Дисертації з теми "Sobol’s indices"
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Nzang, Essono Francine. "Approche géomatique de la variabilité spatio-temporelle de la contamination microbienne des eaux récréatives." Thèse, Université de Sherbrooke, 2016. http://hdl.handle.net/11143/10211.
Повний текст джерелаAbstract : The aim of this study was to predict water faecal contamination from a bayesian probabilistic model, on a watershed scale in a farming area and on a factual scale. This project aims to better understand the influence of hydrological, environmental and temporal factors involved in the explanation of microbial contamination episodes of recreational waters. First, a bayesian probabilistic model: Weight of Evidence was developed to identify and map the probability of water levels to be contaminated by agricultural effluents, on the basis of spectrals data and geomorphologic variables. By this method, we were able to calculate weighted relationships between concentrations of Escherichia coli and distribution of key agronomic, pedologic and climatic parameters that influence the spread of these microorganisms. The results showed that the Bayesian model that was developed can be used as a prediction of microbial contamination of recreational waters. This model, with a success rate of 71%, highlighted the significant role played by the rain, which is the main cause of pollution transport. Secondly, the Bayesian probabilistic model has been the subject of a sensitivity analysis related to spatial parameters, using Sobol indications. This allowed (1) quantification of uncertainties on soil variables, land use and distance and (2) the spread of these uncertainties in the probabilistic model that is to say, the calculation of induced error in the output by the uncertainties of spatial inputs. Lastly, simulation sensitivity analysis to the various sources of uncertainty was performed to assess the contribution of each factor on the overall uncertainty taking into account their interactions. It appears that of all the scenarios, the uncertainty of the microbial contamination is directly dependent on the variability of clay soils. Sobol prime indications analysis showed that among the most likely to influence the microbial factors, the area of farmland is the first important factor in assessing the coliforms. Importance must be given on this parameter in the context of preparation for microbial contamination. Then, the second most important variable is the urban area with sensitivity shares of approximately 30%. Furthermore, estimates of the total indications are better than those of the first order, which means that the impact of parametric interaction is clearly significant for the modeling of microbial contamination. Thirdly, we propose to implement a temporal variability model of microbiological contamination on the watershed of Lake Massawippi, based on the AVSWAT model. This is a model that couples the temporal and spatial components that characterize the dynamics of coliforms. The synthesis of the main results shows that concentrations of Escherichia coli in different sub-watersheds are influenced by rain intensity. Research also concluded that best performance is obtained by multi-objective optimization. The results of these studies show the prospective of operationally providing a comprehensive understanding of the dynamics of microbial contamination of surface water.
Chastaing, Gaëlle. "Indices de Sobol généralisés pour variables dépendantes." Phd thesis, Université de Grenoble, 2013. http://tel.archives-ouvertes.fr/tel-00930229.
Повний текст джерелаChastaing, Gaëlle. "Indices de Sobol généralisés par variables dépendantes." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM046.
Повний текст джерелаA mathematical model aims at characterizing a complex system or process that is too expensive to experiment. However, in this model, often strongly non linear, input parameters can be affected by a large uncertainty including errors of measurement of lack of information. Global sensitivity analysis is a stochastic approach whose objective is to identify and to rank the input variables that drive the uncertainty of the model output. Through this analysis, it is then possible to reduce the model dimension and the variation in the output of the model. To reach this objective, the Sobol indices are commonly used. Based on the functional ANOVA decomposition of the output, also called Hoeffding decomposition, they stand on the assumption that the incomes are independent. Our contribution is on the extension of Sobol indices for models with non independent inputs. In one hand, we propose a generalized functional decomposition, where its components is subject to specific orthogonal constraints. This decomposition leads to the definition of generalized sensitivity indices able to quantify the dependent inputs' contribution to the model variability. On the other hand, we propose two numerical methods to estimate these constructed indices. The first one is well-fitted to models with independent pairs of dependent input variables. The method is performed by solving linear system involving suitable projection operators. The second method can be applied to more general models. It relies on the recursive construction of functional systems satisfying the orthogonality properties of summands of the generalized decomposition. In parallel, we illustrate the two methods on numerical examples to test the efficiency of the techniques
Riahi, Hassen. "Analyse de structures à dimension stochastique élevée : application aux toitures bois sous sollicitation sismique." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2013. http://tel.archives-ouvertes.fr/tel-00881187.
Повний текст джерелаMontealegre, Scott Juan. "Initial value problem for a coupled system of Kadomtsev-Petviashvili II equations in Sobolev spaces of negative indices." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95255.
Повний текст джерелаTissot, Jean-Yves. "Sur la décomposition ANOVA et l'estimation des indices de Sobol'. Application à un modèle d'écosystème marin." Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00762800.
Повний текст джерелаTissot, Jean-yves. "Sur la décomposition ANOVA et l'estimation des indices de Sobol'. Application à un modèle d'écosystème marin." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENM064/document.
