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Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients
This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-ρAMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the coarse basis used to define the new two-level method of our interest. We illustrate the performance of this adaptive two-level procedure with a large set of numerical experiments that demonstrate its efficiency over building the solvers from scratch.
SU-F-J-66: Anatomy Deformation Based Comparison Between One-Step and Two-Step Optimization for Online ART
Purpose: This study investigated that how the quality of adapted plan was affected by inter-fractional anatomy deformation by using one-step and two-step optimization for on line adaptive radiotherapy (ART) procedure. Methods: 10 lung carcinoma patients were chosen randomly to produce IMRT plan by one-step and two-step algorithms respectively, and the prescribed dose was set as 60 Gy on the planning target volume (PTV) for all patients. To simulate inter-fractional target deformation, four specific cases were created by systematic anatomy variation; including target superior shift 0.5 cm, 0.3cm contraction, 0.3 cm expansion and 45-degree rotation. Based on these four anatomy deformation, adapted plan, regenerated plan and non-adapted plan were created to evaluate quality of adaptation. Adapted plans were generated automatically by using one-step and two-step algorithms respectively to optimize original plans, and regenerated plans were manually created by experience physicists. Non-adapted plans were produced by recalculating the dose distribution based on corresponding original plans. The deviations among these three plans were statistically analyzed by paired T-test. Results: In PTV superior shift case, adapted plans had significantly better PTV coverage by using two-step algorithm compared with one-step one, and meanwhile there was a significant difference of V95 by comparison with adapted and non-adapted plans (p=0.0025). In target contraction deformation, with almost same PTV coverage, the total lung received lower dose using one-step algorithm than two-step algorithm (p=0.0143,0.0126 for V20, Dmean respectively). In other two deformation cases, there were no significant differences observed by both two optimized algorithms. Conclusion: In geometry deformation such as target contraction, with comparable PTV coverage, one-step algorithm gave better OAR sparing than two-step algorithm. Reversely, the adaptation by using two-step algorithm had higher efficiency and accuracy as target occurred position displacement. We want to thank Dr. Lei Xing and Dr. Yong Yang in the Stanford University School of Medicine for this work. This work was jointly supported by NSFC (61471226), Natural Science Foundation for Distinguished Young Scholars of Shandong Province (JQ201516), and China Postdoctoral Science Foundation (2015T80739, 2014M551949).
G-Mapper: Learning a Cover in the Mapper Construction
The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a “nice” Mapper graph. This paper focuses on selecting the cover parameter. We present an algorithm that optimizes the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on G-means clustering, which searches for the optimal number of clusters in 𝑘-means by iteratively applying the Anderson–Darling test. Our splitting procedure employs a Gaussian mixture model to carefully choose the cover according to the distribution of the given data. In conclusion, experiments for synthetic and real-world datasets demonstrate that our algorithm generates covers so that the Mapper graphs retain the essence of the datasets, while also running significantly faster than a previous iterative method.
Bayesian inference of nuclear-matter density from proton scattering
Background: Proton elastic scattering at intermediate energy is widely employed as a tool for determining the matter radius of atomic nuclei. Here, the sensitivity of the approach relies on high-resolution measurements at small scattering angles and low-momentum transfer. Under these conditions, the Glauber multiple scattering theory accurately describes the proton-nucleus elastic cross section. Purpose: Investigate the sensitivity of the Glauber multiple scattering theory to uncertainties associated with input parameters such as the nuclear-matter density distribution and nucleon-nucleon data. Method: A joint Bayesian inference was performed using 12 angular distributions of elastic scattering at different energies on 58 Ni, 90 Zr, and 208 Pb targets. A Metropolis-Hastings algorithm was implemented to make an uncertainty quantification analysis for the input parameters used in the Glauber multiple scattering theory. Results: The experimental cross sections were fitted simultaneously using a joint Bayesian inference approach. Posterior probability density distributions of 42 input parameters were obtained from the analysis. A moderate correlation between the nuclear density parameters and the nucleon-nucleon cross sections was found. This correlation impacts the extraction of the nuclear-matter radius. Conclusions: The present analysis provided a consistent method for extracting the nuclear-matter density distribution of 58 Ni, 90 Zr, and 208 Pb from data across different incident energies. Due to the correlation of the nucleon-nucleon cross sections with the other input parameters, a constrained Bayesian inference using free nucleon-nucleon cross section data was performed. The nuclear-matter radii obtained from the analysis are in good agreement with multiple results reported in the literature.
