This paper will analyze the effects of using hybrid optimization methods for optimizing objective functions that are determined by computational fluid dynamics solvers for compressible viscous flow for optimal design of airfoils. Previous studies on this topic by the authors had examined the application of deterministic optimization methods and stochastic optimization methods such as Simulated Annealing and Simultaneous Perturbation Stochastic Analysis (SPSA). The studies indicated that SPSA method has a greater or equal efficiency as compared with SA method in reaching optimal airfoil designs for the design problem in question. However, in some situations SPSA method has a tendency to demonstrate an oscillatory behavior in the vicinity of a local optima. To overcome this tendency, a hybrid method designed to take full advantage of SPSA’s high rate of reduction of the objective function at the inception of the design process to drive the design cycles towards the optimal zone at first, and then combining with other methods to perform the final stages of the convergence towards the optimal solutions is considered. SPSA method has been combined with the gradient-based Broydon-Fletcher-Goldfarb-Shanno (BFGS) method as well as Simulated Annealing method for the transonic inverse airfoil design problem that is concerned with the specification of a target airfoil surface pressure distribution and starting from an initial guess of an airfoil shape, the target airfoil shape is reached by way of minimization of a quantity that depends on the difference between the target and current airfoil surface pressure distribution. For a typical transonic flow test case, the effects of using hybrid optimization techniques such as SPSA+BFGS and SPSA+SA as opposed to using SPSA alone can be seen in Figure 1. After 800 design cycles using SPSA, the hybrid SPSA+SA method took 2521 function evaluations of SA while the SPSA+BFGS method took 271 function evaluations to reach similar values which are much better than that reached by using SPSA alone in the entire minimization process. Results indicate that both of the two hybrid methods have capability to find a global optimum more efficiently than the SPSA method. The paper will address issues related to hybridization and its impact on the optimal airfoil shape designs in various contexts. / Singapore-MIT Alliance (SMA)

Analysis of flow and solute transport problem in porous media are affected by uncertainty inbuilt both in boundary conditions and spatial variability in system parameters. The experimental investigation reveals that the parameters may vary in various scales by several orders. These affect the solute plume characteristics in field-scale problem and cause uncertainty in the prediction of concentration. The main focus of the present thesis is to analyze the probabilistic behavior of solute concentration in three dimensional(3-D) heterogeneous porous media. The framework for the probabilistic analysis has been developed using perturbation approach for both spectral based analytical and finite element based numerical method. The results of the probabilistic analysis are presented either in terms of solute plume characteristics or prediction uncertainty of the concentration. After providing a brief introduction on the role of stochastic analysis in subsurface hydrology in chapter 1, a detailed review of the literature is presented to establish the existing state-of-art in the research on the probabilistic analysis of flow and transport in simple and complex heterogeneous porous media in chapter 2. The literature review is mainly focused on the methods of solution of the stochastic differential equation. Perturbation based spectral method is often used for probabilistic analysis of flow and solute transport problem. Using this analytical method a nonlocal equation is solved to derive the expression of the spatial plume moments. The spatial plume moments represent the solute movement, spreading in an average sense. In chapter 3 of the present thesis, local dispersivity if also assumed to be random space function along with hydraulic conductivity. For various correlation coefficients of the random parameters, the results in terms of the field scale effective dispersivity are presented to demonstrate the effect of local dispersivity variation in space. The randomness of local dispersivity is found to reduce the effective fields scale dispersivity. The transverse effective macrodispersivity is affected more than the longitudinal effective macrodispersivity due to random spatial variation of local dispersivity. The reduction in effective field scale longitudinal dispersivity is more for positive correlation coefficient. The applicability of the analytical method, which is discussed in earlier chapter, is limited to the simple boundary conditions. The solution by spectral method in terms of statistical moments of concentration as a function of space and time, require higher dimensional integration. Perturbation based stochastic finite element method(SFEM) is an alternative method for performing probabilistic analysis of concentration. The use of this numerical method for performing probabilistic analysis of concentration. The use of this numerical method is non common in the literature of stochastic subsurface hydrology. The perturbation based SFEM which uses FEM for spatial discretization of the steady state flow and Laplace transform for the solute transport equation, is developed in chapter 4. The SFEM is formulated using Taylor series of the dependent variable upto second-order term. This results in second-order accurate mean and first-order accurate standard deviation of concentration. In this study the governing medium properties viz. hydraulic Conductivity, dispersivity, molecular diffusion, porosity, sorption coefficient and decay coefficient are considered to vary randomly in space. The accuracy of results and computational efficiency