Повний текст джерелаIn the fields of modelization and numerical simulation, simulators generally depend on several input parameters whose impact on the model outputs are not always well known. The main goal of sensitivity analysis is to better understand how the model outputs are sensisitive to the parameters variations. One of the most competitive method to handle this problem when complex and potentially highly non linear models are considered is based on the ANOVA decomposition and the Sobol' indices. More specifically the latter allow to quantify the impact of each parameters on the model response. In this thesis, we are interested in the issue of the estimation of the Sobol' indices. In the first part, we revisit in a rigorous way existing methods in light of discrete harmonic analysis on cyclic groups and randomized orthogonal arrays. It allows to study theoretical properties of this method and to intriduce generalizations. In a second part, we study the Monte Carlo method for the Sobol' indices and we introduce a new approach to reduce the number of simulations of this method. In parallel with this theoretical work, we apply these methods on a marine ecosystem model
Gayrard, Emeline. "Analyse bayésienne de la gerbe d'éclats provoquée pa l'explosion d'une bombe à fragmentation naturelle." Thesis, Université Clermont Auvergne (2017-2020), 2019. http://www.theses.fr/2019CLFAC039/document.
Повний текст джерелаDuring this thesis, a method of statistical analysis on sheaf of bomb fragments, in particular on their masses, has been developed. Three samples of incomplete experimental data and a mechanical model which simulate the explosion of a ring were availables. First, a statistical model based on the mechanical model has been designed, to generate data similar to those of an experience. Then, the distribution of the masses has been studied. The classical methods of analysis being not accurate enough, a new method has been developed. It consists in representing the mass by a random variable built from a basis of chaos polynomials. This method gives good results however it doesn't allow to take into account the link between slivers. Therefore, we decided to model the masses by a stochastic process, and not a random variable. The range of fragments, which depends of the masses, has also been modeled by a process. Last, a sensibility analysis has been carried out on this range with Sobol indices. Since these indices are applied to random variables, it was necessary to adapt them to stochastic process in a way that take into account the links between the fragments. In the last part, it is shown how the results of this analysis could be improved. Specifically, the indices presented in the last part are adapted to dependent variables and therefore, they could be suitable to processes with non independent increases
Gilquin, Laurent. "Échantillonnages Monte Carlo et quasi-Monte Carlo pour l'estimation des indices de Sobol' : application à un modèle transport-urbanisme." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM042/document.
Повний текст джерелаLand Use and Transportation Integrated (LUTI) models have become a norm for representing the interactions between land use and the transportation of goods and people in a territory. These models are mainly used to evaluate alternative planning scenarios, simulating their impact on land cover and travel demand.LUTI models and other mathematical models used in various fields are most of the time based on complex computer codes. These codes often involve poorly-known inputs whose uncertainty can have significant effects on the model outputs.Global sensitivity analysis methods are useful tools to study the influence of the model inputs on its outputs. Among the large number of available approaches, the variance based method introduced by Sobol' allows to calculate sensitivity indices called Sobol' indices. These indices quantify the influence of each model input on the outputs and can detect existing interactions between inputs.In this framework, we favor a particular method based on replicated designs of experiments called replication method. This method appears to be the most suitable for our application and is advantageous as it requires a relatively small number of model evaluations to estimate first-order or second-order Sobol' indices.This thesis focuses on extensions of the replication method to face constraints arising in our application on the LUTI model Tranus, such as the presence of dependency among the model inputs, as far as multivariate outputs.Aside from that, we propose a recursive approach to sequentially estimate Sobol' indices. The recursive approach is based on the iterative construction of stratified designs, latin hypercubes and orthogonal arrays, and on the definition of a new stopping criterion. With this approach, more accurate Sobol' estimates are obtained while recycling previous sets of model evaluations. We also propose to combine such an approach with quasi-Monte Carlo sampling.An application of our contributions on the LUTI model Tranus is presented
Jannet, Basile. "Influence de la non-stationnarité du milieu de propagation sur le processus de Retournement Temporel (RT)." Thesis, Clermont-Ferrand 2, 2014. http://www.theses.fr/2014CLF22436/document.
Повний текст джерелаThe aim of this thesis is to measure and quantify the impacts of uncertainties in the Time Reversal (TR) process. These random variations, coming from diverse sources, can have a huge influence if they happen between the TR steps. On this perspective, the Stochastique Collocation (SC) method is used. Very good results in terms of effectiveness and accuracy had been noticed in previous studies in ElectroMagnetic Compatibility (EMC). The conclusions are still excellent here on TR problems. Although, when the problem dimension rises (high number of Random Variables (RV)), the SC method reaches its limits and the efficiency decreases. Therefore a study on Sensitivity Analysis (SA) techniques has been carried out. Indeed, these methods emphasize the respective influences of the random variables of a model. Among the various quantitative or qualitative SA techniques the Morris method and the Sobol total sensivity indices have been adopted. Since only a split of the inputs (point out of the predominant RV) is expected, they bring results at a lesser cost. That is why a novel method is built, combining SA techniques and the SC method. In a first step, the model is reduced with SA techniques. Then, the shortened model in which only the prevailing inputs remain, allows the SC method to show once again its efficiency with a high accuracy. This global process has been validated facing Monte Carlo results on several analytical and numerical TR cases subjet to random variations
Horiguchi, Akira. "Bayesian Additive Regression Trees: Sensitivity Analysis and Multiobjective Optimization." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1606841319315633.
