Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Modeling some real phenomena by fractional differential equations

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

The influence of self-weight of elastic 2D structures in topology optimization via numerical technique Smooth Evolutionary Structural Optimization (SESO)

This paper deals with topology optimization in plane elastic-linear problems considering the influence of the self weight in efforts in structural elements. For this purpose it is used a numerical technique called SESO (Smooth ESO), which is based on the procedure for progressive decrease of the inefficient stiffness element contribution at lower stresses until he has no more influence. The SESO is applied with the finite element method and is utilized a triangular finite element and high order. This paper extends the technique SESO for application its self weight where the program, in computing the volume and specific weight, automatically generates a concentrated equivalent force to each node of the element. The evaluation is finalized with the definition of a model of strut-and-tie resulting in regions of stress concentration. Examples are presented with optimum topology structures obtaining optimal settings. (C) 2012 CIMNE (Universitat Politecnica de Catalunya). Published by Elsevier Espana, S.L.U. All rights reserved.

A numerical methodology for the multi-objective optimization of the DI Diesel engine combustion

DI Diesel engine are widely used both for industrial and automotive applications due to their durability and fuel economy. Nonetheless, increasing environmental concerns force that type of engine to comply with increasingly demanding emission limits, so that, it has become mandatory to develop a robust design methodology of the DI Diesel combustion system focused on reduction of soot and NOx simultaneously while maintaining a reasonable fuel economy. In recent years, genetic algorithms and CFD three-dimensional combustion simulations have been successfully applied to that kind of problem. However, combining GAs optimization with actual CFD three-dimensional combustion simulations can be too onerous since a large number of calculations is usually needed for the genetic algorithm to converge, resulting in a high computational cost and, thus, limiting the suitability of this method for industrial processes. In order to make the optimization process less time-consuming, CFD simulations can be more conveniently used to generate a training set for the learning process of an artificial neural network which, once correctly trained, can be used to forecast the engine outputs as a function of the design parameters during a GA optimization performing a so-called virtual optimization. In the current work, a numerical methodology for the multi-objective virtual optimization of the combustion of an automotive DI Diesel engine, which relies on artificial neural networks and genetic algorithms, was developed.

Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model

Numerical modelling and structural optimization of multifunctional maritime structures aimed to protect harbours and produce energy

The main objective of this PhD thesis is to optimize a specific multifunctional maritime structure for harbour protection and energy production, named Overtopping Breakwater for Energy Conversion (OBREC), developed by the team of the University of Campania. This device is provided with a sloping plate followed by a unique reservoir, which is linked with the machine room (where the energy conversion occurs) by means of a pipe passing through the crown wall, provided with a parapet on top of it. Therefore, the potential energy of the overtopping waves, collected inside the reservoir located above the still water level, is then converted by means of low – head turbines. In order to improve the understanding of the wave – structure interactions with OBREC, several methodologies have been used and combined together: i. analysis of recent experimental campaigns on wave overtopping discharges and pressures at the crown wall on small – scale OBREC cross sections, carried out in other laboratories by the team of the University of Campania; ii. new experiments on cross sections similar to the OBREC device, planned and carried out in the hydraulic lab at the University of Bologna in the framework of this PhD work; iii. numerical modelling with a 1 – phase incompressible fluid model IH – 2VOF, developed by the University of Cantabria, and with a 2 – phase incompressible fluid model OpenFOAM, both available from the literature; iv. numerical modelling with a new 2 – phase compressible fluid model developed in the OpenFOAM environment within this PhD work; v. analysis of the data gained from the monitoring of the OBREC prototype installation.

Development of numerical tools for the simulation, design and optimization of a Helicon Plasma Thruster

This work thesis focuses on the Helicon Plasma Thruster (HPT) as a candidate for generating thrust for small satellites and CubeSats. Two main topics are addressed: the development of a Global Model (GM) and a 3D self-consistent numerical tool. The GM is suitable for preliminary analysis of HPTs with noble gases such as argon, neon, krypton, and xenon, and alternative propellants such as air and iodine. A lumping methodology is developed to reduce the computational cost when modelling the excited species in the plasma chemistry. A 3D self-consistent numerical tool is also developed that can treat discharges with a generic 3D geometry and model the actual plasma-antenna coupling. The tool consists of two main modules, an EM module and a FLUID module, which run iteratively until a steady state solution is converged. A third module is available for solving the plume with a simplified semi-analytical approach, a PIC code, or directly by integration of the fluid equations. Results obtained from both the numerical tools are benchmarked against experimental measures of HPTs or Helicon reactors, obtaining very good qualitative agreement with the experimental trend for what concerns the GM, and an excellent agreement of the physical trends predicted against the measured data for the 3D numerical strategy.

