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Variance-based sensitivity analysis of dynamic systems with both input and model uncertainty
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The cluster decomposition of the configurational energy of multicomponent alloys
Abstract The cluster expansion method (CEM) is a widely used lattice-based technique in the study of multicomponent alloys. Despite its prevalent use, a clear understanding of expansion terms is lacking. We present a modern mathematical formalism of the CEM and introduce thecluster decomposition—a unique and basis-independent decomposition for functions of the atomic configuration in a crystal. We identify the cluster decomposition as an invariant ANOVA decomposition; and demonstrate how functional analysis of variance and sensitivity analysis can be used to interpret interactions among species. Furthermore, we show how the mathematical structure of the cluster decomposition enables numerical evaluation that scales with the number of clusters and is independent of the number of species. Overall, our work enables rigorous interpretations of interactions among species, provides opportunities to explore parameter estimation beyond linear regression, introduces a numerical efficient implementation, and enables analysis of cluster expansions based on established mathematical and statistical principles.
UAV-Based High Resolution Thermal Imaging for Vegetation Monitoring, and Plant Phenotyping Using ICI 8640 P, FLIR Vue Pro R 640, and thermoMap Cameras
The growing popularity of Unmanned Aerial Vehicles (UAVs) in recent years, along with decreased cost and greater accessibility of both UAVs and thermal imaging sensors, has led to the widespread use of this technology, especially for precision agriculture and plant phenotyping. There are several thermal camera systems in the market that are available at a low cost. However, their efficacy and accuracy in various applications has not been tested. In this study, three commercially available UAV thermal cameras, including ICI 8640 P-series (Infrared Cameras Inc., USA), FLIR Vue Pro R 640 (FLIR Systems, USA), and thermoMap (senseFly, Switzerland) have been tested and evaluated for their potential for forest monitoring, vegetation stress detection, and plant phenotyping. Mounted on multi-rotor or fixed wing systems, these cameras were simultaneously flown over different experimental sites located in St. Louis, Missouri (forest environment), Columbia, Missouri (plant stress detection and phenotyping), and Maricopa, Arizona (high throughput phenotyping). Thermal imagery was calibrated using procedures that utilize a blackbody, handheld thermal spot imager, ground thermal targets, emissivity and atmospheric correction. A suite of statistical analyses, including analysis of variance (ANOVA), correlation analysis between camera temperature and plant biophysical and biochemical traits, and heritability were utilized in order to examine the sensitivity and utility of the cameras against selected plant phenotypic traits and in the detection of plant water stress. In addition, in reference to quantitative assessment of image quality from different thermal cameras, a non-reference image quality evaluator, which primarily measures image focus that is based on the spatial relationship of pixels in different scales, was developed. Our results show that (1) UAV-based thermal imaging is a viable tool in precision agriculture and (2) the three examined cameras are comparable in terms of their efficacy for plant phenotyping. Overall, accuracy, when compared against field measured ground temperature and estimating power of plant biophysical and biochemical traits, the ICI 8640 P-series performed better than the other two cameras, followed by FLIR Vue Pro R 640 and thermoMap cameras. Our results demonstrated that all three UAV thermal cameras provide useful temperature data for precision agriculture and plant phenotying, with ICI 8640 P-series presenting the best results among the three systems. Cost wise, FLIR Vue Pro R 640 is more affordable than the other two cameras, providing a less expensive option for a wide range of applications.
Statistical analysis of Thematic Mapper Simulator data for the geobotanical discrimination of rock types in southwest Oregon
An evaluation of Thematic Mapper Simulator (TMS) data for the geobotanical discrimination of rock types based on vegetative cover characteristics is addressed in this research. A methodology for accomplishing this evaluation utilizing univariate and multivariate techniques is presented. TMS data acquired with a Daedalus DEI-1260 multispectral scanner were integrated with vegetation and geologic information for subsequent statistical analyses, which included a chi-square test, an analysis of variance, stepwise discriminant analysis, and Duncan's multiple range test. Results indicate that ultramafic rock types are spectrally separable from nonultramafics based on vegetative cover through the use of statistical analyses.
