Probabilistic optimal design in the presence of random fields

This article describes a methodology to incorporate a random field in a probabilistic optimization problem. The approach is based on the extraction of the features of a random field using a reduced number of experimental observations. This is achieved by proper orthogonal decomposition. Using Lagrange interpolation, a modified random field is obtained by changing the contribution of each feature. The contributions are controlled using scalar parameters, which can be considered as random variables. This allows one to perform a random-field-based probabilistic optimization with few random variables. The methodology is demonstrated on a tube impacting a rigid wall for which a random field modifies the planarity of the tube's wall.