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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

SU-D-BRD-07: Evaluation of the Effectiveness of Statistical Process Control Methods to Detect Systematic Errors For Routine Electron Energy Verification

Purpose: To evaluate the ability of statistical process control methods to detect systematic errors when using a two dimensional (2D) detector array for routine electron beam energy verification. Methods: Electron beam energy constancy was measured using an aluminum wedge and a 2D diode array on four linear accelerators. Process control limits were established. Measurements were recorded in control charts and compared with both calculated process control limits and TG-142 recommended specification limits. The data was tested for normality, process capability and process acceptability. Additional measurements were recorded while systematic errors were intentionally introduced. Systematic errors included shifts in the alignment of the wedge, incorrect orientation of the wedge, and incorrect array calibration. Results: Control limits calculated for each beam were smaller than the recommended specification limits. Process capability and process acceptability ratios were greater than one in all cases. All data was normally distributed. Shifts in the alignment of the wedge were most apparent for low energies. The smallest shift (0.5 mm) was detectable using process control limits in some cases, while the largest shift (2 mm) was detectable using specification limits in only one case. The wedge orientation tested did not affect the measurements as this did not affect the thickness of aluminum over the detectors of interest. Array calibration dependence varied with energy and selected array calibration. 6 MeV was the least sensitive to array calibration selection while 16 MeV was the most sensitive. Conclusion: Statistical process control methods demonstrated that the data distribution was normally distributed, the process was capable of meeting specifications, and that the process was centered within the specification limits. Though not all systematic errors were distinguishable from random errors, process control limits increased the ability to detect systematic errors using routine measurement of electron beam energy constancy.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2015

SU-E-P-13: Quantifying the Geometric Error Due to Irregular Motion in Four-Dimensional Computed Tomography (4DCT)

Purpose: Respiratory correlated 4DCT images are generated under the assumption of a regular breathing cycle. This study evaluates the error in 4DCT-based target position estimation in the presence of irregular respiratory motion. Methods: A custom-made programmable externally-and internally-deformable lung motion phantom was placed inside the CT bore. An abdominal pressure belt was placed around the phantom to mimic clinical 4DCT acquisitio and the motion platform was programmed with a sinusoidal (±10mm, 10 cycles per minute) motion trace and 7 motion traces recorded from lung cancer patients. The same setup and motion trajectories were repeated in the linac room and kV fluoroscopic images were acquired using the on-board imager. Positions of 4 internal markers segmented from the 4DCT volumes were overlaid upon the motion trajectories derived from the fluoroscopic time series to calculate the difference between estimated (4DCT) and “actual” (kV fluoro) positions. Results: With a sinusoidal trace, absolute errors of the 4DCT estimated markers positions vary between 0.78mm and 5.4mm and RMS errors are between 0.38mm to 1.7mm. With irregular patient traces, absolute errors of the 4DCT estimated markers positions increased significantly by 100 to 200 percent, while the corresponding RMS error values have much smaller changes. Significant mismatches were frequently found at peak-inhale or peak-exhale phase. Conclusion: As expected, under conditions of well-behaved, periodic sinusoidal motion, the 4DCT yielded much better estimation of marker positions. When an actual patient trace is used 4DCT-derived positions showed significant mismatches with the fluoroscopic trajectories, indicating the potential for geometric and therefore dosimetric errors in the presence of cycle-to-cycle respiratory variations.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-769: T-Test Based Prior Error Estimate and Stopping Criterion for Monte Carlo Dose Calculation in Proton Therapy

Purpose: The Monte Carlo (MC) method is a gold standard for dose calculation in radiotherapy. However, it is not a priori clear how many particles need to be simulated to achieve a given dose accuracy. Prior error estimate and stopping criterion are not well established for MC. This work aims to fill this gap. Methods: Due to the statistical nature of MC, our approach is based on one-sample t-test. We design the prior error estimate method based on the t-test, and then use this t-test based error estimate for developing a simulation stopping criterion. The three major components are as follows.First, the source particles are randomized in energy, space and angle, so that the dose deposition from a particle to the voxel is independent and identically distributed (i.i.d.).Second, a sample under consideration in the t-test is the mean value of dose deposition to the voxel by sufficiently large number of source particles. Then according to central limit theorem, the sample as the mean value of i.i.d. variables is normally distributed with the expectation equal to the true deposited dose.Third, the t-test is performed with the null hypothesis that the difference between sample expectation (the same as true deposited dose) and on-the-fly calculated mean sample dose from MC is larger than a given error threshold, in addition to which users have the freedom to specify confidence probability and region of interest in the t-test based stopping criterion. Results: The method is validated for proton dose calculation. The difference between the MC Result based on the t-test prior error estimate and the statistical Result by repeating numerous MC simulations is within 1%. Conclusion: The t-test based prior error estimate and stopping criterion are developed for MC and validated for proton dose calculation. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

