# VO 328.032/UE 325.065 Identification - Experimental Modeling

## Content

Mathematical models are now the basis for simulations, some of which replace experimental tests or make predictions possible in the first place. Such models can basically be determined in two different ways. The establishment of mathematical equations based on physical, chemical or other relationships is referred to as theoretical modeling. However, the acquisition of the functional relationships and their parameterization is often very difficult and time-consuming due to the complexity of real processes. In this case, experimental modeling becomes more important. It is based on mathematical models with a suitably specified structure, but tries to determine their parameters with the help of measurement data in such a way that the corresponding relationships between the input and output signals are mapped as best as possible. This system identification generally refers to the determination of the quantitative dependency of the output and input variables of a system.

With powerful and cheap hardware, even complex (non-linear, dynamic, multi-input/multi-output) models can now be obtained from large amounts of data. The important aspects of a correct model validation and a systematic implementation from the experiment to the documentation are also important skills that are taught in the course.

The lectures impart knowledge of the mathematical basics as well as practical application with the help of software tools. Graduates should be able to independently solve and document technically relevant identification tasks. In addition, a theoretical foundation for further studies in this field is imparted. As an introduction, the most important stochastic basics of parameter estimation and stochastic processes are presented. The ergodic theorem as a basis for identifying dynamic systems from time series is taught. There is also a place for spectral estimation.

Then the main methods of linear identification are presented. The importance of noise models for the modeling of the measurement noise is emphasized, and the least squares estimation as the core of the parameter estimation is presented. Particular value is placed on teaching the practical procedure, which is trained using software and concrete examples. Another important section are the artificial neural networks (ANN), which deal with non-linear system dynamics. Based on a biological analogy, ANNs can learn and reproduce any (also dynamic) non-linear relationships. Different types of neural networks are presented and the common methods of training are taught. A presentation of the methods for nonlinear optimization introduces the basis for these training methods.

The lecture is supported by extensive examples that are available to students as complete MATLAB/Simulink packages (e.g. Identification Toolbox and Neural Network Toolbox). The comprehensive use of MATLAB/Simulink by the students is an essential part of the courses and conveys competence in practical application. However, the theoretical knowledge imparted at the same time allows a critical evaluation of the results of the software tools and enables the independent study of further literature.

## Contact

TU Wien

Institute of Mechanics and Mechatronics

Research Unit of Control and Process Automation

Getreidemarkt 9 / E325-04 / 6th floor

1060 Vienna

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