The relationship between kurtosis- and envelope-based indexes for the diagnostic of rolling element bearings

The coupling of kurtosis based-indexes and envelope analysis represents one of the most successful and widespread procedures for the diagnostics of incipient faults on rolling element bearings. Kurtosis-based indexes are often used to select the proper demodulation band for the application of envelope-based techniques. Kurtosis itself, in slightly different formulations, is applied for the prognostic and condition monitoring of rolling element bearings, as a standalone tool for a fast indication of the development of faults. This paper shows for the first time the strong analytical connection which holds for these two families of indexes. In particular, analytical identities are shown for the squared envelope spectrum (SES) and the kurtosis of the corresponding band-pass filtered analytic signal. In particular, it is demonstrated how the sum of the peaks in the SES corresponds to the raw 4th order moment. The analytical results show as well a link with an another signal processing technique: the cepstrum pre-whitening, recently used in bearing diagnostics. The analytical results are the basis for the discussion on an optimal indicator for the choice of the demodulation band, the ratio of cyclic content (RCC), which endows the kurtosis with selectivity in the cyclic frequency domain and whose performance is compared with more traditional kurtosis-based indicators such as the protrugram. A benchmark, performed on numerical simulations and experimental data coming from two different test-rigs, proves the superior effectiveness of such an indicator. Finally a short introduction to the potential offered by the newly proposed index in the field of prognostics is given in an additional experimental example. In particular the RCC is tested on experimental data collected on an endurance bearing test-rig, showing its ability to follow the development of the damage with a single numerical index.

Testing second order cyclostationarity in the squared envelope spectrum of non-white vibration signals

Cyclostationary models for the diagnostic signals measured on faulty rotating machineries have proved to be successful in many laboratory tests and industrial applications. The squared envelope spectrum has been pointed out as the most efficient indicator for the assessment of second order cyclostationary symptoms of damages, which are typical, for instance, of rolling element bearing faults. In an attempt to foster the spread of rotating machinery diagnostics, the current trend in the field is to reach higher levels of automation of the condition monitoring systems. For this purpose, statistical tests for the presence of cyclostationarity have been proposed during the last years. The statistical thresholds proposed in the past for the identification of cyclostationary components have been obtained under the hypothesis of having a white noise signal when the component is healthy. This need, coupled with the non-white nature of the real signals implies the necessity of pre-whitening or filtering the signal in optimal narrow-bands, increasing the complexity of the algorithm and the risk of losing diagnostic information or introducing biases on the result. In this paper, the authors introduce an original analytical derivation of the statistical tests for cyclostationarity in the squared envelope spectrum, dropping the hypothesis of white noise from the beginning. The effect of first order and second order cyclostationary components on the distribution of the squared envelope spectrum will be quantified and the effectiveness of the newly proposed threshold verified, providing a sound theoretical basis and a practical starting point for efficient automated diagnostics of machine components such as rolling element bearings. The analytical results will be verified by means of numerical simulations and by using experimental vibration data of rolling element bearings.

A new procedure for using envelope analysis for rolling element bearing diagnostics in variable operating conditions

In the field of rolling element bearing diagnostics envelope analysis, and in particular the squared envelope spectrum, have gained in the last years a leading role among the different digital signal processing techniques. The original constraint of constant operating speed has been relaxed thanks to the combination of this technique with the computed order tracking, able to resample signals at constant angular increments. In this way, the field of application of squared envelope spectrum has been extended to cases in which small speed fluctuations occur, maintaining the effectiveness and efficiency that characterize this successful technique. However, the constraint on speed has to be removed completely, making envelope analysis suitable also for speed and load transients, to implement an algorithm valid for all the industrial application. In fact, in many applications, the coincidence of high bearing loads, and therefore high diagnostic capability, with acceleration-deceleration phases represents a further incentive in this direction. This paper is aimed at providing and testing a procedure for the application of envelope analysis to speed transients. The effect of load variation on the proposed technique will be also qualitatively addressed.

