Mean Estimation and Nominal Device Selection with the Pairwise Midpoint Method
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Adams, Jason Ross↗
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Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method
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BANERJEE, KAUSHIK .↗
Groundwater recharge estimation in arid hardrock-alluvium aquifers using combined water-table fluctuation and groundwater balance approaches
This article proposes an approach to estimate groundwater recharge using an optimization-based water-table fluctuation method combined with a groundwater balance model in an arid hardrock-alluvium region, located at the Oman–United Arab Emirates border. Here, we introduce an “effective hardrock thickness” term to identify the percentage of the considered hardrock thickness in which effective groundwater flow takes place. The proposed method is based upon a Thiessen polygon zoning approach. The method includes subpolygons to represent specific geologic units and to enhance the confidence of the estimated groundwater recharge. Two linear and 1 nonlinear submodels were developed to evaluate the model components for the calibration (October 1996 to September 2008) and validation (October 2008 to September 2013) periods. Long-term annual groundwater recharge from rainfall and return flow over the model domain are estimated as 24.62 and 5.71 Mm 3 , respectively, while the effective groundwater flow circulation is found to occur in the upper 7% of the known hardrock thickness (42 m), confirming conclusions of previous field studies. Considering a total difference in groundwater levels between eastern and western points of the study area of the order of 220 m and a 12-year monthly calibration period, a weighted root mean squared error in predicted groundwater elevation of 2.75 m is considered quite reasonable for the study area characterized by remarkable geological and hydrogeological diversity. The proposed approach provides an efficient and robust method to estimate groundwater recharge in regions with a complex geological setting in which interaction between fractured and porous media cannot be easily assessed.
58 GEOSCIENCES↗
Robust Period Estimation Using Mutual Information for Multiband Light Curves in the Synoptic Survey Era
The Large Synoptic Survey Telescope (LSST) will produce an unprecedented amount of light curves using six optical bands. Robust and efficient methods that can aggregate data from multidimensional sparsely sampled time-series are needed. Here, we present a new method for light curve period estimation based on quadratic mutual information (QMI). The presented method does not assume a particular model for the light curve nor its underlying probability density and it is robust to non-Gaussian noise and outliers. By combining the QMI from several bands the true period can be estimated even when no single-band QMI yields the period. Period recovery performance as a function of average magnitude and sample size is measured using 30,000 synthetic multiband light curves of RR Lyrae and Cepheid variables generated by the LSST Operations and Catalog simulators. The results show that aggregating information from several bands is highly beneficial in LSST sparsely sampled time-series, obtaining an absolute increase in period recovery rate up to 50%. We also show that the QMI is more robust to noise and light curve length (sample size) than the multiband generalizations of the Lomb–Scargle and AoV periodograms, recovering the true period in 10%–30% more cases than its competitors. A python package with efficient Cython implementations of the QMI and other methods is provided.
