Francois Baccelli INRIA ENS Information Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements Authors Venkat Anantharam Francois Baccelli
86 Pages
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Francois Baccelli INRIA ENS Information Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements Authors Venkat Anantharam Francois Baccelli


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Learn more
86 Pages


Abstracts – Francois Baccelli (INRIA ,ENS) Information-Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements Authors : Venkat Anantharam, Francois Baccelli Abstract : This paper studies the Shannon regime for the random displacement of stationary point processes. Let each point of some initial stationary point process in Rn give rise to one daughter point, the location of which is obtained by ad- ding a random vector to the coordinates of the mother point, with all displacement vectors independently and identically distributed for all points. The decoding problem is then the following one : the whole mother point process is known as well as the coordinates of some daughter point ; the displa- cements are only known through their law ; can one find the mother of this daughter point ? The Shannon regime is that where the dimension n tends to infinity and where the loga- rithm of the intensity of the point process is proportional to n. We show that this problem exhibits a sharp threshold : if the sum of the proportionality factor and of the differen- tial entropy rate of the noise is positive, then the probability of finding the right mother point tends to 0 with n for all point processes and decoding strategies. If this sum is nega- tive, there exist mother point processes, for instance Poisson, and decoding strategies, for instance maximum likelihood, for which the probability of finding the right mother tends to 1 with n.

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th6 International Conference
Acoustical and Vibratory
Surveillance Methods and Diagnostic Techniques
UTC Compiègne

Tuesday 25 october 2011
Plenary Session

Christian Cremona
Technical Centre for Bridges and Structures (CTOA),Technical Department for Transport, Roads
and Bridges (SETRA),Ministry of Ecology, sustainable Development, Transport and Housing
(MEDDTL), Bagneux, France.
The management of structures is a very important economic issue. France has been aware of this
for many years. In 2006, after the parliament vote of decentralization law, the State considered as
critical to rationalize the maintenance and the management of the remaining national asset. Since
the past 5 years, a lot of procedures and guidelines for bridge maintenance have been revised for
the national bridge stock. In addition opportunity was given to introduce new concepts such
focalized inspection, risk-based assessment. These changes or upgrades are made to take better
account in the decision-making process of socio-economic aspects (disruption for road users in
particular) and the effect of decisional choices and to introduce more elaborate structural condition
assessment methods which will give a more reliable estimate of the current and predicted
condition of the bridges asset. This paper presents the current procedures used for managing the
national bridge stock and the proposed enhancements or dominant future works.

Stilios Fassois Stochastic Mechanical Systems and Automation (SMSA) University of Patras,
Non–stationary random vibration signals exhibit time–dependent characteristics, thus requiring
time-dependent models and corresponding identification methods. In this talk parametric models
are distinguished into three main classes: unstructured, stochastic, and deterministic parameter
evolution. The main identification methods pertinent to each class are presented, along with recent
advances on “automated” and “complete” methods aiming at the concurrent handling of the model
structure and parameter estimation subproblems. Comparisons of the various methods via a
benchmark study, employing a laboratory bridge–like structure with a moving mass, are made.
Snapshots from the application of the methods to the modeling and identification of mechanism,
robot arm, and wind turbine vibrations, as well as earthquake ground motion are presented. An
outlook on upcoming and future developments is finally provided.

Schematic diagram of wind turbine indicating measurement locations and estimated frozen-type
time-dependent Power Spectral Density function (SP-TARMA method).

th6 International Conference
Acoustical and Vibratory
Surveillance Methods and Diagnostic Techniques
UTC Compiègne

Tuesday 25 october 2011
Morning session 1A
Signal processing : Cyclostationarity

Q. Leclere,N. Hamzaoui
INSA Lyon, LaboratoireVibrations Acoustique,
Cyclostationarity is a property of vibration and acoustic signals recorded on rotating machines operating at
constant speed. It states that the statistic properties of signals are periodic: the random process defined by
the signal observed at a given position in the cycle is stationary, the cycle being defined as the angle
interval between two identical configurations of the mechanical system. The cyclostationary theory allows
for example the division of the signal into the deterministic part (expected value of a cycle realization, also
called periodic part) and a random part (the centered signal). In some cases, the cyclostationarity property
is not fully satisfied. Mechanical events in the cycle can exhibit different periodicities, for example because
of transmission ratios or rolling elements. If those periodicities are incommensurable, it means that the
mechanical system never recovers periodically strictly identical configurations. Cyclostationarity is also not
fully satisfied if the signals are acquired in the time domain on rotating machines with a fluctuating rotation
speed. Indeed, if the instantaneous rotation speed is not purely periodic, it means that time samples taken
at a constant time interval (equal to the average cycle duration) do not correspond exactly to an angle in
the cycle. In this particular case, a synchronous averaging of cycle realizations can still be processed to
estimate a periodic part using a predefined trigger angle to align cycle realizations before the averaging
process. The time window of each realization is thus defined as two time portions before and after this
synchronization angle (practically, by a number of points of the time-sampled signal before and after the
trigger). In these conditions,the synchronousaverage dependsonthe chosen synchronization angle: each
point of the synchronous average is an estimate of the expected value of the signal at a given time
preceding or following the synchronization angle. The synchronous average can be computed in function of
the synchronization angle, varying over an entire cycle. The result is a moving synchronous average that
can be post-processed for diagnosis purposes. For example, a time frequencyrepresentation of the moving
synchronous average can be computed, and the synchronization angle maximizing each point of the time
frequencymap can be easily extracted. Under certain conditions of instantaneous speed fluctuations, this
analysis allows the precise localization of different mechanical events in the cycle, as well as their
contributions in the analyzed vibration or acoustic signal.

