Optimal operation of plants is becoming more important due to increasing competition and small and changing profit margins for many products. One major reason has been the realization by industry that potentially large savings can be achieved by improving processes. Growth rates and profitability are much lower now, and international competition has increased greatly. The industry is faced with a need to manufacture quality products, while minimizing production costs and complying with a variety of safety and environmental regulations. As industry is confronted with the challenge of moving toward a clearer and more sustainable path of production, new technologies are needed to achieve industrial requirements. In this research, a new methodology is proposed to integrate so-called new technologies into existing processes. Research shows that the new technologies must be carefully selected and adopted to match the complex requirements of an existing process. The new proposed methodology is based on four major steps. If the improvement in the process is not sufficient to meet business needs, new technologies can be considered. Application of a new technology is always perceived as a potential threat; therefore, financial risk assessment and reliability risk analysis help alleviate risk of investment. An industrial case study from the literature was selected to implement and validate the new methodology. The case study is a planning problem to plan the layout or design of a fleet of generating stations owned and operated by the electric utility company, Ontario Power Generation (OPG). The impact of new technology integration on the performance of a power grid consisting of a variety of power generation plants was evaluated. The reduction in carbon emissions is projected to be accomplished through a combination of fuel switching, fuel balancing and switching to new technologies: carbon capture and sequestration. The fuel-balancing technique is used to decrease carbon emissions by adjusting the operation of the fleet of existing electricity-generating stations; the technique of fuel-switching involves switching from carbon-intensive fuels to less carbon-intensive fuels, for instance, switching from coal to natural gas; carbon capture and sequestration are applied to meet carbon emission reduction requirements. Existing power plants with existing technologies consist of fossil fuel stations, nuclear stations, hydroelectric stations, wind power stations, pulverized coal stations and a natural gas combined cycle, while hypothesized power plants with new technologies include solar stations, wind power stations, pulverized coal stations, a natural gas combined cycle and an integrated gasification combined cycle with and without capture and sequestration. The proposed methodology includes financial risk management in the framework of a two stage stochastic programme for energy planning under uncertainty: demands and fuel price. A deterministic mixed integer linear programming formulation is extended to a two-stage stochastic programming model in order to take into account random parameters, which have discrete and finite probabilistic distributions. Thus, the expected value of the total costs of power generation is minimized, while the objective of carbon emission reduction is achieved. Furthermore, conditional value at risk (CVaR), a most preferable risk measure in the financial risk management, is incorporated within the framework of two-stage mixed integer programming. The mathematical formulation, which is called mean-risk model, is applied for the purpose of minimizing expected value. The process is formulated as a mixed integer linear programming model, implemented in GAMS (General Algebraic Modeling System) and solved using the CPLEX algorithm, a commercial solver embedded in GAMS. The computational results demonstrate the effectiveness of the proposed new methodology. The optimization model is applied to an existing Ontario Power Generation (OPG) fleet. Four planning scenarios are considered: a base load demand, a 1.0% growth rate in demand, a 5.0% growth rate in demand, a 10% growth rate in demand and a 20% growth rate in demand. A sensitivity analysis study is accomplished in order to investigate the effect of parameter uncertainties, such as uncertain factors on coal price and natural gas price. The optimization results demonstrate how to achieve the carbon emission mitigation goal with and without new technologies, while minimizing costs affects the configuration of the OPG fleet in terms of generation mix, capacity mix and optimal configuration. The selected new technologies are assessed in order to determine the risks of investment. Electricity costs with new technologies are lower than with the existing technologies. 60% CO2 reduction can be achieved at 20% growth in base load demand with new technologies. The total cost of electricity increases as we increase CO2 reduction or increase electricity demand. However, there is no significant change in CO2 reduction cost when CO2 reduction increases with new technologies. Total cost of electricity increases when fuel price increases. The total cost of electricity increases with financial risk management in order to lower the risk. Therefore, more electricity is produced for the industry to be on the safe side.