79 ASTRONOMY AND ASTROPHYSICS↗
Infrared imaging diagnostics for intense pulsed electron beam
Infrared imaging diagnostic method for two-dimensional calorimetric diagnostics has been developed for intense pulsed electron beam (IPEB). By using a 100-μm-thick tungsten film as the infrared heat sink for IPEB, the emitting uniformity of the electron source can be analyzed to evaluate the efficiency and stability of the diode system. Two-dimensional axisymmetric finite element method heat transfer simulation, combined with Monte Carlo calculation, was performed for error estimation and optimization of the method. The test of the method was finished with IPEB generated by explosive emission electron diode with pulse duration (FWHM) of 80 ns, electron energy up to 450 keV, and a total beam current of over 1 kA. The results showed that it is possible to measure the cross-sectional energy density distribution of IPEB with energy sensitivity of 0.1 J/cm{sup 2} and spatial resolution of 1 mm. The technical details, such as irradiation protection of bremsstrahlung γ photons and the functional extensibility of the method were discussed in this work.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Marker-free registration of forest terrestrial laser scanner data pairs with embedded confidence metrics
Terrestrial laser scanning (TLS) has emerged as an effective tool for rapid comprehensive measurement of object structure. Registration of TLS data is an important prerequisite to overcome the limitations of occlusion. However, due to the high dissimilarity of point cloud data collected from disparate viewpoints in the forest environment, adequate marker-free registration approaches have not been developed. The majority of studies instead rely on the utilization of artificial tie points (e.g., reflective tooling balls) placed within a scene to aid in coordinate transformation. We present a technique for generating view-invariant feature descriptors that are intrinsic to the point cloud data and, thus, enable blind marker-free registration in forest environments. To overcome the limitation of initial pose estimation, we employ a voting method to blindly determine the optimal pairwise transformation parameters, without an a priori estimate of the initial sensor pose. To provide embedded error metrics, we developed a set theory framework in which a circular transformation is traversed between disjoint tie point subsets. This provides an upper estimate of the Root Mean Square Error (RMSE) confidence associated with each pairwise transformation. Output RMSE errors are commensurate with the RMSE of input tie points locations. Thus, while the mean output RMSE=16.3cm, improved results could be achieved with a more precise laser scanning system. This study 1) quantifies the RMSE of the proposed marker-free registration approach, 2) assesses the validity of embedded confidence metrics using receiver operator characteristic (ROC) curves, and 3) informs optimal sample spacing considerations for TLS data collection in New England forests. Furthermore, while the implications for rapid, accurate, and precise forest inventory are obvious, the conceptual framework outlined here could potentially be extended to built environments.
47 OTHER INSTRUMENTATION↗
Robust Matrix Completion State Estimation in Distribution Systems
Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage by exploring the low-rank characteristics of the matrix. This paper proposes a robust matrix completion state estimation (RMCSE) to estimate the voltage in a distribution system under a low-observability condition. Tradition state estimation weighted least squares (WLS) method requires full observability to calculate the states and needs redundant measurements to proceed a bad data detection. The proposed method improves the robustness of the MCSE to bad data by minimizing the rank of the matrix and measurements residual with different weights. It can estimate the system state in a low-observability system and has robust estimates without the bad data detection process in the face of multiple bad data. The method is numerically evaluated on the IEEE 33-node radial distribution system. The estimation performance and robustness of RMCSE are compared with the WLS with the largest normalized residual bad data identification (WLS-LNR), and the MCSE.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Robust Matrix Completion State Estimation in Distribution Systems: Preprint
Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage by exploring the low-rank characteristics of the matrix. This paper proposes a robust matrix completion state estimation (RMCSE) to estimate the voltage in a distribution system under a low-observability condition. Tradition state estimation weighted least squares (WLS) method requires full observability to calculate the states and needs redundant measurements to proceed a bad data detection. The proposed method improves the robustness of the MCSE to bad data by minimizing the rank of the matrix and measurements residual with different weights. It can estimate the system state in a low-observability system and has robust estimates without the bad data detection process in the face of multiple bad data. The method is numerically evaluated on the IEEE 33-node radial distribution system. The estimation performance and robustness of RMCSE are compared with the WLS with the largest normalized residual bad data identification (WLS-LNR), and the MCSE.
