Signalverarbeitungsverfahren und virtuelle Instrumente zur Messung von elektrischen Signalen und zur Fehlerdiagnose an Maschinen

Es wird in dieser Arbeit gezeigt, dass sich die Chirp-z-Transformation (CZT) und das Zeropadding-Verfahren (ZP), kombiniert mit der Anwendung geeigneter Fensterfunktionen, zur Bestimmung der Größen von Spannungs- und Stromsignalen bezüglich der Zuverlässigkeit bei kurzen Messzeiten eignen. Die allgemeinen Bedingungen für die Anwendung der CZT bzw. des ZP bei reellen Multifrequenz-Signalen unter dem Einsatz der Fensterfunktionen dargestellt. Der Einfluß eines reellen weißen Rauschsignals auf die geschätzten Größen eines reellen Multifrequenz-Signals wurde untersucht. Das TDA-Verfahren wird zur Verarbeitung der harmonischen Komponenten der Ausgangssignale eines Frequenzumformers untersucht. Zur Detektion und Messung der interharmonischen Komponenten wird ein digitales Differenz-Filter vorgestellt. Die Anwendbarkeit des TDA-Verfahrens und des digitalen Differenz-Filters wird durch die Ergebnisse aus Simulationen und praktischen Anwendungen gezeigt. Virtuelle Instrumente wurden zur Fehldiagnose und Schwingungsanalyse an Planetengetrieben entwickelt. Die praktischen Anwendungen zeigen, dass das Spektrum der demodulierten hochfrequenten mechanischen Schwingungen – Hüllkurvenspektrum – eine spektrale Struktur bei den Frequenzen enthält, die mit den Fehlern auf Innenring- oder Außenringlaufbahn in Verbindung stehen.It will be shown that the chirp-z-transform and zero-padding, combined with a appropriate window, are suitable for the estimation of the parameters of the voltage and current signals with moderate computational complexity. Through the analysis of the spectral interference in the discrete time Fourier transform the conditions for the simultaneous use of the windows and the chirp-z-transform or zero-padding will be presented. The statistical errors of the estimations will be discussed. The time domain averaging will be here investigated to process harmonic components in the output signals of frequency converters. For the detection and measurement of interharmonics a digital difference-filter will be proposed. Simulations and field test results are provided to illustrate the utility of the time domain averaging and the difference-filter. Based on the analysis of the faults of gears and rolling bearings the virtual instruments for the fault diagnosis and vibration analysis in epicyclic gearboxes are developed. The practical applications show that the spectrum of the demodulated high-frequency vibration – envelope spectrum – contains a pattern of spectral lines at frequencies which can be related to the faults on the inner or outer race of rolling bearings

A Time-Dependent Dirichlet-Neumann Method for the Heat Equation

We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration involves subdomain solves with Dirichlet boundary conditions followed by subdomain solves with Neumann boundary conditions. However, each subdomain problem is now in space and time, and the interface conditions are also time-dependent. Using a Laplace transform argument, we show for the heat equation that when we consider finite time intervals, the Dirichlet-Neumann method converges, similar to the case of Schwarz waveform relaxation algorithms. The convergence rate depends on the length of the subdomains as well as the size of the time window. In this discussion, we only stick to the linear bound. We illustrate our results with numerical experiments.Comment: 9 pages, 5 figures, Lecture Notes in Computational Science and Engineering, Vol. 98, Springer-Verlag 201

Reduced-Order Modeling based on Approximated Lax Pairs

A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where the solution is searched for evolves according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive waves or front propagation. Numerical examples are shown for the KdV and FKPP (nonlinear reaction diffusion) equations, in one and two dimensions

Recognition and reconstruction of coherent energy with application to deep seismic reflection data

Reflections in deep seismic reflection data tend to be visible on only a limited number of traces in a common midpoint gather. To prevent stack degeneration, any noncoherent reflection energy has to be removed. In this paper, a standard classification technique in remote sensing is presented to enhance data quality. It consists of a recognition technique to detect and extract coherent energy in both common shot gathers and fi- nal stacks. This technique uses the statistics of a picked seismic phase to obtain the likelihood distribution of its presence. Multiplication of this likelihood distribution with the original data results in a “cleaned up” section. Application of the technique to data from a deep seismic reflection experiment enhanced the visibility of all reflectors considerably. Because the recognition technique cannot produce an estimate of “missing” data, it is extended with a reconstruction method. Two methods are proposed: application of semblance weighted local slant stacks after recognition, and direct recognition in the linear tau-p domain. In both cases, the power of the stacking process to increase the signal-to-noise ratio is combined with the direct selection of only specific seismic phases. The joint application of recognition and reconstruction resulted in data images which showed reflectors more clearly than application of a single technique

Time-scale analysis of abrupt changes corrupted by multiplicative noise

Multiplicative Abrupt Changes (ACs) have been considered in many applications. These applications include image processing (speckle) and random communication models (fading). Previous authors have shown that the Continuous Wavelet Transform (CWT) has good detection properties for ACs in additive noise. This work applies the CWT to AC detection in multiplicative noise. CWT translation invariance allows to define an AC signature. The problem then becomes signature detection in the time-scale domain. A second-order contrast criterion is defined as a measure of detection performance. This criterion depends upon the first- and second-order moments of the multiplicative process's CWT. An optimal wavelet (maximizing the contrast) is derived for an ideal step in white multiplicative noise. This wavelet is asymptotically optimal for smooth changes and can be approximated for small AC amplitudes by the Haar wavelet. Linear and quadratic suboptimal signature-based detectors are also studied. Closed-form threshold expressions are given as functions of the false alarm probability for three of the detectors. Detection performance is characterized using Receiver Operating Characteristic (ROC) curves computed from Monte-Carlo simulations