[pt] O trabalho tem como objetivo desenvolver uma formulação matemática para o problema de projeto de redes logísticas que seja integrado e flexível de modo a contemplar escolhas de localização de instalações, transporte, produção e estoques. O projeto de redes considera seleção de fornecedores, plantas e armazéns e de opções de transportes, com alocação de produtos para plantas de manufatura e armazéns, e ainda consideram questões de estocagem na rede logística como custos de manutenção e de obtenção de estoques. A formulação resultante é um modelo de programação não linear inteira mista, feita para um único período com a demanda estocástica. Por ser um problema NP-Difícil, para a resolução do problema proposto foi utilizado o algoritmo Outer-Approximation, que foi testando por meio do dimensionamento de três classes distintas. / [en] This thesis aims to develop a mathematical formulation to an integrated and flexible logistics network design that include choices of facility locations, transportation, production and inventories. The network designs consider vendors, plants, warehouses and transportation modes choices. The proposed model considers products assignment to plants and warehouses, inventory holding and procurement costs. The mathematical formulation of the model is a Mixer Integer Non Linear Program (MINLP) problem, referring to a single period with stochastic demand. The problem is NP-Hard and we used the Outer-Approximation algorithmic as the method to resolve the model proposed. We tested the algorithmic for three different instances (scenarios).

Les programmes de sélection visent à produire des reproducteurs de bonnes valeurs génétiques pour la filière. La connaissance de marqueurs moléculaires du génome des individus et de mutations d’intérêt ouvrent des perspectives en termes d’organisation de la sélection. A l’aide de simulations déterministes et stochastiques, l’intérêt technique et économique de l’utilisation d’un panel de marqueurs moléculaires très basse densité a été évalué dans les populations ovines et caprines en sélection et permis d’obtenir les résultats suivants : i) utiliser un tel panel pour accroître, quand elle est limitée, la quantité de filiations paternelles n’est pas toujours rentable, ii) la stratégie de gestion des gènes d’ovulation qui maximise la rentabilité économique du plan de sélection a été déterminée par optimisation et des stratégies simples à implémenter, qui donnent des rentabilités proches de la rentabilité maximale, ont été proposées, iii) un programme de sélection génomique basé sur un panel très basse densité, permet à coût constant une efficacité supérieure aux programmes basés actuellement sur le testage sur descendance des mâles. / Breeding programs aim to transfer high genetic value breeding stock to the industry. The knowledge of molecular markers of individual’s genome and causal mutations allow to conceive new breeding program designs. Based on deterministic and stochastic simulations, the technical and economic benefits of using a very low density molecular markers panel were assessed in sheep and goat populations. Following results were obtained: i) using such a panel to increase female paternal filiations in case of incomplete pedigree is not always profitable, ii) a method of optimization has been used to derive the maximal profits of managing ovulation genes, and practical management giving profits close to the maximal profits have been determined, iii) at similar cost, a genomic design based on a very low density panel is more efficient than the current design based on progeny testing.