MO-F-CAMPUS-T-05: Correct Or Not to Correct for Rotational Patient Set-Up Errors in Stereotactic Radiosurgery

Purpose: To quantify the effect of patient rotation in stereotactic radiation therapy and establish a threshold where rotational patient set-up errors have a significant impact on target coverage. Methods: To simulate rotational patient set-up errors, a Matlab code was created to rotate the patient dose distribution around the treatment isocentre, located centrally in the lesion, while keeping the structure contours in the original locations on the CT and MRI. Rotations of 1°, 3°, and 5° for each of the pitch, roll, and yaw, as well as simultaneous rotations of 1°, 3°, and 5° around all three axes were applied to two types of brain lesions: brain metastasis and acoustic neuroma. In order to analyze multiple tumour shapes, these plans included small spherical (metastasis), elliptical (acoustic neuroma), and large irregular (metastasis) tumour structures. Dose-volume histograms and planning target volumes were compared between the planned patient positions and those with simulated rotational set-up errors. The RTOG conformity index for patient rotation was also investigated. Results: Examining the tumour volumes that received 80% of the prescription dose in the planned and rotated patient positions showed decreases in prescription dose coverage of up to 2.3%. Conformity indices for treatments with simulated rotational errors showed decreases of up to 3% compared to the original plan. For irregular lesions, degradation of 1% of the target coverage can be seen for rotations as low as 3°. Conclusions: This data shows that for elliptical or spherical targets, rotational patient set-up errors less than 3° around any or all axes do not have a significant impact on the dose delivered to the target volume or the conformity index of the plan. However the same rotational errors would have an impact on plans for irregular tumours.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-D-BRA-03: Analysis of Systematic Errors with 2D/3D Image Registration for Target Localization and Treatment Delivery in Stereotactic Radiosurgery

Purpose: Determine systematic deviations between 2D/3D and 3D/3D image registrations with six degrees of freedom (6DOF) for various imaging modalities and registration algorithms on the Varian Edge Linac. Methods: The 6DOF systematic errors were assessed by comparing automated 2D/3D (kV/MV vs. CT) with 3D/3D (CBCT vs. CT) image registrations from different imaging pairs, CT slice thicknesses, couch angles, similarity measures, etc., using a Rando head and a pelvic phantom. The 2D/3D image registration accuracy was evaluated at different treatment sites (intra-cranial and extra-cranial) by statistically analyzing 2D/3D pre-treatment verification against 3D/3D localization of 192 Stereotactic Radiosurgery/Stereotactic Body Radiation Therapy treatment fractions for 88 patients. Results: The systematic errors of 2D/3D image registration using kV-kV, MV-kV and MV-MV image pairs using 0.8 mm slice thickness CT images were within 0.3 mm and 0.3° for translations and rotations with a 95% confidence interval (CI). No significant difference between 2D/3D and 3D/3D image registrations (P>0.05) was observed for target localization at various CT slice thicknesses ranging from 0.8 to 3 mm. Couch angles (30, 45, 60 degree) did not impact the accuracy of 2D/3D image registration. Using pattern intensity with content image filtering was recommended for 2D/3D image registration to achieve the best accuracy. For the patient study, translational error was within 2 mm and rotational error was within 0.6 degrees in terms of 95% CI for 2D/3D image registration. For intra-cranial sites, means and std. deviations of translational errors were −0.2±0.7, 0.04±0.5, 0.1±0.4 mm for LNG, LAT, VRT directions, respectively. For extra-cranial sites, means and std. deviations of translational errors were - 0.04±1, 0.2±1, 0.1±1 mm for LNG, LAT, VRT directions, respectively. 2D/3D image registration uncertainties for intra-cranial and extra-cranial sites were comparable. Conclusion: The Varian Edge radiosurgery 6DOF-based system, can perform 2D/3D image registration with high accuracy for target localization in image-guided stereotactic radiosurgery. The work was supported by a Research Scholar Grant, RSG-15-137-01-CCE from the American Cancer Society.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-320: Assessing Placement Error of Optically Stimulated Luminescent in Vivo Dosimeters Using Cone-Beam Computed Tomography