of the SFEM are compared with Monte Carle Simulation method(MCSM) for both I-D and 3-D problems. The comparison of results obtained hby SFEM and MCSM indicates that SFEM is capable in providing reasonably accurate mean and standard deviation of concentration. The Laplace transform based SFEM is simpler and advantageous since it does not require any stability criteria for choosing the time step. However it is not applicable for nonlinear transport problems as well as unsteady flow conditions. In this situation, finite difference method is adopted for the time discretization. The first part of the Chapter 5, deals with the formulation of time domain SFEM for the linear solute transport problem. Later the SFEM is extended for a problem which involve uncertainty of both system parameters and boundary/source conditions. For the flow problem, the randomness in the boundary condition is attributed by the random spatial variation of recharge at the top of the domain. The random recharge is modeled using mean, standard deviation and 2-D spatial correlation function. It is observed that even for the deterministic recharge case, the behavior of prediction uncertainty of concentration in the space is affected significantly due to the variation of flow field. When the effect of randomness of recharge condition is included, the standard deviation of concentration increases further. For solute transport, the concentration input at the source is modeled as a time varying random process. Two types of random source at the source is modeled as a time varying random process. Two types of random source condition are considered, firstly the amount of solute mass released at uniform time interval is random and secondly the source is treated as a Poission process. For the case of multiple random mass releases, the stochastic response function due to stochastic system is obtained by using SFEM. Comparing the results for the two type of random sources, it sis found that the prediction uncertainty is more when it is modeled as a Poisson process. The probabilistic analysis of nonlinear solute transport problem using MCSM is often requires large computational cost. The formulation of the alternative efficient method, SFEM, for nonlinear solute transport problem is presented in chapter 6. A general Langmuir-Freundlich isotherm is considered to model the equilibrium mass transfer between aqueous and sorbed phase. In the SFEM formulation, which uses the Taylor Series expansion, the zeroth-order derivatives of concentration are obtained by solving nonlinear algebraic equation. The higher order derivatives are obtained by solving linear equation. During transport, the nonlinear sorbing solutes is characterized by sharp solute fronts with a traveling wave behavior. Due to this the prediction uncertainty is significantly higher. The comparison of accuracy and computational efficiency of SFEM with MCSM for I-D and 3-D problems, reveals that the performance of SFEM for nonlinear problem is good and similar to the linear problem. In Chapter 7, the nonlinear SFEM is extended for probabilistic analysis of biodegrading solute, which is modeled by a set of PDEs coupled with nonlinear Monod type source/sink terms. In this study the biodegradation problem involves a single solute by a single class of microorganisms coupled with dynamic microbial growth is attempted using this methods. The temporal behavior of mean and standard deviation of substrate concentration are not monotonic, they show peaks before reaching lower steady state value. A comparison between the SFEM and MCSM for the mean and standard deviation of concentration is made for various stochastic cases of the I-D problem. In most of the cases the results compare reasonably well. The analysis of probabilistic behavior of substrate concentration for different correlation coefficient between the physical parameters(hydraulic conductivity, porosity, dispersivity and diffusion coefficient) and the biological parameters(maximum substrate utilization rate and the coefficient of cell decay) is performed. It is observed that the positive correlation between the two sets of parameters results in a lower mean and significantly higher standard deviation of substrate concentration. In the previous chapters, the stochastic analysis pertaining to the prediction uncertainty of concentration has been presented for simple problem where the system parameters are modeled as statistically homogeneous random. The experimental investigations in a small watershed, point towards a complex in geological substratum. It has been observed through the 2-D electrical resistivity imaging that the interface between the layers of high conductive weathered zone and low conductive clay is very irregular and complex in nature. In chapter 8 a theoretical model based on stochastic approach is developed to stimulate the complex geological structure of the weathered zone, using the 2-D electrical image. The statistical parameters of hydraulic conductivity field are estimated using the data obtained from the Magnetic Resonance Sounding(MRS) method. Due to the large complexity in the distribution of weathered zone, the stochastic analysis of seepage flux has been carried out by using MCSM. A batter characterization of the domain based on sufficient experimental data and suitable model of the random conductivity field may help to use the efficient SFEM. The flow domain is modeled as (i) an unstructured random field consisting of a single material with spatial heterogeneity, and (ii) a structured random field using 2-D electrical imaging which is composed of two layers of different heterogeneous random hydraulic properties. The simulations show that the prediction uncertainty of seepage flux is comparatively less when structured modeling framework is used rather than the unstructured modeling. At the end, in chapter 9 the important conclusions drawn from various chapters are summarized.