Application of cepstrum pre-whitening for the diagnosis of bearing faults under variable speed conditions

Diagnostics of rolling element bearings involves a combination of different techniques of signal enhancing and analysis. The most common procedure presents a first step of order tracking and synchronous averaging, able to remove the undesired components, synchronous with the shaft harmonics, from the signal, and a final step of envelope analysis to obtain the squared envelope spectrum. This indicator has been studied thoroughly, and statistically based criteria have been obtained, in order to identify damaged bearings. The statistical thresholds are valid only if all the deterministic components in the signal have been removed. Unfortunately, in various industrial applications, characterized by heterogeneous vibration sources, the first step of synchronous averaging is not sufficient to eliminate completely the deterministic components and an additional step of pre-whitening is needed before the envelope analysis. Different techniques have been proposed in the past with this aim: The most widely spread are linear prediction filters and spectral kurtosis. Recently, a new technique for pre-whitening has been proposed, based on cepstral analysis: the so-called cepstrum pre-whitening. Owing to its low computational requirements and its simplicity, it seems a good candidate to perform the intermediate pre-whitening step in an automatic damage recognition algorithm. In this paper, the effectiveness of the new technique will be tested on the data measured on a full-scale industrial bearing test-rig, able to reproduce the harsh conditions of operation. A benchmark comparison with the traditional pre-whitening techniques will be made, as a final step for the verification of the potentiality of the cepstrum pre-whitening.

Fault symptoms of rolling element bearings under variable operating conditions - a multi domain analysis

Diagnostics of rolling element bearings have been traditionally developed for constant operating conditions, and sophisticated techniques, like Spectral Kurtosis or Envelope Analysis, have proven their effectiveness by means of experimental tests, mainly conducted in small-scale laboratory test-rigs. Algorithms have been developed for the digital signal processing of data collected at constant speed and bearing load, with a few exceptions, allowing only small fluctuations of these quantities. Owing to the spreading of condition based maintenance in many industrial fields, in the last years a need for more flexible algorithms emerged, asking for compatibility with highly variable operating conditions, such as acceleration/deceleration transients. This paper analyzes the problems related with significant speed and load variability, discussing in detail the effect that they have on bearing damage symptoms, and propose solutions to adapt existing algorithms to cope with this new challenge. In particular, the paper will i) discuss the implication of variable speed on the applicability of diagnostic techniques, ii) address quantitatively the effects of load on the characteristic frequencies of damaged bearings and iii) finally present a new approach for bearing diagnostics in variable conditions, based on envelope analysis. The research is based on experimental data obtained by using artificially damaged bearings installed on a full scale test-rig, equipped with actual train traction system and reproducing the operation on a real track, including all the environmental noise, owing to track irregularity and electrical disturbances of such a harsh application.

The combination of empirical mode decomposition and minimum entropy deconvolution for roller bearing diagnostics in non-stationary operation

Diagnostics is based on the characterization of mechanical system condition and allows early detection of a possible fault. Signal processing is an approach widely used in diagnostics, since it allows directly characterizing the state of the system. Several types of advanced signal processing techniques have been proposed in the last decades and added to more conventional ones. Seldom, these techniques are able to consider non-stationary operations. Diagnostics of roller bearings is not an exception of this framework. In this paper, a new vibration signal processing tool, able to perform roller bearing diagnostics in whatever working condition and noise level, is developed on the basis of two data-adaptive techniques as Empirical Mode Decomposition (EMD), Minimum Entropy Deconvolution (MED), coupled by means of the mathematics related to the Hilbert transform. The effectiveness of the new signal processing tool is proven by means of experimental data measured in a test-rig that employs high power industrial size components.