Purpose: Optically-stimulated luminescent dosimeters (OSLDs) are increasingly utilized for in vivo dosimetry of complex radiation delivery techniques such as intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT). Evaluation of clinical uncertainties such as placement error has not been performed. This work retrospectively investigates the magnitude of placement error using conebeam computed tomography (CBCT) and its effect on measured/planned dose agreement. Methods: Each OSLD was placed at a physicist-designated location on the patient surface on a weekly basis. The location was given in terms of a gantry angle and two-dimensional offset from central axis. The OSLDs were placed before daily image guidance. We identified 77 CBCTs from 25 head-and-neck patients who received IMRT or VMAT, where OSLDs were visible on the CT image. Grossly misplaced OSLDs were excluded (e.g. wrong laterality). CBCTs were registered with the treatment plan and the distance between the planned and actual OSLD location was calculated in two dimensions in the beam’s eye view. Distances were correlated with measured/planned dose percent differences. Results: OSLDs were grossly misplaced for 5 CBCTs (6.4%). For the remaining 72 CBCTs, average placement error was 7.0±6.0 mm. These errors were not correlated with measured/planned dose percent differences (R{sup 2}=0.0153). Generalizing the dosimetric effect of placement errors may be unreliable. Conclusion: Correct placement of OSLDs for IMRT and VMAT treatments is critical to accurate and precise in vivo dosimetry. Small placement errors could produce large disagreement between measured and planned dose. Further work includes expansion to other treatment sites, examination of planned dose at the actual point of OSLD placement, and the influence of imageguided shifts on measured/planned dose agreement.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TU-H-CAMPUS-JeP1-05: Dose Deformation Error Associated with Deformable Image Registration Pathways

Purpose: To evaluate errors associated with using different deformable image registration (DIR) pathways to deform dose from planning CT (pCT) to cone-beam CT (CBCT). Methods: Deforming dose is controversial because of the lack of quality assurance tools. We previously proposed a novel metric to evaluate dose deformation error (DDE) by warping dose information using two methods, via dose and contour deformation. First, isodose lines of the pCT were converted into structures and then deformed to the CBCT using an image based deformation map (dose/structure/deform). Alternatively, the dose matrix from the pCT was deformed to CBCT using the same deformation map, and then the same isodose lines of the deformed dose were converted into structures (dose/deform/structure). The doses corresponding to each structure were queried from the deformed dose and full-width-half-maximums were used to evaluate the dose dispersion. The difference between the FWHM of each isodose level structure is defined as the DDE. Three head-and-neck cancer patients were identified. For each patient, two DIRs were performed between the pCT and CBCT, either deforming pCT-to-CBCT or CBCT-to-pCT. We evaluated the errors associated by using either of these pathways to deform dose. A commercially available, Demons based DIR was used for this study, and 10 isodose levels (20% to 105%) were used to evaluate the errors in various dose levels. Results: The prescription dose for all patients was 70 Gy. The mean DDE for CT-to-CBCT deformation was 1.0 Gy (range: 0.3–2.0 Gy) and this was increased to 4.3 Gy (range: 1.5–6.4 Gy) for CBCT-to-CT deformation. The mean increase in DDE between the two deformations was 3.3 Gy (range: 1.0–5.4 Gy). Conclusion: The proposed DDF was used to quantitatively estimate dose deformation errors caused by different pathways to perform DIR. Deforming dose using CBCT-to-CT deformation produced greater error than CT-to-CBCT deformation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Putting error bars on density functional theory dataset

This dataset contains submission files and raw output files from high-throughput DFT simulations to analyze the systemic errors in lattice constant, bulk moduli and formation energy predictions for a range of binary and ternary oxides using four exchange correlation functionals (LDA, PBE, PBEsol and vdW-DF-C09). This data was then used as the basis for employing materials informatics methods to predict the expected errors in the lattice constants of the studied compounds. Predicted errors were also used to better the DFT-predicted lattice parameters. Our results emphasize the link between the computed errors and the electron density and hybridization errors of a functional. In essence, these results provide “error bars” for choosing a functional for the creation of high-accuracy, high-throughput datasets as well as avenues for the development of XC functionals with enhanced performance, thereby enabling the accelerated discovery and design of new materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - I : Theory