Повний текст джерелаKamari, Halaleh. "Qualité prédictive des méta-modèles construits sur des espaces de Hilbert à noyau auto-reproduisant et analyse de sensibilité des modèles complexes." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASE010.
Повний текст джерелаIn this work, the problem of estimating a meta-model of a complex model, denoted m, is considered. The model m depends on d input variables X1 , ..., Xd that are independent and have a known law. The meta-model, denoted f ∗ , approximates the Hoeffding decomposition of m, and allows to estimate its Sobol indices. It belongs to a reproducing kernel Hilbert space (RKHS), denoted H, which is constructed as a direct sum of Hilbert spaces (Durrande et al. (2013)). The estimator of the meta-model, denoted f^, is calculated by minimizing a least-squares criterion penalized by the sum of the Hilbert norm and the empirical L2-norm (Huet and Taupin (2017)). This procedure, called RKHS ridge group sparse, allows both to select and estimate the terms in the Hoeffding decomposition, and therefore, to select the Sobol indices that are non-zero and estimate them. It makes possible to estimate the Sobol indices even of high order, a point known to be difficult in practice.This work consists of a theoretical part and a practical part. In the theoretical part, I established upper bounds of the empirical L2 risk and the L2 risk of the estimator f^. That is, upper bounds with respect to the L2-norm and the empirical L2-norm for the f^ distance between the model m and its estimation f into the RKHS H. In the practical part, I developed an R package, called RKHSMetaMod, that implements the RKHS ridge group sparse procedure and a spacial case of it called the RKHS group lasso procedure. This package can be applied to a known model that is calculable in all points or an unknown regression model. In order to optimize the execution time and the storage memory, except for a function that is written in R, all of the functions of the RKHSMetaMod package are written using C++ libraries GSL and Eigen. These functions are then interfaced with the R environment in order to propose an user friendly package. The performance of the package functions in terms of the predictive quality of the estimator and the estimation of the Sobol indices, is validated by a simulation study
Broto, Baptiste. "Sensitivity analysis with dependent random variables : Estimation of the Shapley effects for unknown input distribution and linear Gaussian models." Electronic Thesis or Diss., université Paris-Saclay, 2020. http://www.theses.fr/2020UPASS119.
Повний текст джерелаSensitivity analysis is a powerful tool to study mathematical models and computer codes. It reveals the most impacting input variables on the output variable, by assigning values to the the inputs, that we call "sensitivity indices". In this setting, the Shapley effects, recently defined by Owen, enable to handle dependent input variables. However, one can only estimate these indices in two particular cases: when the distribution of the input vector is known or when the inputs are Gaussian and when the model is linear. This thesis can be divided into two parts. First, the aim is to extend the estimation of the Shapley effects when only a sample of the inputs is available and their distribution is unknown. The second part focuses on the linear Gaussian framework. The high-dimensional problem is emphasized and solutions are suggested when there are independent groups of variables. Finally, it is shown how the values of the Shapley effects in the linear Gaussian framework can estimate of the Shapley effects in more general settings
Abily, Morgan. "Modélisation hydraulique à surface libre haute-résolution : utilisation de données topographiques haute-résolution pour la caractérisation du risque inondation en milieux urbains et industriels." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4121/document.
Повний текст джерелаHigh Resolution (infra-metric) topographic data, including LiDAR photo-interpreted datasets, are becoming commonly available at large range of spatial extent, such as municipality or industrial site scale. These datasets are promising for High-Resolution (HR) Digital Elevation Model (DEM) generation, allowing inclusion of fine aboveground structures that influence overland flow hydrodynamic in urban environment. DEMs are one key input data in Hydroinformatics to perform free surface hydraulic modelling using standard 2D Shallow Water Equations (SWEs) based numerical codes. Nonetheless, several categories of technical and numerical challenges arise from this type of data use with standard 2D SWEs numerical codes. Objective of this thesis is to tackle possibilities, advantages and limits of High-Resolution (HR) topographic data use within standard categories of 2D hydraulic numerical modelling tools for flood hazard assessment purpose. Concepts of HR topographic data and 2D SWE based numerical modelling are recalled. HR modelling is performed for : (i) intense runoff and (ii) river flood event using LiDAR and photo-interpreted datasets. Tests to encompass HR surface elevation data in standard modelling tools ranges from industrial site scale to a megacity district scale (Nice, France). Several standard 2D SWEs based codes are tested (Mike 21, Mike 21 FM, TELEMAC-2D, FullSWOF_2D). Tools and methods for assessing uncertainties aspects with 2D SWE based models are developed to perform a spatial Global Sensitivity Analysis related to HR topographic data use. Results show the importance of modeller choices regarding ways to integrate the HR topographic information in models
Heredia, Guzman Maria Belen. "Contributions to the calibration and global sensitivity analysis of snow avalanche numerical models." Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALU028.
Повний текст джерелаSnow avalanche is a natural hazard defined as a snow mass in fast motion. Since the thirties, scientists have been designing snow avalanche models to describe snow avalanches. However, these models depend on some poorly known input parameters that cannot be measured. To understand better model input parameters and model outputs, the aims of this thesis are (i) to propose a framework to calibrate input parameters and (ii) to develop methods to rank input parameters according to their importance in the model taking into account the functional nature of outputs. Within these two purposes, we develop statistical methods based on Bayesian inference and global sensitivity analyses. All the developments are illustrated on test cases and real snow avalanche data.First, we propose a Bayesian inference method to retrieve input parameter distribution from avalanche velocity time series having been collected on experimental test sites. Our results show that it is important to include the error structure (in our case the autocorrelation) in the statistical modeling in order to avoid bias for the estimation of friction parameters.Second, to identify important input parameters, we develop two methods based on variance based measures. For the first method, we suppose that we have a given data sample and we want to estimate sensitivity measures with this sample. Within this purpose, we develop a nonparametric estimation procedure based on the Nadaraya-Watson kernel smoother to estimate aggregated Sobol' indices. For the second method, we consider the setting where the sample is obtained from acceptance/rejection rules corresponding to physical constraints. The set of input parameters become dependent due to the acceptance-rejection sampling, thus we propose to estimate aggregated Shapley effects (extension of Shapley effects to multivariate or functional outputs). We also propose an algorithm to construct bootstrap confidence intervals. For the snow avalanche model application, we consider different uncertainty scenarios to model the input parameters. Under our scenarios, the release avalanche position and volume are the most crucial inputs.Our contributions should help avalanche scientists to (i) account for the error structure in model calibration and (ii) rankinput parameters according to their importance in the models using statistical methods
Lu, Rong. "Statistical Methods for Functional Genomics Studies Using Observational Data." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1467830759.
Повний текст джерелаChristian, Steve Clarence. "A sensitivity analysis of a heuristic model used for the placement allocation of utilities in transportation right-of-way corridors." [Tampa, Fla.] : University of South Florida, 2004. http://purl.fcla.edu/fcla/etd/SFE0000501.
Повний текст джерелаNiang, Ibrahima. "Quantification et méthodes statistiques pour le risque de modèle." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSE1015/document.
Повний текст джерелаIn finance, model risk is the risk of loss resulting from using models. It is a complex risk which recover many different situations, and especially estimation risk and risk of model misspecification. This thesis focuses: on model risk inherent in yield and credit curve construction methods and the analysis of the consistency of Sobol indices with respect to stochastic ordering of model parameters. it is divided into three chapters. Chapter 1 focuses on model risk embedded in yield and credit curve construction methods. We analyse in particular the uncertainty associated to the construction of yield curves or credit curves. In this context, we derive arbitrage-free bounds for discount factor and survival probability at the most liquid maturities. In Chapter 2 of this thesis, we quantify the impact of parameter risk through global sensitivity analysis and stochastic orders theory. We analyse in particular how Sobol indices are transformed further to an increase of parameter uncertainty with respect to the dispersive or excess wealth orders. Chapter 3 of the thesis focuses on contrast quantile index. We link this latter with the risk measure CTE and then we analyse on the other side, in which circumstances an increase of a parameter uncertainty in the sense of dispersive or excess wealth orders implies and increase of contrast quantile index. We propose finally an estimation procedure for this index. We prove under some conditions that our estimator is consistent and asymptotically normal
Causse, Mathieu. "Contributions à l'extension de la méthode des Sparse Grids pour les calculs de fiabilité en modélisation de processus." Toulouse 3, 2010. http://www.theses.fr/2010TOU30336.
Повний текст джерелаThe aim of this thesis is to show the efficiency of Sparse Grid approximation method applied to high dimensional real-life problems. For that kind of problems main parameters detection is fundamental. First we introduce Sparse Grid approximation method and emphasize its adaptive form. Then we show the efficiency of the method on standard test functions to show Sparse Grid specificities in main parameters detection. Due to excellent performance properties of the method, we apply it to a real-life problem and obtain accurate results with a reduced computation cost. The first application is dedicated to a pollutant diffusion problem, the second one aims to evaluate the performance of a power network
Solís, Maikol. "Conditional covariance estimation for dimension reduction and sensivity analysis." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2354/.
