1,720,992 research outputs found
Power Grid Simulation with GPU-Accelerated Iterative Solvers and Preconditioners
No full textThis thesis deals with two research problems. The first research problem is motivated by the numerical computation involved in the Time Domain Simulation (TDS) of Power Grids. Due to the ever growing size and complexity of Power Grids such as the China National Grid, accelerating TDS has become a stringent need for the online analysis of these large systems. Hence the first part of the research includes the acceleration of the TDS by means of Iterative Solvers and Preconditioners which exploit the sparsity structure of the Power Grid. The second research problem is motivated by the recent trend of using Graphics Processing Units (GPUs) in High Performance Computing (HPC). By using TDS as a sample application, the second part of research involves the design and implementation of Krylov subspace solvers and general-purpose preconditioner which can fully exploit the performance potential of GPUs. TDS is of crucial importance to the analysis and control of Power Grids. The mathematical model of the Power Grid can be represented by a series of nonlinear Differential Algebraic Equations. With numerical time integration by an implicit scheme and linearization by Newton's Method, the major computation in TDS is the solution of a series of Jacobian matrices based linear systems. With the large size of the Power Grid and the need for fast simulation for online analysis, it is desirable to use iterative solvers and preconditioners for the solution of these linear systems. This thesis tackles the numerical problem in TDS from two aspects: design of high-performance preconditioner to the specific characterization of the TDS problem, and development of multi-step techniques for the iterative solution of a series of linear systems based on the Jacobian matrices. We start with the analysis of the sparsity pattern of the Jacobian matrix and its relationship to the Power Network and admittance matrix. The parts in the Jacobian matrix which corresponds to the dynamic parts (i.e., the differential equations) of the Power Grid and has a block-diagonal form. The Schur complement of the dynamic part has virtually no fill-in in the algebraic part which corresponds to the connectivity of the buses in the Power Network. We then formulate a multilevel preconditioner for the Jacobian matrix based on the static sparsity pattern in the matrix and the analysis of the network topology. We show that multilevel structure based on independent sets (\INDSET) can serve as an efficient preconditioners for TDS in terms of both memory efficiency and convergence property. To accommodate matrix and right hand side changes during the simulation, we further transform the Jacobian matrix in an additive form of , where is a static matrix and is a block-diagonal, low rank matrix which changes from linear system to linear system. Based on this transformation, effective preconditioner re-use, also called preconditioner updating, is derived, through dynamically adopting the changes of into the preconditioner initially constructed for itself. This results in much more efficient iterative methods for TDS of Power Grid. Furthermore, we explore the potential of matrix spectral deflation as another multi-step technique for TDS. To accommodate dynamic changes in the linear operator, \GCRODR is used. With the additive form of , we achieve a more computationally feasible form for the updates of the deflation matrices in \GCRODR. Spectral analysis shows that eigenvalues of both large and very small magnitude appear for the preconditioned TDS matrices, hence we propose the use of a heuristics to dynamically choose among the largest and smallest eigenvalues (or Rits values) used for deflation. The experiments show that the dynamic eigenvalue choice could greatly benefit convergence due to the dynamic changes in the matrix spectra of TDS. We also show that preconditioner updates and deflation can be used together which leads to a combined effect on the reduction of the total iteration count in TDS. GPU based accelerated HPC systems are becoming popular due to the high performance potential and good efficiency of GPUs. Iterative Algorithm and Preconditioners are the two fundamental components of Krylov subspace solvers. However, porting them to GPU platform remain a challenge especially for preconditioners. In this thesis we target at porting of Krylov subspace solvers on GPU and the design of GPU-efficient preconditioners. Firstly we discuss the two major parts of computation involved in Krylov solvers: (1) the generation of Krylov subspace basis through Sparse Matrix-Vector multiplications (\SpMV), and (2) orthogonalization by modified Gram-Schmidt method. We show that both parts can be efficiently implemented on GPU with high performance. On GPU platform, incomplete factorization based preconditioners, such as Incomplete LU or Incomplete Cholesky, have not been successfully implemented due to the ``sequentialness" and limited parallelism in their preconditioning process. While inverse form based preconditioner such as -biconjugate allows higher parallelism and better performance on GPUs, it introduces too much fill-ins. We aim to design a preconditioner that can achieve high performance while maintaining good memory efficiency and convergence property of the incomplete factorizations. We use recursive multilevel structure retrieved from the elimination tree and -biconjugate algorithm to achieve this. Multilevel structure is constructed based on \INDSET{s} by symbolic analysis of the elimination tree. For the preconditioning of the last-level reduced system, we use -biconjugation. The proposed preconditioner, denoted as \MLAINV, features preconditioning operation which involve a series of matrix-vector products. Through experiments with TDS problems and test matrices from various other applications, we show that \MLAINV achieves the design goal in both aspects: (1) its good convergence property is similar to incomplete factorizations, and (2) it obtains high performance by \SpMV based preconditioning on GPUs.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc
