The hysteretic nonlinear dependence of pre-sliding friction force on displacement is modeled using different physics-based and black-box approaches including various Maxwell-slip models, NARX models, neural networks, nonparametric (local) models and dynamical networks. The efficiency and accuracy of these identification methods is compared for an experimental time series where the observed friction force is predicted from the measured displacement. All models, although varying in their degree of accuracy, show good prediction capability of pre-sliding friction. Finally, we show that even better results can be achieved by using an ensemble of the best models for prediction.
In the past few years a new learning method called Support Vector Machines (SVMs) has enjoyed increasing popularity. Based on statistical learning theory it shows very good generalization abilities. Though SVMs are mainly used for classification tasks, they are also applicable to regression problems and thus to modeling the dynamics of a time series. However when regression techniques are used to build dynamical models caution is advisable if the data are noisy. Due to correlations between data points, estimates of model parameters deviate systematically from the true values. An approach is presented to reduce such bias in SVM parameters.
IntroductionEvery day we are confronted with a multitude of new facts that we have to include in our decision making. Media, like television, radio, or newspapers inform us about current events from politics and economics. We are provided with the latest prices from the stock markets as well as the newest results from sports. In scientific journals we are informed about new research achievements with myriads of data and facts that support the presented theories. In magazines we read about the newest software and hardware issues in the field of computer technology, about new fashion trends, about the latest medical advices, about the best way to invest money, and so on. To refer to all the different kinds of information in a complete manner would simply be impossible. Especially with the growing popularity of the Internet in the last decade, one can say that there is virtually no information that we cannot access.Since human beings depend on information to plan ahead and decide their course of action, it seems that we live in heavenly times. With the infinite pool of facts that can be accessed day and night everybody should be able to make the best possible decisions. Curiously enough, this is not what is happening. Instead of using the information to their advantage, people are often overwhelmed by it. The sheer amount of facts makes it impossible to filter the important things from the unimportant and to prioritize the results. It is not a question of whether but of how many important decisions in the politics, industry, or in private households are made in the wrong way because vital information could not be found or was simply overlooked.Clearly, the people need help managing information nowadays, and researchers all over the world are working on solutions. Concepts like 'Data mining' and 'Data warehouse' have become buzzwords in recent years. These concepts do not try to produce new data but are simply meant to manage the data that is already there in a meaningful way and to reveal information that is hidden in the data pool. This is done by searching for common patterns, by interpolating and extrapolating among data points, and by developing models that can extract the essential laws behind them. Although the nomenclature
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