Machine learning to build reduced order models of solid mechanic models with uncertainty

Abstract

In civil engineering, mining and the petroleum industry in-situ stress state knowledge is fundamental. To estimate the stress state in-situ methods are applied, these methods are not sufficient to fully estimate the stress field in 3D due to the sparsity of observations and the paucity of stress measurements. In the current master’s thesis, a framework is developed through Reduced-Order Models (ROM) to predict the vertical displacement field, and consequently the stress state, when variations in the material and geometric properties of the problem are introduced. To achieve this, four different methods are tested in four different examples, one of them with uncertainty in the properties of the material and the last three with geometric uncertainties. The four methods tested are Artificial Neural Network with Levenberg Marquardt training algorithm (LM), Artificial Neural Network with Gradi-ent Descent with Momentum training algorithm (GDM), Proper Orthogonal Decom-position (POD) and Encapsulated Proper Generalized Decomposition (Encapsulated PGD) The developed framework consists of three parts. First, the data generator module creates a series of samples through Latin Hypercube Sampling varying the geometric or material properties of the problem and then obtains the vertical displacement field by the Finite Element Method (FEM) simulations. The second module applies any of the four methods to build a reduced-order model and finally, the third module is applied, if necessary, to reconstruct the vertical displacement field.