>Magister Scientiae - MSc / HIV/AIDS is nowadays considered as the greatest public health disaster of modern time. Its progression has challenged the global population for decades. Through mathematical modelling, researchers have studied different interventions on the HIV pandemic, such as treatment, education, condom use, etc. Our research focuses on different compartmental models with emphasis on the effect of public health education. From the point of view of statistics, it is well known how the public health educational programs contribute towards the reduction of the spread of HIV/AIDS epidemic. Many models have been studied towards understanding the dynamics of the HIV/AIDS epidemic. The impact of ARV treatment have been observed and analysed by many researchers. Our research studies and investigates a compartmental model of HIV with treatment and education campaign. We study the existence of equilibrium points and their stability. Original contributions of this dissertation are the modifications on the model of Cai et al. [1], which enables us to use optimal control theory to identify optimal roll-out of strategies to control the HIV/AIDS. Furthermore, we introduce randomness into the model and we study the almost sure exponential stability of the disease free equilibrium. The randomness is regarded as environmental perturbations in the system. Another contribution is the global stability analysis on the model of Nyabadza et al. in [3]. The stability thresholds are compared for the HIV/AIDS in the absence of any intervention to assess the possible community benefit of public health educational campaigns. We illustrate the results by way simulation The following papers form the basis of much of the content of this dissertation, [1 ] L. Cai, Xuezhi Li, Mini Ghosh, Boazhu Guo. Stability analysis of an HIV/AIDS epidemic model with treatment, 229 (2009) 313-323. [2 ] C.P. Bhunu, S. Mushayabasa, H. Kojouharov, J.M. Tchuenche. Mathematical Analysis of an HIV/AIDS Model: Impact of Educational Programs and Abstinence in Sub-Saharan Africa. J Math Model Algor 10 (2011),31-55. [3 ] F. Nyabadza, C. Chiyaka, Z. Mukandavire, S.D. Hove-Musekwa. Analysis of an HIV/AIDS model with public-health information campaigns and individual with-drawal. Journal of Biological Systems, 18, 2 (2010) 357-375. Through this dissertation the author has contributed to two manuscripts [4] and [5], which are currently under review towards publication in journals, [4 ] G. Abiodun, S. Maku Vyambwera, N. Marcus, K. Okosun, P. Witbooi. Control and sensitivity of an HIV model with public health education (under submission). [5 ] P.Witbooi, M. Nsuami, S. Maku Vyambwera. Stability of a stochastic model of HIV population dynamics (under submission).

In this paper, we discuss methods for developing a stochastic model which incorporates behavior differences in the predation movements of Anelosimus studiosus (a subsocial spider). Stochastic models for animal movement and, in particular, spider predation movement have been developed previously; however, this paper focuses on the development and implementation of the necessary mathematical and statistical methods required to expand such a model in order to capture a variety of distinct behaviors. A least squares optimization algorithm is used for parameter estimation to fit a single stochastic model to an individual spider during predation resulting in unique parameter values for each spider. Similarities and variations between parameter values across the spiders are analyzed and used to estimate probability distributions for the variable parameter values. An aggregate stochastic model is then created which incorporates the individual dynamics. The comparison between the optimal individual models to the aggregate model indicate the methodology and algorithm developed in this paper are appropriate for simulating a range of individualistic behaviors.

