Winfried Theis

Multivariate Classification of Business Phases

We propose multivariate classification as a statistical tool to describe business cycles. These cycles are often analyzed as a univariate phenomenon in terms of GNP or industrial net production ignoring additional information in other economic variables. Multivariate classification overcomes these limitations by reducing dimension in a way suitable for human perception. Based on a four phase scheme (upswing, upper turning point, downswing, lower turning point) we demonstrate the potential of classification methods by determining the important economic variables (stylized facts) for the German business cycle.

Monitoring a Drilling Process Using Residual Control Charts

ABSTRACT Deep-hole drilling methods are used for producing holes with a high length-to-diameter ratio, good surface finish, and straightness. The process is subject to dynamic disturbances that are classified as either chatter vibration or spiraling. In this article, control charts are used to monitor a drilling process in order to detect chatter vibration and to secure production with high quality. These control charts use the residuals obtained from a model that describes the variation in the amplitudes of the relevant frequencies of the process. The results showed that the start of the transition from stable drilling to chatter vibration is detected and that some alarm signals are related to changing physical conditions of the process.

Statistics, Dynamics and Quality - Improving BTA-deep-hole drilling

In this paper we present how statistical experimental design, time series analysis and non-linear dynamic models have been applied to gain a deeper insight into BTA-deep-hole drilling process. BTA-deep-hole drilling process is used to produce long holes of a length to diameter ratio larger than 5. This process normally produces holes of high quality with regard to straightness, smoothness of the boring walls and roundness. However, two dynamic disturbances, chatter and spiralling, are sometimes observed in the process. While chatter mainly results in increased wear of the cutting edges of the tool but may also damage boring walls, spilling damages the workpiece severely. In our study we applied experimental design to gain insight into the connection between process parameters and quality measures like roughness and roundness, while at the same time creating a database for dynamic modelling of the processes. This turned out ot be a very helpful approach because we observed all kinds of dynamic disturbances. In this paper we will focus on chatter which turned out to be dominated by a few (eigen-) frequencies. Two models were proposed to describe the variation of the amplitudes of these frequencies, on the one hand a stochastic differential equation and on the other hand a descriptive model based on piecewise periodogramms. In the latter model the knowledge of the underlying experimental design was used to distinguish between the effects of the assembly of the machine, like damping by the starting bush on the tool, and effects of the dynamics and stochastic influences. Because this model is completely data-driven it can be used as a starting point for the development of a suitable dynamic model of a process.

Clustering Techniques for the Detection of Business Cycles

In this paper business cycles are considered as a multivariate phenomenon and not as a univariate one determined e.g. by the GNP. The subject is to look for the number of phases of a business cycle, which can be motivated by the number of clusters in a given dataset of macro-economic variables. Different approaches to distances in the data are tried in a fuzzy cluster analysis to pursue this goal.

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.

Monitoring of the BTA Deep Hole Drilling Process Using Residual Control Charts

Deep hole drilling methods are used for producing holes with a high lengthto- diameter ratio, good surface finish and straightness. The process is subject to dynamic disturbances usually classified as either chatter vibration or spiralling. In this work, we propose to monitor the BTA drilling process using control charts to detect chatter as early as possible and to secure production with high quality. These control charts use the residuals obtained from a model which describes the variation in the amplitude of the relevant frequencies of the process. The results showed that chatter is detected and some alarm signals are related to changing physical conditions of the process.

Application and Use of Multivariate Control Charts in a BTA Deep Hole Drilling Process

Deep hole drilling methods are used for producing holes with a high length-to-diameter ratio, good surface finish and straightness. The process is subject to dynamic disturbances usually classified as either chatter vibration or spiralling. In this paper, we will focus on the application and use of multivariate control charts to monitor the process in order to detect chatter vibrations. The results showed that chatter is detected and some alarm signals occurs at time points which can be connected to physical changes of the process.

Comparing Time Series from Experiments with and without Spiralling

In this paper we compare data from BTA deep-hole drilling experiments conducted according to an experimental design, which had to be repeated due to the development of spiralling in all experiments in the first repetition. We compare the time series of the drilling torque and the bending moment with respect to the development of the maximal Lyapunov-Exponent and the overall relevant frequencies and the relevant frequencies on sections of the process.

Descriptive Studies on Stylized Facts of the German Business Cycle

Thirteen Stylized Facts of the german economy are studied with different descriptive statistical methods. The results of this study are considered with respect to other results from Project B3 Multivariate Bestimmung und Untersuchung von Konjunkturzyklen.

Two connected models for varying amplitudes in BTA-deep-hole-drilling

Two models are proposed to roughly approximate the observed behavior of the amplitude of the drilling torque in the BTA-deep-hole-drilling process. It is schown that these models are closely connected.