Повний текст джерелаThis thesis will be focused in the estimation of conditional covariance matrices and their applications, in particular, in dimension reduction and sensitivity analyses. In Chapter 2, we are in a context of high-dimensional nonlinear regression. The main objective is to use the sliced inverse regression methodology. Using a functional operator depending on the joint density, we apply a Taylor decomposition around a preliminary estimator. We will prove two things: our estimator is asymptotical normal with variance depending only the linear part, and this variance is efficient from the Cramér-Rao point of view. In the Chapter 3, we study the estimation of conditional covariance matrices, first coordinate-wise where those parameters depend on the unknown joint density which we will replace it by a kernel estimator. We prove that the mean squared error of the nonparametric estimator has a parametric rate of convergence if the joint distribution belongs to some class of smooth functions. Otherwise, we get a slower rate depending on the regularity of the model. For the estimator of the whole matrix estimator, we will apply a regularization of type "banding". Finally, in Chapter 4, we apply our results to estimate the Sobol or sensitivity indices. These indices measure the influence of the inputs with respect to the output in complex models. The advantage of our implementation is that we can estimate the Sobol indices without use computing expensive Monte-Carlo methods. Some illustrations are presented in the chapter showing the capabilities of our estimator
Masinde, Brian. "Birds' Flight Range. : Sensitivity Analysis." Thesis, Linköpings universitet, Institutionen för datavetenskap, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-166248.
Повний текст джерелаAndrianandraina. "Approche d'éco-conception basée sur la combinaison de l'analyse de cycle de vie et de l'analyse de sensibilité : Cas d'application sur le cycle de vie du matériau d'isolation thermique biosourcé, le béton de chanvre." Ecole centrale de Nantes, 2014. http://www.theses.fr/2014ECDN0005.
Повний текст джерелаThe purpose of this PhD thesis is to establish an ecodesign method based on Life Cycle Assessment, that should allow identifying action levers specific for each economic actor of the life cycle of a product, for improved environmental performances. Life Cycle Assessment was coupled with two methods of sensitivity analysis in five steps: (i) definition of objectives and system, (ii) modeling calculation of inventory and impact indicators with different approaches according to foreground and background sub-systems, (iii) characterization of parameters using a typology specific to possibilities of control of the considered economic actor, (iv) application of two sensitivity analysis methods (Morris and Sobol) and (v) results interpretation in order to identify potential efficient improvements. The approach was applied on the hemp concrete insulation product, including agricultural production, industrial transformation of hemp fibers, and use of hemp concrete as a thermal insulator for buildings. The approach provides potential technological scenarios improving environmental performances for each single economic actor of the product’s life cycle. Performing the method presently requires additional information, but will probably be paid back in the future by driving more robust choices for a given product
Noto, Raffaella. "Flussi in mezzi porosi a saturazione variabile generati da canali superficiali disperdenti: analisi numerica bidimensionale." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017.
Знайти повний текст джерелаNovák, Lukáš. "Pravděpodobnostní modelování smykové únosnosti předpjatých betonových nosníků: Citlivostní analýza a semi-pravděpodobnostní metody návrhu." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2018. http://www.nusl.cz/ntk/nusl-372051.
Повний текст джерелаNodet, Maëlle. "Problèmes inverses pour l'environnement : outils, méthodes et applications." Habilitation à diriger des recherches, Université de Grenoble, 2013. http://tel.archives-ouvertes.fr/tel-00930102.
Повний текст джерелаRodrigues, Diogo Castanhas. "Técnicas de análise de sensibilidade aplicadas ao processo de estampagem de uma taça quadrada." Master's thesis, 2021. http://hdl.handle.net/10316/96098.
Повний текст джерелаCom o aumento da competitividade industrial é crucial conhecer bem os processos de conformação de chapas metálicas, de modo a que estes possam ser otimizados e consequentemente reduzir os tempos e custos de produção. Assim, nesta dissertação é aplicada uma análise de sensibilidade ao processo de estampagem de uma taça quadrada, com o objetivo de compreender como as propriedades do material e condições do processo podem influenciar a estampagem. É estudada a influência da variabilidade do módulo de Young, do coeficiente de Poisson, dos coeficientes de anisotropia, dos parâmetros constitutivos da lei de Swift, da espessura inicial da chapa, do coeficiente de atrito e da força do cerra chapas. O objetivo é avaliar a influência da variabilidade destes parâmetros de entrada, na deformação plástica equivalente, na alteração de geometria, na redução de espessura, na força do punção e no retorno elástico. A análise de sensibilidade é realizada por duas técnicas distintas, índices de Sobol e índices PAWN.Antes de ser aplicada a análise de sensibilidade, é importante perceber quais as zonas da taça mais sujeitas à variabilidade dos parâmetros de entrada. Concluiu-se que a aba da taça e a zona próxima ao raio de curvatura da matriz são as zonas mais afetadas, sendo a base da taça a zona menos afetada pela variabilidade nos parâmetros de entrada.Posteriormente, avaliou-se a estabilização dos índices de sensibilidade e concluiu-se que, para a mesma precisão de resultados, os índices PAWN requerem apenas 7,7% a 12,8% das simulações utilizadas para avaliar os índices de Sobol. Da análise de sensibilidade constatou-se que os parâmetros de entrada com mais influência na variabilidade dos parâmetros de saída são: o coeficiente de encruamento, o parâmetro C da lei de Swift e o coeficiente de anisotropia a 90º. Ambos os índices de sensibilidade fornecem resultados semelhantes para todos os parâmetros de saída, exceto para o retorno elástico, para o qual se mostrou que os índices PAWN são mais precisos quando aplicados a um conjunto de dados que segue uma distribuição multimodal.
With the industrial competitiveness increasing day by day, it is crucial to have knowledge about the processes of conformation of metallic plates, in order to optimize that process and consequently decrease time and costs of production. In this dissertation it is applied a sensitivity analysis to the stamping process of a square cup with the aim of understanding how the material properties and the process conditions can influence that same process. The variability influence of the Young’s module, Poisson’s coefficient, anisotropy coefficients, constitutive parameters of Swift’s law, sheet thickness, friction coefficient and blank-holder force is studied. The objective is to evaluate the variability influence of these input parameters, on the variability of equivalent plastic strain, geometry change, thickness reduction, punch force and springback. This sensitivity analysis is made using two techniques: PAWN indices and Sobol indices.Before applying the sensitivity analysis, it is important to understand which zones of the square cup were more affected by inputs variability. It was concluded that the cup flange and the region near the curvature radius of the die are the most affected regions, and the cup base is the region least affected by the variability in the input parameters.Afterwards, the stabilization of the sensitivity indices was evaluated and it was concluded that, for the same results precision, the PAWN indices require only 7.7% to 12.8% of the simulations used to evaluate the Sobol indices. The sensitivity analysis showed that the input parameters with more influence on the variability of the output parameters are: the hardening coefficient, the parameter C of Swift’s law and the anisotropy coefficient at 90º. Both sensitivity indices provide similar results for all outputs, except springback, for which we can conclude that PAWN indices are more accurate than Sobol indices when the data follows a multimodal distribution.
Ruivo, Miguel António Fernandes Pereira. "Estudo numérico do processo de estampagem de uma taça quadrada: uma análise estocástica." Master's thesis, 2020. http://hdl.handle.net/10316/92101.
Повний текст джерелаIn the industry, it is becoming more and more important to guarantee the quality of the produced components. To ensure this quality, it is important to define which parameters should be considered important and which ones’ control must be prioritized. With this goal, in this dissertation is presented a numerical study about the influence of the variability of the parameters associated with the mechanical behavior of the material and the process conditions, in the stamping results of a square cup. In this analysis is assumed variability in the elastic properties, Swift law constitutive parameters, anisotropy coefficients, sheet thickness, friction coefficient and in the blank-holder force. The effect of these parameters’ variability is evaluated in the punch force, equivalent plastic strain, thickness reduction, change of geometry and in the springback.Firstly, the quasi-Monte Carlo method was used to evaluate the average and standard deviation values of the simulation outputs, considering the variability of the input parameters. With this analysis, it was possible to conclude that the change of geometry and the springback are the outputs most sensible to the variability of the input parameters; and that the top of the square cup is the zone where the effect of the variability is more significant.Afterwards, a variance-based sensitivity analysis was done. In this analysis, first order Sobol indices were used to identify the input parameters with more effect in the output’s variability, and total Sobol indices were used to estimate the effect of the interactions between the different input parameters in the outputs’ variability. It was concluded that the input parameters with more effect are the Swift law coefficients, n and C, the anisotropy coefficient r_90 and that the effect of the interactions is only relevant for the geometry change. Furthermore, it was verified that the Sobol indices are not suitable to evaluate the influence of the input parameters in the springback, since this output have a multimodal distribution, thus different sensitivity indices must be used.With the goal to reduce the number of necessary simulations to compute the Sobol indices, a Polynomial Chaos Expansion metamodel is utilized. The values obtained for the Sobol indices using this metamodel were compared to the ones obtained with the quasi-Monte Carlo method. It was concluded that the use of the metamodel allowed to significantly reduce the computation time associated to the sensitivity analysis, without compromising the results.