[pt] A filtração profunda de suspensões particuladas ocorre em muitos processos industriais e ambientais, como filtração de água e contaminação do solo. Na indústria petrolífera, a filtração profunda ocorre próximo ao poço injetor durante a injeção de água, causando redução de injetividade. A captura de partículas no meio poroso pode ser causada por diferentes mecanismos físicos (exclusão pelo tamanho, forças elétricas, gravidade (sedimentação), etc.). No caso do mecanismo de exclusão pelo tamanho, quanto maiores forem as partículas e menores forem os poros, mais intensa será a captura. Conseqüentemente, maior será o dano à formação. Entretanto, o modelo tradicional não considera as distribuições de tamanho de partículas e de poros. Assumindo que as partículas são capturadas pelo mecanismo de exclusão pelo tamanho, foram deduzidas as equações básicas para o transporte de suspensões particuladas no meio poroso considerando as distribuições de tamanho de poros e de partículas. Apenas o fluxo de água via poros acessíveis transporta partículas, ou seja, as partículas não podem acessar poros menores do que elas. No presente trabalho, os efeitos da redução do fluxo de partículas e da inacessibilidade devido ao fluxo seletivo de diferentes tamanhos de partículas são incluídos no modelo estocástico para a filtração profunda. As soluções analíticas obtidas mostram um comportamento físico mais realístico do que o previsto pelo modelo tradicional. O modelo de medição (concentrações totais) obtido difere substancialmente do modelo tradicional para a filtração profunda. Vários dados experimentais foram tratados, mostrando boa concordância e validando o modelo proposto. Um sistema de equações estocásticas para modelar a formação do reboco externo foi proposto e soluções analíticas foram obtidas, permitindo tratar a filtração profunda e a formação do reboco externo, utilizando o mesmo formalismo matemático. / [en] Deep bed filtration of water with particles occurs in several industrial and environmental processes like water filtration and soil contamination. In petroleum industry, deep bed filtration occurs near to injection wells during water injection, causing injectivity reduction. It also takes place during well drilling, sand production control, produced water disposal in aquifers, etc. The particle capture in porous media can be caused by different physical mechanisms (size exclusion, electrical forces, bridging, gravity (sedimentation), etc.). In case of size exclusion mechanism, the larger are the particles and the smaller are the pores, the more intensive is the capture and the larger is the formation damage. Nevertheless, the widely used traditional model does not account for particle and pore size distributions. Considering that particles are captured due to size exclusion mechanism, we derived basic equations for transport of particulate suspensions in porous media, accounting for particle and pore radii distributions. Particles are carried by water flowing through the accessible pore space only, i.e. particles cannot access smaller pores. In the current work, the effects of porous space accessibility and particle flux reduction due to selective flow of different size particles are included into the stochastic deep bed filtration model. The particle and pore ensembles for analytical solutions of the derived system show more realistic physics behaviour than that of the traditional model. Averaging of the derived stochastic equations leads to a new deep bed filtration model that significantly differs from the classical deep bed filtration system. Treatment of several experimental data shows good agreement between the laboratory and modelling data and validates the proposed model. The derived stochastic model has been extended to model formation of external filter cake by particles from the injected polydispersed suspension, allowing treating both deep bed filtration and external filter cake formation in the framework of the same system of governing equations.

[pt] A Igualdade de Jarzynski (IJ) é um tipo especial de Teorema de Flutuação, de trabalho, que caracteriza sistemas termodinâmicos microscópicos fora do equilíbrio. A IJ pode ser usada como uma calibração de experimentos e simulações, o que nos permite estudar comportamentos não triviais da dinâmica desses sistemas. Um desses comportamentos é a troca de entropia e informação que o sistema realiza junto a um banho térmico de contato. Neste ensejo, modelamos via uma dinâmica não-Markoviana, i.e., uma dinâmica com memória, que leva a fluxos reversos de informação do reservatório para o sistema. / [en] The Jarzynski Equality (JE) is a special kind of Fluctuation Theorem, of work, which characterizes non-equilibrium small thermodynamics systems. The JE can be used as gauge of experiments and simulations allowing us to study the non-trivial behaviours of these systems dynamics. One of these behaviours is the entropy and information flow the system makes in contact with a thermal bath. In this framework, we modelled through a non-Markovian dynamic, i.e., with a memory effect, leading to reverse flows of information from the reservoir to the system.

No description available.