This paper discusses two cross section interpolation methods commonly found in popular nodal codes; the partial derivatives and multiple tables models. The motivation for choosing a model, and thus a case matrix structure, is a trade off between accuracy and computational cost. Due to decades of experience, there are default structures that are sufficient for current light water reactor analysis. However, this is not necessarily the case for advanced reactor designs. Therefore, it is advantageous to understand the sources of error in cross section interpolation models so that the quality of a case matrix may be improved. A mathematical framework for these models is presented in this work that provides a more rigorous connection between the nuclear engineering field's cross section interpolation methods and the broader mathematical field of function approximation. The two cross section models examined in this paper were found to utilize Lagrange interpolation and are a subset of Lagrange tensor products. Classical results of Lagrange polynomial error analysis were then applied to the partial derivative and multiple tables models to derive expressions for the total point-wise error. The analytical results classify the total error into two parts: the model form error and interpolation error. Finally, based on our observations, a better foundation for improving the quality of a case matrix is proposed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Correction of confidence intervals in excess relative risk models using Monte Carlo dosimetry systems with shared errors

Introduction: Measurement errors are ubiquitous in epidemiological studies, especially for doses arising from environmental and occupational exposures, which are difficult to assess. Correction methods for independent measurement errors, have been comprehensively described elsewhere, including regression calibration, simulation extrapolation (SIMEX), etc. However, when exposure estimates are constructed using complicated physical and biological models, uncertainties in the dosimetry system can become very complex. In such systems, uncertainties in some parameters may affect a large group of study participants simultaneously, and hence are “shared” as opposed to independent dosimetric uncertainties. Representing the structure of the uncertainty in the dosimetry by providing multiple realizations of possible dose has been described for several studies. The goal of this paper is to implement, and explore the properties of, a generalized estimating equation-based approach to shared uncertainties based on principles described in an earlier paper. Methods: The effects of shared and unshared dosimetry error on parameter estimates and confidence intervals in a generalized excess relative risk model are examined. A post-hoc correction method is implemented that constructs corrected confidence intervals based on an underlying variance structure described in an earlier paper. In this correction method it is assumed that the estimated slope parameter in a linear excess relative risk model is distributed as a mixture of normal and lognormal components. A simulation study of the behavior of this correction was developed based on multiple realizations provided by the Monte Carlo dosimetry system used for the plutonium exposures in the Mayak Worker Cohort and a risk model with close similarity to that used in analyses of lung cancer data in that cohort. Results: In the simulation study we found that shared dose errors severely degraded the coverage probabilities of confidence limits for the slope parameter in the linear excess relative risk model relating uncertain exposure to lung cancer risk. Using our correction method to adjust the confidence intervals provided much improved coverage probabilities for this parameter. A smaller amount of degradation in confidence interval coverage for other parameters (e.g. those in the baseline and dose modification terms) was noted, and the proposed correction method also improved coverage for these parameters as well. Discussion: Compared to other recently described methods our proposed correction method relies on relatively familiar software to fit dose response models. The basic modeling philosophy described here first uses existing Poisson regression methods to estimate parameters in the excess relative risk model; in this first stage mean dose (computed from the multiple realizations) is used as the independent variable in the regression. Once the model is fit we then correct (widen) the standard errors for all parameters using the proposed correction method. The simulation studies indicate that the methods described here are an important contribution to the available tools for dealing with shared measurement errors in complex risk analysis.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2022

Error-Bounded Learned Scientific Data Compression with Preservation of Derived Quantities

Scientific applications continue to grow and produce extremely large amounts of data, which require efficient compression algorithms for long-term storage. Compression errors in scientific applications can have a deleterious impact on downstream processing. Thus, it is crucial to preserve all the “known” Quantities of Interest (QoI) during compression. To address this issue, most existing approaches guarantee the reconstruction error of the original data or primary data (PD), but cannot directly control the problem of preserving the QoI. In this work, we propose a physics-informed compression technique that is composed of two parts: (i) reduction of the PD with bounded errors and (ii) preservation of the QoI. In the first step, we combine tensor decompositions, autoencoders, product quantizers, and error-bounded lossy compressors to bound the reconstruction error at high levels of compression. In the second step, we use constraint satisfaction post-processing followed by quantization to preserve the QoI. To illustrate the challenges of reducing the reconstruction errors of the PD and QoI, we focus on simulation data generated by a large-scale fusion code, XGC, which can produce tens of petabytes in a single day. The results show that our approach can achieve a high compression amount while accurately preserving the QoI within scientifically acceptable bounds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Stochastic Error Cancellation in Analog Quantum Simulation

Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can be simulated. In our work, we consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian we want to simulate by small local perturbations, which are assumed to be random and unbiased. We analyze the error accumulated in observables in this setting and show that, due to stochastic error cancellation, with high probability the error scales as the square root of the number of qubits instead of linearly. We explore the concentration phenomenon of this error as well as its implications for local observables in the thermodynamic limit. Moreover, we show that stochastic error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise. This indicates that, to reach a certain fidelity, more noise can be tolerated than implied by the worst-case bound if the noise comes from many statistically independent sources.

Analog quantum simulation↗
DOE OSTI2019

Application of the Clear-Sky Spectral Error for Radiometer Classification in ISO 9060: Preprint

A recent update of the ISO 9060 standard for the classification of solar radiometers introduces the use of the clear sky spectral error. The spectral error is the change in responsivity that may occur when the spectral distribution of the incident solar radiation differs from the spectral distribution present at the time of calibration. Spectral errors may occur if the radiometer does not have a completely uniform spectral responsivity. This use of the clear sky spectral error is a significant change compared to the previous version of the 9060 standard as now not only thermopile radiometers, but also photodiode radiometers are covered by the standard. We explain the method used to derive the spectral error and present spectral errors for several radiometers of different technologies. The results demonstrate that the new method is helpful to classify radiometers, distinguishing between different radiometer types and excluding inappropriate instruments from the classification as pyranometers and pyrheliometers. We recommend that the method is also used for WMO's radiometer classification which up to our knowledge is currently not fulfilled by any field pyrheliometer and many pyranometers on the market due to its demanding requirements for the spectral responsivity.

14 SOLAR ENERGY↗
DOE OSTI2013

A new indirect measure of diffusion model error

We define a new indirect measure of the diffusion model error called the diffusion model error source. When this model error source is added to the diffusion equation, the transport solution for the angular-integrated intensity is obtained. This source represents a means by which a transport code can be used to generate information relating to the adequacy of diffusion theory for any given problem without actually solving the diffusion equation. The generation of this source does not relate in any way to acceleration of the iterative convergence of transport solutions. Perhaps the most well-known indirect measure of the diffusion model error is the variable-Eddington tensor. This tensor provides a great deal of information about the angular dependence of the angular intensity solution, but it is not always simple to interpret. In contrast, our diffusion model error source is a scalar that is conceptually easy to understand. In addition to defining the diffusion model error source analytically, we show how to generate this source numerically relative to the S{sub n} radiative transfer equations with linear-discontinuous spatial discretization. This numerical source is computationally tested and shown to reproduce the Sn solution for a Marshak-wave problem. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Determination of a Generic Human Error Probability Distribution, Part 1: A Dynamic Formulation of SPAR-H

