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Uncertainty quantification through the Monte Carlo method in a cloud computing setting

The Monte Carlo (MC) method is the most common technique used for uncertainty quantification, due to its simplicity and good statistical results. However, its computational cost is extremely high, and, in many cases, prohibitive. Fortunately, the MC algorithm is easily parallelizable, which allows its use in simulations where the computation of a single realization is very costly. This work presents a methodology for the parallelization of the MC method, in the context of cloud computing. This strategy is based on the MapReduce paradigm, and allows an efficient distribution of tasks in the cloud. This methodology is illustrated on a problem of structural dynamics that is subject to uncertainties. The results show that the technique is capable of producing good results concerning statistical moments of low order. It is shown that even a simple problem may require many realizations for convergence of histograms, which makes the cloud computing strategy very attractive (due to its high scalability capacity and low-cost). Additionally, the results regarding the time of processing and storage space usage allow one to qualify this new methodology as a solution for simulations that require a number of MC realizations beyond the standard.

Modeling and Quantification of Physical Systems Uncertainties in a Probabilistic Framework

Uncertainty quantification (UQ) is a multidisciplinary area, that deals with quantitative characterization and reduction of uncertainties in applications. It is essential to certify the quality of numerical and experimental analyses of physical systems. The present manuscript aims to provide the reader with an introductory view about modeling and quantification of uncertainties in physical systems. In this sense, the text presents some fundamental concepts in UQ, a brief review of probability basics notions, discusses, through a simplistic example, the fundamental aspects of probabilistic modeling of uncertainties in a physical system, and explains what is the uncertainty propagation problem.

On the nonlinear dynamics of an inverted double pendulum over a vehicle suspension subject to random excitations

This paper deals with the nonlinear dynamics of a mechanical system which consists of an agricultural tower pulverizer, coupled with a vehicle suspension that is subject to random excitations due to soil irregularities. A deterministic mathematical model, where tower is considered as an inverted double pendulum over an vehicle suspension, with three degrees of freedom (one translation and two rotations) is constructed. To take into account the random loadings due to soil variabilities, a parametric probabilistic approach is employed, where the external force is assumed to be a harmonic random process. This stochastic process has random amplitude and frequency, which are modeled as random variables, and a sinusoidal shape in time. Once experimental data are not available for adjusting consistent distributions for these random variables, their distributions are constructed based only on theoretical information, using the maximum entropy principle. This procedure result in a system of stochastic ordinary differential equations, which defines a stochastic model for the problem. The propagation of uncertainties through the stochastic model is computed using the Monte Carlo method. Numerical simulations show large discrepancies in the system response obtained with the mean of the stochastic model and with the nominal (deterministic) model, and a high level of uncertainty associated. Also, an analysis of the system response probability distributions shows that they present asymmetries with respect to mean and unimodal behavior.

Zika virus in Brazil: calibration of an epidemic model for 2016 outbreak

This work deals with the development and calibration of an epidemic model to describe the 2016 outbreak of Zika virus in Brazil. A mathematical model with 8 differential equations and 7 parameters is employed. Nominal values for the model parameters are estimated from the literature. An inverse problem associated to the model identification is formulated and solved. The calibrated model obtained presents realistic parameters and returns reasonable predictions, with the curve shape similar to the outbreak evolution and peak value close to the maximum number of infected people during 2016.

Calibration of a SEIR–SEI epidemic model to describe the Zika virus outbreak in Brazil

Multiple instances of Zika virus epidemic have been reported around the world in the last two decades, turning the related illness into an international concern. In this context the use of mathematical models for epidemics is of great importance, since they are useful tools to study the underlying outbreak numbers and allow one to test the effectiveness of different strategies used to combat the associated diseases. This work deals with the development and calibration of an epidemic model to describe the 2016 outbreak of Zika virus in Brazil. A system of 8 differential equations with 8 parameters is employed to model the evolution of the infection through two populations. Nominal values for the model parameters are estimated from the literature. An inverse problem is formulated and solved by comparing the system response to real data from the outbreak. The calibrated results presents realistic parameters and returns reasonable descriptions, with the curve shape similar to the outbreak evolution and peak value close to the highest number of infected people during 2016. Considerations about the lack of data for some initial conditions are also made through an analysis over the response behavior according to their change in value.

Maximization of the electrical power generated by a piezo-magneto-elastic energy harvesting device

This work deals with the maximization of the mean power in a piezoelectric energy harvesting device. The voltages are acquired by applying different force amplitudes and initial positions for the system. These signals are treated in order to identify and separate chaotic from regular (non chaotic) results, through 0-1 test for chaos. An optimization problem is numerically solved in order to identify an optimal configuration of parameters.

Uso do método de superfície de resposta para estimar um modelo estocástico de uma viga não linear com rigidez cúbica

A meta deste trabalho e identificar funcoes densidade de probabilidade associadas aos parâmetros que descrevem o comportamento vibratorio em regime linear e nao linear de uma viga assumindo as incertezas existentes. O metodo e testado em uma viga de aluminio com condicao de contorno engastada-livre com forte mecanismo de nao linearidade polinomial associado a endurecimento da rigidez. Este comportamento nao lineare lineare acionado atraves da interacao magnetica entre uma massa de ferro conectada na ponta livre da viga e imas presos na extremidade livre da estrutura. O processo de identificacao utilizado e hibrido e nao parametrico. Com baixos niveis de amplitude da forca de excitacao, a forca elastica de restauracao e nula. Nestas condicoes de operacao, tecnicas de analise modal sao utilizadas para extrair parâmetros modais. Ja para elevados niveis de excitacao a forca de restauracao deve incluir termos nao lineares. Assim, a identificacao do coeficiente nao linear sera feita pelo metodo de superficie de resposta. Os testes experimentais foram realizados diversas vezes considerando diferentes dias e condicoes para considerar incertezas nos dados adquiridos e com os pa-râmetros identificados para cada realizacao. Assim, se estimam funcoes densidades de probabilidade de cada parâmetro identificado com cada metodo. Um modelo estocastico do sistema e obtido e validado com as repostas experimentais previstas para verificacao da confiabilidade do modelo frente a diferentes regimes de vibracao. Palavras-chave: Vibracao Nao Linear, Quantificacao de Incertezas, Metodo de Superficie de Resposta.

Mathematical modeling of horizontal drillstrings subjected to friction and shocks effects

During the process of oil prospection, an equipment called drillstring is used to drill the soil. This device presents a three-dimensional nonlinear dynamics subjected to effects of fric- tion and shock. This work aims to analyze the nonlinear dynamics of a drillstring in horizontal configuration. For this purpose, the drillstring is modeled as a beam theory with rotatory inertia and shear deformation of the the cross section, undergoing large displacements. This model also takes into account the effects of friction and shock, induced by the lateral impacts between the drillstring and the borehole wall. The model equations are discretized using the Galerkin/finite element method, and the resulting initial value problem is integrated using the Newmark method. Numerical simulations are conducted to investigate the effects of the lateral shock in nonlinear dynamic of the column.

Uncertainty analysis in Volterra series applied in a nonlinear system

The goal of this paper is to verify the influence of uncertainties in the identification of Volterra kernels applied in a single degree-of-freedom nonlinear model with cubic stiffness. Stochastic modelling and Monte-Carlo simulations were performed for the identification of the Volterra kernels considering variations in the parameters of the motion equations, with the aim of verify how the kernels change with the presence of uncertainties. The results are evaluated by establishing confidence intervals in the kernels. These results allow to propose a statistical decision if the the kernels are representative of the nonlinear behavior of the systems even with uncertainties