Numerical comparison between conventional dispersion compensating fibers and photonic crystal fibers as lumped Raman amplifiers

In this paper we discuss the use of photonic crystal fibers (PCFs) as discrete devices for simultaneous wideband dispersion compensation and Raman amplification. The performance of the PCFs in terms of gain, ripple, optical signal-to-noise ratio (OSNR) and required fiber length for complete dispersion compensation is compared with conventional dispersion compensating fibers (DCFs). The main goal is to determine the minimum PCF loss beyond which its performance surpasses a state-of-the-art DCF and justifies practical use in telecommunication systems. (C) 2009 Optical Society of America

Effective Electromechanical Coupling Coefficients of Piezoelectric Adaptive Structures: Critical Evaluation and Optimization

This work presents a critical analysis of methodologies to evaluate the effective (or generalized) electromechanical coupling coefficient (EMCC) for structures with piezoelectric elements. First, a review of several existing methodologies to evaluate material and effective EMCC is presented. To illustrate the methodologies, a comparison is made between numerical, analytical and experimental results for two simple structures: a cantilever beam with bonded extension piezoelectric patches and a simply-supported sandwich beam with an embedded shear piezoceramic. An analysis of the electric charge cancelation effect on the effective EMCC observed in long piezoelectric patches is performed. It confirms the importance of reinforcing the electrodes equipotentiality condition in the finite element model. Its results indicate also that smaller (segmented) and independent piezoelectric patches could be more interesting for energy conversion efficiency. Then, parametric analyses and optimization are performed for a cantilever sandwich beam with several embedded shear piezoceramic patches. Results indicate that to fully benefit from the higher material coupling of shear piezoceramic patches, attention must be paid to the configuration design so that the shear strains in the patches are maximized. In particular, effective square EMCC values higher than 1% were obtained embedding nine well-spaced short piezoceramic patches in an aluminum/foam/aluminum sandwich beam.

Mitigation of the torque ripple of a switched reluctance motor through a multiobjective optimization

The purpose of this work is to perform a multiobjective optimization in a 4:2 switched reluctance motor aiming both to maximize the mitigation of the torque ripple and to minimize the degradations of the starting and mean torques. To accomplish this task the Pareto Archived Evolution Strategy was implemented jointly with the Kriging Method, which acts as a surrogate function. The technique was applied on the optimization of some rotor geometrical parameters with the aid of finite element simulations to evaluate the approximation points for the Kriging model. The numerical results were compared to those from tests.

Finite Element Analysis and Optimization of a Single-Axis Acoustic Levitator

A finite element analysis and a parametric optimization of single-axis acoustic levitators are presented. The finite element method is used to simulate a levitator consisting of a Langevin ultrasonic transducer with a plane radiating surface and a plane reflector. The transducer electrical impedance, the transducer face displacement, and the acoustic radiation potential that acts on small spheres are determined by the finite element method. The numerical electrical impedance is compared with that acquired experimentally by an impedance analyzer, and the predicted displacement is compared with that obtained by a fiber-optic vibration sensor. The numerical acoustic radiation potential is verified experimentally by placing small spheres in the levitator. The same procedure is used to optimize a levitator consisting of a curved reflector and a concave-faced transducer. The numerical results show that the acoustic radiation force in the new levitator is enhanced 604 times compared with the levitator consisting of a plane transducer and a plane reflector. The optimized levitator is able to levitate 3, 2.5-mm diameter steel spheres with a power consumption of only 0.9 W.

Multi-actuated functionally graded piezoelectric micro-tools design: A multiphysics topology optimization approach

Micro-tools offer significant promise in a wide range of applications Such as cell Manipulation, microsurgery, and micro/nanotechnology processes. Such special micro-tools consist of multi-flexible structures actuated by two or more piezoceramic devices that must generate output displacements and forces lit different specified points of the domain and at different directions. The micro-tool Structure acts as a mechanical transformer by amplifying and changing the direction of the piezoceramics Output displacements. The design of these micro-tools involves minimization of the coupling among movements generated by various piezoceramics. To obtain enhanced micro-tool performance, the concept of multifunctional and functionally graded materials is extended by, tailoring elastic and piezoelectric properties Of the piezoceramics while simultaneously optimizing the multi-flexible structural configuration using multiphysics topology optimization. The design process considers the influence of piezoceramic property gradation and also its polarization sign. The method is implemented considering continuum material distribution with special interpolation of fictitious densities in the design domain. As examples, designs of a single piezoactuator, an XY nano-positioner actuated by two graded piezoceramics, and a micro-gripper actuated by three graded piezoceramics are considered. The results show that material gradation plays an important role to improve actuator performance, which may also lead to optimal displacements and coupling ratios with reduced amount of piezoelectric material. The present examples are limited to two-dimensional models because many of the applications for Such micro-tools are planar devices. Copyright (c) 2008 John Wiley & Sons, Ltd.

A generalized multi-period mean-variance portfolio optimization with Markov switching parameters

In this paper, we deal with a generalized multi-period mean-variance portfolio selection problem with market parameters Subject to Markov random regime switchings. Problems of this kind have been recently considered in the literature for control over bankruptcy, for cases in which there are no jumps in market parameters (see [Zhu, S. S., Li, D., & Wang, S. Y. (2004). Risk control over bankruptcy in dynamic portfolio selection: A generalized mean variance formulation. IEEE Transactions on Automatic Control, 49, 447-457]). We present necessary and Sufficient conditions for obtaining an optimal control policy for this Markovian generalized multi-period meal-variance problem, based on a set of interconnected Riccati difference equations, and oil a set of other recursive equations. Some closed formulas are also derived for two special cases, extending some previous results in the literature. We apply the results to a numerical example with real data for Fisk control over bankruptcy Ill a dynamic portfolio selection problem with Markov jumps selection problem. (C) 2008 Elsevier Ltd. All rights reserved.