<p dir="ltr">At airports, aircraft taxi time may have effect on congestion, engine pollutants, and aircraft fuel consumption. An End-Around Taxiway (EAT) improves airport runway efficiencies and safety by providing a path for aircraft to move from one side of the runway to the other side without crossing that runway (FAA, 2022). The EAT has been implemented in four airports in the U.S.: Dallas/Fort Worth International Airport (KDFW), Hartsfield-Jackson International Airport (KATL), Detroit Metro Airport (KDTW), and Miami International Airport (KMIA) (Le, 2014). Currently, all the EATs are implemented at parallel runways. Previous research have shown that EAT on parallel runways has the potential to improve airport capacity and reduce fuel consumption (Fala et al., 2014; Feng & Johnson, 2021). There was no published application or research found about implementing EAT on crossing runways. This research is an explanatory study that focuses on analyzing the effect of EATs on airports with crossing runways. This research uses dynamic discrete event stochastic simulation software to build simulation models to analyze the effects of implementing EAT at crossing runways. Using a fictional airport loosely based on existing commercial service airports, the effect of EATs on a crossing runway airport was studied. The research has three experiments to measure the effects of the EAT in terms of taxi-in time, taxi-out time, and number of operations completed.</p><p dir="ltr">The major findings of the research are: 1) using EAT for taxi-in operations significantly reduces the taxi-in time and taxi-out time at the fictional airport with crossing runways; 2) using EAT for taxi-out operation significantly increases taxi-in time at the fictional airport with crossing runways; 3) using EAT for taxi-out operations significantly reduces taxi-out times at the fictional airport with crossing runways; 4) there is no statistical significance found when implementing EAT at the fictional airport with crossing runways in terms of number of operations completed per day. The configuration of the airport, the number of operations, the weather, and other factors may affect the transfer of these results to other airports with crossing runways.</p><p dir="ltr">Current EATs are only implemented and proposed at parallel runway airports. As aviation demand grows, this research may provide insights about a novel usage and operation strategy of EATs. The simulation model in this research is subject to assumptions and limitations. Future research is needed to improve the simulation model and further explore the effect of EATs on crossing runways.</p>

Uncertainties in both loading and structural characteristics can adversely affect the response and reliability of a structure. Parameter uncertainties in structural dynamics can arise due to several sources. These include variations due to intrinsic material property variability, measurement errors, manufacturing and assembly errors, differences in modeling and solution procedures. Problems of structural dynamics with randomly distributed spatial inhomogeneities in elastic, mass, and damping properties, have been receiving wide attention. Several mathematical and computational issues include discretization of random fields, characterization of random eigensolutions, inversion of random matrices, solutions of stochastic boundary-value problems, and description of random matrix products. Difficulties are encountered when one has to include interaction between nonlinear and stochastic system characteristics, or if one is interested in controlling the system response. The study of structural systems including the effects of system nonlinearity in the presence of parameter uncertainties presents serious challenges and difficulties to designers and reliability engineers. In the analysis of large structures, the situation for substructuring frequently arises due to the repetition of identical assemblages (substructures), within a structure, and the general need to reduce the size of the problem, particularly in the case of non-linear inelastic dynamic analysis. A small reduction in the model size can have a large effect on the storage and time requirement. A primary structural dynamic system may be coupled to subsystems such as piping systems in a nuclear reactor or in a chemical plant. Usually subsystem in itself is quite complex and its modeling with finite elements may result in a large number of degrees of freedom. The reduced subsystem model should be of low-order yet capturing the essential dynamics of the subsystem for useful integration with the primary structure. There are two major issues to be studied: one, techniques for analyzing a complex structure into component subsystems, analyzing the individual sub-system dynamics, and from thereon determining the dynamics of the structure after assembling the subsystems. The nonlinearity due to support gap effects such as supports for piping system in nuclear reactors further complicates the problem. The second is the issue of reviewing the methods for reducing the model-order of the component subsystems such that the order of the global dynamics, after assembly, is within some predefined limits. In the reliability analysis of complex engineering structures, a very large number of the system parameters have to be considered as random variables. The parameter uncertainties are modeled as random variables and are assumed to be time independent. Here the problem would be to reduce the number of random variables without sacrificing the accuracy of the reliability analysis. The procedure involves the reduction of the size of the vector of random variables before the calculation of failure probability. The objectives of this thesis are: 1.To use the available model reduction techniques in order to effectively reduce the size of the finite element model, and hence, compare the dynamic responses from such models. 