24 POWER TRANSMISSION AND DISTRIBUTION↗
SU-G-IeP2-15: Virtual Insertion of Digital Kidney Stones Into Dual-Source, Dual- Energy CT Projection Data
Purpose: In order to investigate novel methods to more accurately estimate the mineral composition of kidney stones using dual energy CT, it is desirable to be able to combine digital stones of known composition with actual phantom and patient scan data. In this work, we developed and validated a method to insert digital kidney stones into projection data acquired on a dual-source, dual-energy CT system. Methods: Attenuation properties of stones of different mineral composition were computed using tabulated mass attenuation coefficients, the chemical formula for each stone type, and the effective beam energy at each evaluated tube potential. A previously developed method to insert lesions into x-ray CT projection data was extended to include simultaneous dual-energy CT projections acquired on a dual-source gantry (Siemens Somatom Flash). Digital stones were forward projected onto both detectors and the resulting projections added to the physically acquired sinogram data. To validate the accuracy of the technique, digital stones were inserted into different locations in the ACR CT accreditation phantom; low and high contrast resolution, CT number accuracy and noise properties were compared before and after stone insertion. The procedure was repeated for two dual-energy tube potential pairs in clinical use on the scanner, 80/Sn140 kV and 100/Sn140 kV, respectively. Results: The images reconstructed after the insertion of digital kidney stones were consistent with the images reconstructed from the scanner. The largest average CT number difference for the 4 insert in the CT number accuracy module of the phantom was 3 HU. Conclusion: A framework was developed and validated for the creation of digital kidney stones of known mineral composition, and their projection-domain insertion into commercial dual-source, dual-energy CT projection data. This will allow a systematic investigation of the impact of scan and reconstruction parameters on stone attenuation and dual-energy behavior under rigorously controlled conditions. Dr. McCollough receives research support from Siemens Healthcare.
60 APPLIED LIFE SCIENCES↗
Large-Scale Inference of Multivariate Regression for Heavy-Tailed and Asymmetric Data
Large-scale multivariate regression is a fundamental statistical tool with a wide range of applications. Here, this study considers the problem of simultaneously testing a large number of general linear hypotheses, encompassing covariate-effect analysis, analysis of variance, and model comparisons. The challenge that accompanies a large number of tests is the ubiquitous presence of heavy-tailed and/or highly skewed measurement noise, which is the main reason for the failure of conventional least squares-based methods. For large-scale multivariate regression, we develop a set of robust inference methods to explore data features such as heavy tailedness and skewness, which are not visible to least squares methods. The new testing procedure is based on the data-adaptive Huber regression and a new covariance estimator of regression estimates. Under mild conditions, we show that our methods produce consistent estimates of the false discovery proportion. Extensive numerical experiments and an empirical study on quantitative linguistics demonstrate the advantage of the proposed method over many state-of-the-art methods when the data are generated from heavy-tailed and/or skewed distributions.
97 MATHEMATICS AND COMPUTING↗
Neptunium transition probabilities estimated through laser induced breakdown spectroscopy (LIBS) measurements
in tis report calibration free–laser induced breakdown spectroscopy (CF-LIBS) approaches are promising for the analysis of radioactive materials; however, a lack of reported fundamental properties for these materials is an obstacle to implementation. Spectra of laser induced plasmas containing Np and Sr, along with Saha–Boltzmann methods, were used to estimate the first reported transition probabilities (TPs) of Np. These TPs enabled the first attempt at CF-LIBS analysis of radioactive samples to predict Np/Sr ratios with a mean error of 3.86%. The presented methodology of TP estimation will be applied to the study of other actinides and allow broader applications of CF-15 LIBS in the nuclear field.
74 ATOMIC AND MOLECULAR PHYSICS↗
CAMERA: A method for cost-aware, adaptive, multifidelity, efficient reliability analysis
Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distributions, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. Here, we propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest at the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set and probability estimation on synthetic test functions and two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier-Stokes equations. We show that our method predicts the failure boundary and probability more accurately and at a fraction of the computational cost compared with using just a single expensive high-fidelity model. Finally, we show that our sequential approach is guaranteed to asymptotically converge to the true failure boundary with high probability.
