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Implementation and demonstration of characteristic diagram as well as structure model based correction of thermo-elastic tool center point displacements

Putz M., Ihlenfeldt S., Kauschinger B., Naumann C., Thiem X., Riedel M.

Journal of Machine Engineering

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2016

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Vol. 16, No. 3

88--101

EN

In milling machines, waste heat from motors, friction effects on guides and most importantly the milling process itself greatly affect positioning accuracy and thus production quality. Therefore, active cooling and lead time are used to reach thermal stability. A cheaper and more energy-efficient approach is to gather sensor data from the machine tool to predict and correct the resulting tool center point displacement. Two such approaches are the characteristic diagram based and the structure model based correction algorithms which are briefly introduced in this paper. Both principles have never been directly compared on the same demonstration machine, under the equal environmental conditions and with the same measurement setup. The paper accomplishes this comparison ona hexapod kinematics examined in a thermal chamber,where the effectiveness of both approaches is measured and the strengths and weaknesses of both are pointed out.

2

Building the library of RNA 3D nucleotide conformations using the clustering approach

Zok T., Antczak M., Riedel M., Nebel D., Villmann T., Lukasiak P., Blazewicz J., Szachniuk M.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 3

689--700

EN

An increasing number of known RNA 3D structures contributes to the recognition of various RNA families and identification of their features. These tasks are based on an analysis of RNA conformations conducted at different levels of detail. On the other hand, the knowledge of native nucleotide conformations is crucial for structure prediction and understanding of RNA folding. However, this knowledge is stored in structural databases in a rather distributed form. Therefore, only automated methods for sampling the space of RNA structures can reveal plausible conformational representatives useful for further analysis. Here, we present a machine learning-based approach to inspect the dataset of RNA three-dimensional structures and to create a library of nucleotide conformers. A median neural gas algorithm is applied to cluster nucleotide structures upon their trigonometric description. The clustering procedure is two-stage: (i) backbone- and (ii) ribose-driven. We show the resulting library that contains RNA nucleotide representatives over the entire data, and we evaluate its quality by computing normal distribution measures and average RMSD between data points as well as the prototype within each cluster.

3

Aspects in Classification Learning - Review of Recent Developments in Learning Vector Quantization

Kaden M, Lange M., Nebel D, Riedel M, Geweniger T, Villmann T.

Foundations of Computing and Decision Sciences

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2014

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Vol. 39, No. 2

79--105

EN

Classification is one of the most frequent tasks in machine learning. However, the variety of classification tasks as well as classifier methods is huge. Thus the question is coming up: which classifier is suitable for a given problem or how can we utilize a certain classifier model for different tasks in classification learning. This paper focuses on learning vector quantization classifiers as one of the most intuitive prototype based classification models. Recent extensions and modifications of the basic learning vector quantization algorithm, which are proposed in the last years, are highlighted and also discussed in relation to particular classification task scenarios like imbalanced and/or incomplete data, prior data knowledge, classification guarantees or adaptive data metrics for optimal classification.

4

Periodic observations of harmonizable symmetric stable sequences

Klotz L., Riedel M.

Probability and Mathematical Statistics

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2005

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Vol. 25, Fasc. 2

289--306

EN

For harmonizable symmetric stable sequences we solve the following prediction problem: Assume that the values of the sequence are known at all odd integers. Compute the metric projection of an unknown value onto the space spanned by the known values as well as the corresponding approximation error. We study several questions related to this prediction problem such as regularity and singularity, Wold type decomposition, interrelations between the spaces spanned by the values at the even and odd integers, respectively.

5

Spectral representation and extrapolation of stationary random processes on linear spaces

Klotz L., Riedel M.

Probability and Mathematical Statistics

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2001

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Vol. 21, Fasc. 1

179--197

EN

The paper deals with continuous Banach-space-valued stationary random processes on linear spaces. From von Waldenfels’ [13] integral representation of positive definite functions on a linear space L we derive an analogue of Stone’s theorem for a group of unitary operators over L. It is used to obtain spectral representations of a general Banach-space-valued stationary random process over L and its covariance function. For the special class of Hilbert-Schmidt operator-valued stationary processes the explicit form of Kolmogorov’s isomorphism theorem between temporal space and spectral space is established and with its aid there are studied some prediction problems. Our prediction results are similar to those proved in [5] for multivariate stationary processes on groups.