Hydraulic instability onset detection in Kaplan turbines by monitoring shaft vibrations

Design of hydraulic turbines has often to deal with hydraulic instability. It is well-known that Francis and Kaplan types present hydraulic instability in their design power range. Even if modern CFD tools may help to define these dangerous operating conditions and optimize runner design, hydraulic instabilities may fortuitously arise during the turbine life and should be timely detected in order to assure a long-lasting operating life. In a previous paper, the authors have considered the phenomenon of helical vortex rope, which happens at low flow rates when a swirling flow, in the draft tube conical inlet, occupies a large portion of the inlet. In this condition, a strong helical vortex rope appears. The vortex rope causes mechanical effects on the runner, on the whole turbine and on the draft tube, which may eventually produce severe damages on the turbine unit and whose most evident symptoms are vibrations. The authors have already shown that vibration analysis is suitable for detecting vortex rope onset, thanks to an experimental test campaign performed during the commissioning of a 23 MW Kaplan hydraulic turbine unit. In this paper, the authors propose a sophisticated data driven approach to detect vortex rope onset at different power load, based on the analysis of the vibration signals in the order domain and introducing the so-called "residual order spectrogram", i.e. an order-rotation representation of the vibration signal. Some experimental test runs are presented and the possibility to detect instability onset, especially in real-time, is discussed.

Order tracking for discrete-random separation in variable speed conditions

The transmission path from the excitation to the measured vibration on the surface of a mechanical system introduces a distortion both in amplitude and in phase. Moreover, in variable speed conditions, the amplification/attenuation and the phase shift, due to the transfer function of the mechanical system, varies in time. This phenomenon reduces the effectiveness of the traditionally tachometer based order tracking, compromising the results of a discrete-random separation performed by a synchronous averaging. In this paper, for the first time, the extent of the distortion is identified both in the time domain and in the order spectrum of the signal, highlighting the consequences for the diagnostics of rotating machinery. A particular focus is given to gears, providing some indications on how to take advantage of the quantification of the disturbance to better tune the techniques developed for the compensation of the distortion. The full theoretical analysis is presented and the results are applied to an experimental case.

Bearing Fault Diagnostics Using the Spectral Pattern Recognition

In the field of diagnostics of rolling element bearings, the development of sophisticated techniques, such as Spectral Kurtosis and 2nd Order Cyclostationarity, extended the capability of expert users to identify not only the presence, but also the location of the damage in the bearing. Most of the signal-analysis methods, as the ones previously mentioned, result in a spectrum-like diagram that presents line frequencies or peaks in the neighbourhood of some theoretical characteristic frequencies, in case of damage. These frequencies depend only on damage position, bearing geometry and rotational speed. The major improvement in this field would be the development of algorithms with high degree of automation. This paper aims at this important objective, by discussing for the first time how these peaks can draw away from the theoretical expected frequencies as a function of different working conditions, i.e. speed, torque and lubrication. After providing a brief description of the peak-patterns associated with each type of damage, this paper shows the typical magnitudes of the deviations from the theoretical expected frequencies. The last part of the study presents some remarks about increasing the reliability of the automatic algorithm. The research is based on experimental data obtained by using artificially damaged bearings installed in a gearbox.

Diagnostic of Rolling Element Bearings with Envelope Analysis in Non-Stationary Conditions

In the field of rolling element bearing diagnostics, envelope analysis has gained in the last years a leading role among the different digital signal processing techniques. The original constraint of constant operating speed has been relaxed thanks to the combination of this technique with the computed order tracking, able to resample signals at constant angular increments. In this way, the field of application of this technique has been extended to cases in which small speed fluctuations occur, maintaining high effectiveness and efficiency. In order to make this algorithm suitable to all industrial applications, the constraint on speed has to be removed completely. In fact, in many applications, the coincidence of high bearing loads, and therefore high diagnostic capability, with acceleration-deceleration phases represents a further incentive in this direction. This chapter presents a procedure for the application of envelope analysis to speed transients. The effect of load variation on the proposed technique will be also qualitatively addressed.

