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.

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) |

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. |
Ex07-Framework |

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

The final exam consists of two parts.

- 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.
- 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**.

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