Characterization of vegetation by microwave and optical remote sensing
Two series of carefully controlled experiments were conducted. First, plots of important crops (corn, soybeans, and sorghum), prairie grasses (big bluestem, switchgrass, tal fescue, orchardgrass, bromegrass), and forage legumes (alfalfa, red clover, and crown vetch) were manipulated to produce wide ranges of phytomass, leaf area index, and canopy architecture. Second, coniferous forest canopies were simulated using small balsam fir trees grown in large pots of soil and arranged systematically on a large (5 m) platform. Rotating the platform produced many new canopies for frequency and spatial averaging of the backscatter signal. In both series of experiments, backscatter of 5.0 GHz (C-Band) was measured as a function of view angle and polarization. Biophysical measurements included leaf area index, fresh and dry phytomass, water content of canopy elements, canopy height, and soil roughness and moisture content. For a subset of the above plots, additional measurements were acquired to exercise microwave backscatter models. These measurements included size and shape of leaves, stems, and fruit and the probability density function of leaf and stem angles. The relationships of the backscattering coefficients and the biophysical properties of the canopies were evaluated using statistical correlations, analysis of variance, and regression analysis. Results from the corn density and balsam fir experiments are discussed and analyses of data from the other experiments are summarized.
Comments on the statistical analysis of excess variance in the COBE differential microwave radiometer maps
Cosmic anisotrophy produces an excess variance sq sigma(sub sky) in the Delta maps produced by the Differential Microwave Radiometer (DMR) on cosmic background explorer (COBE) that is over and above the instrument noise. After smoothing to an effective resolution of 10 deg, this excess sigma(sub sky)(10 deg), provides an estimate for the amplitude of the primordial density perturbation power spectrum with a cosmic uncertainty of only 12%. We employ detailed Monte Carlo techniques to express the amplitude derived from this statistic in terms of the universal root mean square (rms) quadrupole amplitude, (Q sq/RMS)(exp 0.5). The effects of monopole and dipole subtraction and the non-Gaussian shape of the DMR beam cause the derived (Q sq/RMS)(exp 0.5) to be 5%-10% larger than would be derived using simplified analytic approximations. We also investigate the properties of two other map statistics: the actual quadrupole and the Boughn-Cottingham statistic. Both the sigma(sub sky)(10 deg) statistic and the Boughn-Cottingham statistic are consistent with the (Q sq/RMS)(exp 0.5) = 17 +/- 5 micro K reported by Smoot et al. (1992) and Wright et al. (1992).
Effect of altered sensory conditions on multivariate descriptors of human postural sway
Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.
Parameters Impacting Columnated Granular Soil Pneumatic Seal Performance
The ability of a column of loose granular soil to form a pneumatic seal was investigated by varying the diameter of the soil column, the effective column height, and the level of compaction in the soil. The soil column diameter was tested at three levels using pipes with inner diameters measuring 5.08, 10.16, and 15.24 centimeters (2, 4, and 6 inches). Soil was filled in each pipe to form 15, 30, and 45 centimeter (6, 12, and 18 inch) tall soil columns. Each diameter/height configuration was also tested at three levels of soil compaction, compared by calculating the bulk density of the soil with mass and volume measurements. GRC-1a simulant was used, with approximate low/medium/high bulk densities of 1.6, 1.75, and 1.9 g/cc achieved with a combination of vibration and tamping. The order of tests for a given column diameter was randomized and repeated three times. With the top of the soil open to atmosphere at room temperature, compressed air was injected through a small diffuser at the column base with several small downward-facing holes. The number and size of these holes was scaled such that a constant total inlet orifice area to column cross sectional area ratio was maintained for each column diameter. Inlet air pressure was slowly increased via a precision regulator to preserve quasi-static equilibrium in the soil column to minimize the impact of dynamics. Air pressure was increased all the way through the static and bubbling regimes until slugging or turbulent behavior was observed in the soil to ensure that the entire static regime had been captured during data collection. A three-factor, three-level analysis of variance (ANOVA) statistical analysis was performed on the resulting data to determine the extent to which each physical parameter impacted the soil column seal performance. It was concluded that there is statistically significant evidence that column height, and the interaction between column height and diameter impact soil seal performance. In all other cases there was insufficient data to identify a statistically significant causal relationship. Additionally, plots were generated comparing experimental data to the predictive formula developed by Ogino et al. for fluidized beds in 1993. Because this model was developed for industrial spouted fluidized beds, the accuracy of its output prior to fluidization in the static seal ‘edge case’ is unknown, especially considering in this application the working gas was diffused across the column base rather than being injected through a spout. Further, the fidelity of the model had not yet been tested with lunar soil simulants. Plotting the Ogino et al. model alongside test data allows for a more intuitive sense of the impact of test parameters on soil seal performance, as well as providing a quick means to further tune this predictive model for more accurate use with static seals across granular lunar soil simulants. The model provided by Ogino et al. was further tuned using test data to determine the degree to which a spouted bed model could be applied to a slightly modified set of testing conditions: lunar soil simulants and a more diffuse, homogeneous application of pneumatic pressure. A Matlab script was created to test different values for the leading coefficient and exponents in Ogino’s formula. The script swept preset ranges, then iterated with higher resolutions across narrower ranges to converge on the optimal value for each parameter. The resulting adjusted model was compared to the original, as well as test data with noticeable improvements across the entire test domain.
