Optimization of Gaussian Random Fields

TL;DR

This paper develops a gradient-based optimization framework to adjust the mean and covariance of Gaussian random fields, enabling control over system output statistics in engineering applications.

Contribution

It introduces a novel sensitivity analysis method for the statistics of system outputs with respect to Gaussian random field parameters, integrated into an optimization process.

Findings

Successfully optimized variance in a model problem.

Optimized manufacturing tolerances for a gas turbine blade.

Demonstrated effective control of output statistics through parameter adjustments.

Abstract

Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of the system outputs. We present an approach for computing the sensitivity of the statistics of system outputs with respect to the parameters describing the mean and covariance of the distributed uncertainty. This sensitivity information is then incorporated into a gradient-based optimizer to optimize the structure of the distributed uncertainty to achieve desired output statistics. This framework is applied to perform variance optimization for a model problem and to optimize the manufacturing tolerances of a gas turbine compressor blade.