Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.

Diferentes métodos de aglutinação para melhoria de processos com múltiplas respostas

Pós-graduação em Engenharia Mecânica - FEG

Damage detection in beams by using artificial neural networks and dynamical parameters

In this paper is presented a multilayer perceptron neural network combined with the Nelder-Mead Simplex method to detect damage in multiple support beams. The input parameters are based on natural frequencies and modal flexibility. It was considered that only a number of modes were available and that only vertical degrees of freedom were measured. The reliability of the proposed methodology is assessed from the generation of random damages scenarios and the definition of three types of errors, which can be found during the damage identification process. Results show that the methodology can reliably determine the damage scenarios. However, its application to large beams may be limited by the high computational cost of training the neural network.

An ordinal logistic regression model with misclassification of the outcome variable and categorical covariate

Ordinal outcomes are frequently employed in diagnosis and clinical trials. Clinical trials of Alzheimer's disease (AD) treatments are a case in point using the status of mild, moderate or severe disease as outcome measures. As in many other outcome oriented studies, the disease status may be misclassified. This study estimates the extent of misclassification in an ordinal outcome such as disease status. Also, this study estimates the extent of misclassification of a predictor variable such as genotype status. An ordinal logistic regression model is commonly used to model the relationship between disease status, the effect of treatment, and other predictive factors. A simulation study was done. First, data based on a set of hypothetical parameters and hypothetical rates of misclassification was created. Next, the maximum likelihood method was employed to generate likelihood equations accounting for misclassification. The Nelder-Mead Simplex method was used to solve for the misclassification and model parameters. Finally, this method was applied to an AD dataset to detect the amount of misclassification present. The estimates of the ordinal regression model parameters were close to the hypothetical parameters. β1 was hypothesized at 0.50 and the mean estimate was 0.488, β2 was hypothesized at 0.04 and the mean of the estimates was 0.04. Although the estimates for the rates of misclassification of X1 were not as close as β1 and β2, they validate this method. X 1 0-1 misclassification was hypothesized as 2.98% and the mean of the simulated estimates was 1.54% and, in the best case, the misclassification of k from high to medium was hypothesized at 4.87% and had a sample mean of 3.62%. In the AD dataset, the estimate for the odds ratio of X 1 of having both copies of the APOE 4 allele changed from an estimate of 1.377 to an estimate 1.418, demonstrating that the estimates of the odds ratio changed when the analysis includes adjustment for misclassification. ^

A hybrid Particle Swarm Optimization - Simplex algorithm (PSOS) for structural damage identification

This study proposes a new PSOS-model based damage identification procedure using frequency domain data. The formulation of the objective function for the minimization problem is based on the Frequency Response Functions (FRFs) of the system. A novel strategy for the control of the Particle Swarm Optimization (PSO) parameters based on the Nelder-Mead algorithm (Simplex method) is presented; consequently, the convergence of the PSOS becomes independent of the heuristic constants and its stability and confidence are enhanced. The formulated hybrid method performs better in different benchmark functions than the Simulated Annealing (SA) and the basic PSO (PSO(b)). Two damage identification problems, taking into consideration the effects of noisy and incomplete data, were studied: first, a 10-bar truss and second, a cracked free-free beam, both modeled with finite elements. In these cases, the damage location and extent were successfully determined. Finally, a non-linear oscillator (Duffing oscillator) was identified by PSOS providing good results. (C) 2009 Elsevier Ltd. All rights reserved

Utilização de pulsos de radiofrequência fortemente modulados no processamento de informação quântica via ressonância magnética nuclear

Nesta dissertação apresentamos um trabalho de desenvolvimento e utilização de pulsos de radiofreqüência modulados simultaneamente em freqüência, amplitude e fase (pulsos fortemente modulados, SMP, do inglês Strongly Modulated Pulses) para criar estados iniciais e executar operações unitárias que servem como blocos básicos para processamento da informação quântica utilizando Ressonância Magnética Nuclear (RMN). As implementações experimentais foram realizas em um sistema de 3 q-bits constituído por spins nucleares de Césio 133 (spin nuclear 7/2) em uma amostra de cristal líquido em fase nemática. Os pulsos SMP´s foram construídos teoricamente utilizando um programa especialmente desenvolvido para esse fim, sendo o mesmo baseado no processo de otimização numérica Simplex Nelder-Mead. Através deste programa, os pulsos SMP foram otimizados de modo a executarem as operações lógicas desejadas com durações consideravelmente menores que aquelas realizadas usando o procedimento usual de RMN, ou seja, seqüências de pulsos e evoluções livres. Isso tem a vantagem de reduzir os efeitos de descoerência decorrentes da relaxação do sistema. Os conceitos teóricos envolvidos na criação dos SMPs são apresentados e as principais dificuldades (experimentais e teóricas) que podem surgir devido ao uso desses procedimentos são discutidas. Como exemplos de aplicação, foram produzidos os estados pseudo-puros usados como estados iniciais de operações lógicas em RMN, bem como operações lógicas que foram posteriormente aplicadas aos mesmos. Utilizando os SMP\'s também foi possível realizar experimentalmente os algoritmos quânticos de Grover e Deutsch-Jozsa para 3 q-bits. A fidelidade das implementações experimentais foi determinadas utilizando as matrizes densidade experimentais obtidas utilizando um método de tomografia da matriz densidade previamente desenvolvido.

