@article{SitzSchwarzKurths2004, author = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen}, title = {The unscented Kalman filter : a powerful tool for data analysis}, year = {2004}, language = {en} } @article{WesselKonvickaWeidermannetal.2004, author = {Wessel, Niels and Konvicka, Jan and Weidermann, Frank and Nestmann, S. and Neugebauer, R. and Schwarz, U. and Wessel, A. and Kurths, J{\"u}rgen}, title = {Predicting thermal displacements in modular tool systems}, issn = {1054-1500}, year = {2004}, abstract = {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 inducedaccuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems. errors can be estimated with 1-2 micrometer}, language = {en} } @article{WesselAssmusWeidermannetal.2004, author = {Wessel, Niels and Aßmus, Joerg and Weidermann, Frank and Konvicka, Jan and Nestmann, S. and Neugebauer, R. and Schwarz, Udo and Kurths, J{\"u}rgen}, title = {Modeling thermal displacements in modular tool systems}, year = {2004}, abstract = {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.}, language = {en} } @article{VossTimmerKurths2004, author = {Voss, Henning U. and Timmer, Jens and Kurths, J{\"u}rgen}, title = {Modeling and identification of nonlinear systems}, issn = {0218-1274}, year = {2004}, language = {en} } @article{SpahnKrivovSremcevicetal.2003, author = {Spahn, Frank and Krivov, Alexander V. and Sremcevic, Miodrag and Schwarz, U. and Kurths, J{\"u}rgen}, title = {Stochastic forces in circumplanetary dust dynamics}, year = {2003}, abstract = {Charged dust grains in circumplanetary environments experience, beyond various deterministic forces, also stochastic perturbations caused, by fluctuations of the magnetic field, the charge of the grains, by chaotic rotation of aspherical grains, etc. Here we investigate the dynamics of a dust population in a circular orbit around a planet which is perturbed by a stochastic planetary magnetic field B', modeled by an isotropically Gaussian white noise. The resulting perturbation equations give rise to a modified diffusion of the inclinations i and eccentricities e. The diffusion coefficient is found to be D proportional to w^2 O /n^2 , where the gyrofrequency, the Kepler frequency, and the synodic frequency are denoted by w , O, and n, respectively. This behavior has been checked against numerical simulations. We have chosen dust grains (1 m in radius) ejected from Jupiter's satellite Europa in circular equatorial orbits around Jupiter and integrated numerically their trajectories over their typical lifetimes (100 years). The particles were exposed to a Gaussian fluctuating magnetic field B' with the same statistical properties as in the analytical treatment. These simulations have confirmed the analytical results. The theoretical studies showed the statistical properties of B' to be of decisive importance. To estimate them, we analyzed the magnetic field data obtained by the Galileo spacecraft magnetometer at Jupiter and found almost Gaussian fluctuations of about 5\% of the mean field and exponentially decaying correlations. This results in a diffusion of orbital inclinations and eccentricities of the dust grains of about ten percent over the lifetime of the particles. For smaller dusty motes or for close-in particles (e.g., in Jovian gossamer rings) stochastics might well dominate the dynamics.}, language = {en} } @article{WesselSchwarzSaparinetal.2002, author = {Wessel, Niels and Schwarz, Udo and Saparin, Peter and Kurths, J{\"u}rgen}, title = {Symbolic dynamics for medical data analysis}, isbn = {3-936142-09-2}, year = {2002}, abstract = {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.}, language = {en} } @article{EbelingMolgedeyKurthsetal.2002, author = {Ebeling, Werner and Molgedey, Lutz and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Entropy, complexity, predictability, and data analysis of time series and letter sequences}, isbn = {3-540-41324-3}, year = {2002}, abstract = {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.}, language = {en} } @unpublished{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Characterizing the dynamics of stochastic bistable systems by measures of complexity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14556}, year = {1997}, abstract = {The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.}, language = {en} } @unpublished{WittKurthsKrauseetal.1994, author = {Witt, Annette and Kurths, J{\"u}rgen and Krause, F. and Fischer, K.}, title = {On the validity of a model for the reversals of the Earth's magnetic field}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13460}, year = {1994}, abstract = {We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.}, language = {en} } @unpublished{KurthsVossWittetal.1994, author = {Kurths, J{\"u}rgen and Voss, A. and Witt, Annette and Saparin, P. and Kleiner, H. J. and Wessel, Niels}, title = {Quantitative analysis of heart rate variability}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13470}, year = {1994}, abstract = {In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.}, language = {en} }