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A Bayesian method to remove correlated noise from multi-channel measurements is introduced. It is based on Bayesian factor analysis coupled with prior but uncertain knowledge of the correlation structure of the noise. This technique is well suited to denoise cross-spectral matrices measured in the frame of aeroacoustic experiments when background noise measurements are available, because it allows separating the engine noise contribution from the turbulent boundary layer and uniform noise components that are all sensed by in-flow microphones. In-flight data measured on flush-mounted microphones on an aircraft fuselage are denoised using this method. It is shown that it has a significant benefit for studying the broadband shock-associated noise generated by the engines in realistic flight conditions.

International audience; Instantaneous speed estimation has become a key part of many condition monitoring procedures for rotating machinery. The ability to track the rotational speed of a system is a critical requirement for the majority of vibration-based condition monitoring methods. Information about the speed enables compensating for potential speed variations that would otherwise impair conventional frequency-based methods. The problem of instantaneous speed estimation based on the vibration signals themselves is one that has received a significant amount of attention in recent years. Installing encoders or tachometers has become a lot less attractive due to the potential cost savings that can be obtained by simply utilizing an accelerometer instead. However, trying to find a speed estimation method that fits a certain application “best” is not so straightforward if one inspects the available literature. It turns out that there are many articles that present slight variations or extensions to already existing techniques. This paper targets a general overview of the available knowledge regarding vibration-based speed estimation techniques. It also aims to review some of the most commonly used techniques by means of a performance comparison of seven speed estimation methods on three different experimental data sets. The resulting speed estimation data of all tested methods is made publicly available such that it can help in forming a benchmark for future speed estimation methods.

International audience; A lightweight numerical method is developed to predict the sound absorption coefficient of resonators whose cross-section dimensions are significantly larger compared to the viscous and thermal boundary layer’s thicknesses. This method is based on the boundary layer theory and on the perturbations theory. According to the perturbations theory, in acoustical domains with large dimensions, the fluid viscosity and thermal conductivity only affect the boundary layers. The model proposed in this article combines the lossless Helmholtz wave equation derived from a perfect fluid hypothesis, with viscosity and thermal conductivity values of a real fluid to compute the sound dissipation of geometrical acoustical attenuators (e.g. resonators). It is therefore referred to as a “Hybrid model”. This model is computationally very efficient with regard to visco-thermal models such as the FLNS (Full Linearized Navier-Stokes) model. It remains valid and efficient in a wide range of geometries even when reduced models such as the LRF (Low Reduced Frequency) model cannot be applied. The performances of the Hybrid model was tested on several differently shaped acoustical absorbers based on quarter-wave resonators. The Hybrid model results have been compared with experimental data and FLNS simulations and proved to be accurate and very efficient.

International audience; This paper deals with the dynamic characterisation of plate structures with elliptical orthotropic stiffness properties, using an equivalent thin plate theory using a wave fitting approach. The method consists in projecting the experimentally determined transverse displacement field of a plate on an analytical Green’s function of an elliptical orthotropic plate based on Hankel’s functions. The error between the projected and measured fields is then minimized, varying the characteristics of the function until an optimal fit is reached. The thus obtained characteristics are the two flexural rigidities defining the elliptical orthotropy of the plate, and the orthotropy angle. This fitting procedure is applied at each frequency, enabling the determination of frequency dependent dynamic material properties. The method is applied to a honeycomb sandwich panel to validate the proposed fitting approach. The identified flexural rigidities are compared to the estimations obtained by means of an analytical model and the IWC (Inhomogeneous Wave Correlation) method assuming three different type of plate characteristics (anisotropic, orthotropic and elliptical orthotropic). For the elliptical orthotropic assumption, consistent results are observed between the methods and the model over a large frequency range (from 1 to 50 kHz).

International audience; The aim of this paper is to propose a methodology for identifying the pressure field applied on a laminated composite plate from its measured vibration response. The general framework of this study is the Corrected Force Analysis Technique (CFAT), which was previously used on isotropic plates. This method estimates the spatial derivatives of the equation of motion with a finite difference scheme and corrects the bias error generated by this approximation. The paper presents an extension of this technique to deal with laminated panels. In a first instance, the finite difference scheme has been expanded to allow the identification of the 5 spatial derivatives that compose the equation of motion of such structures. The correction, considered in the wavenumber domain, has also been adapted and is now calculated numerically. In a second instance, the effect of measurement noise has been treated with the implementation of a regularisation technique based on the adaptation of the size of the scheme as function of the frequency. Numerical simulations and contact-less measurements have been conducted on different carbon fibers composite plates. Results are presented in terms of identified pressure fields and input force magnitude.

International audience; A smartphone is a low-cost pocket wireless multichannel multiphysical data acquisition system: the use of such a device for noise and vibration analysis is a challenging task. To what extent is it possible to carry out relevant analysis from it? The Survishno conference, held in Lyon in July 2019, proposed a contest to participants based on this subject. Two challenges were proposed, wherein each a mute video showing an object moving/excited at different frequencies was provided. Due to the frequencies set and the video sampling characteristics, special effects occurred and are visible on both videos. From the first video, participants were asked to estimate the Instantaneous Angular Speed (IAS) of a rotating fan. From the second video, they were asked to perform the modal analysis of a cantilever beam. This paper gathers the interesting ideas proposed by the contestants and proposes a global method to solve these two problems. One major point of the paper might be the advantageous use of the rolling shutter effect, a well-known artefact of smartphone videos, to perform advanced mechanical analyses: the consideration of the unavoidable slight phase shift between the acquisition of each pixel opens up the possibility to perform a dynamic analysis at frequencies that are much higher than the video frame rate.

