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At least 73 records · Page 4

Analysis of modeling errors in system identification

This paper is concerned with the identification of a system in the presence of several error sources. Following some basic definitions, the notion of 'near-equivalence in probability' is introduced using the concept of near-equivalence between a model and process. Necessary and sufficient conditions for the identifiability of system parameters are given. The effect of structural error on the parameter estimates for both deterministic and stochastic cases are considered.

Hadaegh, F. Y.↗

Equipping Neural Network Surrogates with Uncertainty for Propagation in Physical Systems

Coarse-grained or filtered models typically rely on closure models to account for unresolved scales. For instance, large eddy simulation for modeling turbulent fluid flows explicitly resolves the largest scales, but requires modeling closure terms to account for the sub-filter scales. With the vast amount of data available from high-fidelity simulations, there are unique opportunities to leverage data-driven modeling techniques to formulate expressive and flexible closure models. Despite their flexibility, data-driven models struggle in domain shift settings, i.e. when deployed in configurations not captured in the training dataset. In particular, the efficacy of neural network surrogates is difficult to assess a priori due to the deterministic, point-estimate nature of predictions. In high-consequence applications, such models require reliable uncertainty estimates in the data-informed and out-of-distribution regimes. To quantify uncertainties in both regimes, we employ Bayesian neural networks which are able to capture both epistemic and aleatoric uncertainties. We will discuss challenges associated with the training and evaluation of these networks. Furthermore, we will discuss uncertainty embedding strategies to enable efficient sampling and propagation of uncertainty through high-fidelity simulations.

Bayesian neural networks↗

Ensemble Kalman Filter for Dynamic State Estimation of Power Grids Stochastically Driven by Time-correlated Mechanical Input Power

State and parameter estimation of power transmission networks is important for monitoring power grid operating conditions and analyzing transient stability. Wind power generation depends on fluctuating input power levels, which are correlated in time and contribute to uncertainty in turbine dynamical models. The ensemble Kalman filter (EnKF), a standard state estimation technique, uses a deterministic forecast and does not explicitly model time-correlated noise in parameters such as mechanical input power. However, this uncertainty affects the probability of fault-induced transient instability and increased prediction bias. Here a novel approach is to model input power noise with time-correlated stochastic fluctuations, and integrate them with the network dynamics during the forecast. While the EnKF has been used to calibrate constant parameters in turbine dynamical models, the calibration of a statistical model for a time-correlated parameter has not been investigated. In this study, twin experiments on a standard transmission network test case are used to validate our time-correlated noise model framework for state estimation of unsteady operating conditions and transient stability analysis, and a methodology is proposed for the inference of the mechanical input power time-correlation length parameter using time-series data from PMUs monitoring power dynamics at generator buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Validation of a Monte Carlo model for the MLC-Elekta Precise with MCNP6 - Paper 76

Cancer treatment using radiotherapy techniques needs an accurate prediction of the dose delivered to the patient at each position. Treatment planning systems (TPS) allow the optimization of the dose delivered to the tumor volume while minimizing the dose absorbed by the surrounding healthy tissue. Commercial treatment planning systems use empirical deterministic algorithms that do not correctly estimate the dose in the surroundings of heterogeneities. This lack of accuracy is taken into account as bigger security margins in the treatment, reducing the potential effect of the treatment. However, Monte Carlo (MC) simulation techniques have proved to predict the dose distribution more accurately and also representing experimental data better. Nevertheless, the clinical application of these techniques has been limited by the long calculation times they require. As high performance computers decrease in cost MC simulations become more feasible to be used in TPS. The present work improves a simplified model of the MLC-Elekta Precise linear accelerator (linac or unit from now on) previously developed and correctly validated by the group. A multileaf collimator (MLC) has been modelled according to the manufacturer specifications and added to the previous model to allow higher conformity in the studies. The full geometry has been entered to the MCNP6 Monte Carlo code to simulate the transport of particles through the linac. The geometry also includes a cubic water phantom for dosimetry studies and validation with experimental data. The experimental data employed for the dose distribution comparison has been measured at the linac from the linac Hospital Universitari Clinic de Valencia (Spain). Additionally, particles are stored in a phase space surface before their entrance in the water to be analyzed and for performance optimization. Given the results presented, we conclude that this first approach to validate a model of the Elekta Precise linac from the Hospital Cl nic Universitari de Valancia represents well the depth-dose distribution, but fails at representing the dose profiles. It has been shown that they predict too much penumbra, probably caused by the filtration between the leaves. In order to solve this problems, further work is needed to improve the simulated model. This work will mainly focus on the multileaf collimator. Also, the codes developed by the group to analyze phase space files produced by MCNP6 have proven highly useful. As work progress and the codes are debugged, they will be published so that the community can take advantage of them.