The aim of this thesis is to estimate the volatility function of continuoustime stochastic models. The estimation of the volatility of the following wellknown international stock market indexes is presented as an application: Dow Jones Industrial Average, Standard and Poor’s 500, NIKKEI 225, CAC 40, DAX 30, FTSE 100 and IBEX 35. This estimation is studied from two different perspectives: a) assuming that the volatility of the stock market indexes displays shortrange dependence (SRD), and b) extending the previous model for processes with longrange dependence (LRD), intermediaterange dependence (IRD) or SRD. Under the efficient market hypothesis (EMH), the compatibility of the Vasicek, the CIR, the Anh and Gao, and the CKLS models with the stock market indexes is being tested. Nonparametric techniques are presented to test the affinity of these parametric volatility functions with the volatility observed from the data. Under the assumption of possible statistical patterns in the volatility process, a new estimation procedure based on the Whittle estimation is proposed. This procedure is theoretically and empirically proven. In addition, its application to the stock market indexes provides interesting results.

Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 2003. / "January 2003" Includes bibliographical references (leaves 120-129).

Dans cette Thèse, la conception robuste avec un modèle incertain d'un système électromécanique avec vibro-impact est fait. Le système électromécanique est constitué d'un chariot, dont le mouvement est excité par un moteur à courant continu et un marteau embarqué dans ce chariot. Le marteau est relié au chariot par un ressort non linéaire et par un amortisseur linéaire, de façon qu'un mouvement relatif existe entre eux. Une barrière flexible linéaire, placé à l'extérieur du chariot limite les mouvements de marteau. En raison du mouvement relatif entre le marteau et la barrière, impacts peuvent se produire entre ces deux éléments. Le modèle du système développé prend en compte l'influence du courant continu moteur dans le comportement dynamique du système. Certains paramètres du système sont incertains, tels comme les coefficients de rigidité et d'amortissement de la barrière flexible. L'objectif de la Thèse est de réaliser une optimisation de ce système électromécanique par rapport aux paramètres de conception afin de maximiser l'impact puissance sous la contrainte que la puissance électrique consommée par le moteur à courant continu est inférieure à une valeur maximale. Pour choisir les paramètres de conception dans le problème d'optimisation, une analyse de sensibilité a été réalisée afin de définir les paramètres du système les plus sensibles. L'optimisation est formulée dans le cadre de la conception robuste en raison de la présence d'incertitudes dans le modèle. Les lois de probabilités liées aux variables aléatoires du problème sont construites en utilisant le Principe du Maximum l'Entropie et les statistiques de la réponse stochastique du système sont calculées en utilisant la méthode de Monte Carlo. L'ensemble d'équations non linéaires sont présentés, et un solveur temporel adapté est développé. Le problème d'optimisation non linéaire stochastique est résolu pour différents niveaux d'incertitudes, et aussi pour le cas déterministe. Les résultats sont différents, ce qui montre l'importance de la modélisation stochastique / In this Thesis, the robust design with an uncertain model of a vibro-impact electromechanical system is done. The electromechanical system is composed of a cart, whose motion is excited by a DC motor (motor with continuous current), and an embarked hammer into this cart. The hammer is connected to the cart by a nonlinear spring component and by a linear damper, so that a relative motion exists between them. A linear flexible barrier, placed outside of the cart, constrains the hammer movements. Due to the relative movement between the hammer and the barrier, impacts can occur between these two elements. The developed model of the system takes into account the influence of the DC motor in the dynamic behavior of the system. Some system parameters are uncertain, such as the stiffness and the damping coefficients of the flexible barrier. The objective of the Thesis is to perform an optimization of this electromechanical system with respect to design parameters in order to maximize the impact power under the constraint that the electric power consumed by the DC motor is lower than a maximum value. To chose the design parameters in the optimization problem, an sensitivity analysis was performed in order to define the most sensitive system parameters. The optimization is formulated in the framework of robust design due to the presence of uncertainties in the model. The probability distributions of random variables are constructed using the Maximum Entropy Principle and statistics of the stochastic response of the system are computed using the Monte Carlo method. The set of nonlinear equations are presented, and an adapted time domain solver is developed. The stochastic nonlinear constrained design optimization problem is solved for different levels of uncertainties, and also for the deterministic case. The results are different and this show the importance of the stochastic modeling

