Explore chapters and articles related to this topic
Review of The Theory of Stochastic Modelling of Subsurface Porous Flow and Transport
Published in Amro M.M. Elfeki, Gerard J.M. Uffink, Frans B.J. Barends, Groundwater Contaminant Transport, 2017
Amro M.M. Elfeki, Gerard J.M. Uffink, Frans B.J. Barends
Random fields are multi-dimensional stochastic processes. Some researchers consider random fields as a more general theory from which the uni-dimensional stochastic process is a special case. A random field is defined as a mathematical way to describe spatial variations of properties of a physical phenomenon. These spatial variations can be studied by means of stochastic processes representing these variations in a continuous sense over the space considered or at discrete points in it.
Measuring stiffness of soils in situ
Published in Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto, Computer Methods and Recent Advances in Geomechanics, 2014
Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto
Multiple realizations of random fields can be generated by using different random seeds. In this study, 400 realizations of random fields were generated using Monte Carlo simulation. These same realizations were used in the lower bound limit analysis, upper bound limitanalysis, and the finite elementanalysis allowing comparison of results.
Inelastic static and dynamic seismic response assessment of frames with stochastic properties
Published in Structure and Infrastructure Engineering, 2021
Georgios Balokas, Michalis Fragiadakis
The stochastic analysis accounts for uncertainty in several parameters, including material properties, geometry and loads, which are represented by stochastic fields. A stochastic (or random) field is a mapping from a random outcome to a function of space (or time). If is the expected value of the model parameter of interest k (e.g. Young’s modulus E, yield stress σy), the spatial uncertainty is provided by the following random field: where is a zero-mean field. There are few experimental databases for the statistical characterisation of material properties, while it is common belief that their probabilistic characteristics are closer to non-Gaussian rather than Gaussian. In order to generate such a field, a Gaussian one has to be first generated and then it should be transformed to non-Gaussian.
Reliability assessment of large hydraulic structures with spatially distributed measurements
Published in Structure and Infrastructure Engineering, 2020
Sebastian Geyer, Iason Papaioannou, Claus Kunz, Daniel Straub
Spatially variable properties are probabilistically modelled as random fields. A random field can be defined as a collection of random variables indexed by a spatial coordinate , where Ω is a one-, two- or three-dimensional spatial domain. At each point in space, is a random variable with probability density function (PDF) . This results in an infinite number of random variables that define the random field and hence discretization approaches are needed to represent random fields in practice. The spatial correlation of the random field at different points is described by the autocorrelation function (Vanmarcke, 2010).
Influence of different sources of microstructural heterogeneity on the degradation of asphalt mixtures
Published in International Journal of Pavement Engineering, 2018
Silvia Caro, Daniel Castillo, Masoud Darabi, Eyad Masad
Random fields is a stochastic tool that generates probable, spatially correlated distributions of numbers (e.g. values of a parameter) within a spatial domain (Vanmarcke 1983). Hereby, ‘spatially correlated’ means that the values assigned to near locations are similar. In other words, random fields permit the generation of matrices, ‘maps’ or ‘fields’ of a certain parameter of interest that follows certain spatial correlation. The magnitudes of the parameter are randomly generated and the location of the generated values within the spatial domain is also randomly assigned after following specific correlation patterns. Previous applications of random fields to model heterogeneous materials in airfield pavements, clay deposits and flexible pavements include the works by Lua and Sues (1996), Stuedlein et al. (2012), Castillo and Caro (2014) and Lea and Harvey (2015).