Na indústria, cada vez mais é dada importância à qualidade final dos componentes produzidos. De forma a garantir esta qualidade, é importante definir quais os parâmetros a considerar como sendo importantes e cujo controlo deve ser prioritário. Com isto em vista, nesta dissertação é apresentado um estudo numérico sobre a influência da variabilidade dos parâmetros associados ao comportamento mecânico do material e às condições do processo, nos resultados da estampagem de uma taça quadrada. Nesta análise assume-se variabilidade nas propriedades elásticas, nos parâmetros constitutivos da lei de Swift, nos coeficientes de anisotropia, na espessura da chapa, no coeficiente de atrito e na força de aperto do cerra-chapas. O efeito da variabilidade destes parâmetros é avaliado na força do punção, na deformação plástica equivalente, na redução de espessura, na alteração de geometria e no retorno elástico. Inicialmente, utilizou-se o método de quase-Monte Carlo para avaliar a média e o desvio padrão dos resultados das simulações, tendo em conta a variabilidade nos parâmetros de entrada. Com base nesta análise foi possível concluir que a alteração de geometria e o retorno elástico são as respostas mais sensíveis à variabilidade nos parâmetros de entrada; sendo que a zona da aba da taça é aquela cujo efeito da variabilidade é mais significativo. Posteriormente, realizou-se uma análise de sensibilidade com base na variância. Nesta análise, foram utilizados índices de Sobol de primeira ordem, para identificar os parâmetros de entrada com maior efeito na variabilidade dos resultados, e também índices de Sobol totais, para estimar o efeito das interações entre os vários parâmetros na variabilidade dos resultados. Concluiu-se que os parâmetros mais importantes são o n e o C da lei de Swift, o coeficiente de anisotropia r_90 e que o efeito das interações apenas é relevante para a alteração de geometria. Para além disso, verificou-se que os índices de Sobol não são adequados para avaliar a influência no retorno elástico, uma vez que esta resposta tem uma distribuição multimodal, pelo que devem ser utilizadas outros índices de sensibilidade.Com o objetivo de reduzir o número de simulações necessário à computação dos índices de Sobol, é utilizado o metamodelo Polynomial Chaos Expansion. Os resultados dos índices de Sobol obtidos com o metamodelo foram comparados com os obtidos através do método de quase-Monte Carlo. Concluiu-se que a utilização do metamodelo permitiu reduzir significativamente o tempo de computação associado à análise de sensibilidade, sem prejudicar os resultados da mesma.
Brito, Miguel Abranches e. Menezes Peixoto de. "Análise de variabilidade na simulação numérica do processo de estampagem de um perfil em U." Master's thesis, 2020. http://hdl.handle.net/10316/92244.
Повний текст джерелаOs processos de conformação estão entre os mais utilizados na indústria automóvel, aeronáutica e metalomecânica. A procura por produtos com melhor qualidade e menores custos de produção tem incentivado o interesse crescente por um robusto desenvolvimento e otimização destes processos, que tem em conta a variabilidade inerente aos mesmos. De forma a perceber quais as fontes de variabilidade mais importantes na estampagem de um perfil em U, esta tese apresenta um estudo numérico que visa analisar a influência da variabilidade de onze parâmetros de entrada diferentes (módulo de Young, coeficiente de Poisson, coeficientes de anisotropia, parâmetros da lei de Swift, espessura inicial da chapa, coeficiente de atrito e força do cerra-chapas) nos resultados de conformação (Deformação Plástica Equivalente, Redução de Espessura, Retorno Elástico, Alteração de Geometria e Força do Punção).Inicialmente foi utilizado o método de quasi-Monte Carlo com uma sequência de Sobol para analisar a influência da variabilidade dos parâmetros de entrada na variabilidade dos resultados do processo. Nesta fase, conclui-se que a variabilidade dos parâmetros de entrada afeta todos os resultados do perfil em U, principalmente a Alteração de Geometria. De seguida, através do cálculo dos índices de Sobol, é estimada a influência de cada um dos parâmetros de entrada nos valores máximos das variáveis de saída. Com esta análise foi possível concluir que o coeficiente de atrito, a espessura inicial da chapa, o coeficiente de encruamento e a constante C da lei de Swift, são os parâmetros de entrada que mais influenciam os resultados em estudo, sendo que as interações entre parâmetros de entrada só são relevantes na Alteração de Geometria. Por último, foram calculadas as distribuições dos índices de Sobol para todos os nós, de forma a analisar a influência dos parâmetros de entrada nos resultados ao longo do perfil em U. Esta análise permitiu concluir que o coeficiente de atrito, a constante C da lei de Swift e o coeficiente de encruamento são os parâmetros com mais influência na zona da aba e da curvatura superior, que o coeficiente de atrito é o parâmetro com mais influência na zona da curvatura inferior e que a espessura inicial e o coeficiente de atrito são os parâmetros com mais influência na zona da parede do perfil em U.
