Statistical inference of empirical constituents in partitioned analysis from integral-effect experiments

Garrison N. Stevens (AMPP-4 Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA)
Sez Atamturktur (Department of Mechanical Engineering, Clemson University, Clemson, South Carolina, USA)
D. Andrew Brown (Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, USA)
Brian J. Williams (CCS-6 Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA)
Cetin Unal (W-13 Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA)

Engineering Computations

ISSN: 0264-4401

Publication date: 16 April 2018



Partitioned analysis is an increasingly popular approach for modeling complex systems with behaviors governed by multiple, interdependent physical phenomena. Yielding accurate representations of reality from partitioned models depends on the availability of all necessary constituent models representing relevant physical phenomena. However, there are many engineering problems where one or more of the constituents may be unavailable because of lack of knowledge regarding the underlying principles governing the behavior or the inability to experimentally observe the constituent behavior in an isolated manner through separate-effect experiments. This study aims to enable partitioned analysis in such situations with an incomplete representation of the full system by inferring the behavior of the missing constituent.


This paper presents a statistical method for inverse analysis infer missing constituent physics. The feasibility of the method is demonstrated using a physics-based visco-plastic self-consistent (VPSC) model that represents the mechanics of slip and twinning behavior in 5182 aluminum alloy. However, a constituent model to carry out thermal analysis representing the dependence of hardening parameters on temperature is unavailable. Using integral-effect experimental data, the proposed approach is used to infer an empirical constituent model, which is then coupled with VPSC to obtain an experimentally augmented partitioned model representing the thermo-mechanical properties of 5182 aluminum alloy.


Results demonstrate the capability of the method to enable model predictions dependent upon relevant operational conditions. The VPSC model is coupled with the empirical constituent, and the newly enabled thermal-dependent predictions are compared with experimental data.


The method developed in this paper enables the empirical inference of a functional representation of input parameter values in lieu of a missing constituent model. Through this approach, development of partitioned models in the presence of uncertainty regarding a constituent model is made possible.



Garrison N. Stevens, Sez Atamturktur, D. Andrew Brown, Brian J. Williams and Cetin Unal (2018) "Statistical inference of empirical constituents in partitioned analysis from integral-effect experiments", Engineering Computations, Vol. 35 No. 2, pp. 672-691

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