Parallelization of Ensemble Kalman Filter (EnKF) for Oil Reservoirs
No full textThis thesis describes the design and implementation of a parallel algorithm for data assimilation with ensemble Kalman filter (EnKF) for oil reservoir management. The implemented application works on large number of observations from time-lapse seismic, which lead to a large turnaround time for the analysis step, in addition to the time consuming simulations of the realizations. Provided that parallel resources are used for the parallel simulations of the realizations, the analysis step also deserves parallelization. Our experiments show that parallelization of the analysis step in addition to the forecast step also scales well, exploiting the same set of resources with some additional efforts.Computer Simulations for Science and EngineeringApplied mathematicsElectrical Engineering, Mathematics and Computer Scienc
A Methodology for the Parallel Direct Solution of Finite Element Systems
No full textElectrical Engineering, Mathematics and Computer Scienc
Modelleren van verkeer en transport in verkeersnetwerken
No full textIn de wereld waarin we leven is verkeer niet meer weg te denken. Mensen en goederen verplaatsen zich per auto, boot, vliegtuig, openbaar vervoer, enzovoorts. Dit moet ook nog eens in zo'n kort mogelijke tijd. Er wordt dan ook veel onderzoek gedaan om het verkeer te optimaliseren. Zo worden er verkeersmodellen gemaakt om het verkeer bijvoorbeeld te analyseren, voorspellen, besturen en zo zijn er nog meer redenen. Dit project richt zich op het modelleren van verkeersnetwerken bestaande uit wegen, kruispunten, instroom- en uitstroompunten en bijbehorende variabelen. Dit soort verkeersnetwerken worden eerst gedefinieerd. Hierna wordt besproken wat elektrische netwerken zijn en worden deze vergeleken met verkeersnetwerken. Door gebruik te maken van wetten en transformaties uit de elektrotechniek, kan een complex wegennetwerk gereduceerd worden tot een simpel netwerk waarin de totale reistijd over het netwerk makkelijk te berekenen is. Ook zal er gekeken worden hoe de verdeling van het verkeer over een netwerk berekend kan worden.Electrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied Mathematic
An inexact splitting method for the subspace segmentation from incomplete and noisy observations
No full textSubspace segmentation is a fundamental issue in computer vision and machine learning, which segments a collection of high-dimensional data points into their respective low-dimensional subspaces. In this paper, we first propose a model for segmenting the data points from incomplete and noisy observations. Then, we develop an inexact splitting method for solving the resulted model. Moreover, we prove the global convergence of the proposed method. Finally, the inexact splitting method is implemented on the clustering problems in synthetic and benchmark data, respectively. Numerical results demonstrate that the proposed method is computationally efficient, robust as well as more accurate compared with the state-of-the-art algorithms.Accepted author manuscriptMathematical Physic
Optimalisatie en modellering van vertraging in verkeersnetwerken
No full textIn dit verslag worden twee verschillende modellen bekeken om vertraging die opgelopen wordt door weggebruikers in verkeersnetwerken te modelleren en te minimaliseren. De modellen worden gecontroleerd en geverifieerd met onder andere Maple en de stelling van Tellegen. Bij beide modellen worden voorbeelden gegeven en uitgerekend. Dit gebeurt zowel analytisch als met Matlab. De paradox van Braess wordt aangetoond en toegelicht. Verder worden er aanpassingen gedaan aan de modellen zodat deze beter werken en meer netwerken kunnen dienen en opdat de paradox van Braess omzeild kan worden. Er dienen nog een aantal aspecten verbetert te worden. Deze kunnen gevonden worden in de discussie.Applied mathematicsElectrical Engineering, Mathematics and Computer Scienc
Dust storm emission inversion using data assimilation
No full textSevere dust storms present great threats to the environment, property and human health over the areas in the downwind of arid regions. Several dynamical dust models have been developed to predict the dust concentrations in the atmosphere. Currently, the accuracy of these models is limited mainly due to the imperfect modeling of dust emissions. Along with the progress in the dust and aerosol modeling, the advances in sensor technologies have made large-scale aerosol measurements feasible. The rich measurements provide opportunities to estimate uncertain emission fields, and subsequently, to improve the forecast skill. Such process of emission optimization conditioned on measurements is usually referred as emission inversion. Here, the termof emission inversion specially represents the way of deriving estimates from observations through the use of an atmospheric chemical transport model and a data assimilationmethod.Mathematical Physic
Variational data assimilation of satellite observations to estimate volcanic ash emissions