M. El Badaoui, F. Bonnardot 1Université de Lyon,; Université de Saint Etienne, LASPI, France
Rotating machines produces cyclic signals. When the machine parameters (load, speed, …) are almost
onstant or slowly vary,this cycles will introduce periodicity into acceleration (ie the acceleration signal
exhibits cyclostationarity). Since the cycle is linked to the angular part, it seems natural to use the angle as
a sampling variable instead of the time. Therefore, signal becomes synchronised to machine cycle. The
use of angular (or synchronous) sampling have shown very interesting results.Unfortunately, the
synchronisation with mechanical events obtained by angular sampling is not suitable to study the impulse
response associated to these events (or some structural damage). Therefore, it exists a dilemma in the
choice between angular sampling and classical temporal sampling.In the past, degradation of
cyclostationarity property introduced by the influence of temporal ing was studied. The purpose of
this paper was to study the influence of angular sampling on impulse response and time domain relative
signals.An experimental bench described in figure 1 was constructed. This bench uses a synchronous
data acquisition board. The time domain signal comes from an arbitrary generator (sine wave). The
synchronous sampler is driven by an external clock. Our external clock generator creates a square wave
with a tunable jitter δi (see Figure 2). Each sample are taken during the rising edge. The sampled signal is
digitized and analysed by Labview and MatLab.In order to check our random clock generator, a counter is
used to characterized precisely the sampling signal by measuring each period (T1, T2, …). The data
acquisition board is also capable of making both synchronous and temporal acquisition for comparison.

Experimentations are performed by using various period fluctuations (from 0,1 % to 20 %) and are
corroborated by theoretical studies.The first experimentation was to compare the spectrum of the signal
with period fluctuation vs without period fluctuation (temporal sampling). A comparison of the two spectra
is available in figure 3. Surprisingly, the fluctuation does not alter the peak in the spectrum even with high
fluctuation (the attenuation of the magnitude is very small). Nevertheless, the noise level significantly
increased when the fluctuation percentage increased. This result,confirmed by our theoretical study,
shows that the synchronous sampling hazard is not to distort the signal but to mask the information. A low
pass filter effect exists, but it is marginal.

Figure 3 : Effect of speed
fluctuation on spectra (Speed
fluctuation of 10%)
G. D' Eliaa, S. Delvecchioa, M. Cocconcellib, G. Dalpiaza University of Ferrara Italy
This work seeks to study the potential effectiveness of the Blind Signal Extraction as a pre-
processing tool for the detection of distributed faults in rolling bearings. In literature, most of the
authors focus their attention on the detection if incipient localized defects. In that case classical
techniques (i.e. envelope analysis) are robust in recognizing the presence of the fault and its
characteristic frequency. However, when the fault grows, the usual approach fails, due to the
change of the fault signature. De facto, in this case the signal does not contain impulses at the
fault characteristic frequency, but more complex components with strong non-stationary contents.
Moreover, signals acquired from complex machines often contain contributions from several
different components as well as noise; thus the fault signature can be hidden in the complex
system vibration. Therefore, pre-processing tools are needed in order to extract the bearing
signature, from the raw system vibration. In this paper authors focalize their attention on the
application of Blind Signal Extraction (BSE) in order to extract the bearing signature from the raw
vibration of a gearbox. The effectiveness and sensitivity of BSE is here exploited on the basis of
both simulated and real signals. Firstly a simulated signal including the effect of gear meshing as
well as a localized fault in bearings is introduced in order to tune the parameters of the BSE
algorithm. Next, real vibration signals acquired from a gearbox where tow degreased bearing
developed accelerated wear are analysed. In particular, the BSE is compared with the usual pre-
processing technique for the analysis of cyclostationary signals, i.e. the extraction of the residual
signal. The fault detection is carried out by the computation of the Integrated Cyclic Modulation
Spectrum (ICMS) on the extracted signals. The results indicate that the extracted signals via BSE
clearly highlight the distributed fault signature, in particular both the appearance of the faults as
well as their development are detected, whilst noise still hides fault grow in the residual signals.

