Model Calibration Using Optimization Techniques

Fatma Koçer-Poyraz –  Director of Business Development

Introduction

When we think of optimization, we naturally think of finding the design with minimum cost, maximum performance, etc. However, we can use optimization methods for objectives other than minimizing or maximizing. One of these use cases is to meet a set of target values; so we need neither to minimize a response nor maximize it. We instead need to make sure that it achieves the target value.

A typical application comprises model calibration problems, such as simulation material model calibration to match to test data. We can formulate these cases as minimizing the difference between sets of data leading us down the path to use optimization methods for efficient and effective solution- finding.  How we calculate the difference may depend on the application, but a very common calculation that works well for most problems is to minimize the sum of normalized-difference-squared. Another common calculation may involve calculating the area between two curves.

The first aspect of solving such problems easily is the method selection. The second aspect is the ease of setup, and the third aspect is the post-processing. In HyperStudy, we have an objective function formulation called System Identification. System identification allows users to set target values to a number of responses and automatically creates the difference equation and uses it as the objective function. In the pos- processing site, HyperStudy lists the values of all objectives, the delta between them, and the targets and the normalized deltas. We will now go through an application that uses system identification for material model calibration.

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