61 RADIATION PROTECTION AND DOSIMETRY↗

Geomechanics-Based Stochastic Analysis of Injection- Induced Seismicity

The production of geothermal energy from dry and low permeability reservoirs is achieved by water circulation in natural and/or man-made fractures, and is referred to as enhanced or engineered geothermal systems (EGS). Often, the permeable zones have to be created by stimulation, a process which involves fracture initiation and/or activation of discontinuities such as faults and joints due to pore pressure and the in-situ stress perturbations. The stimulation of a rock mass is often accompanied by multiple microseismic events. Micro-seismic events associated with rock failure in shear, and shear slip on new or pre-existing fracture planes and possibly their propagations. The microseismic signals contain information about the sources of energy that can be used for understanding the hydraulic fracturing process and the created reservoir properties. Detection and interpretation of microseismic events is useful for estimating the stimulated zone, created reservoir permeability and fracture growth, and geometry of the geological structures and the in-situ stress state. The process commonly is referred to as seismicity-based reservoir characterization (SBRC). Although, progress has been made by scientific & geothermal communities for quantitative and qualitative analysis of reservoir stimulation using SBRC several key questions remain unresolved in the analysis of micro-seismicity namely, variation of seismic activity with injection rate, delayed micro-seismicity, and the relation of stimulated zone to the injected volume and its rate, and the resulting reservoir permeability. In addition, the current approach to SBRC does not consider the full range of relevant poroelastic and thermoelastic phenomena and neglects the uncertainty in rock properties and in-situ stress in the data inversion process. The objective of this research and technology developments was to develop a 3D SBRC model that addresses these shortcomings by taking into account hydro-thermo-poro-mechanical mechanisms associated with injection and utilizing a state-of-the-art stochastic inversion procedure. The approach proposed herein is innovative and significantly improves the existing SBCR technology (e.g., Shapiro et al. 2003) for geothermal reservoirs in several ways. First, the current scope of the SBRC is limited with respect to the physical processes considered and the rock properties used. Usually, the geomechanics analyses within SBRC is limited to the pore pressure diffusion in the rock mass, which is modeled using a time-dependent parabolic equation and solved using a finite element algorithm with either a line or a point source. However, water injection induces both poroelastic and thermoelastic stresses in the rock mass which affect the stress state. In fact, it has been suggested that thermoelastic stresses can play a dominant role in reservoir seismicity (Ghassemi et al., 2007). We include these important effects by using a fully-coupled poro-thermoelastic constitutive equations for the rock mass which will be solved using a 3D finite element model with more realistic injection geometries such as multiple injection/extraction sources (and in fractures), uncertainty in the material parameters and the in-situ stress distribution to better reflect the pore pressure and stress distributions. In addition, we developed a 3D stochastic fracture network model to study MEQ generation in fracture rocks. The model was verified using laboratory experiments, and calibrated and applied to Newberry EGS stimulation. In previous SBRC approaches, the triggering of micro-seismicity is modeled base on the assumption that the prior stochastic criticality model of the rock mass is a valid and adequate description. However, this assumption often does not hold in the field. Thus, we improved upon the current SBRC approach by using the micro-seismic responses to estimate the hydraulic diffusivity as well as the criticality distribution itself within the field. In this way, instead of relying on our a priori knowledge of criticality distribution, we combine an initial probabilistic description of criticality with the information contained in microseismic measurements to arrive at criticality solutions that are conditioned on both field data and our prior knowledge. Previous SBRC have relied upon a deterministic inversion approach to estimate the permeability, and the extent of the stimulated zone, whereas a stochastic inversion algorithm that recognizes and quantifies the uncertainties in the prior model, the time evolution of pore pressure distributions (modeling errors), and the observed seismic events is developed and used herein to realistically assess the quality of the solution. Finally, we developed a technique for processing discrete MEQ data to estimate fracture network properties such as dip and dip directions. The approach was successfully applied to the Fenton Hill HRD experiment and the Newberry EGS with results in good agreement with field observations.

15 GEOTHERMAL ENERGY↗

A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L 2 -consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L 2 -inconsistent calibration. This L 2 -inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L 2 calibration, is proposed and proven to be L 2 -consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L 2 -inconsistency problem.