Quantum noise properties of CT images with anatomical textured backgrounds across reconstruction algorithms: FBP and SAFIRE
Purpose: Quantum noise properties of CT images are generally assessed using simple geometric phantoms with uniform backgrounds. Such phantoms may be inadequate when assessing nonlinear reconstruction or postprocessing algorithms. The purpose of this study was to design anatomically informed textured phantoms and use the phantoms to assess quantum noise properties across two clinically available reconstruction algorithms, filtered back projection (FBP) and sinogram affirmed iterative reconstruction (SAFIRE). Methods: Two phantoms were designed to represent lung and soft-tissue textures. The lung phantom included intricate vessel-like structures along with embedded nodules (spherical, lobulated, and spiculated). The soft tissue phantom was designed based on a three-dimensional clustered lumpy background with included low-contrast lesions (spherical and anthropomorphic). The phantoms were built using rapid prototyping (3D printing) technology and, along with a uniform phantom of similar size, were imaged on a Siemens SOMATOM Definition Flash CT scanner and reconstructed with FBP and SAFIRE. Fifty repeated acquisitions were acquired for each background type and noise was assessed by estimating pixel-value statistics, such as standard deviation (i.e., noise magnitude), autocorrelation, and noise power spectrum. Noise stationarity was also assessed by examining the spatial distribution of noise magnitude. The noise properties were compared across background types and between the two reconstruction algorithms. Results: In FBP and SAFIRE images, noise was globally nonstationary for all phantoms. In FBP images of all phantoms, and in SAFIRE images of the uniform phantom, noise appeared to be locally stationary (within a reasonably small region of interest). Noise was locally nonstationary in SAFIRE images of the textured phantoms with edge pixels showing higher noise magnitude compared to pixels in more homogenous regions. For pixels in uniform regions, noise magnitude was reduced by an average of 60% in SAFIRE images compared to FBP. However, for edge pixels, noise magnitude ranged from 20% higher to 40% lower in SAFIRE images compared to FBP. SAFIRE images of the lung phantom exhibited distinct regions with varying noise texture (i.e., noise autocorrelation/power spectra). Conclusions: Quantum noise properties observed in uniform phantoms may not be representative of those in actual patients for nonlinear reconstruction algorithms. Anatomical texture should be considered when evaluating the performance of CT systems that use such nonlinear algorithms.
MICADO: Parallel implementation of a 2D-1D iterative algorithm for the 3D neutron transport problem in prismatic geometries
The large increase in computing power over the past few years now makes it possible to consider developing 3D full-core heterogeneous deterministic neutron transport solvers for reference calculations. Among all approaches presented in the literature, the method first introduced in [1] seems very promising. It consists in iterating over resolutions of 2D and ID MOC problems by taking advantage of prismatic geometries without introducing approximations of a low order operator such as diffusion. However, before developing a solver with all industrial options at EDF, several points needed to be clarified. In this work, we first prove the convergence of this iterative process, under some assumptions. We then present our high-performance, parallel implementation of this algorithm in the MICADO solver. Benchmarking the solver against the Takeda case shows that the 2D-1D coupling algorithm does not seem to affect the spatial convergence order of the MOC solver. As for performance issues, our study shows that even though the data distribution is suited to the 2D solver part, the efficiency of the ID part is sufficient to ensure a good parallel efficiency of the global algorithm. After this study, the main remaining difficulty implementation-wise is about the memory requirement of a vector used for initialization. An efficient acceleration operator will also need to be developed. (authors)
Development of Application Function Blocks for Power-Hardware-in-the-Loop Testing of Grid-Connected Inverters: Preprint
Stability and accuracy of the PHIL platform has been a common problem and challenging issue for a long time, thus continuous efforts and research have been devoted to developing interface algorithms to improve upon this. Some of existing works exhibit promising solutions to compensate the errors in the PHIL platform. However, there is a need to harmonize various solutions into a standard framework that provides a general solution for various PHIL test beds and that can be reused with minimum modifications to avoid extra effort. A good way to do this is by using application function blocks (AFBs), which are model-based and can be developed as a standard library component, thus achieving satisfactory reusability and reconfigurability for various platforms. Since PHIL simulation has the flexibility of the software simulation, proper functions can be easily implemented in the digital real-time simulator (DRTS) to preprocess the reference signal before sending it to the power amplifier. Therefore, this paper aims to develop standard AFBs in DRTS for the PHIL interface to test grid-connected inverters. The PHIL interface algorithm is separated into five AFBs that will be presented in detail in this paper.
