TY  - JOUR
A1  - Wessel, Niels
A1  - Schwarz, Udo
A1  - Saparin, Peter
A1  - Kurths, Jürgen
T1  - Symbolic dynamics for medical data analysis
N2  - Observational data of natural systems, as measured in medical measurements are typically quite different from those obtained in laboratories. Due to the peculiarities of these data, wellknown characteristics, such as power spectra or fractal dimension, often do not provide a suitable description. To study such data, we present here some measures of complexity, which are basing on symbolic dynamics. Firstly, a motivation for using symbolic dynamics and measures of complexity in data analysis based on the logistic map is given and next, two applications to medical data are shown. We demonstrate that symbolic dynamics is a useful tool for the risk assessment of patients after myocardial infarction as well as for the evaluation of th e architecture of human cancellous bone.
Y1  - 2002
UR  - http://www.agnld.uni-potsdam.de/~shw/Paper/EUROATTRACTOR2000.ps
SN  - 3-936142-09-2
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Aßmus, Joerg
A1  - Weidermann, Frank
A1  - Konvicka, Jan
A1  - Nestmann, S.
A1  - Neugebauer, R.
A1  - Schwarz, Udo
A1  - Kurths, Jürgen
T1  - Modeling thermal displacements in modular tool systems
N2  - In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally induced errors can be estimated with 1-2${mu m}$ accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.
Y1  - 2004
ER  -