Variance-Based Sensitivity Analysis to Support Simulation-Based Design Under Uncertainty
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Minimum variance technique for the analysis of ionospheric data acquired in satellite retarding potential analyzer experiments.
Minimum variance technique for analysis of ionospheric data acquired by satellite retarding potential analyzer
Use of Sobol’ Variance-Based Global Sensitivity Analysis and Multidimensional Legendre Polynomial Fitting for Reduced Order Modeling
Sandia National Laboratories (SNL) has developed a novel reduced order modeling approach. Prioritization of inputs is accomplished using Sobo' indices obtained through a more efficient variance-based global sensitivity analysis. To determine the Sobo' functions, simulated input values are aligned to collocation points to permit the use of Gauss-Lobatto integration, thereby reducing the number of simulation trials needed by more than an order of magnitude compared to standard Monte Carlo approaches. Furthermore, by leveraging the orthogonality of Legendre polynomials in conjunction with those same simulations at the collocation nodes, an efficient fitting method is developed to represent the Sobo' functions from which a reduced order model (ROM) is constructed. The developed method is both more efficient computationally, and the resulting ROM is more accurate. The efficacy of this technique is demonstrated on a nonlinear polynomial test function as well as the nonlinear Ishigami and Sobo' g functions.
A Computational Approach for Model Update of an LS-DYNA Energy Absorbing Cell
NASA and its contractors are working on structural concepts for absorbing impact energy of aerospace vehicles. Recently, concepts in the form of multi-cell honeycomb-like structures designed to crush under load have been investigated for both space and aeronautics applications. Efforts to understand these concepts are progressing from tests of individual cells to tests of systems with hundreds of cells. Because of fabrication irregularities, geometry irregularities, and material properties uncertainties, the problem of reconciling analytical models, in particular LS-DYNA models, with experimental data is a challenge. A first look at the correlation results between single cell load/deflection data with LS-DYNA predictions showed problems which prompted additional work in this area. This paper describes a computational approach that uses analysis of variance, deterministic sampling techniques, response surface modeling, and genetic optimization to reconcile test with analysis results. Analysis of variance provides a screening technique for selection of critical parameters used when reconciling test with analysis. In this study, complete ignorance of the parameter distribution is assumed and, therefore, the value of any parameter within the range that is computed using the optimization procedure is considered to be equally likely. Mean values from tests are matched against LS-DYNA solutions by minimizing the square error using a genetic optimization. The paper presents the computational methodology along with results obtained using this approach.
Low-dimensional Representation of Error Covariance
Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.
Assessment of Interfraction Patient Setup for Head-and-Neck Cancer Intensity Modulated Radiation Therapy Using Multiple Computed Tomography-Based Image Guidance
Purpose: Various image guidance systems are commonly used in conjunction with intensity modulated radiation therapy (IMRT) in head-and-neck cancer irradiation. The purpose of this study was to assess interfraction patient setup variations for 3 computed tomography (CT)-based on-board image guided radiation therapy (IGRT) modalities. Methods and Materials: A total of 3302 CT scans for 117 patients, including 53 patients receiving megavoltage cone-beam CT (MVCBCT), 29 receiving kilovoltage cone-beam CT (KVCBCT), and 35 receiving megavoltage fan-beam CT (MVFBCT), were retrospectively analyzed. The daily variations in the mediolateral (ML), craniocaudal (CC), and anteroposterior (AP) dimensions were measured. The clinical target volume-to-planned target volume (CTV-to-PTV) margins were calculated using 2.5Σ + 0.7 σ, where Σ and σ were systematic and random positioning errors, respectively. Various patient characteristics for the MVCBCT group, including weight, weight loss, tumor location, and initial body mass index, were analyzed to determine their possible correlation with daily patient setup. Results: The average interfraction displacements (± standard deviation) in the ML, CC, and AP directions were 0.5 ± 1.5, −0.3 ± 2.0, and 0.3 ± 1.7 mm (KVCBCT); 0.2 ± 1.9, −0.2 ± 2.4, and 0.0 ± 1.7 mm (MVFBCT); and 0.0 ± 1.8, 0.5 ± 1.7, and 0.8 ± 3.0 mm (MVCBCT). The day-to-day random errors for KVCBCT, MVFBCT, and MVCBCT were 1.4-1.6, 1.7, and 2.0-2.1 mm. The interobserver variations were 0.8, 1.1, and 0.7 mm (MVCBCT); 0.5, 0.4, and 0.8 mm (MVFBCT); and 0.5, 0.4, and 0.6 mm (KVCBCT) in the ML, CC, and AP directions, respectively. The maximal calculated uniform CTV-to-PTV margins were 5.6, 6.9, and 8.9 mm for KVCBCT, MVFBCT, and MVCBCT, respectively. For the evaluated patient characteristics, the calculated margins for different patient parameters appeared to differ; analysis of variance (ANOVA) and/or t test analysis found no statistically significant setup difference in any direction. Conclusions: Daily random setup errors and CTV-to-PTV margins for treatment of head-and-neck cancer were affected by imaging quality. Our data indicated that larger margins were associated with MVFBCT and MVCBCT, compared with smaller margins for KVCBCT. IGRT modalities with better image quality are encouraged in clinical practice.
