Object Shape Error Modelling and Simulation During Early Design Phase by Morphing Gaussian Random Fields

Gaussian Random Vector Fields in Trajectory Modelling

This paper proposes the use of Gaussian random vector fields as a generative model to describe a set of observed trajectories in a 2-dimensional space. The observed trajectories are sequences of points in space sampled from continuous trajectories that are assumed to have been generated by an underlying velocity field. Given the observed velocities connecting the trajectory points, a vector fie...

Numerical Simulation of Non-Gaussian Random Fields

The non-Gaussian random fields are used to modelling some dynamic loads generated by wind turbulence, ocean waves, earthquake ground motion etc. These fields also represent the uncertain properties of different materials (reinforced concrete, composite, soils etc.). This paper presents some methods and the corresponding algorithms to the numerical simulation of stationary non-Gaussian random fi...

Efficient Modelling and Simulation of Random Fields

The application of random fields to real-world problems, e.g. for assessing the robustness and reliability of structural components with geometrical or material tolerances, has gained much interest recently. However, the large number of random variables involved inhibits the use of accurate and efficient methods to compute failure probabilities. Several measures to handle the large dimension or...

Modelling Gaussian Fields and Geostatistical Data Using Gaussian Markov Random Fields

Information geometry, simulation and complexity in Gaussian random fields

Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this paper, we propose to quantify how changes in the spatial dependence structure affect the Riemannian metric tensor that equips the model’s parametric space. Defi...