Jacek Urbanek, Jerome Antoni, Tomasz Barszcz Analysis of the vibration signals generated by the
machinery has proven its usefulness in industrial condition monitoring. In the recent years, the use of
vibrodiagnostics has expanded to many branches of industry and has found application in the number of
types of the machinery. This fact raise the demand for application of vibrodiagnostic tools to more complex
objects, frequently operating under nonstationary conditions and in harsh environment. n the paper, the
authors propose the method for extracting second order cyclostationary components from a vibration signal.
For a known cyclic frequency, the proposed algorithm allows to estimate the amount of energy of each
cyclic component of interest in time-frequency domain. In this way, the resulted representation contains
only the chosen second order cyclostationary component that manifests itself as a number of carrier
frequencies modulated by the harmonic signal of selected frequency. The main concept of the algorithm is
to track down the energy flow of the spectral components that manifest cyclic behavior on the time-
frequency plane using pattern recognition method supported by the information from time domain averaged
instantaneous power spectrum (AIPS). The obtained filter is created to cover only desired energy
alternations. Such approach allows to achieve relatively selective results of extraction of second order
cyclostaionarities in both time and frequency domain with significantly reduced background noise level and
free of the influence of other cyclic components that were not meant to be extracted. A significant
advantage of the proposed algorithm is that it allows to extract the desired components from the vibration
signals generated by the machinery operating under variable load. The energy of the vibrations generated
by the operating machinery depends mostly on the load. By extracting only the pure second order
cyclostationary component the information about the variable energy level might be lost. Since this
information appears to be very useful in signal interpretation, its preservation is crucial in the extraction
process. Because the variation of the load is frequently connected with the variation of the machine
rotational speed, the proposed method permits limited fluctuations of the speed. In terms of variable energy
and the variable cycle length, it may be stated that the method described in the article allows to extract not
only cyclostationary but also second order quasicyclostationary components of desired quasi cyclic
frequency within known fluctuations range. The paper introduces the model of vibration signals generated
under variable operational conditions and the nature of second order cyclostationary signals generated by
rotating machinery. Next, the description of extraction method is proposed together with the method for
calculation of the AIPS. The applicability and the limitations are described. Subsequently, the method is
tested on the simulated signal and the experimental data from the test rig. Finally, as the example of the
machinery operating under variable operational conditions, the results from the case study of the industrial
wind turbine with defected rolling element bearing are presented.

1École de Technologie Supérieur de Montréal, Québec, Canada
2 LASPI, Université Jean Monnet de St Etienne, Roanne, France
In manufacturing, the current evolution towards productivity improvement and cost effectiveness has led to
the adoption of high speed machining. However, the use of high speed can cause a loss of work-piece
quality due to dynamic problems, such as tool wear and self-excited vibrations that produce chatter. Most of
the known chatter and tool wear detection methods are based on the assumption of stationarity. On this
basis, scalar time descriptors and spectral analysis are often employed to extract information on the cutting
tool health. However, most rotating machineries undergo non-stationary operations. In fact, even under
cutting conditions of pseudo-constant operations (speed, torque, temperature…), repetitive shocks and
friction due to the action of the tool and the work-piece during machining exhibit non stationary phenomena
during each cycle of the machine. The study of the cyclostationarity of the vibratory signals in milling
operations allows for taking into account the random effect that can be produced between each tool
revolution. The statistical properties of machine-tool vibratory signals are periodic with regard to the basic
cycle. This periodicity is inferred by the cyclic operation of the machine. New vectorial indicators based on
the property of cyclostationarity for identifying the angular position where specific phenomena can occur
are presented in this paper. These angular indicators were employed for the detection of slight chatter and
tool wear. For the tested conditions, the use of the angular power, the angular kurtosis, the angular
spectrum and the Wigner-Ville Spectrum (WVS) of the residual part of signal showed their efficiency for the
detection of the tool wear and the detection of chatter in the machining operation. The results reveal that
tool wear reduces the angular Kurtosis, but increases its power and the projection of the WVS presents a
good mean to analyze the tool wear especially for broken tooth. In addition, the angle-frequency of Wigner-
Ville representation of the residual signal shows that the energy corresponding to the tooth passing
decreases when a chatter phenomenon happens. The effect of tool wear and the number of broken teeth
on the excitation of structure resonances appears on the Wigner-Ville Spectrum. Angular power and
kurtosis spectrum are also used for analyzing chatter phenomena. By machining in the unstable region,
chatter is produced that results in flat angle kurtosis and flat angle power, such as a pseudo (white) random
signal with flat spectrum. Since a vectorial feature is difficult to manipulate for an efficient diagnosis, new
scalar indicators were developed. The Kurto Angular Power (KAP) and the Kurto Angular Kurtosis (KAK)
were used to analyze and detect chatter phenomena. These news scalars indicators are calculated from
the angular features in order to evaluate the severity of damage. These new indicators are useful for an
intelligent monitoring of the chatter and tool wear in high speed machining.

th6 International Conference
Acoustical and Vibratory
Surveillance Methods and Diagnostic Techniques
UTC Compiègne

Tuesday 25 october 2011
Morning session 1B
Structural health monitoring