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Parameteridentifikation (5)

Contents

The identification of model parameters is of utmost importance for accurate numerical simulations of complex materials and structures. Usually, the model parameters are computed by minimizing the distance between experimental data and their numerical counterparts, e.g., by employing a least-squares method.

In order to solve the aforementioned minimization problems, the fundamentals of non-linear optimization are introduced in the first part of the course. Both theoretical as well as numerical aspects are covered. In addition to gradient-based approaches, generic algorithms are also presented. While unconstrained problems are considered first, the extensions necessary for constrained optimization are subsequently discussed. In addition to the fundamentals, the application of the algorithms to solids mechanics is also addressed, e.g., the parameter identification of elasto-plastic solids. This application includes the parameter identification based on (initial) boundary value problems which are characterized by inhomogeneous fields (such as the strains). 

After successfully participating in the course, the students are able to apply methods of parameter identification to different classes of materials and to implement the respective algorithms in computer codes. These algorithms – as well as their underlying fundamentals – can be transferred to a broad variety of other technical and scientific problems.


Lecture

 

Semester Lecturer Dates Location
SS 2019 Prof. Dr.-Ing. Jörn Mosler Mondays, 08:30-10:00
Wednesdays, 08:30-10:00
MB I, Room 165


In the following you find the presentation slides from the lecture:

Documents Contents
Chapter 0 Motivation
Chapter 1 Preliminaries
Chapter 2.1 Unconstrained non-linear optimization - step size strategies
Chapter 2.2 Unconstrained non-linear optimization - descent directions
Chapter 3 Constrained non-linear optimization
Chapter 4 Uniqueness of model parameters
Chapter 5 Parameter identification (for mechanical problems)




Exercise

 

Semester Dates Location
SS 2019 Mondays, 08:30-10:00
Wednesdays, 08:30-10:00
MB I, Room 163
(CIP-Pool)

 

The exact dates of the exercises are are flexibly coordinated with the lecture dates as required and are usually announced in the lecture or exercise, respectively. 

The following documents are suitable for the preparation of the respective exercise. All participants are advised to familiarize themselves with the documents before the exercise takes place. This ensures that all participants are at a comparable level at the beginning of each exercise.

 

Date

Topic

Coding-Framework

15.04. Exercise 1 - The Method of Steepest Descent Ex01-Framework
17.04. Exercise 1 - The Method of Steepest Descent -
06.05. Exercise 2 - The Conjugate Gradient Method Ex02-Framework
27.05. Exercise 3 - The Active Set strategy -
29.05. Exercise 4 - Implementation of the Active Set Strategy Ex04-Framework
12.06. Exercise 5 - Implementation of the Augmented Lagrange Algorithm Ex05-Framework
19.06. Exercise 6 - Parameter Identification for 1D Elasto-Plasticity Ex06-Framework
26.06.

Exercise 7 - Parameter Identification for 3D Elasto-Plasticity

additional background information (cf. Introduction to Theory of Materials, aka. Materialtheorie)
- Material model
- Voigt-Notation
- Driver algorithm
- Objective funciton

Ex07-Framework
01.07. Exercise 8 - Parameter Identification using the Matlab Toolbox Ex08-Framework




Exam

The final exam consists of two parts.

  1. All students will be assigned a programming task in the context of parameter identification. This project and the corresponding results have to be presented in a short presentation. 
  2. The participants have to take an oral exam.

The assignments were discussed and given out on Wednesday, July 10, 2019, at 08:30 a.m. in MBI, room 165. Both, the presentation and the oral examination will take place on Tuesday, August 27, 2019.