97 MATHEMATICS AND COMPUTING↗
Five Year Comparison of Mixing Height Determinations at the Savannah River Site
Air quality dispersion modeling is performed for the Savannah River Site (SRS) to demonstrate compliance with applicable regulations. The AMS/EPA Regulatory Model (AERMOD) modeling system is an EPA recommended model for air quality applications with a data preprocessor (AERMET) to incorporate meteorological data collected on site. AERMET parameterizes or calculates meteorological variables that are not directly measured onsite. One of the parameters estimated by AERMET is the atmospheric mixing height. While the mixing height is not currently a measurement input into AERMET, SRS has the capability to measure the local mixing height. The Savannah River National Laboratory (SRNL) operates a Vaisala CL31 Lidar Ceilometer which estimates mixing height from aerosol backscatter. This study compares the parameterized mixing height from AERMET to the ceilometer estimated mixing height for the current regulatory period at SRS incorporating data from 2015-2019. Results from this study showed the average daily minimum values (morning) from AERMET were an order of magnitude lower than the commonly used Holzworth (1972) method and the ceilometer estimated mixing heights. Additionally, on average, the ceilometer exhibited a daily maximum mixing height value that occurred 1-3 hours later than the AERMET estimated maximum. This difference is likely due to the nighttime atmospheric mixing height assumptions and calculations used by AERMET. The AERMET algorithm cuts off mixing height growth at sunset while the ceilometer data show ongoing evening convection typical of the southeastern United States. These results suggest that the AERMET parametrization scheme assumptions may not be representative of a forested landscape and evening convection which could account for more mixing overnight. The results obtained in this study are significant for air dispersion modeling applications for regulatory purposes and worker safety. Mixing height can impact model estimated pollutant concentrations. A greater mixing height will provide more volume for pollutant dispersion. This report documents efforts to quantify the dependence of mixing height inputs toward a conservative estimated pollutant concentration.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
CheKiPEUQ Intro 1: Bayesian Parameter Estimation Considering Uncertainty or Error from both Experiments and Theory**
A common goal is extraction of physico-chemical parameter values such as pre-exponentials and activation energies from experiment. Ever increasing knowledge from experiments and computations is enabling semi-quantitative prior predictions of such values. When prior knowledge of physically realistic ranges is available, a method named Bayesian parameter estimation (BPE) enables more physically realistic parameter estimation relative to unsophisticated fitting by seeking the most probable value when considering together the uncertainties from prior knowledge, experimental data, and approximations in the model. An impediment to widespread use of BPE is a lack of understanding, training, and user-friendly software. Along with this invited publication, a general software package for BPE is being released that is user-friendly and that does not require understanding of the math behind the methodology. Overall, two previously unpublished catalysis science examples are provided along with considerations and guidelines for successful application of BPE. Following this work, BPE can become more widespread to enable extraction of physically meaningful parameter values.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
On the time growth of the error of the DG method for advective problems
Abstract In this paper we derive a priori $L^{\infty }(L^{2})$ and L2(L2) error estimates for a linear advection–reaction equation with inlet and outlet boundary conditions. The goal is to derive error estimates for the discontinuous Galerkin method that do not blow up exponentially with respect to time, unlike the usual case when Gronwall’s inequality is used. While this is possible in special cases, such as divergence-free advection fields, we take a more general approach using exponential scaling of the exact and discrete solutions. Here we use a special scaling function, which corresponds to time taken along individual pathlines of the flow. For advection fields, where the time that massless particles carried by the flow spend inside the spatial domain is uniformly bounded from above by some $\widehat{T}$, we derive $\mathcal{O}$(hp+1/2) error estimates where the constant factor depends only on $\widehat{T}$, but not on the final time T. This can be interpreted as applying Gronwall’s inequality in the error analysis along individual pathlines (Lagrangian setting), instead of physical time (Eulerian setting).