A produção de frango de corte tem impressionado pelo dinamismo e pela competência conquistada nas últimas décadas, destacando-se o Brasil como o segundo maior produtor dessa proteína animal. O ganho de produtividade, associado à coordenação da cadeia avícola, colocou o País como um dos mais eficientes produtores. Entretanto, a significativa especialização da atividade tende a excluir do processo produtivo os pequenos avicultores e os produtores menos eficientes. Assim, o estudo buscou medir a eficiência econômica dos produtores de frango de corte das regiões Sul e Centro-Oeste do Brasil, identificando quais fatores influenciam essa medida de desempenho. Para isso, usou-se uma função fronteira de lucro estocástica em um estágio (modelo 2) em que os coeficientes da fronteira e os efeitos da ineficiência são obtidos simultaneamente, assumindo que os termos de erro não são identicamente distribuídos. Concluiu-se que para a região Sul, o preço da mão-de-obra contratada interfere significativamente na lucratividade das unidades produtivas, o que seria um dos fatores associados ao maior uso do trabalho familiar no desenvolvimento das atividades. Além disso, os resultados sugerem a presença de uma melhor utilização das áreas ocupadas com a produção avícola. Os efeitos da ineficiência são sentidos principalmente no baixo nível de educação dos que tomam as decisões e nos índices elevados de conversão alimentar. Já no Centro-Oeste, os coeficientes indicaram que o maior uso de mão-de-obra familiar poderia elevar a lucratividade dos produtores. Pelo fato de ser uma região relativamente nova e possuir condições favoráveis ao investimento em capital e tecnologia, estaria indicando um maior lucro na atividade. Não se identificou ganho de escala por meio do modelo estocástico. Embora não se observa uma tendência contínua associada à escala de eficiência, no Centro-Oeste parece existirem ganhos de eficiência relevante nos estratos de médio e alto escala de produção para os padrões regionais. / The dynamism and ability acquired through the last decade by the broiler production is very impressive. The productivity rate gain associated to the good management of poultry chain in Brazil led the country to be the second biggest producer of this animal’s protein. However, the significant specialization of this activity tend to exclude the smaller producers and those who are lesser efficient in the productive process. In view of that, this study intends to precise the economic efficiency of the broiler producers in the Southerner and Center-Southerner regions of Brazil. For that, the main factors that influence the economic efficiency were identified. To reach those results, it was considered the stochastic profit function in a stage (model 2) where the coefficients of the frontier and the inefficiency effects are obtained simultaneously, since the terms of error are not identical distributing. It was possible to conclude that in the Southerner region of Brazil, the contracted labor force influence significantly the profitability of the productive farms. That’s one of the factors that explain the great use of the familiar labor force in that region. Moreover, the results pointed a better utilization of the broiler producing areas in Brazil. The effects of the inefficiency are present mainly in the producers and players with low educational level, and also in the high food conversion ratio. In the Center-Westerner of Brazil, the coefficients pointed that the better use of the familiar manpower could raise the probability of the producers. For been a new region that present positive conditions for the investments in capital and technology, it also obtained a larger profit with the activity. It was not identified gains by the stochastic model. None successively trend associated to the efficiency scale were pointed in the Center-Westerner of Brazil. Even so, the region shows efficiency gains in the middle and high scales of production in regional terms.

