# Uncertainty Modelling in Engineering

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

Presentation: PPTX

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

Presentation: PDF

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

Presentation: PDF

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: Adaptive procedure for meta-model updating & Uniform space-filling design of experiments in hyperspheres

Presentation: PDF

The talk is focused on an adaptive parallel two-criterial procedure for updating of the meta-model. It is done by addition of new design points into the design of experiments which serves as base for the meta-model construction. New points are added into unsampled regions and in the vicinity of the limit state. Because the meta-model covers only limited domain it is needed to improve the procedure so that the relevant points from the outside of the domain can also be added into the design. The second part of the talk is aimed on the generation of uniform designs in hyperspheres. The clustering tool and an algorithm for removal of superfluous points from the intentionally overcrowded initial design are employed.

##### 15:00-15:30 Adéla Pospíšilová: Inverse Reliability Optimization

Presentation: PDF

A multi-objective Reliability-Based Design Optimization (RBDO) deals with a search for a set of optimal trade-off solutions with a minimum weight and the maximum reliability of the structure (or the minimum probability of failure). The performance measure as a difference between the value of the limit state function and zero level is constant in the classical RBDO formulation. From a different point of view, some tasks require a fixed probability of failure and finding the compromising solutions for the minimization of costs and maximization of the performance measure to find the most advantageous solutions. This task is called an inverse Reliability-Based Design Optimization (iRBDO) and is formulated in a multi-objective sense in this talk. To evaluate the performance measure, the inverse Monte Carlo is utilized.