Improving PLDA speaker verification with limited development data

This paper analyses the probabilistic linear discriminant analysis (PLDA) speaker verification approach with limited development data. This paper investigates the use of the median as the central tendency of a speaker’s i-vector representation, and the effectiveness of weighted discriminative techniques on the performance of state-of-the-art length-normalised Gaussian PLDA (GPLDA) speaker verification systems. The analysis within shows that the median (using a median fisher discriminator (MFD)) provides a better representation of a speaker when the number of representative i-vectors available during development is reduced, and that further, usage of the pair-wise weighting approach in weighted LDA and weighted MFD provides further improvement in limited development conditions. Best performance is obtained using a weighted MFD approach, which shows over 10% improvement in EER over the baseline GPLDA system on mismatched and interview-interview conditions.

A Human identification technique using images of the iris and wavelet transform

A new approach for recognizing the iris of the human eye is presented. Zero-crossings of the wavelet transform at various resolution levels are calculated over concentric circles on the iris, and the resulting one-dimensional (1-D) signals are compared with model features using different dissimilarity functions.

An efficient proactive route maintenance process for reliable data transmissions in sensor networks

For industrial wireless sensor networks, maintaining the routing path for a high packet delivery ratio is one of the key objectives in network operations. It is important to both provide the high data delivery rate at the sink node and guarantee a timely delivery of the data packet at the sink node. Most proactive routing protocols for sensor networks are based on simple periodic updates to distribute the routing information. A faulty link causes packet loss and retransmission at the source until periodic route update packets are issued and the link has been identified as broken. We propose a new proactive route maintenance process where periodic update is backed-up with a secondary layer of local updates repeating with shorter periods for timely discovery of broken links. Proposed route maintenance scheme improves reliability of the network by decreasing the packet loss due to delayed identification of broken links. We show by simulation that proposed mechanism behaves better than the existing popular routing protocols (AODV, AOMDV and DSDV) in terms of end-to-end delay, routing overhead, packet reception ratio.

Local inter-session variability modelling for object classification

Object classification is plagued by the issue of session variation. Session variation describes any variation that makes one instance of an object look different to another, for instance due to pose or illumination variation. Recent work in the challenging task of face verification has shown that session variability modelling provides a mechanism to overcome some of these limitations. However, for computer vision purposes, it has only been applied in the limited setting of face verification. In this paper we propose a local region based intersession variability (ISV) modelling approach, and apply it to challenging real-world data. We propose a region based session variability modelling approach so that local session variations can be modelled, termed Local ISV. We then demonstrate the efficacy of this technique on a challenging real-world fish image database which includes images taken underwater, providing significant real-world session variations. This Local ISV approach provides a relative performance improvement of, on average, 23% on the challenging MOBIO, Multi-PIE and SCface face databases. It also provides a relative performance improvement of 35% on our challenging fish image dataset.

Rodent Scope: A User-Configurable Digital Wireless Telemetry System for Freely Behaving Animals

This paper describes the design and implementation of a wireless neural telemetry system that enables new experimental paradigms, such as neural recordings during rodent navigation in large outdoor environments. RoSco, short for Rodent Scope, is a small lightweight user-configurable module suitable for digital wireless recording from freely behaving small animals. Due to the digital transmission technology, RoSco has advantages over most other wireless modules of noise immunity and online user-configurable settings. RoSco digitally transmits entire neural waveforms for 14 of 16 channels at 20 kHz with 8-bit encoding which are streamed to the PC as standard USB audio packets. Up to 31 RoSco wireless modules can coexist in the same environment on non-overlapping independent channels. The design has spatial diversity reception via two antennas, which makes wireless communication resilient to fading and obstacles. In comparison with most existing wireless systems, this system has online user-selectable independent gain control of each channel in 8 factors from 500 to 32,000 times, two selectable ground references from a subset of channels, selectable channel grounding to disable noisy electrodes, and selectable bandwidth suitable for action potentials (300 Hz–3 kHz) and low frequency field potentials (4 Hz–3 kHz). Indoor and outdoor recordings taken from freely behaving rodents are shown to be comparable to a commercial wired system in sorting for neural populations. The module has low input referred noise, battery life of 1.5 hours and transmission losses of 0.1% up to a range of 10 m.