Forming processes are among the most used in the automotive, aeronautic and metalworking industry. The demand for quality enhanced products and lower production costs has encouraged the growing interest for a robust development and optimization of these processes which takes into account the inherent variability in them. In order to understand which are the most important sources of variability of a U-rail stamping process, this thesis presents a numerical study that aims to analyse the influence of the variability of eleven different input parameters (Young’s modulus, Poisson’s coefficient, anisotropy coefficients, parameters of Swift’s hardening law, initial thickness of the sheet metal, friction coefficient and Blank Holder force) in the forming process results (Equivalent Plastic Strain, Thickness Reduction, Springback, Geometry Modification and Punch Force).Initially the quasi-Monte Carlo method with a Sobol sequence was used to analyse the influence of the variability of the input parameters on the variability of the process results. In this phase, it is concluded that the variability of the input parameters affects all the results of the U-rail, mainly the Geometry Modification. Then the influence of each of the input parameters, for the maximum values of the output variables, is estimated by calculating the Sobol indices. With this analysis it was possible to conclude that the friction coefficient, the initial thickness of the sheet metal, the hardening coefficient and the Swift’s Law constant, C, are the input parameters that most influence the results under study, and the interactions between input parameters are only relevant for the Geometry Modification. Lastly, distributions of the Sobol indices were calculated for all nodes, in order to analyse the influence of the input parameters throughout the U-rail geometry. This analysis allowed to conclude that the friction coefficient, Swift’s law constant C and the hardening coefficient are the parameters with the most influence in the tab and upper curvature areas, that the friction coefficient is the parameter with the most influence in the lower curvature area and that the initial thickness and the friction coefficient are the parameters with the most influence in the wall area of the U-rail.
Câmara, Bernardo Monteiro dos Santos de Aguiar da. "Análise de sensibilidade do ensaio biaxial em provete cruciforme." Master's thesis, 2021. http://hdl.handle.net/10316/94300.
Повний текст джерелаNeste trabalho é realizada uma análise de sensibilidade para avaliar a influência dos parâmetros do material nos resultados do ensaio biaxial em provete cruciforme. Esta análise é feita com auxílio dos índices de Sobol de 1ª ordem, que permitem quantificar a sensibilidade de cada parâmetro do material, e dos índices de Sobol totais, que permitem avaliar a influência das interações entre esses parâmetros. Nesta análise foram estudados os parâmetros s0, k e n da lei de encruamento de Swift, e F, G e N do critério de plasticidade anisotrópico de Hill’48. A influência desses parâmetros é avaliada nos resultados do ensaio biaxial (variáveis de saída), nomeadamente, as forças máximas segundo 0x e 0y, as deformações principais e1 e e2, a deformação plástica equivalente eeq, a redução de espessura e a trajetória de deformação. Todos estes resultados do ensaio biaxial foram obtidos numericamente, com recurso ao programa de elementos finitos DD3IMP.Inicialmente, recorreu-se à análise de sensibilidade para avaliar a influência dos parâmetros do material nos valores máximos das variáveis de saída. Desta análise concluiu-se que: os parâmetros K e n da lei de Swift são os mais influentes no valor máximo das forças e da deformação principal e1; o valor máximo da deformação plástica equivalente é afetado principalmente pelos parâmetros G e n, embora os restantes parâmetros também tenham uma influência relevante; os valores máximos de e2 e da redução de espessura são essencialmente afetados pelo parâmetro G do critério de Hill’48.Posteriormente analisou-se os parâmetros que mais influenciam os resultados do ensaio em cada região do provete. Desta análise concluiu-se no geral que: G é o parâmetro que mais influencia as variáveis de saída no centro do provete e no braço do eixo 0x; F é o parâmetro que mais influencia as variáveis de saída no braço do eixo 0y; as variáveis de saída na zona do raio de curvatura do provete são mais sensíveis aos parâmetros n, N e G. No geral, pode-se afirmar que os parâmetros do critério de plasticidade Hill’48 são os que mais influenciam os resultados ao longo do provete cruciforme.
In this work, a sensitivity analysis is performed to evaluate the influence of the material parameters on the results of the biaxial test on a cruciform specimen. This analysis is done with the help of 1st order Sobol indices, which quantify the sensitivity of each material parameter, and total Sobol indices, which allow to evaluate the influence of the interactions between these parameters. In this analysis, the parameters s0, K and n of the Swift hardening law, and the parameters F, G and N of the Hill'48 anisotropic yield criterion were studied. The influence of these parameters is evaluated on the results of the biaxial test (output variables, namely, the maximum forces along 0x and 0y, the principal strains e1 and e2, the equivalent plastic strain eeq, the thickness reduction and the strain paths. All these results of the biaxial test were numerically obtained, resorting to the finite element software DD3IMP.Initially, the sensitivity analysis was used to assess the influence of the material parameters on the maximum values of the output parameters. From this analysis, it was concluded that: the parameters K and n of Swift's law are the most influential in the maximum values of the forces and the principal strain e1; the maximum value of the equivalent plastic strain is mainly affected by G and n, although the remaining parameters also have a relevant influence; the maximum values of e2 and thickness reduction are essentially affected by the parameter G of the Hill’48 criterion.Afterwards, the parameters that most influence the test results in each specimen region were analyzed. From this analysis, it was concluded in general that: G is the parameter that most influences the output variables in the center of the specimen and in the 0x arm; F is the parameter that most influences the output variables in the 0y arm; the output variables in the radius of curvature of the specimen are more sensitive to the parameters n, N and G. In general, it can be stated that the parameters of the Hill’48 yield criterion are the ones that most influence the results along the cruciform specimen.