A Taylor Expansion Approach for Computing Structural Performance Variation From Population-Based Shape Data

Abstract

Rapid advancement of sensor technologies and computing power has led to wide availability of massive population-based shape data. In this paper, we present a Taylor expansion-based method for computing structural performance variation over its shape population. The proposed method consists of four steps: (1) learning the shape parameters and their probabilistic distributions through the statistical shape modeling (SSM), (2) deriving analytical sensitivity of structural performance over shape parameter, (3) approximating the explicit function relationship between the finite element (FE) solution and the shape parameters through Taylor expansion, and (4) computing the performance variation by the explicit function relationship. To overcome the potential inaccuracy of Taylor expansion for highly nonlinear problems, a multipoint Taylor expansion technique is proposed, where the parameter space is partitioned into different regions and multiple Taylor expansions are locally conducted. It works especially well when combined with the dimensional reduction of the principal component analysis (PCA) in the statistical shape modeling. Numerical studies illustrate the accuracy and efficiency of this method.