A Robust Load Shedding Strategy for Microgrid Islanding Transition
A microgrid is a group of interconnected loads and distributed energy resources. It can operate in either gridconnected mode to exchange energy with the main grid or run autonomously as an island in emergency mode. However, the transition of microgrid from grid-connected mode to islanded mode is usually associated with excessive load (or generation), which should be shed (or spilled). Under this condition, this paper proposes an robust load shedding strategy for microgrid islanding transition, which takes into account the uncertainties of renewable generation in the microgrid and guarantees the balance between load and generation after islanding. A robust optimization model is formulated to minimize the total operation cost, including fuel cost and penalty for load shedding. The proposed robust load shedding strategy works as a backup plan and updates at a prescribed interval. It assures a feasible operating point after islanding given the uncertainty of renewable generation. The proposed algorithm is demonstrated on a simulated microgrid consisting of a wind turbine, a PV panel, a battery, two distributed generators (DGs), a critical load and a interruptible load. Numerical simulation results validate the proposed algorithm.
Vectorization techniques for probability distribution functions using VecCore
Probability distribution functions (PDFs) are very used in modeling random processes and physics simulations. Improving the performance of algorithms that generate many random numbers under complex PDFs is often a very challenging task when methods as direct functions are not available. In this work we present general strategies on how to vectorize some PDFs using VecCore library. We show the results for the Exponential, Gaussian, discrete Poisson and Gamma probability distributions.
Phase Identification in Real Distribution Networks with High PV Penetration Using Advanced Metering Infrastructure Data
Many distribution network monitoring and control applications - including state estimation, volt/VAR optimization, and network reconfiguration - rely on accurate network models; however, the network models maintained by utilities can become outdated because of restoration activities, network reconfiguration, and missing data. With the widespread deployment of advanced metering infrastructure (AMI), abundant measurement data from low-voltage secondary networks are available. The AMI measurement data can be used for phase identification to improve the network models. Although the existing phase identification techniques work well in passive distribution feeders that do not have photovoltaic (PV) generation, they can fail to accurately identify the phases in the presence of PV. This paper proposes a robust phase identification algorithm based on supervised machine learning that accurately identifies the AMI meter phase connectivity in the presence of significant PV generation. The proposed algorithm does not require network topology information or feeder head measurement data. The algorithm is validated using the AMI measurement data collected in the field and the field-validated phase connectivity database on two real distribution feeders from San Diego Gas & Electric Company that have significant PV generation.
Phase Identification in Real Distribution Networks with High PV Penetration Using Advanced Metering Infrastructure Data: Preprint
Many distribution network monitoring and control applications - including state estimation, volt/VAR optimization, and network reconfiguration - rely on accurate network models; however, the network models maintained by utilities can become outdated because of restoration activities, network reconfiguration, and missing data. With the widespread deployment of advanced metering infrastructure (AMI), abundant measurement data from low-voltage secondary networks are available. The AMI measurement data can be used for phase identification to improve the network models. Although the existing phase identification techniques work well in passive distribution feeders that do not have photovoltaic (PV) generation, they can fail to accurately identify the phases in the presence of PV. This paper proposes a robust phase identification algorithm based on supervised machine learning that accurately identifies the AMI meter phase connectivity in the presence of significant PV generation. The proposed algorithm does not require network topology information or feeder head measurement data. The algorithm is validated using the AMI measurement data collected in the field and the field-validated phase connectivity database on two real distribution feeders from San Diego Gas & Electric Company that have significant PV generation.
Phase Identification in Real Distribution Networks with High PV Penetration Using Advanced Metering Infrastructure Data
Many distribution network monitoring and control applications - including state estimation, Volt/VAr optimization, and network reconfiguration - rely on accurate network models; however, the network models maintained by utilities can become outdated because of restoration activities, network reconfiguration, and missing data. With the widespread deployment of advanced metering infrastructure (AMI), abundant measurement data from low-voltage secondary networks are available. The AMI measurement data can be used for phase identification to improve the network models. Although the existing phase identification techniques work well in passive distribution feeders that do not have photovoltaic (PV) generation, they can fail to accurately identify the phases in the presence of PV. This paper proposes a robust phase identification algorithm based on supervised machine learning that accurately identifies the AMI meter phase connectivity in the presence of significant PV generation. The proposed algorithm does not require network topology information or feeder-head measurement data. The algorithm is validated using the AMI measurement data collected in the field and the field-validated phase connectivity database on two real distribution feeders from San Diego Gas & Electric Company that have significant PV generation.