Mathematics↗
Constrained partitioning of autotrophic and heterotrophic respiration reduces model uncertainties of forest ecosystem carbon fluxes but not stocks
Abstract We partitioned the soil carbon dioxide flux ( R s ) into its respective autotrophic and heterotrophic components in a mature temperate‐boreal forest (Howland Forest in Maine, USA). We combined automated chamber measurements of R s with two different partitioning methods: (1) a classic root trenching experiment and (2) a radiocarbon ( 14 C) mass balance approach. With a model‐data fusion approach, we used these data to constrain a parsimonious ecosystem model (FöBAAR), and we investigated differences in modeled C fluxes and pools under both current and future climate scenarios. The trenching experiment indicated that heterotrophic respiration accounted for 53 ± 11% of total R s . In comparison, using the 14 C method, the heterotrophic contribution was 42 ± 9%. For both current and future model runs, incorporating the partitioning data as constraints substantially reduced the uncertainties of autotrophic and heterotrophic respiration fluxes. Moreover, with best fit model parameters, the two partitioning methods yielded fundamentally different estimates of the relative contributions of autotrophic and heterotrophic respiration to total R s , especially at the annual time scale. Surprisingly, however, modeled soil C and biomass C pool size trajectories did not differ significantly between model runs based on the different methods. Instead, model differences in partitioning were compensated for by changes in C allocation, resulting in similar, but still highly uncertain, soil C pool trajectories. Our findings show that incorporating constraints on the partitioning of R s can reduce model uncertainties of fluxes but not pools, and the results are sensitive to the partitioning method used.
Carbone, Mariah S.↗
Hypothesis tests for the detection of constant speed radiation moving sources
Radiation Portal Monitors are deployed in linear network to detect radiological material in motion. As a complement to single and multichannel detection algorithms, inefficient under too low signal to noise ratios, temporal correlation algorithms have been introduced. Test hypothesis methods based on empirically estimated mean and variance of the signals delivered by the different channels have shown significant gain in terms of a tradeoff between detection sensitivity and false alarm probability. This paper discloses the concept of a new hypothesis test for temporal correlation detection methods, taking advantage of the Poisson nature of the registered counting signals, and establishes a benchmark between this test and its empirical counterpart. The simulation study validates that in the four relevant configurations of a pedestrian source carrier under respectively high and low count rate radioactive background, and a vehicle source carrier under the same respectively high and low count rate radioactive background, the newly introduced hypothesis test ensures a significantly improved compromise between sensitivity and false alarm, while guaranteeing the stability of its optimization parameter regardless of signal to noise ratio variations between 2 to 0.8. (authors)
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Statistical change detection of building energy consumption: Applications to savings estimation
The surge in interval meter data availability and associated activity in energy data analytics has inspired new interest in advanced methods for building efficiency savings estimation. Statistical and machine learning approaches are being explored to improve the energy baseline models used to measure and verify savings. One outstanding challenge is the ability to identify and account for operational changes that may confound savings estimates. In the measurement and verification (M&V) context, ‘non-routine events’ (NREs) cause changes in building energy use that are not attributable to installed efficiency measures, and not accounted for in the baseline model’s independent variables. In the M&V process NREs must be accounted for as ‘adjustments’ to appropriately attribute the estimated energy savings to the specific efficiency interventions that were implemented. Currently this is a manual and custom process, conducted using professional judgment and engineering expertise. As such it remains a barrier in scaling and standardizing meter-based savings estimation. Here in this work, a data driven methodology was developed to (partially) automate, and therefore streamline the process of detecting NREs in the post-retrofit period and making associated savings adjustments. The proposed NRE detection algorithm is based on a statistical change point detection method and a dissimilarity metric. The dissimilarity metric measures the proximity between the actual time series of the post-retrofit energy consumption and the projected baseline, which is generated using a statistical baseline model. The suggested approach for NRE adjustment involves the NRE detection algorithm, the M&V practitioner, and a regression modeling algorithm. The performance of the detection and adjustment algorithm was evaluated using a simulation-generated test data set, and two benchmark algorithms. Results show a high true positive detection rate (75%-100% across the test cases), higher than ideal false positive detection rates (20%-70%), and low errors in energy adjustment (<0.7%). These results indicate that the algorithm holds for helping M&V practitioners to streamline the process of handling NREs. Moreover, the change point algorithm and underlying statistical principles could prove valuable for other building analytics applications such as anomaly detection and fault diagnostics.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