In almost all major nuclear power plants (NPP) events include a significant human error component. As an example, in Fukushima Daiichi (2011) nuclear meltdown, the human actions related to the high-pressure injection cooling strongly affected accident evolution. Furthermore, in the Three Mile Island accident (1979) (which was initiated by a stuck open valve and thus was triggered a loss of coolant accident) the unit operators made decisions based upon false assumptions that contributed negatively to the accident. Given these premises, the ability to accurately model human interactions with plant evolution and, in particular, dynamically calculate human error probability (HEP) plays a major role in a probabilistic risk analysis (PRA). Human reliability analysis (HRA) identifies and models the causes of human errors, and quantifies HEP by applying different methodologies. HRA methods identify errors and reflect on the understanding of error-prone people and systems. There are a number of HRA methods available that assist in identifying the vulnerabilities in the system and provide guidance in determining the HEP. HEP is the probability of a human failure event (HFE), and quantification of HEPs under various situations is utilized in PRA of large complex systems. One of the more prominent HRA methods is the Standardized Plant Analysis Risk-Human Reliability Analysis (SPAR-H) method that was developed to estimate HEPs for the use in the Standardized Plant Analysis Risk (SPAR) PRA models employed in U.S. NPPs. SPAR-H is implemented in U.S. NPPs by regulators at the U.S. Nuclear Regulatory Commission (NRC) to determine the HEP based on expert estimation through the use of calculation worksheets. In SPAR-H, the nominal HEPs (NHEPs) are multiplied by performance shaping factors (PSF) multiplier values to obtain the overall error probability. PSFs encompass the human components, individual characteristics, their environment, and aspects of the task. With PSFs, the goal is to capture all factors that can affect human performance. In SPAR-H there are eight PSFs used, each having respective levels corresponding to multipliers: Available Time, Stress/Stressors, Complexity, Experience/Training, Procedures, Ergonomics/Human Machine Interface, Fitness for Duty, and Work Processes. The PSF multipliers indicate enhanced, nominal, or degraded human performance. The SPAR-H method estimates the HEP through multiplying a NHEP with PSFs. Hence, SPAR-H is a traditional HRA method that assesses human performance at a fixed, or static, point in time. In a dynamic HRA framework, human performance is assessed on a continuous time basis. SPAR-H can be used within a dynamic PRA framework through the use of simulation and stochastic models. The goal of dynamic HRA is to build a more realistic model of the human-system interaction to enhance calculation of reliability, risk and safety analysis. The progression of events in dynamic SPAR-H considers that some PSFs may experience gradual change, while other change can be sudden due to individualistic differences or rapid plant status changes. The PSF changes are caused by contextual changes in the scenario. For example, as more time passes, the realization that a task should be completed sooner may cause the operator more stress. In another example, a sudden relay of information about sickness of a family member may alter the operator's general stress level and fitness for duty. Each PSF has a different dynamic nature; PSFs like stress and complexity change more quickly over the course of a task than experience and training. While the experience of an operator changes over the course of attaining the objective, the amount that this added experience changes the HEP is very minimal. In contrast, the stress, complexity, and procedures PSFs may change quite a bit over the course of task completion.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

The impact of response measurement error on the analysis of designed experiments

This study considers the analysis of designed experiments when there is measurement error in the true response or so-called response measurement error. We consider both additive and multiplicative response measurement errors. Through a simulation study, we investigate the impact of ignoring the response measurement error in the analysis, that is, by using a standard analysis based on t-tests. In addition, we examine the role of repeat measurements in improving the quality of estimation and prediction in the presence of response measurement error. We also study a Bayesian approach that accounts for the response measurement error directly through the specification of the model, and allows including additional information about variability in the analysis. We consider the impact on power, prediction, and optimization. Copyright © 2015 John Wiley & Sons, Ltd.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Interior energy error estimates for the weak Galerkin finite element method

Consider the Poisson equation in a polytopal domain ΩRC d (d=2,3) as the model problem. In this paper, we study interior energy error estimates for the weak Galerkin finite element approximation to elliptic boundary value problems. In particular, we show that the interior error in the energy norm is bounded by three components: the best local approximation error, the error in negative norms, and the trace error on the element boundaries. This implies that the interior convergence rate can be polluted by solution singularities on the domain boundary, even when the solution is smooth in the interior region. Numerical results are reported to support the theoretical findings. Lastly, to the best of our knowledge, this is the first local energy error analysis that applies to general meshes consisting of polytopal elements and hanging nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Characterizing the impact of model error in hydrologic time series recovery inverse problems

Hydrologic models are commonly over-smoothed relative to reality, owing to computational limitations and to the difficulty of obtaining accurate high-resolution information. When used in an inversion context, such models may introduce systematic biases which cannot be encapsulated by an unbiased “observation noise” term of the type assumed by standard regularization theory and typical Bayesian formulations. Despite its importance, model error is difficult to encapsulate systematically and is often neglected. In this paper, model error is considered for an important class of inverse problems that includes interpretation of hydraulic transients and contaminant source history inference: reconstruction of a time series that has been convolved against a transfer function (i.e., impulse response) that is only approximately known. Using established harmonic theory along with two results established here regarding triangular Toeplitz matrices, upper and lower error bounds are derived for the effect of systematic model error on time series recovery for both well-determined and over-determined inverse problems. It is seen that use of additional measurement locations does not improve expected performance in the face of model error. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. Finally, a possible diagnostic criterion for blind transfer function characterization is also uncovered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