Aplicação de retroanálise em obras subterrâneas

Dissertação para obtenção do Grau de Mestre em Engenharia Civil - Perfil Geotecnia

Optimização de esforços em estruturas: influência da localização e rigidez dos apoios

Dissertação para obtenção do Grau de Mestre em Engenharia Civil - Perfil Estruturas

Technical Note: Dissolved organic matter fluorescence a finite mixture approach to deconvolve excitation-emission matrices

The analysis of the shape of excitation-emission matrices (EEMs) is a relevant tool for exploring the origin, transport and fate of dissolved organic matter (DOM) in aquatic ecosystems. Within this context, the decomposition of EEMs is acquiring a notable relevance. A simple mathematical algorithm that automatically deconvolves individual EEMs is described, creating new possibilities for the comparison of DOM fluorescence properties and EEMs that are very different from each other. A mixture model approach is adopted to decompose complex surfaces into sub-peaks. The laplacian operator and the Nelder-Mead optimisation algorithm are implemented to individuate and automatically locate potential peaks in the EEM landscape. The EEMs of a simple artificial mixture of fluorophores and DOM samples collected in a Mediterranean river are used to describe the model application and to illustrate a strategy that optimises the search for the optimal output.

On the optical flow model selection through metaheuristics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Studio di un algoritmo di controllo di temperatura per ganasce termosigillanti in macchine per packaging

Gli obiettivi dell'elaborato sono lo studio e la programmazione di un algoritmo di controllo di temperatura per le superfici termosaldanti di macchine per il packaging (confezionatrici in film a file multiple) prodotte dal committente, OMAG srl. L'algoritmo è implementato tramite il software SoMachineMotion v.4.2, prodotto da Schneider Electrics spa. Il controllo è di tipo in anello chiuso in retroazione, con temocoppie e resistenze di riscaldamento con modulazione PWM. Ci si è inizialmente occupati di testare su banco prova varie tipologie di regolatori: a relay, a isteresi, a ricerca diretta del duty cycle, TBH, con approccio misto TBH/integratore di Clegg, PID. I diversi metodi di regolazione sono stati valutati sulla base di una serie di metri di giudizio (precisione dell'inseguimento, prestazioni statiche e dinamiche, flessibilità, peso computazionale, facilità implementativa), pesati secondo i requisiti imposti dal committente. Le metodologie selezionate sono state PID e TBH/Clegg integrator; quest'ultima ha dato risultati assai soddisfacenti, pur essendo un metodo monoparametrico. Si sono quindi studiate diverse modalità per la taratura del regolatore PID, in particolare: tuning in anello chiuso con metodo a relay per la fase di pretuning, algoritmo di Nelder-Mead, per la ricerca diretta continua dei valori che minimizzano l'errore integrale, per un selftuning adattivo. Si è infine proceduto ad implementare le soluzioni individuate in un software robusto, che rispetti gli standard del settore e si sono inoltre sviluppate una serie di funzionalità aggiuntive, quali: modulazione software PWM, preriscaldamento, handling errori/warning, filtraggio segnali in/out. Si è addizionalmente sviluppato un modello matematico predittivo dell'evoluzione del sistema, che potrebbe servire, in un futuro sviluppo, come base per un controllo model-based in cascata al controllo in retroazione studiato.

A novel hybrid swarm based approach for curriculum based course timetabling problem

This work applies a hybrid approach in solving the university curriculum-based course timetabling problem as presented as part of the 2nd International Timetabling Competition 2007 (ITC2007). The core of the hybrid approach is based on an artificial bee colony algorithm. Past methods have applied artificial bee colony algorithms to university timetabling problems with high degrees of success. Nevertheless, there exist inefficiencies in the associated search abilities in term of exploration and exploitation. To improve the search abilities, this work introduces a hybrid approach entitled nelder-mead great deluge artificial bee colony algorithm (NMGD-ABC) where it combined additional positive elements of particle swarm optimization and great deluge algorithm. In addition, nelder-mead local search is incorporated into the great deluge algorithm to further enhance the performance of the resulting method. The proposed method is tested on curriculum-based course timetabling as presented in the ITC2007. Experimental results reveal that the proposed method is capable of producing competitive results as compared with the other approaches described in literature

USO DA EQUAÇÃO DE ESTADO DE PENG-ROBINSON COM REGRA DE MISTURA DEPENDENTE DA COMPOSIÇÃO NA PREDIÇÃO DO EQUILÍBRIO DE FASES DO SISTEMA TERNÁRIO CO2-LIMONENO-CITRAL

Dados de equilíbrio de fases a pressões elevadas dos sistemas binários CO2-Limoneno e CO2-Citral e do sistema ternário CO2-Limoneno-Citral foram coletados da literatura e usados na modelagem termodinâmica que emprega a equação de estado de PENG-ROBINSON [1] com: 1) Regra de mistura clássica; 2) Regra de mistura dependente da composição de STRYJEK & VERA [2]. Os parâmetros de interação binária entre CO2-Limoneno e CO2-Citral foram obtidos pelo ajuste dos modelos a dados experimentais, fazendo uso de dois programas computacionais, os quais envolvem a minimização de uma função objetivo, pelo método Simplex de NELDER & MEAD (3), que foi escrita em termos dos desvios relativos entre os pontos experimentais e os calculados pelos modelos. O equilíbrio de fases do sistema ternário foi calculado utilizando-se os parâmetros de interação binária ajustados previamente e considerando parâmetros nulos entre os componentes Limoneno e Citral. A análise dos resultados indica, para as condições supercríticas, que os dois modelos foram capazes de predizer qualitativamente o sistema ternário, fornecendo resultados compatíveis, em ordem de grandeza, com os valores experimentais.