Bayesian sensitivity analysis of a nonlinear finite element model

A major problem in uncertainty and sensitivity analysis is that the computational cost of propagating probabilistic uncertainty through large nonlinear models can be prohibitive when using conventional methods (such as Monte Carlo methods). A powerful solution to this problem is to use an emulator, which is a mathematical representation of the model built from a small set of model runs at specified points in input space. Such emulators are massively cheaper to run and can be used to mimic the “true” model, with the result that uncertainty analysis and sensitivity analysis can be performed for a greatly reduced computational cost. The work here investigates the use of an emulator known as a Gaussian process (GP), which is an advanced probabilistic form of regression. The GP is particularly suited to uncertainty analysis since it is able to emulate a wide class of models, and accounts for its own emulation uncertainty. Additionally, uncertainty and sensitivity measures can be estimated analytically, given certain assumptions. The GP approach is explained in detail here, and a case study of a finite element model of an airship is used to demonstrate the method. It is concluded that the GP is a very attractive way of performing uncertainty and sensitivity analysis on large models, provided that the dimensionality is not too high.

► An uncertainty analysis technique, new to structural dynamics, is shown. ► A Gaussian process emulator is built, using a small number of training runs. ► The emulator is used to analytically infer uncertainty and sensitivity measures. ► There are substantial computational savings compared to Monte Carlo. ► The approach is demonstrated on a finite element model of an airship.