Une nouvelle classe d'opérateurs de Teager-Kaiser multidimensionnels basée sur les dérivées directionnelles d'ordre supérieur

This work aims at introducing some energy operators linked to Teager-Kaiser energy operator and its associated higher order versions and expand them to multidimensional signals. These operators are very useful for analyzing oscillatory signals with time-varying amplitude and frequency (AM-FM). We prove that gradient tensors combined with Kronecker powers allow to express these operators by directional derivatives along any n-D vector. In particular, we show that the construction of a large class of non linear operators for AM-FM multidimensional signal demodulation is possible. Also, a new scalar function using the directional derivative along a vector giving the ”sign” of the frequency components is introduced. An application of this model to local n-D AM-FM signal is presented and related demodulation error rates estimates. To show the effectiveness and the robustness of our method in term of envelope and frequency components extraction, results obtained on synthetic and real data are compared to multi-dimensional energy separation algorithm and to our recently introduced n-D operator

Fuzzy determination of informative frequency band for bearing fault detection

Detecting early faults in rolling element bearings is a crucial measure for the health maintenance of rotating machinery. As faulty features of bearings are usually demodulated into a high-frequency band, determining the informative frequency band (IFB) from the vibratory signal is a challenging task for weak fault detection. Existing approaches for IFB determination often divide the frequency spectrum of the signal into even partitions, one of which is regarded as the IFB by an individual selector. This work proposes a fuzzy technique to select the IFB with improvements in two aspects. On the one hand, an IFB-specific fuzzy clustering method is developed to segment the frequency spectrum into meaningful sub-bands. Considering the shortcomings of the individual selectors, on the other hand, three commonly-used selectors are combined using a fuzzy comprehensive evaluation method to guide the clustering. Among all the meaningful sub-bands, the one with the minimum comprehensive cost is determined as the IFB. The bearing faults, if any, can be detected from the demodulated envelope spectrum of the IFB. The proposed fuzzy technique was evaluated using both simulated and experimental data, and then compared with the state-of-the-art peer method. The results indicate that the proposed fuzzy technique is capable of generating a better IFB, and is suitable for detecting bearing faults

Modulation parameter estimation of LFM interference for direct sequence spread spectrum communication system in alpha-stable noise

The linear frequency modulation (LFM) interference is one of the typical broadband interferences in direct sequence spread spectrum (DSSS) communication system. In this article, a novel modulation parameter estimation method of LFM interference is proposed for the DSSS communication system in alpha-stable noise. To accurately estimate the modulation parameters, the alpha-stable noise should be eliminated first. Thus, we formulate a new generalized extended linear chirplet transform to suppress the alpha-stable noise, for a robust time-frequency, transformation of LFM interference is realized. Then, using the Radon transform, the maximum value after transformation and the chirp rate according to the angle related to the maximum value are estimated. In addition, a generalized Fourier transform is introduced to estimate the initial frequency of the LFM interference. For the performance analysis, the Cramér-Rao lower bounds of the estimated chirp rate and the initial frequency of the LFM interference in the presence of alpha-stable noise are derived. Moreover, the asymptotic properties of the modulation parameter estimator are analyzed. Simulation results demonstrate that the performance of the proposed parameter estimation method significantly outperforms existing methods, especially in a low SNR regime

Phase Synchrony Analysis of Rolling Bearing Vibrations and Its Application to Failure Identification

As the failure-induced component (FIC) in the vibration signals of bearings transmits through housings and shafts, potential phase synchronization is excited among multichannel signals. As phase synchrony analysis (PSA) does not involve the chaotic behavior of signals, it is suitable for characterizing the operating state of bearings considering complicated vibration signals. Therefore, a novel PSA method was developed to identify and track the failure evolution of bearings. First, resonance demodulation and variational mode decomposition (VMD) were combined to extract the mono-component or band-limited FIC from signals. Then, the instantaneous phase of the FIC was analytically solved using Hilbert transformation. The generalized phase difference (GPD) was used to quantify the relationship between FICs extracted from different vibration signals. The entropy of the GPD was regarded as the indicator for quantifying failure evolution. The proposed method was applied to the vibration signals obtained from an accelerated failure experiment and a natural failure experiment. Results showed that phase synchronization in bearing failure evolution was detected and evaluated effectively. Despite the chaotic behavior of the signals, the phase synchronization indicator could identify bearing failure during the initial stage in a robust manner

Observer-biased bearing condition monitoring: from fault detection to multi-fault classification

Bearings are simultaneously a fundamental component and one of the principal causes of failure in rotary machinery. The work focuses on the employment of fuzzy clustering for bearing condition monitoring, i.e., fault detection and classification. The output of a clustering algorithm is a data partition (a set of clusters) which is merely a hypothesis on the structure of the data. This hypothesis requires validation by domain experts. In general, clustering algorithms allow a limited usage of domain knowledge on the cluster formation process. In this study, a novel method allowing for interactive clustering in bearing fault diagnosis is proposed. The method resorts to shrinkage to generalize an otherwise unbiased clustering algorithm into a biased one. In this way, the method provides a natural and intuitive way to control the cluster formation process, allowing for the employment of domain knowledge to guiding it. The domain expert can select a desirable level of granularity ranging from fault detection to classification of a variable number of faults and can select a specific region of the feature space for detailed analysis. Moreover, experimental results under realistic conditions show that the adopted algorithm outperforms the corresponding unbiased algorithm (fuzzy c-means) which is being widely used in this type of problems. (C) 2016 Elsevier Ltd. All rights reserved.Grant number: 145602

Submillimeter Polarimetry with PolKa, a reflection-type modulator for the APEX telescope

Imaging polarimetry is an important tool for the study of cosmic magnetic fields. In our Galaxy, polarization levels of a few up to $\sim$10\% are measured in the submillimeter dust emission from molecular clouds and in the synchrotron emission from supernova remnants. Only few techniques exist to image the distribution of polarization angles, as a means of tracing the plane-of-sky projection of the magnetic field orientation. At submillimeter wavelengths, polarization is either measured as the differential total power of polarization-sensitive bolometer elements, or by modulating the polarization of the signal. Bolometer arrays such as LABOCA at the APEX telescope are used to observe the continuum emission from fields as large as \sim0\fdg2 in diameter. %Here we present the results from the commissioning of PolKa, a polarimeter for Here we present PolKa, a polarimeter for LABOCA with a reflection-type waveplate of at least 90\% efficiency. The modulation efficiency depends mainly on the sampling and on the angular velocity of the waveplate. For the data analysis the concept of generalized synchronous demodulation is introduced. The instrumental polarization towards a point source is at the level of $\sim0.1$\%, increasing to a few percent at the $-10$db contour of the main beam. A method to correct for its effect in observations of extended sources is presented. Our map of the polarized synchrotron emission from the Crab nebula is in agreement with structures observed at radio and optical wavelengths. The linear polarization measured in OMC1 agrees with results from previous studies, while the high sensitivity of LABOCA enables us to also map the polarized emission of the Orion Bar, a prototypical photon-dominated region