97 MATHEMATICS AND COMPUTING↗

Stress Rupture Life Reliability Measures for Composite Overwrapped Pressure Vessels

Composite Overwrapped Pressure Vessels (COPVs) are often used for storing pressurant gases onboard spacecraft. Kevlar (DuPont), glass, carbon and other more recent fibers have all been used as overwraps. Due to the fact that overwraps are subjected to sustained loads for an extended period during a mission, stress rupture failure is a major concern. It is therefore important to ascertain the reliability of these vessels by analysis, since the testing of each flight design cannot be completed on a practical time scale. The present paper examines specifically a Weibull statistics based stress rupture model and considers the various uncertainties associated with the model parameters. The paper also examines several reliability estimate measures that would be of use for the purpose of recertification and for qualifying flight worthiness of these vessels. Specifically, deterministic values for a point estimate, mean estimate and 90/95 percent confidence estimates of the reliability are all examined for a typical flight quality vessel under constant stress. The mean and the 90/95 percent confidence estimates are computed using Monte-Carlo simulation techniques by assuming distribution statistics of model parameters based also on simulation and on the available data, especially the sample sizes represented in the data. The data for the stress rupture model are obtained from the Lawrence Livermore National Laboratories (LLNL) stress rupture testing program, carried out for the past 35 years. Deterministic as well as probabilistic sensitivities are examined.

Murthy, Pappu L. N.↗

Predictability of phases and magnitudes of natural decadal climate variability phenomena in CMIP5 experiments with the UKMO HadCM3, GFDL-CM2.1, NCAR-CCSM4, and MIROC5 global earth system models

Data from decadal hindcast experiments conducted under CMIP5 were used to assess the ability of CM2.1, HadCM3, MIROC5, and CCSM4 Earth System Models (ESMs) to hindcast sea-surface temperature (SST) indices of the Pacific Decadal Oscillation (PDO), the tropical Atlantic SST gradient (TAG) variability, and the West Pacific Warm Pool (WPWP) SST variability from 1961 to 2010. The ESMs were initialized at specific times with observed data to make 10- and 30-year hindcasts/forecasts. Deterministic and probabilistic skill estimates show predictability of detrended WPWP index to 5 years’ lead time and of non-detrended WPWP index to 10 years’ lead time. These estimates also show atypical skill dependence of PDO and TAG indices on lead times, with increasing skill in the middle to end of 10-year hindcasts. The skill of ESMs to hindcast an observed DCV index (signal skill) is surprisingly greater than the skill to hindcast their own DCV index (noise skill) at some lead times. All ESMs hindcast occurrence frequencies of positive and negative phases of the indices, and probabilities of same-phase transitions from one year to the next reasonably well. Four, major, low-latitude volcanic eruptions are associated with phase transitions of all observed and some of the ensemble-average hindcast indices. All ESMs’ WPWP index hindcasts respond correctly to all eruptions as do three observed PDO phase transitions. No one of the ESMs’ hindcasts of the TAG index responds correctly to these eruptions. Some of the ESMs hindcast correct phase transitions in the absence of eruptions also, implying that initializations with observed data are beneficial in predicting phase transitions. The skills of DCV indices’ phase prediction up to at least two years in advance can be used to inform societal impacts adaptation decisions in water resources management and agriculture. The Atlantic region’s responses in these ESMs appear to be fundamentally incorrect.

54 ENVIRONMENTAL SCIENCES↗

Tipping point analysis of atmospheric oxygen concentration

We apply tipping point analysis to nine observational oxygen concentration records around the globe, analyse their dynamics and perform projections under possible future scenarios, leading to oxygen deficiency in the atmosphere. The analysis is based on statistical physics framework with stochastic modelling, where we represent the observed data as a composition of deterministic and stochastic components estimated from the observed data using Bayesian and wavelet techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effects of structural error on the estimates of parameters of dynamical systems

In this paper, the notion of 'near-equivalence in probability' is introduced for identifying a system in the presence of several error sources. Following some basic definitions, necessary and sufficient conditions for the identifiability of parameters are given. The effects of structural error on the parameter estimates for both the deterministic and stochastic cases are considered.

Hadaegh, F. Y.↗

Ideal State Reconstructor For Control System

Ideal state reconstructor is conceptual subsystem of deterministic digital control system estimating state of controlled plant periodically at discrete sampling intervals of duration T. Does not add new states, eigenvalues, or dynamics. Based on concepts described in "State-Variable Representations For Moving-Average Sampling" (MFS-28405).

Polites, Michael E.↗

Evaluating NMME Seasonal Forecast Skill for use in NASA SERVIR Hub Regions

The U.S. National Multi-Model Ensemble seasonal forecasting system is providing hindcast and real-time data streams to be used in assessing and improving seasonal predictive capacity. The coupled forecasts have numerous potential applications, both national and international in scope. The NASA / USAID SERVIR project, which leverages satellite and modeling-based resources for environmental decision making in developing nations, is focusing on the evaluation of NMME forecasts specifically for use in driving applications models in hub regions including East Africa, the Hindu Kush- Himalayan (HKH) region and Mesoamerica. A prerequisite for seasonal forecast use in application modeling (e.g. hydrology, agriculture) is bias correction and skill assessment. Efforts to address systematic biases and multi-model combination in support of NASA SERVIR impact modeling requirements will be highlighted. Specifically, quantilequantile mapping for bias correction has been implemented for all archived NMME hindcasts. Both deterministic and probabilistic skill estimates for raw, bias-corrected, and multi-model ensemble forecasts as a function of forecast lead will be presented for temperature and precipitation. Complementing this statistical assessment will be case studies of significant events, for example, the ability of the NMME forecasts suite to anticipate the 2010/2011 drought in the Horn of Africa and its relationship to evolving SST patterns.