Orientador: Pedro Jose Catuogno / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-09T00:50:27Z (GMT). No. of bitstreams: 1 Stelmastchuk_SimaoNicolau_D.pdf: 537546 bytes, checksum: f06c81c8cd3b758c84d267af8373abdd (MD5) Previous issue date: 2007 / Resumo: Neste trabalho estudamos os martingales no fibrado de bases e suas relações com os martingales no fibrado tangente. Caracterizamos as aplicações harmônicas a valores no fibrado de bases e as relacionamos com as aplicações harmônicas a valores no fibrado tangente. Numa segunda parte estudamos a harmonicidade das seções de um fibrado via geometria estocástica. Seja P(M;G) um fibrado principal e E(M;N; G; P) um fibrado associado a P(M;G). Entre outros resultados obtemos que: uma seção s : M - E é harmônica se, e somente se, o seu levantamento eqüivariante Fs : P - N é horizontalmente harmônico; e se a ação à esquerda de G × N em N não fixa pontos então não existe seção s : M - E harmônica ou toda seção harmônica é nula / Abstract: Neste trabalho estudamos os martingales no fibrado de bases e suas relações com os martingales no fibrado tangente. Caracterizamos as aplicações harmônicas a valores no fibrado de bases e as relacionamos com as aplicações harmônicas a valores no fibrado tangente. Numa segunda parte estudamos a harmonicidade das seções de um fibrado via geometria estocástica. Seja P(M;G) um fibrado principal e E(M;N; G; P) um fibrado associado a P(M;G). Entre outros resultados obtemos que: uma seção s : M - E é harmônica se, e somente se, o seu levantamento eqüivariante Fs : P - N é horizontalmente harmônico; e se a ação à esquerda de G × N em N não fixa pontos então não existe seção s : M - E harmônica ou toda seção harmônica é nula / Doutorado / Geometria Estocastica / Doutor em Matemática

Dans cette Thèse, la conception robuste avec un modèle incertain d'un système électromécanique avec vibro-impact est fait. Le système électromécanique est constitué d'un chariot, dont le mouvement est excité par un moteur à courant continu et un marteau embarqué dans ce chariot. Le marteau est relié au chariot par un ressort non linéaire et par un amortisseur linéaire, de façon qu'un mouvement relatif existe entre eux. Une barrière flexible linéaire, placé à l'extérieur du chariot limite les mouvements de marteau. En raison du mouvement relatif entre le marteau et la barrière, impacts peuvent se produire entre ces deux éléments. Le modèle du système développé prend en compte l'influence du courant continu moteur dans le comportement dynamique du système. Certains paramètres du système sont incertains, tels comme les coefficients de rigidité et d'amortissement de la barrière flexible. L'objectif de la Thèse est de réaliser une optimisation de ce système électromécanique par rapport aux paramètres de conception afin de maximiser l'impact puissance sous la contrainte que la puissance électrique consommée par le moteur à courant continu est inférieure à une valeur maximale. Pour choisir les paramètres de conception dans le problème d'optimisation, une analyse de sensibilité a été réalisée afin de définir les paramètres du système les plus sensibles. L'optimisation est formulée dans le cadre de la conception robuste en raison de la présence d'incertitudes dans le modèle. Les lois de probabilités liées aux variables aléatoires du problème sont construites en utilisant le Principe du Maximum l'Entropie et les statistiques de la réponse stochastique du système sont calculées en utilisant la méthode de Monte Carlo. L'ensemble d'équations non linéaires sont présentés, et un solveur temporel adapté est développé. Le problème d'optimisation non linéaire stochastique est résolu pour différents niveaux d'incertitudes, et aussi pour le cas déterministe. Les résultats sont différents, ce qui montre l'importance de la modélisation stochastique / In this Thesis, the robust design with an uncertain model of a vibro-impact electromechanical system is done. The electromechanical system is composed of a cart, whose motion is excited by a DC motor (motor with continuous current), and an embarked hammer into this cart. The hammer is connected to the cart by a nonlinear spring component and by a linear damper, so that a relative motion exists between them. A linear flexible barrier, placed outside of the cart, constrains the hammer