TY - JOUR A1 - Sitz, Andre A1 - Schwarz, Udo A1 - Kurths, Jürgen T1 - The unscented Kalman filter : a powerful tool for data analysis Y1 - 2004 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 - 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 - Ebeling, Werner A1 - Molgedey, Lutz A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Entropy, complexity, predictability, and data analysis of time series and letter sequences N2 - The structure of time series and letter sequences is investigated using the concepts of entropy and complexity. First conditional entropy and transinformation are introduced and several generalizations are discussed. Further several measures of complexity are introduced and discussed. The capability of these concepts to describe the structure of time series and letter sequences generated by nonlinear maps, data series from meteorology, astrophysics, cardiology, cognitive psychology and finance is investigated. The relation between the complexity and the predictability of informational strings is discussed. The relation between local order and the predictability of time series is investigated. Y1 - 2002 UR - http://www.pik-potsdam.de/~kropp/myown/book.html SN - 3-540-41324-3 ER - TY - JOUR A1 - Palus, Milan A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Novotná, Dagmar A1 - Charvátová, Ivanka T1 - Is the solar activity cycle synchronized with the solar inertial motion? N2 - The 300 year record of the yearly sunspot numbers and numerically generated trajectory of the solar inertial motion (SIM) were subjects of a synchronization analysis. Phase synchronization of the sunspot cycle and a fast component of the SIM have been found and confirmed with statistical significance in three epochs (1727-1757, 1802-1832 and 1863-1922) of the entire 1700-1997 record. This result can be considered as a quantitative support for the hypothesis that there is a weak interaction of gravity and solar activity. Y1 - 2001 UR - http://ejournals.wspc.com.sg/ijbc/10/1011/S0218127400001766.html ER - TY - JOUR A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Nichtlineare Wissenschaften - neue Paradigmen und Konzepte N2 - In den letzten 2 Jahrzehnten des 20. Jahrhunderts hat sich mit der rasanten Entwicklung der Nichtlinearen Wissenschaften ein weiterer Umbruch vollzogen, der eine ausgepraegte Nachhaltigkeit in Wissenschaft und Technik ebenso wie in der Gesellschaft erwarten laesst. Die Nichtlinearen Wissenschaften werden auch als Nichtlineare Dynamik, Wissenschaft Komplexer Systeme oder etwas eingegrenzt Chaostheorie bezeichnet. Y1 - 2001 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/2001ArtChaos.pdf SN - 0177- 3674 ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Lange, Holger A1 - Hauhs, M. T1 - Conceptual model of runoff from a forested catchment N2 - We investigate the relationship between precipitation and runoff data from a small forested catchment in the Harz mountains (Germany). For this purpose, we develop a conceptual model including memory effects to predict the runoff signal using the precipitation data as input. An enhanced variant of the model also includes air temperature as input variable. We show in terms of correlation functions that this model describes main dynamical properties of the runoff, especially the delay between rain event and runoff response as the annual persistence in the runoff data. Y1 - 2001 UR - http://journals.worldscientific.com.sg/ijbc/11/1110/S0218127401003619.html ER - TY - JOUR A1 - Sitz, Andre A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Maus, Doris A1 - Wiese, Michael A1 - Warnecke, Günter T1 - Signatures of acoustic emission signals generated during high speed cutting N2 - Acoustic emission signals generated during high speed cutting of steel are investigated. The data are represen ted in time-folded form. Several methods from linear and nonlinear data analysis based on time- and frequency- domain are applied to the data and reveal signatures of the observed acoustic emission signal. These investiga tions are necessary for modeling the cutting process by means of differential equations. Y1 - 2001 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/21618.pdf ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Hasinger, Günther A1 - Belloni, Tomaso T1 - Nonlinear Time series analysis of the X-ray flux of compact objects N2 - We analyse the X-ray light curves of compact objects using linear and nonlinear time series analysis methods. A Power Density Spectrum (PDS) describes the overall second order properties of the observed data well. To look beyond we propose the nonlinear Q-statistic to detect an asymmetry of the time series. This allows us to find relevant time scales. This method even grants a subclassification of the known states of X-ray sources. Y1 - 2001 SN - 0004-640x ER - TY - JOUR A1 - Timmer, Jens A1 - Schwarz, Udo A1 - Voss, Henning U. A1 - Wardinski, Ingo A1 - Belloni, Tomaso A1 - Hasinger, Günther A1 - VanDerKlis, Michael A1 - Kurths, Jürgen T1 - Linear and Nonlinear Time Series Analysis of the Black Hole Candidate Cygnus X-1 N2 - We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data. Y1 - 2000 UR - http://pre.aps.org/ ER -