2.Study of propagation of uncertainties in the reduced order/coupled stochastic finite element dynamic models. 3.Addressing the localized nonlinearities due to support gap effects in the built up structures, and also in cases of sudden change in soil behaviour under the footings. The irregularity in soil behaviour due to lateral escape of soil due to failure of quay walls/retaining walls/excavation in neighbouring site, etc. 4.To evolve a procedure for the reduction of size of the vector containing the random variables before the calculation of failure probability. In the reliability analysis of complex engineering structures, a very large number of the system parameters are considered to be random variables. Here the problem would be to reduce the number of random variables without sacrificing the accuracy of the reliability analysis. 5.To analyze the reduced nonlinear stochastic dynamic system (with phase space reduction), and effectively using the network pruning technique for the solution, and also to use filter theory (wavelet theory) for reducing the input earthquake record to save computational time and cost. It is believed that the techniques described provide highly useful insights into the manner structural uncertainties propagate. The cross-sectional area, length, modulus of elasticity and mass density of the structural components are assumed as random variables. Since both the random and design variables are expressed in a discretized parameter space, the stochastic sensitivity function can be modeled in a parallel way. The response of the structures in frequency domain is considered. This thesis is organized into seven chapters. This thesis deals with the reduced order models of the stochastic structural systems under deterministic/random loads. The Chapter 1 consists of a brief introduction to the field of study. In Chapter 2, an extensive literature survey based on the previous works on model order reduction and the response variability of the structural dynamic systems is presented. The discussion on parameter uncertainties, stochastic finite element method, and reliability analysis of structures is covered. The importance of reducing mechanical models for dynamic response variability, the systems with high-dimensional variables and reduction in random variables space, nonlinearity issues are discussed. The next few chapters from Chapter 3 to Chapter 6 are the main contributions in this thesis, on model reduction under various situations for both linear and nonlinear systems. After forming a framework for model reduction, local nonlinearities like support gaps in structural elements are considered. Next, the effect of reduction in number of random variables is tackled. Finally influence of network pruning and decomposition of input signals into low and high frequency parts are investigated. The details are as under. In Chapter 3, the issue of finite element model reduction is looked into. The generalized finite element analysis of the full model of a randomly parametered structure is carried out under a harmonic input. Different well accepted finite element model reduction techniques are used for FE model reduction in the stochastic dynamic system. The structural parameters like, mass density and modulus of elasticity of the structural elements are considered to be non-Gaussian random variables. Since the variables considered here are strictly positive, the probabilistic distribution of the random variables is assumed to be lognormal. The sensitivities in the eigen solutions are compared. The response statistics based on response of models in frequency domain are compared. The dynamic responses of the full FE model, separated into real and imaginary parts, are statistically compared with those from reduced FE models. Monte Carlo simulation is done to validate the analysis results from SFEM. In Chapter 4, the problem of coupling of substructures in a large and complex structure, and FE model reduction, e.g., component mode synthesis (CMS) is studied in the stochastic environment. Here again, the statistics of the response from full model and reduced models are compared. The issues of non-proportional damping, support gap effects and/local nonlinearity are considered in the stochastic sense. Monte Carlo simulation is done to validate the analysis results from SFEM. In Chapter 5, the reduction in size of the vector of random variables in the reliability analysis is attempted. Here, the relative entropy/ K-L divergence/mutual information, between the random variables is considered as a measure for ranking of random variables to study the influence of each random variable on the response/reliability of the structure. The probabilistic distribution of the random variables is considered to be lognormal. The reliability analysis is carried out with the well known Bucher and Bourgund algorithm (1990), along with the probabilistic model reduction of the stochastic structural dynamic systems, within the framework of response surface method. The reduction in number of random variables reduces the computational effort required to construct an approximate closed form expression in response surface approach. In Chapter 6, issues regarding the nonlinearity effects in the reduced stochastic structural dynamic systems (with phase space reduction), along with network pruning are attempted. The network pruning is also adopted for reduction in computational effort. The earthquake accelerogram is decomposed using Fast Mallat Algorithm (Wavelet theory) into smaller number of points and the dynamic analysis of structures is carried out against these reduced points, effectively reducing the computational time and cost. Chapter 7 outlines the contributions made in this thesis, together with a few suggestions made for further research. All the finite element codes were developed using MATLAB5.3. Final pages of the thesis contain the references made in the preparation of this thesis.