs but are not constrained well by existing data. By employing ecological models of varying complexity, databases, and network methods, we identify the key parameters responsible for limited model accuracy. They should be prioritized for future data sampling to reduce model uncertainty.

54 ENVIRONMENTAL SCIENCES↗

Impacts of climate change on subannual hydropower generation: a multi-model assessment of the United States federal hydropower plant

Abstract Hydropower is a low-carbon emission renewable energy source that provides competitive and flexible electricity generation and is essential to the evolving power grid in the context of decarbonization. Assessing hydropower availability in a changing climate is technically challenging because there is a lack of consensus in the modeling representation of key dynamics across scales and processes. Focusing on 132 US federal hydropower plants, in this study we evaluate the compounded impact of climate and reservoir-hydropower models’ structural uncertainties on monthly hydropower projections. In particular, instead of relying on one single regression-based hydropower model, we introduce another conceptual reservoir operations-hydropower model in the assessment framework. This multi-model assessment approach allows us to partition uncertainties associated with both climate and hydropower models for better clarity. Results suggest that while at least 70% of the uncertainties at the annual scale and 50% at the seasonal scale can be attributed to the choice of climate models, up to 50% of seasonal variability can be attributed to the choice of hydropower models, particularly in regions over the western US where the reservoir storage is substantial. The analysis identifies regions where multi-model assessments are needed and presents a novel approach to partition uncertainties in hydropower projections. Another outcome includes an updated evaluation of Coupled Model Intercomparison Project Phase 5 (CMIP5)-based federal hydropower projection, at the monthly scale and with a larger ensemble, which can provide a baseline for understanding future assessments based on CMIP6 and beyond.

54 ENVIRONMENTAL SCIENCES↗

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↗