TY - CHAP A1 - Most, Thomas A1 - Bucher, Christian ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - ADAPTIVE RESPONSE SURFACE APPROACH USING ARTIFICIAL NEURAL NETWORKS AND MOVING LEAST SQUARES N2 - In engineering science the modeling and numerical analysis of complex systems and relations plays an important role. In order to realize such an investigation, for example a stochastic analysis, in a reasonable computational time, approximation procedure have been developed. A very famous approach is the response surface method, where the relation between input and output quantities is represented for example by global polynomials or local interpolation schemes as Moving Least Squares (MLS). In recent years artificial neural networks (ANN) have been applied as well for such purposes. Recently an adaptive response surface approach for reliability analyses was proposed, which is very efficient concerning the number of expensive limit state function evaluations. Due to the applied simplex interpolation the procedure is limited to small dimensions. In this paper this approach is extended for larger dimensions using combined ANN and MLS response surfaces for evaluating the adaptation criterion with only one set of joined limit state points. As adaptation criterion a combination by using the maximum difference in the conditional probabilities of failure and the maximum difference in the approximated radii is applied. Compared to response surfaces on directional samples or to plain directional sampling the failure probability can be estimated with a much smaller number of limit state points. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29922 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER - TY - JOUR A1 - Most, Thomas A1 - Bucher, Christian T1 - Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization JF - International Journal for Numerical and Analytical Methods in Geomechanics N2 - Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2007 SP - 285 EP - 305 ER - TY - JOUR A1 - Most, Thomas T1 - A natural neighbour-based moving least-squares approach for the element-free Galerkin method JF - International Journal for Numerical Methods in Engineering N2 - A natural neighbour-based moving least-squares approach for the element-free Galerkin method KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2007 SP - 224 EP - 252 ER - TY - JOUR A1 - Most, Thomas A1 - Bucher, Christian T1 - Probabilistic analysis of concrete cracking using neural networks and random fields JF - Probabilistic Engineering Mechanics N2 - Probabilistic analysis of concrete cracking using neural networks and random fields KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2007 SP - 219 EP - 229 ER - TY - JOUR A1 - Most, Thomas A1 - Ishii, H. A1 - Geng, X. A1 - Bolzern, P. A1 - Colaneri, P. A1 - De Nicolao, G. T1 - Discussion on Almost sure stability of stochastic linear systems with ergodic parameters JF - European Journal of Control N2 - Discussion on Almost sure stability of stochastic linear systems with ergodic parameters KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2008 SP - 124 EP - 130 ER - TY - JOUR A1 - Most, Thomas A1 - Bucher, Christian T1 - New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares JF - Engineering Analysis with Boundary Elements N2 - New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2008 SP - 461 EP - 470 ER - TY - JOUR A1 - Bucher, Christian A1 - Most, Thomas T1 - A comparison of approximate response functions in structural reliability analysis JF - Probabilistic Engineering Mechanics N2 - A comparison of approximate response functions in structural reliability analysis KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2008 SP - 154 EP - 163 ER - TY - CHAP A1 - Most, Thomas ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - ESTIMATING UNCERTAINTIES FROM INACCURATE MEASUREMENT DATA USING MAXIMUM ENTROPY DISTRIBUTIONS N2 - Modern engineering design often considers uncertainties in geometrical and material parameters and in the loading conditions. Based on initial assumptions on the stochastic properties as mean values, standard deviations and the distribution functions of these uncertain parameters a probabilistic analysis is carried out. In many application fields probabilities of the exceedance of failure criteria are computed. The out-coming failure probability is strongly dependent on the initial assumptions on the random variable properties. Measurements are always more or less inaccurate data due to varying environmental conditions during the measurement procedure. Furthermore the estimation of stochastic properties from a limited number of realisation also causes uncertainties in these quantities. Thus the assumption of exactly known stochastic properties by neglecting these uncertainties may not lead to very useful probabilistic measures in a design process. In this paper we assume the stochastic properties of a random variable as uncertain quantities caused by so-called epistemic uncertainties. Instead of predefined distribution types we use the maximum entropy distribution which enables the description of a wide range of distribution functions based on the first four stochastic moments. These moments are taken again as random variables to model the epistemic scatter in the stochastic assumptions. The main point of this paper is the discussion on the estimation of these uncertain stochastic properties based on inaccurate measurements. We investigate the bootstrap algorithm for its applicability to quantify the uncertainties in the stochastic properties considering imprecise measurement data. Based on the obtained estimates we apply standard stochastic analysis on a simple example to demonstrate the difference and the necessity of the proposed approach. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Architektur KW - Computerunterstütztes Verfahren KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28732 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER -