Application of Functional Regression in Modeling Mechanical Properties of Materials

• Activity Number: 267
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Hao Ji* and Ana Kupresanin and Sejin Oh and Ian Darnell
• Companies: UC Davis and Lawrence Livermore National Laboratory and Lawrence Livermore National Laboratory and Lawrence Livermore National Laboratory
• Keywords: Functional Data Analysis ; Functional Quasi-likelihood Regression ; Functional Principal Component Analysis ; Uncertainty Quantification

Abstract

The predictive modeling of the deformation of materials under extreme conditions of pressure and temperature is important. Description of material response in this regime is difficult because laboratory testing is very expensive and often impossible.

We analyze data collected from compression tests of an insensitive high explosive material. There are 72 compression tests conducted on the material. Different experiment regimes (temperature and strain rate), different histories of material specimens used, along with the stress-strain curves are recorded for these experiments. The goal is to characterize uncertainties in the maximal stress and the corresponding strain under different experimental regimes and with specimens of different histories.

Standard statistical models do not perform well due to lack of experimental design. In order to utilize the similar patterns of the stress-strain curves, we treat them as functional data, and regress the curves on the vectors of predictors using functional quasi-likelihood regression and functional principal component analysis. Confidence regions for maximal stress-strain coordinates are obtained.