No full textVolcanic eruptions release a large amount of volcanic ash, which can pose hazard to human and animal health, land transportation, and aviation safety. Volcanic Ash Transport and Dispersion (VATD) models are critical tools to provide advisory information and timely volcanic ash forecasts. Due to the complexity and the uncertainty of many dynamic processes involved in the volcanic ash distribution, even the most advanced VATDs today are not capable to reproduce the reality accurately. It is necessary to integrate available observations in the models for more accurate predictions by employing data assimilation techniques.In addition to a valid VATD, ash emissions, usually used as input so the model, are crucial for the forecasts of the locations and shapes of the ash cloud. In general, the eruption source parameters for the construction of the emission are poorly known, which include Plume Height (PH), Mass Eruption Rate (MER) and vertical distribution of the emission rate. Even when PH can be obtained from ground-based observations in some cases, the emission source computed from this PH and a MER empirically related to this PH remains highly uncertain. Not to mention the volcanoes which are unmonitored or hardly accessible, the PH can merely be retrieved from satellite data with a large uncertainty and temporal insufficiency. Fortunately, satellite instruments are able to observe the movement of an ash cloud with a global coverage. Therefore, this thesis focuses on the estimation of the volcanic ash emissions by assimilating Ash Mass Loadings (AMLs) retrieved from satellite data to improve the accuracy of forecasts. Among all available data assimilation approaches, Four Dimensional Variational assimilation (4D-Var) approach was chosen as a suitable one. 4D-Var seeks an optimal set of parameters, including model states, initial conditions and systematic parameters, by minimizing a cost function which combines the model simulations and observations over a period according to their statistic properties. 4D-Var with a standard form of the cost function is tested in a twin experiment framework, where synthetic observations of ash columns computed from model simulated 3D ash concentrations are used. The results show that Standard 4DVar (Std4DVar) is unable to reconstruct the vertical profile of the emission. The injection layer containing the maximal amount of emission rate cannot be accurately determined. This failure is attributed to the fact that AML data lacks vertical resolution. Using the AMLs, it is difficult to reconstruct the volcanic ash emission presented in forms of an eruption column.To deal with this problem, a Trajectory-based 4D-Var (Trj4DVar) approach is proposed. Trj4DVar reformulates the cost function in a regression type which computes the total difference between observed ash columns and a linear combination of simulated trajectories coupled with a priori emission knowledge. The results of twin experiments show that, for most cases, Trj4DVar is capable of estimating the input emission column when a large assimilation window (> 6 hours) is used. The twin experiments is repeated where different values of noise are given in the synthetic observations or perturbations are used in the meteorologic data. The outcomes show that there is still a small possibility that Trj4DVar fails to determine the injection height accurately. Being disturbed by the weather condition (light and cloud, etc) at that moment, satellite instrument can be hampered to observe the ash cloud, which may increase the possibility of failure for the use of Trj4DVar. To remedy this, Trj4DVar is modified to incorporate observations of PH and MER in addition to satellite AMLs. The modified Trj4DVar is shown to be able accurately estimate the injection height based on the results of twin experiments.When it comes to using real-life field data, the situation is more complicated. The detection of volcanic ash can be disturbed by the weather condition such as water vapor. This will result in observations of undetected or wrongly-detected ash. Besides, many sensors ,such as UV and visible sensors, have limited temporal coverage which can only observe during daylight. In order to find effective method in dealing with the temporal and sometimes spatial insufficiency of the data, investigations are carried out on how to use the data properly to benefit more and produce a reasonable estimate. A prepossessing procedure and guidance on the proper use of satellite data are presented.Finally, a deeper analysis is given on the failure of using Std4DVar in this application. It is found that using Std4DVar to assimilate remote sensing data can be tricky. Remote sensing measures quantities that combine several state variables. This creates Sensor-Induced Correlations between the state variables which share the same observation variable and may be physically unrelated. This may cause numerical problems resulting in a low convergence rate or inaccurate estimates of parameters using gradient-based variational assimilation if an erroneous or improper specification of error statistics is adopted. These problems are usually ignored when a reasonable result is obtained, or are avoided by reducing the 3D model to a 2D model. However, it results in significantly unreliable and misguiding estimates for the application in this thesis. Two criteria are proposed to quantify the negative effects of the SICs, which give indications of the effectiveness of the assimilation process and the forecast quality. They are simple to implement and very practical for the use of remote sensing data. They are tested in the twin experiments. The results show that they are able to give evaluation on the design and configuration of the assimilation system with remote sensing data
Improving volcanic ash forecasts with ensemble-based data assimilation