Roberts, J. Brent↗

Stochastic Waveform Estimation at the Fundamental Quantum Limit

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit: the extended-channel quantum Cramér-Rao bound. In the experimentally relevant regime in which losses dominate, we prove that non-Gaussian-state preparation and measurement are required to achieve this fundamental limit and we determine numerically the optimal non-Gaussian protocol. We discuss how this scheme could accelerate searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

Axions↗

H(sub infinity)-type filter for spacecraft attitude estimation

A nonlinear filtering theory from a deterministic point of view is presented and an application to attitude determination is considered. The approach that is taken in this paper is motivated largely by the H(sun infinity) control and estimation theory for linear systems which has been evolved within the last decade. Rather than formulating the estimation problem as a game played by two adversaries, as has been done in the linear case, we employ in this work some notions from the theory of dissipative systems as a vehicle for arriving at certain Hamilton-Jacobi inequality, which in turn, provides a solution to the filtering problem, whenever it is satisfied. Application of this method to a linear estimation problem and to the problem of estimating a spacecraft attitude quaternion and gyro drift bias vector are presented. In limiting cases, these give the Kalman filter and the extended Kalman filter, respectively. The main advantages of this approach over its probabilistic counterpart are that this approach does not require a prior knowledge of any statistics, and that in general it is more amenable to a quantitative assessment regarding approximations such as linearization, and that in certain cases this approach yields an exact solution to the nonlinear filtering.

Markley, F. Landis↗

Wind estimation using air data probe measurements to evaluate meteorological measurements made during Space Shuttle entries

Deterministic and weighted least squares methods for obtaining estimates of the horizontal winds encountered during the Shuttle entry phase are described. The estimates are based on in situ Air Data System (ADS) measurements of angle-of-attack, side-slip angle and true airspeed, in conjunction with inertial trajectory parameters obtained from the post flight trajectory reconstruction. Accuracies in the wind estimates obtained from each method are assessed using both theoretical arguments and flight results. Comparisons of derived winds with meteorological measurements taken during the first three Shuttle entries have demonstrated: (1) the usefulness of the wind estimators for evaluating meteorological measurements below 50 kft, and (2) the potential for adequate wind determinations in the absence of independent wind measurements. Comparisons of STS-3 flight-derived L/D versus predicted values from the LaRC aerodynamic data base are presented from 50 kft to touchdown. These results exemplify the importance of such determinations to enhance the ongoing Shuttle aerodynamic and aerothermodynamic research.

Kelly, G. M.↗

Final STS-35 Columbia descent BET products and results for LaRC OEX investigations

Final STS-35 'Columbia' descent Best Estimate Trajectory (BET) products have been developed for Langley Research Center (LaRC) Orbiter Experiments (OEX) investigations. Included are the reconstructed inertial trajectory profile; the Extended BET, which combines the inertial data and, in this instance, the National Weather Service atmospheric information obtained via Johnson Space Center; and the Aerodynamic BET. The inertial BET utilized Inertial Measurement Unit 1 (IMU1) dynamic measurements for deterministic propagation during the ENTREE estimation process. The final estimate was based on the considerable ground based C-band tracking coverage available as well as Tracking Data and Relay Satellite System (TDRSS) Doppler data, a unique use of the latter for endo-atmospheric flight determinations. The actual estimate required simultaneous solutions for the spacecraft position and velocity, spacecraft attitude, and six IMU parameters - three gyro biases and three accelerometer scale factor correction terms. The anchor epoch for this analysis was 19,200 Greenwich Mean Time (GMT) seconds which corresponds to an initial Shuttle altitude of approximately 513 kft. The atmospheric data incorporated were evaluated based on Shuttle derived considerations as well as comparisons with other models. The AEROBET was developed based on the Extended BET, the measured spacecraft configuration information, final mass properties, and the final Orbiter preoperation databook. The latter was updated based on aerodynamic consensus incrementals derived by the latest published FAD. The rectified predictions were compared versus the flight computed values and the resultant differences were correlated versus ensemble results for twenty-two previous STS entry flights.

Oakes, Kevin F.↗

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.

Rodriguez, G.↗