Characterization of a novel 2D array dosimeter for patient-specific quality assurance with volumetric arc therapy
Purpose: In this study, the authors are evaluating a new, commercially available 2D array that offers 3D dose reconstruction for patient specific intensity modulated radiation therapy quality assurance (IMRT QA).Methods: The OCTAVIUS 4D system and its accompanying software (VERISOFT) by PTW were evaluated for the accuracy of the dose reconstruction for patient specific pretreatment IMRT QA. OCTAVIUS 4D measures the dose plane at the linac isocenter as the phantom rotates synchronously with the gantry, maintaining perpendicularity with the beam, by means of an inclinometer and a motor. The measurements collected during a volumetric modulated arc therapy delivery (VMAT) are reconstructed into a 3D dose volume. The VERISOFT application is used to perform the analysis, by comparing the reconstructed dose against the 3D dose matrix from the treatment planning system (TPS) that is computed for the same geometry and beam arrangement as that of the measurement. In this study, the authors evaluated the 3D dose reconstruction algorithm of this new system using a series of tests. Using the Octavius 4D phantom as the patient, dose distributions for various field sizes, beam orientations, shapes, and combination of fields were calculated using the Pinnacle3, TPS, and the respective DICOMRT dose was exported to the VERISOFT analysis software. Measurements were obtained by delivering the test treatment plans and comparisons were made based on gamma index, dose profiles, and isodose distribution analysis. In addition, output factors were measured and the dose linearity of the array was assessed. Those measurements were compared against measurements in water using a single, calibrated ionization chamber as well as calculations from Pinnacle for the same delivery geometries.Results: The number of voxels that met the 3%/3 mm criteria for the volumetric 3D gamma index analysis ranged from 92.3% to 98.9% for all the patient plans that the authors evaluated. 2D gamma analysis in the axial, sagittal, and coronal planes produced similar results to those in the 3D gamma analysis. The new detector system does not require an angular dependence correction because it rotates in synchrony with the gantry and the detector array maintains a constant SAD while always perpendicular to the beam axis. Output factors were within 2% when compared to ionization chamber measurements and Pinnacle calculations. Similar agreement was observed when testing the MU linearity (for MU values above 2) as well as dose rate effect.Conclusions: The OCTAVIUS 4D system has some unique characteristics that can potentially improve the patient specific pretreatment IMRT QA data collection and analysis. The ability of the software to reconstruct from the measurements the true 3D dose distribution in the phantom, provides a unique perspective for the medical physicist that evaluates a patient's QA plan.
Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra
In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. In conclusion, the posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.
Multi channel thermal hydraulic analysis of gas cooled fast reactor using genetic algorithm
There are three analyzes to be done in the design process of nuclear reactor i.e. neutronic analysis, thermal hydraulic analysis and thermodynamic analysis. The focus in this article is the thermal hydraulic analysis, which has a very important role in terms of system efficiency and the selection of the optimal design. This analysis is performed in a type of Gas Cooled Fast Reactor (GFR) using cooling Helium (He). The heat from nuclear fission reactions in nuclear reactors will be distributed through the process of conduction in fuel elements. Furthermore, the heat is delivered through a process of heat convection in the fluid flow in cooling channel. Temperature changes that occur in the coolant channels cause a decrease in pressure at the top of the reactor core. The governing equations in each channel consist of mass balance, momentum balance, energy balance, mass conservation and ideal gas equation. The problem is reduced to finding flow rates in each channel such that the pressure drops at the top of the reactor core are all equal. The problem is solved numerically with the genetic algorithm method. Flow rates and temperature distribution in each channel are obtained here.
Distribution of centrality measures on undirected random networks via the cavity method
The Katz centrality of a node in a complex network is a measure of the node’s importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its “global” character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P ( K ) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank- 1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.
Achieving precise multiparameter measurements with distributed optical fiber sensor using wavelength diversity and deep neural networks
The development of advanced distributed optical fiber sensing systems that are capable of performing accurate and spatially resolved multiparameter measurements is of great interest to a wide range of scientific and industrial applications. Here, in this paper, we propose and experimentally demonstrate a wavelength diversity based advanced distributed optical fiber sensor system to accomplish multiparameter sensing while greatly enhancing measurement accuracy. A suite of deep neural network (DNN) algorithms are developed and verified for data denoising, rapid Brillouin frequency shift estimation, and vibration data event classification. As a proof-of-concept, we demonstrate the effectiveness of the proposed advanced wavelength diversity distributed fiber sensor system assisted by DNN for simultaneous, independent measurements of static strain, temperature, and acoustic vibrations over a 25 km long sensing fiber at 3 m spatial resolution. These results suggest the potential for an intelligent multiparameter monitoring system with enhanced performance in advanced structural health monitoring applications.