movements. Due to the relative movement between the hammer and the barrier, impacts can occur between these two elements. The developed model of the system takes into account the influence of the DC motor in the dynamic behavior of the system. Some system parameters are uncertain, such as the stiffness and the damping coefficients of the flexible barrier. The objective of the Thesis is to perform an optimization of this electromechanical system with respect to design parameters in order to maximize the impact power under the constraint that the electric power consumed by the DC motor is lower than a maximum value. To chose the design parameters in the optimization problem, an sensitivity analysis was performed in order to define the most sensitive system parameters. The optimization is formulated in the framework of robust design due to the presence of uncertainties in the model. The probability distributions of random variables are constructed using the Maximum Entropy Principle and statistics of the stochastic response of the system are computed using the Monte Carlo method. The set of nonlinear equations are presented, and an adapted time domain solver is developed. The stochastic nonlinear constrained design optimization problem is solved for different levels of uncertainties, and also for the deterministic case. The results are different and this show the importance of the stochastic modeling

No description available.

<div>In the past two decades, the pharmaceutical industry has been engaged in modernization of its drug development and manufacturing strategies, spurred onward by changing market pressures, regulatory encouragement, and technological advancement. Concomitant with these changes has been a shift toward new modalities of manufacturing in support of patient-centric medicine and on-demand production. To achieve these objectives requires manufacturing platforms which are both flexible and scalable, hence the interest in development of small-scale, continuous processes for synthesis, purification and drug product production. Traditionally, the downstream steps begin with a crystalline drug powder – the effluent of the final purification steps – and convert this to tablets or capsules through a series of batch unit operations reliant on powder processing. As an alternative, additive manufacturing technologies provide the means to circumvent difficulties associated with dry powder rheology, while being inherently capable of flexible production.</div><div>Through the combination of physical knowledge, experimental work, and data-driven methods, a framework was developed for ink formulation and process operation in drop-on-demand manufacturing with non-Brownian suspensions. Motivated by the challenges at hand, application of novel computational image analysis techniques yielded insight into the effects of non-Brownian particles and fluid properties on rheology. Furthermore, the extraction of modal and statistical information provided insight into the stochastic events which appear to play a notable role in drop formation from such suspensions. These computer vision algorithms can readily be applied by other researchers interested in the physics of drop coalescence and breakup in order to further modeling efforts.</div><div>Returning to the realm of process development to deal with challenges of monitoring and quality control initiated by suspension-based manufacturing, these machine vision algorithms were combined with Bayesian modeling to enact a probabilistic control strategy at the level of each dosage unit by utilizing the real-time image data acquired by an online process image sensor. Drawing upon a large historical database which spanned a wide range of conditions, a hierarchical modeling approach was used to incorporate the various sources of uncertainty inherent to the manufacturing process and monitoring technology, therefore providing more reliable predictions for future data at in-sample and out-of-sample conditions.</div><div>This thesis thus contributes advances in three closely linked areas: additive manufacturing of solid oral drug products, computer vision methods for event recognition in drop formation, and Bayesian hierarchical modeling to predict the probability that each dosage unit produced is within specifications.</div><div><br></div>