No full textThe 2010 Eyjafjallajökull volcano eruption had serious consequences to civil aviation. This has initiated a lot of research on volcanic ash forecasting in recent years. For forecasting the volcanic ash transport after eruption onset, a volcanic ash transport and diffusion model (VATDM) needs to be run with Eruption Source Parameters (ESPs) such as plume height and mass eruption rate as input, and with data assimilation techniques to continuously improve the forecast. Reliable and accurate ash measurements are crucial for providing successful ash clouds advices. In the firstphase of this research work, simulated aircraft-based volcanic ash measurements, will be assimilated into a transport model to identify the potential benefit of this kind of observations in an assimilation system. The results show that assimilating aircraft-based measurements can improve the state of ash clouds, and can provide an improved forecast. We also show that for an advice on the aeroplane flying level, aircraft-based measurements should preferably be taken at this level. Furthermoreit is shown that in order to make an acceptable advice for aviation decision makers, accurate knowledge about uncertainties of ESPs and measurements is of great importance.The forecast accuracy of distal volcanic ash clouds is important for providing valid aviation advice during volcanic ash eruptions. However, because the distal part of a volcanic ash plume is far from the volcano, the influence of eruption information on this part becomes rather indirect and uncertain, resulting in inaccurate volcanic ash forecasts in these distal areas. In this thesis, we use real-life aircraft in situ observations, measured in the North-West part of Germany during the 2010 Eyjafjallajökull eruption, in an ensemble-based data assimilation system to investigate the potential improvement on the forecast accuracy with regard to the distal volcanic ash plume. We show that the error of the analyzed volcanic ash state can be significantly reduced by assimilating real-life in situ measurements. After assimilation, it is shown that the model-based aviation advice for Germany, the Netherlands and Luxembourg can be improved. We suggest that with suitable aircrafts measuring once per day across the distal volcanic ash plume, the description and prediction of volcanic ash clouds in these areas can be improved significantly.Among the data assimilation approaches, the ensemble Kalman filter (EnKF) is a well-known and popular method. A proper covariance localization strategy in the analysis step of EnKF is essential for reducing spurious covariances caused by the finite ensemble size, as shown for this application for assimilation of aircraft in situ measurements. After analyzing the characteristics of the physical forecast error covariances, we present a two-way tracking approach to define the localization matrixfor covariance localization. The result shows that the Two-way-tracking Localized EnKF (TL-EnKF) effectively maintains the correctly specified physical covariances and largely reduces the spurious ones. The computational cost of TL-EnKF is also evaluated and is shown to be advantageous for both serial and parallel implementations. Compared to the commonly used distance-based covariance localization, the two-way tracking approach is shown to be more suitable. In addition, the covariance inflation approach is verified as an additional improvement to TL-EnKF to achieve more accurate results.A timely prediction requires that the computations of the data assimilation system can be performed quickly (at least than the Wall-clock). We therefore investigate strategies for accelerating the data assimilation algorithm. Based on evaluations of the computational time, the analysis step of the assimilation turns out to be the most expensive part. After a study on the characteristics of the ensemble ash state, we propose a mask-state algorithm which records the sparsity information of the full ensemble state matrix and transforms the full matrix into a relatively small one. This will reduce the computational cost in the analysis step. Experimental results show the mask-state algorithm significantly speeds up the analysis step. Subsequently, the total amount of computing time for volcanic ash data assimilation is reduced to an acceptable level. The mask-state algorithm is generic and thus can be embedded in any ensemble-based data assimilation framework. Moreover, ensemble-based data assimilation with the mask-state algorithm is promising and flexible, because it implements exactly the standard data assimilation without any approximation and it realizes the satisfying performance without any change of the full model.Infrared satellite measurements of volcanic ash mass loadings are often used asinput observations for the assimilation scheme. However, these satellite-retrieveddata are often two-dimensional (2D), and cannot easily be combined with a three-dimensional (3D) volcanic ash model to improve the volcanic ash state. By integrating available data including ash mass loadings, cloud top heights and thickness information, we propose a satellite observational operator (SOO) that translates satellite-retrieved 2D volcanic ash mass loadings to 3D concentrations at the top layer of the ash cloud. Ensemble-based data assimilation is used to assimilate the extracted measurements of ash concentrations. The results show that satellite data assimilation can force the volcanic ash state to match the satellite observations, and that it improves the forecast of the ash state. Comparison with highly accurate aircraft in situ measurements shows that the effective duration of the improved volcanic ash forecasts is about a half day
Power system stability and frequency control for transient performance improvement
No full textThe electrical power grid is a fundamental infrastructure in today’s society. The synchronization of the frequency to nominal frequency over all the network is essential for the proper functioning of the power grid. The current transition to a more distributed generation by weather dependent renewable power sources, which are inherently more prone to fluctuations, poses great challenges to the functioning of the power grid. Among these fluctuations, the frequency fluctuations negatively affect the power supply and stability of the power grid. In this thesis, we focus on load frequency control laws that can effectively suppress the frequency fluctuations, and methods that can improve the synchronization stability...Mathematical Physic
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