In the context of automatic and preventive condition monitoring of rotating machines, this paper presents a case study of a naturally-worn parallel straight gear by monitoring the evolution of the modulation functions. The Hilbert demodulation is automatically performed considering only the frequency content of the signals detected by the AStrion software. The gear has been worn over 3000 hours with a constant axial load. A particular focus is set on the amplitude modulation function in order to assess its efficiency to characterize both the severity of the wear and the most worn part of the gear. The results are confronted with on-site observation of the teeth. For this purpose, the evolution of both amplitude and phase modulations over several meshing harmonics are compared, as well as demodulation on both original and residual signals. Indicators to automatically classify the wear are discussed.

Spectral analysis of sea level anomalies (SLA) is widely used in the altimetry community to understand the geophysical content of the measured signal, to assess and compare the outputs of different missions. Spectral content of SLA is used to characterize ocean at different scales and to estimate the instrumental noise. Based on the SLA spectrum, one can estimate the spectral slope at medium to large scales (relied to the Surface Quasi-Geostrophic (SQG) ocean dynamics theory) and the measurement noise (observed as a noise plateau at smallest scales). A previous contribution [1] has pointed out the weaknesses of spectral analysis based on Fourier transform, mainly due to : (1) the convolutive bias which results in a biased estimation of the slope, the bias being related to the kind of observation weighting temporal window used and (2) the high variance of estimation leading to averaging several spectral estimations and raising the question of stationarity. To overcome these two drawbacks, a parametric spectral analysis method is proposed. This method is based on Auto-Regressive (AR) modeling [2,3] which is known to provide a spectral estimation with a lower variance than the as outperforming Fourier-based methods in terms of variance, in the case of short observation windows, without any need for choosing a weighting temporal window. Moreover, in order to better match the SLA frequency contents on a log scale to match the log scale interest of the SLA frequency contents , warping is introduced as a preprocessing prior to spectral analysis as it is done in speech coding [4]. Comparisons between the proposed parametric method (called ARWARP) and classical Fourier Fourier-based methods have been performed on both simulated SLA signals obtained from theoretical spectra and real signals from a high-resolution altimeter SARAL/AltiKa at 40 Hz rate (Orbit – Range – Mean Sea Surface). Results on simulated SLA signals highlight the performance of the ARWARPmethod, in terms of bias and variance on spectral estimation. ARWARP can be applied on short segments of SLA signals, providing a local information of the ocean characteristics, which can be of promising use by the wider Cal/Val and altimetry science community.

Spectral analysis of sea level anomalies (SLA) is widely used in the altimetry community to understand the geophysical content of the measured signal, to assess and compare the missions’ performances. Spectral content of SLA is used to characterize the ocean at different scales as well as instrumental noise. Based on the SLA spectrum, one can estimate the spectral slope at medium to large scales (relied to the Surface Quasi-Geostrophic (SQG) ocean dynamics theory) and the measurement noise (observed as a noise plateau at smallest scales). It has already been shown that the spectral slope strongly depends on ocean variability, both in time and space domains [1]. However, spectral analysis based on Fourier transform requires stationary signals and is well-known to suffer from a convolutive bias and a high variance of estimation [2]. Thus, using Fourier transforms for SLA spectral analysis requires mathematical caution and needs to be fully managed. This study aims at reviewing applicability of Fourier transform-based methods to SLA analysis and comparing it to other spectral methods. Such comparison has been performed on both simulated SLA signals obtained from theoretical spectra and real signals from a high-resolution altimeter (Orbit – Range – Mean Sea Surface). Finally, a parametric spectral analysis method is proposed and suggested for use by the wider Cal/Val and altimetry science community. [1] C. Dufau et al., Mesoscale capability of along-track altimeter data in LRM & SARM, OSTST Meeting, 2014. [2] P. Stoica, R. Moses, Introduction to spectral analysis, Prentice Hall, 1997.

Monitoring the drive train of a wind turbine is still a challenge for reducing operationand maintenance costs and therefore decreasing cost of energy. In this paper, astandalone, data-driven and automatic tracking analyzer, entitled AStrion and alreadypresented in this conference, is applied on vibration data acquired during one full yearon a set of sensors located in the nacelle of two wind turbines in a wind farm in thePyrénées (France). These experimentations were realized thanks to KAStrion projectfunded by KIC InnoEnergy program.In the context of a particular case study, the main bearing failure of one of the two windturbines, this paper will highlight three main assets of AStrion strategy. A first asset willbe the application of the data validation module. According to the value of anonstationary index, the data measured on the sensor located on the main bearing closeto the failure have been discarded. This was justified afterwards by a dysfunction of thesensor. Then from the validated data acquired with a more remote sensor, a second assetwill be the trends of global features computed by AStrion which proved a strong linkwith maintenance operations on the mechanical components such as the greasing. Thethird asset will be the reading of other AStrion features associated to one specificcomponent. Indeed the trends of the features of the main bearing show evolutionsthroughout the year. A real time reading would have led to the conclusion of a severeevolution of the condition of this main bearing eight months before the failure and thestop of the machine. This study was carried out thanks to a narrow collaboration withthe operator of the wind farm.

This paper proposes a new Bayesian strategy for the estimation of smooth parameters from nonlinear models. The observed signal is assumed to be corrupted by an independent and non identically (colored) Gaussian distribution. A prior enforcing a smooth temporal evolution of the model parameters is considered. The joint posterior distribution of the unknown parameter vector is then derived. A Gibbs sampler coupled with a Hamiltonian Monte Carlo algorithm is proposed which allows samples distributed according to the posterior of interest to be generated and to estimate the unknown model parameters/hyperparameters. Simulations conducted with synthetic and real satellite altimetric data show the potential of the proposed Bayesian model and the corresponding estimation algorithm for nonlinear regression with smooth estimated parameters.