Experimental Analysis of the Effects of Simulator Complexity on Human Performance
Human Reliability Analysis predicts accidents caused by human errors and is an important factor in Probabilistic Safety Assessment that comprehensively evaluates the safety of nuclear power plants. This study compares and analyzes the human performance of nuclear power plant operators according to the simulator complexity as part of the HRA data collection support method development project conducted by Idaho National Laboratory. This experiment was conducted by setting two types of simulators and scenarios as independent variables. The data collected by conducting the experiments in two different simulators were analyzed using an analysis of variance test and a correlation analysis, and four human performance charts were derived.
Human Performance Analysis Depending on Operator Expertise (Student vs. Operator) and Simulator Complexity (Rancor Microworld vs. Compact Nuclear Simulator)
Human reliability analysis (HRA) evaluates human errors and provides human error probabilities (HEPs) for application in probabilistic safety assessment (PSA), which is a comprehensive safety assessment method for nuclear power plants (NPPs). Generally, HRA methods estimate HEPs based on human reliability data collected from actual historical measurement, simulator experiments, or expert judgement. Most recent HRA data collection studies focus on collecting data via full-scope main control room (MCR) simulators with actual licensed reactor operators. Contrary to this, Idaho National Laboratory (INL) has adopted a different approach, which attempts to collect HRA data based on experiment using simplified simulators and student participants by following the Simplified Human Error Experimental Program (SHEEP). This approach has a couple of advantages compared to full-scope data collection. Representatively, it has relatively low entry point for collecting HRA data, and secures large sample sizes with reasonable cost and labor. In the previous studies, we developed the SHEEP framework, then verified whether the data collected through the framework could support a representative full-scope data collection study, i.e., the Human Reliability Data Extraction (HuREX) study. Also, we analyzed human performance measurements depending on participant type (i.e., student vs. operator). In this paper, we analyze human performance data collected from an experiment comparing operator expertise and simulator complexity when using the more simplified simulator developed by INL, i.e., Rancor Microworld and the less simplified simulator, i.e., Compact Nuclear Simulator (CNS) developed by Korea Atomic Energy Research Institute (KAERI). Analysis of variance (ANOVA) tests and correlation analysis are used for analyzing the experimental data.
WE-E-18A-10: Comparison of Patient Dose and Vessel Visibility Between Antiscatter Grid Removal and Lower Angiographic Radiation Dose Settings for Pediatric Imaging: A Preclinical Investigation
Purpose: To define an alternative to antiscatter grid (ASG) removal in angiographic systems which achieves similar patient dose reduction as ASG removal without degrading image quality during pediatric imaging. Methods: This study was approved by the local institution animal care and use committee (IACUC). Six different digital subtraction angiography settings were evaluated that altered the mAs, (100, 70, 50, 35, 25, 17.5% of reference mAs) with and without ASG. Three pigs of 5, 15, and 20 kg (9, 15, and 17 cm abdominal thickness; smaller than a newborn, average 3 yr old, and average 10 year old human abdomen respectively) were imaged using the six dose settings with and without ASG. Image quality was defined as the order of vessel branch that is visible relative to the injected vessel. Five interventional radiologists evaluated all images. Image quality and patient dose were statistically compared using analysis of variance and receiver operating curve (ROC) analysis to define the preferred dose level and use of ASG for a minimum visibility of 2nd or 3rd order branches of vessel visibility. Results: ASG grid removal reduces dose by 26% with reduced image quality. Only with the ASG present can 3rd order branches be visualized; 100% mAs is required for 9 cm pig while 70% mAs is adequate for the larger pigs. 2nd order branches can be visualized with ASG at 17.5% mAs for all three pig sizes. Without the ASG, 50%, 35% and 35% mAs is required for smallest to largest pig. Conclusion: Removing ASG reduces patient dose and image quality. Image quality can be improved with the ASG present while further reducing patient dose if an optimized radiographic technique is used. Rami Nachabe is an employee of Philips Health Care; Keith Strauss is a paid consultant of Philips Health Care.