Nils Raabe

klaR Analyzing German Business Cycles

Decision making often asks for classification. We will present a new R package klaR including functions to build, check, tune, visualize, and compare classification rules. The software is illustrated by means of a case study of prediction of the German economy’s business cycle phases.

Varying bending eigenfrequencies in BTA deep hole drilling: mechanical modeling using statistical parameter estimation

One serious problem in deep-hole drilling is the formation of a dynamic disturbance called spiralling which causes a multi-lobe shaped distortion of the bore hole cross section. An important factor governing the occurrence of spiralling is the coincidence of a bending eigenfrequency of the boring tool with a multiple of the spindle rotation frequency. This article presents a discrete dynamic model of the tool/boring-bar assembly including a Lanchester-damper and containing free parameters for the unknown stiffness of the tools lateral supports. Furthermore, a method for estimating these parameters by determining the changing eigenfrequencies over the drilling depth from spectrogram data using the maximum likelihood method is proposed.

Spiralling in BTA Deep-hole Drilling: Models of Varying Frequencies

One serious problem in deep-hole drilling is the formation of a dynamic disturbance called spiralling which causes holes with several lobes. Since such lobes are a severe impairment of the bore hole the formation of spiralling has to be prevented. Gessesse et al. (1994) explain spiralling by the coincidence of bending modes and multiples of the rotary frequency. They derive this from an elaborate finite elements model of the process. In online measurements we detected slowly changing frequency patterns similar to those calculated by Gessesse et al. We therefore propose a method to estimate the explanation of spiralling in practice because the finite elements model has to be correctly modified for each machine and tool assembly while the statistical method uses observable measurements. Estimating the variation of the frequencies as good as possible opens up the opportunity to prevent spiralling by e.g. changing the rotary frequency.

Statistical Process Modelling for Machining of Inhomogeneous Mineral Subsoil

Because in the machining process of concrete, tool wear and production time are very cost sensitive factors, the adaption of the tools to the particular machining processes is of major importance.We show how statistical methods can be used to model the influences of the process parameters on the forces affecting the workpiece as well as on the chip removal rate and the wear rate of the used diamond. Based on these models a geometrical simulation model can be derived which will help to determine optimal parameter settings for specific situations.As the machined materials are in general abrasive, usual discretized simulation methods like finite elements models can not be applied. Hence our approach is another type of discretization subdividing both material and diamond grain into Delaunay tessellations and interpreting the resulting micropart connections as predetermined breaking points. Then, the process is iteratively simulated and in each iteration the interesting entities are computed.

Control charts based on models derived from differential equations

The development of technical processes over time can often be adequately modelled by means of differential equations. In order to monitor such processes, control charts may be derived from stochastic models based on such differential equations. In this work, this is demonstrated for a deep-hole drilling process used for producing holes with a high length-to-diameter ratio, good surface finish and straightness. The process is subject to dynamic disturbances classified as either chatter vibration or spiraling. For chatter, a differential equation for the drilling torque and a model known to well approximate processes with similar characteristics are used to set up monitoring procedures. For spiraling a control chart can be based on a statistical model for the spectrum of the structure-born vibrations derived from a differential equation for the deflection of the boring bar. Copyright

Deriving a statistical model for the prediction of spiralling in BTA deep hole drilling from a physical model

One serious problem in deep hole drilling is the occurrence of a dynamic disturbances called spiralling. A common explanation for the occurrence of spiralling is the coincidence of time varying bending eigenfrequencies of the tool with multiples of the spindle rotation frequency. We propose a statistical model for the estimation of the eigenfrequencies derived from a physical model. The major advantage of the statistical model is that it allows to estimate the parameters of the physical model directly from data measured during the process. This represents an efficient way of detecting situations in which spiralling is likely and of deriving countermeasures.

Modelling and Understanding of Chatter

Recent analysis in chatter modelling of BTA deep-hole drilling consisted in phenomenological modelisation of relationships between the observed time series and appearance of chatter during the process. Using the newly developed MEWMA control chart [4, 5], it has even been possible to predict the occurence of chatter about 30 to 50 mm in advance (i.e. up to one minute before the chatter starts). Unfortunately, no relationships between the machine and model parameters have been detected. Therefore, in this paper a physical model of the boring bar is taken into account. Simulation studies of the regenerative process are performed. These simulated time series show the same characteristics as the data recorded during the drilling process and thus support the validity of our model. By running such simulations, we intend to find strategies for chatter prevention in future work.

Prediction of spiralling in BTA deep-hole drilling: estimating the system's eigenfrequencies

One serious problem in deep-hole drilling is the formation of a dynamic disturbance called spiralling which causes holes with several lobes. Since such lobes are a severe impairment of the bore hole quality the formation of spiralling has to be prevented. Gessesse et al. [2] explain spiralling by the coincidence of bending modes and multiples of the rotation frequency. They derive this from an elaborate finite elements model of the process. In online measurements we detected slowly changing frequency patterns similar to those calculated by Gessesse et al. We therefore propose a method to estimate the parameters determining the change of frequencies over time from spectrogram data. This significantly simplifies the explanation of spiralling for practical applications compared to finite elements models which have to be correctly modified for each machine and tool assembly. It turns out that this simpler model achieves to explain the observed frequency patterns quite well. We use this for estimating the variation of the frequencies as good as possible. This opens up the opportunity to prevent spiralling by e.g. changing the rotary frequency.

KMC/EDAM: A new approach for the visualization of K-Means Clustering results

In this work we introduce a method for classification and visualization. In contrast to simultaneous methods like e.g. Kohonen SOM this new approach, called KMC/EDAM, runs through two stages. In the first stage the data is clustered by classical methods like K-means clustering. In the second stage the centroids of the obtained clusters are visualized in a fixed target space which is directly comparable to that of SOM.

Identifying Different Areas of Inhomogenous Mineral Subsoil: Spatial Fluctuation Approaches

We use a recently proposed fluctuation-type procedure for detecting breaks in spatial regions to distinguish between hard and soft areas of inhomogeneous mineral subsoil like additives, air pockets, and adhesion. For a proper application, some refinements of the procedure are necessary. Both simulation evidence of the refinement and the application on the subsoil yield favorable results.