Uncertainty Modelling in Engineering: Difference between revisions
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Macroscopically heterogeneous materials, characterized mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach. It is convenient to introduce stochastic approach with uncertain material parameters quantified as random fields. Nevertheless, introduction of random fields brings higher demands on quality of input data, especially on inputs of covariance functions representing the spatial randomness. The present contribution is devoted to the construction of random fields based on image analysis utilizing statistical descriptors, which were developed to describe the different morphology of two-phase random material. The whole concept is demonstrated on a simple numerical example of stationary heat conduction where interesting phenomena can be clearly understood. | Macroscopically heterogeneous materials, characterized mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach. It is convenient to introduce stochastic approach with uncertain material parameters quantified as random fields. Nevertheless, introduction of random fields brings higher demands on quality of input data, especially on inputs of covariance functions representing the spatial randomness. The present contribution is devoted to the construction of random fields based on image analysis utilizing statistical descriptors, which were developed to describe the different morphology of two-phase random material. The whole concept is demonstrated on a simple numerical example of stationary heat conduction where interesting phenomena can be clearly understood. | ||
===== 14:00-14:30 Eliška Janouchová: | ===== 14:00-14:30 Eliška Janouchová: Probabilistic Estimation of Material Parameters Based on a Set of Experimental Curves ===== | ||
Advances in meta-modelling and increasing computational capacity of modern computers permitted many researches to focus on parameter identification in probabilistic setting. Bayesian approach to parameter identification has several appealing advantages comparing to traditional data fitting, e.g. identification problem is well-posed, results provide probabilistic description of the actual knowledge about the parameters and not just a single value etc. However the obtained distribution from Bayesian inference describes uncertainty in our knowledge of the deterministic values. Now we focus on a reformulation of the Bayesian inference to identify the parameters along with their variations in heterogeneous materials. | |||
===== 14:30-15:00 Eva Myšáková: ===== | ===== 14:30-15:00 Eva Myšáková: ===== | ||
Revision as of 08:27, 27 June 2014
Solid Mechanics Seminar, 13:00-16:00, Friday, 27 June 2014
Uncertainty modelling in Engineering
13:00-13:30 Jan Havelka: Efficient methods for propagation of uncertainty in description of groundwater flow
Diploma thesis supervised by Jan Sýkora
Numerical simulations have become popular approach for solving engineering problems. The progress of computer technology then enables to solve more complex models and consequently to get more information about system behavior. Such a complex problem is here represented by the extension of deterministic material model by uncertain inputs, which may take origin in the lack or inaccuracy of the measurements. Therefore the aim of this work is to create an algorithms and to compare currently used methods for solving partial differential equations with uncertain input parameters in the description of groundwater flow.
13:30-14:00 Anna Kučerová: Stochastic Modelling of Heterogeneous Materials based on Image Analysis
Macroscopically heterogeneous materials, characterized mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach. It is convenient to introduce stochastic approach with uncertain material parameters quantified as random fields. Nevertheless, introduction of random fields brings higher demands on quality of input data, especially on inputs of covariance functions representing the spatial randomness. The present contribution is devoted to the construction of random fields based on image analysis utilizing statistical descriptors, which were developed to describe the different morphology of two-phase random material. The whole concept is demonstrated on a simple numerical example of stationary heat conduction where interesting phenomena can be clearly understood.
14:00-14:30 Eliška Janouchová: Probabilistic Estimation of Material Parameters Based on a Set of Experimental Curves
Advances in meta-modelling and increasing computational capacity of modern computers permitted many researches to focus on parameter identification in probabilistic setting. Bayesian approach to parameter identification has several appealing advantages comparing to traditional data fitting, e.g. identification problem is well-posed, results provide probabilistic description of the actual knowledge about the parameters and not just a single value etc. However the obtained distribution from Bayesian inference describes uncertainty in our knowledge of the deterministic values. Now we focus on a reformulation of the Bayesian inference to identify the parameters along with their variations in heterogeneous materials.