Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Studio, simulazione e verifica sperimentale di tecniche di controllo per convertitori multilivello modulari

L’evoluzione dei componenti elettronici di potenza ed il conseguente sviluppo dei convertitori statici dell’energia elettrica hanno consentito di ottenere un’elevata efficienza energetica, sia nell’ambito degli azionamenti elettrici, sia nell’ambito della trasmissione e distribuzione dell’energia elettrica. L’efficienza energetica è una questione molto importante nell’attuale contesto storico, in quanto si sta facendo fronte ad una elevatissima richiesta di energia, sfruttando prevalentemente fonti di energia non rinnovabili. L’introduzione dei convertitori statici ha reso possibile un notevolissimo incremento dello sfruttamento delle fonti di energia rinnovabili: si pensi ad esempio agli inverter per impianti fotovoltaici o ai convertitori back to back per applicazioni eoliche. All’aumentare della potenza di un convertitore aumenta la sua tensione di esercizio: le limitazioni della tensione sopportabile dagli IGBT, che sono i componenti elettronici di potenza di più largo impiego nei convertitori statici, rendono necessarie modifiche strutturali per i convertitori nei casi in cui la tensione superi determinati valori. Tipicamente in media ed alta tensione si impiegano strutture multilivello. Esistono più tipi di configurazioni multilivello: nel presente lavoro è stato fatto un confronto tra le varie strutture esistenti e sono state valutate le possibilità offerte dall’architettura innovativa Modular Multilevel Converter, nota come MMC. Attualmente le strutture più diffuse sono la Diode Clamped e la Cascaded. La prima non è modulare, in quanto richiede un’apposita progettazione in relazione al numero di livelli di tensione. La seconda è modulare, ma richiede alimentazioni separate e indipendenti per ogni modulo. La struttura MMC è modulare e necessita di un’unica alimentazione per il bus DC, ma la presenza dei condensatori richiede particolare attenzione in fase di progettazione della tecnica di controllo, analogamente al caso del Diode Clamped. Un esempio di possibile utilizzo del convertitore MMC riguarda le trasmissioni HVDC, alle quali si sta dedicando un crescente interesse negli ultimi anni.

Studio e realizzazione di un inverter trifase a tre livelli

Lo scopo di questa tesi è lo studio e la realizzazione di una specifica tipologia di inverter, l’inverter trifase a tre livelli di tipo Cascaded. Il primo capitolo descrive l’inverter a due livelli e quello multilivello, evidenziandone gli aspetti peculiari e le possibili applicazioni. Il secondo capitolo affronta nello specifico l’inverter a trifase a tre livelli, per il quale, nel terzo capitolo, ne è descritta una realizzazione pratica, costruita presso i laboratori del Dipartimento di Ingegneria Elettrica dell’Università di Bologna. Nel quarto capitolo vengono presentate alcune prove sperimentali effettuate sul sistema reale.

Inverters multilivello per il pilotaggio di motori asincroni trifase

In questo lavoro di laurea si presentano le varie famiglie di convertitori multilivello MMC (Modular Multilevel Converter). Questi convertitori sono di ausilio per il condizionamento dei parametri di reti elettriche in media e alta tensione e possono anche essere convenientemente utilizzati nel pilotaggio di motori asincroni trifase. Dopo aver esplicitato i principi di funzionamento, presentato i dispositivi di commutazione, le tipologie conosciute e le rispettive principali tecniche di modulazione, si è presentato il motore asincrono trifase, il suo circuito equivalente e le problematiche di accoppiamento ad un inverter. Successivamente si è simulato un inverter multilivello di tipo Diode-Clamped, con modulazione analogica PWM multiportante, che aziona un motore asincrono commerciale, così da poterne verificare le prestazioni in diversi regimi di velocità.

Variation in partner notification outcomes for chlamydia in UK genitourinary medicine clinics: multilevel study

Objectives To compare different ways of measuring partner notification (PN) outcomes with published audit standards, examine variability between clinics and examine factors contributing to variation in PN outcomes in genitourinary medicine (GUM) clinics in the UK. Methods Reanalysis of the 2007 BASHH national chlamydia audit. The primary outcome was the number of partners per index case tested for chlamydia, as verified by a healthcare worker or, if missing, reported by the patient. Control charts were used to examine variation between clinics considering missing values as zero or excluding missing values. Hierarchical logistic regression was used to investigate factors contributing to variation in outcomes. Results Data from 4616 individuals in 169 genitourinary medicine clinics were analysed. There was no information about the primary outcome in 41% of records. The mean number of partners tested for chlamydia ranged from 0 to 1.5 per index case per clinic. The median across all clinics was 0.47 when missing values were assumed to be zero and 0.92 per index case when missing values were excluded. Men who have sex with men were less likely than heterosexual men and patients with symptoms (4-week look-back period) were less likely than asymptomatic patients (6-month look-back) to report having one or more partners tested for chlamydia. There was no association between the primary outcome and the type of the health professional giving the PN advice. Conclusions The completeness of PN outcomes recorded in clinical notes needs to improve. Further research is needed to identify auditable measures that are associated with successful PN that prevents repeated chlamydia in index cases.

A Fully Bayesian Approach for Combining Multilevel Failure Information in Fault Tree Quantification and Corresponding Optimal Resource Allocation

This paper presents a fully Bayesian approach that simultaneously combines basic event and statistically independent higher event-level failure data in fault tree quantification. Such higher-level data could correspond to train, sub-system or system failure events. The full Bayesian approach also allows the highest-level data that are usually available for existing facilities to be automatically propagated to lower levels. A simple example illustrates the proposed approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.

A MULTILEVEL MODEL TO ADDRESS BATCH EFFECTS IN COPY NUMBER ESTIMATION USING SNP ARRAYS

Submicroscopic changes in chromosomal DNA copy number dosage are common and have been implicated in many heritable diseases and cancers. Recent high-throughput technologies have a resolution that permits the detection of segmental changes in DNA copy number that span thousands of basepairs across the genome. Genome-wide association studies (GWAS) may simultaneously screen for copy number-phenotype and SNP-phenotype associations as part of the analytic strategy. However, genome-wide array analyses are particularly susceptible to batch effects as the logistics of preparing DNA and processing thousands of arrays often involves multiple laboratories and technicians, or changes over calendar time to the reagents and laboratory equipment. Failure to adjust for batch effects can lead to incorrect inference and requires inefficient post-hoc quality control procedures that exclude regions that are associated with batch. Our work extends previous model-based approaches for copy number estimation by explicitly modeling batch effects and using shrinkage to improve locus-specific estimates of copy number uncertainty. Key features of this approach include the use of diallelic genotype calls from experimental data to estimate batch- and locus-specific parameters of background and signal without the requirement of training data. We illustrate these ideas using a study of bipolar disease and a study of chromosome 21 trisomy. The former has batch effects that dominate much of the observed variation in quantile-normalized intensities, while the latter illustrates the robustness of our approach to datasets where as many as 25% of the samples have altered copy number. Locus-specific estimates of copy number can be plotted on the copy-number scale to investigate mosaicism and guide the choice of appropriate downstream approaches for smoothing the copy number as a function of physical position. The software is open source and implemented in the R package CRLMM available at Bioconductor (http:www.bioconductor.org).

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

ON MARGINALIZED MULTILEVEL MODELS AND THEIR COMPUTATION

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate this approach on a cerebrovascular deficiency crossover trial.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.