The installation of a Condition Monitoring System (CMS) on a mechanical machine (e.g., on a wind turbine) aims to reduce the operating costs by applying a predictive maintenance strategy. The CMS is composed of sensors acquiring signals from which system health indicators are computed and monitored. Part of those indicators are predefined depending on the monitored system kinematic and are computed by averaging large or narrow spectral bands. The averaging and the need for predefined thresholds for default detection may induce lots of false alarms while reducing the ability to detect the default early. To get precise health indicators reflecting each local meaningful spectral content, the AStrion software proposes a new data-driven monitoring strategy without any a priori on the measured signals. First, an automatic spectral analysis is applied to detect, characterize and classify the different spectral structures of the successive measured signals. These spectral structures can be either single spectral peaks, either peaks grouped in harmonic series or in modulation sidebands [1]. Second, these spectral structures are characterized by several features, including for example the number of peaks, the characteristic frequencies and the energy. This gives a snapshot of the system health at the signal acquisition time. To perform an automatic diagnosis of the system, the spectral evolution should be tracked along the time snapshots. In this paper, we propose a time tracking method based on McAulay & Quatieri algorithm [2] which has been designed originally for speech signals acquired on a continuous temporal basis. We have adapted [2] in order to account not only for single spectral peak evolution but also for the evolution of more complex structures such as harmonic series or modulation sidebands, even in the case of signals acquired on a non-regular temporal basis, as it is often the case. Moreover, an added sleep state makes the proposed method robust against nondetected spectral structures at a given time. Finally, the temporal evolution of the spectral structure features can be monitored and used as precise health indicators. The following figure is a result of the proposed method applied on real signals coming from a test bench designed in KAStrion project for simulating a wind turbine operation and for which the inner race of the main bearing has been damaged. Above, the time frequency map displays a zoom of the spectral peaks detected (around 20.000 per snapshot, represented by circles) and shows in blue the tracking from 44 to 189 operating hours of a spectral peak at 3.45 Hz. This particular peak evolves at 129 hours to become an harmonic series with more and more peaks and energy. Its energy evolution (plotted below) shows an increase which mirrors out a failure. In a following step [3], this spectral structure has been associated with the ball pass frequency of the inner ring of the main bearing. A dismantling of this bearing has confirmed the failure. This result shows the potential of the proposed data-driven method to create automatically relevant health indicators.

Delay/Doppler radar altimetry is a new technology that has been receiving an increasing interest, especially since the launch of Cryosat-2 in 2010 , the first altimeter using this technique. The Delay/Doppler technique aims at reducing the measurement noise and increasing the along-track resolution in comparison with conventional pulse limited altimetry. A new semi-analytical model with five parameters has been recently introduced for this new technology. However, two of these parameters are highly correlated resulting in bad estimation performance when estimating all parameters. This paper proposes a new strategy improving estimation performance for delay/Doppler altimetry. The proposed strategy exploits all the information contained in the delay/Doppler domain. A comparison with other classical algorithms (using the temporal samples only) allows to appreciate the gain in estimation performance obtained when using both temporal and Doppler data.

This paper introduces a new model for delay/Doppler altimetry, taking into account the effect of antenna mispointing. After defining the proposed model, the effect of the antenna mispointing on the waveform is analyzed with respect to along-track and across-track directions. Two least squaresapproaches are proposed for the estimation of the altimetric parameters. The first algorithm estimates four parameters including the across-track mispointing (which affects the echo’s shape) while the second algorithm considers the mispointing angles provided by the star-trackers and estimates the three remaining parameters. The proposed model and algorithms are validated via simulations conducted on both synthetic and real data.

The concept of delay/Doppler radar altimeter has been under study since the mid 90’s, aiming at reducing the measurement noise and increasing the along-track resolution in comparison with the conventional pulse limited altimeters. This paper introduces a generalized semi-analytical model for the delay/Doppler echo that accounts for antenna mispointing, as well as an associated least squares estimation algorithms. The mean power of a delay/Doppler echo can be expressed by a convolution of three terms that are the probability density function (PDF) of the heights of the specular scatterers, the time/frequency point target response (PTR) of the radar and the flat surface impulse response (FSIR). The first contribution of this paper is the derivation of a generalized analytical model for the FSIR that accounts for antenna mispointing. The proposed analytical expression for the FSIR also considers Earth curvature, a circular antenna pattern and a Gaussian approximation for the antenna gain. The two dimensional delay/Doppler map (DDM) is then obtained by a numerical computation of the convolution between the proposed analytical FSIR expression, the PDF of the sea wave height and the time/frequency PTR. The resulting DDM depends on five altimetric parameters that are the epoch, the significant wave height, the amplitude, the along-track and the across-track mispointing angles. Appropriate processing, including range migration and multi-looking, is applied to the resulting DDM yielding the Doppler echo (also known as the multi-look echo). The second contribution of this paper is the derivation of estimators for the five parameters associated with the multi-look echo. A least squares approach is investigated by means of the Levenberg-Marquardt algorithm. Moreover, the study of the effect of antenna mispointing shows high correlation between the along-track mispointing and the echo's amplitude. Thus, a four parameter estimation strategy has been proposed rather than the mere estimation of the five parameters of interest. In order to evaluate these strategies, we compare their estimation performance to that obtained using the three parameter model derived in a previous paper [1]. Validation of the proposed model and the corresponding algorithms is achieved on simulated and real Cryosat-2 data. The obtained results are very promising and confirm the accuracy of the proposed model.