International audience; Aeroacoustic signals, as typically returned by recordings of pressure fluctuations generated by rotating machines, often exhibit rich mixtures of tonal and broadband components. The separate analysis of these constituents is important from an engineering point of view, as they relate to different physical mechanisms. This paper is concerned with the extraction of tonal components. The characteristics of aeroacoustic signals can make this task challenging, because tones are numerous, nonharmonically related, and subjected to random modulations. A solution is proposed based on the theory of angle-time cyclostationarity, which seems flexible enough to deal with these constraints. A special effort is made to render the methodology as standalone as possible. This is achieved by automatically setting up the leading parameters with data-driven strategies. The methodology is illustrated on counter-rotating open rotor data that are known to be challenging.

International audience; The multiple coherence is a spectral analysis tool allowing the estimation of the contribution of several, possibly partially, coherent inputs to one or several outputs. This type of analysis can be conducted using a waterfall substraction approach (Conditioned Spectral Analysis framework) or using an eigenvalue analysis of the input correlation matrix (Virtual Source Analysis approaches). Those techniques are well established when dealing with converged cross-spectral estimates. In practice, this is never the case because of the finite nature of time records, and it can bring interpretation issues, particularly when increasing the number of references. The significance of the estimated coherence plays a central role in the present work. It involves the implementation of an hypothesis test based upon the statistical behavior of the estimated coherence between incoherent signals. This test, whose principle is to put to zero an estimated coherence that is below a significance threshold, is extended in this work to the multiple coherence case. The TMC (Thresholded Multiple Coherence) is first illustrated in the frame of a numerical benchmark, and then validated in a laboratory wind tunnel test where the interest for denoising purpose is demonstrated. The approach is finally applied to signals recorded inside and outside the cabin of an aircraft during a flight test. The TMC is used either from outside to inside microphones, to analyse the contribution of outside noise sources to the interior noise, or alternatively from inside to outside sensors, for flow noise rejection purpose.

This paper investigates the efficacy and reliability of three different state-of-the-art rotation speed estimation techniques on a very large set of experimental vibration data originating from thirty offshore wind turbine gearboxes. The three methods include the multi-order probabilistic approach, the phase demodulation method based on the frequency-domain energy operator, and the multi-harmonic demodulation technique. The goal is twofold: to assess statistically the performance of present-day vibration-based rotation speed estimation techniques on challenging experimental data, and to establish indirect rotation speed estimation through vibration data as a viable alternate solution to the conventional solution involving a direct measurement with a physical device such as a tachometer or an angle encoder. The results show that while all three techniques attain satisfying results, the multi-harmonic demodulation technique produces the most accurate speed estimate for the majority of all measurements whilst also being flexible in its usage.

International audience; The wall pressure measured by an array of flush mounted microphones subject to a flow results from two components. The first one is due to the pressure fluctuations generated by vortices convected by the flow in the turbulent boundary layer developed on the wall, and the second one results from acoustic waves that are emitted by some acoustic sources. Different type of sensor arrays can be used to characterize the first or second components, or even both. In all cases, a major difficulty is to separate as well as possible their contributions to the measurements. Different techniques are reviewed in this chapter to achieve this goal, based on either the measurement device itself or the post processing method. All approaches are implemented in a unique experimental setup, conducted in the frame of the ADAPT Clean Sky 2 project, allowing to objectively highlight their advantages and drawbacks.

International audience; This paper deals with the structural damping of mutilayered plates. Three definitions of loss factor are studied. The first one uses an equivalent methodology which assumes that the structure behaves as a Love-Kirchhoff's thin plate. The second approach links the spatial decay rate to the spatial decay rate by means of the group velocity of the wave to account for the dynamic behavior of the structure (shearing effect of the layers). The third approach relies on an energetic method based on the Modal Strain Energy (MSE) method. The loss factors according to these definitions are compared by means of an analytical model of multilayered plates for a typical sandwich structure. Experimental measurements are conducted on constrained-layer damping sandwich plates to validate the definitions. The loss factor is identified using three different protocols based on modal analysis (ESPRIT method), time decay rate estimation and displacement field analysis (CFAT method) and compared to the predictions of the analytical model.

This paper presents the modelling and the dynamic characterisation of laminated composite plates and sandwich structures in terms of stiffness and damping. The developments used in this paper are based on the analytical multilayer model of Guyader and Lesueur (JSV, 1978). The model considers linear shear, membrane and bending effects in each layer. The characteristics of the structure are determined by means of an equivalent thin plate methodology. The first main novelty of this paper consists in adapting this methodology for laminated plates (orthotropic multilayers with arbitrary orthotropic angle per layer). An experimental validation of this adaptation is presented for a laminated composite plate. Concerning the modelling of the structural loss factor, a space domain definition based on the spatial attenuation of a plane wave is compared to an energetic method and an equivalent definition based on the thin plate theory. The results show that the equivalent definition overestimates the loss factor in high frequencies since the thin plate theory only considers the flexural behaviour of the structure. On the contrary, the space domain definition (which give similar results as compared to the energetic one for lightly damped structures) considers the frequency dependent variation of the dynamic behaviour of the structure by means of the ratio between the group and phase velocities. The latter approach is considered to be more correct. The second main novelty of this article is on the experimental validation of this space domain definition. The structural loss factors of two sandwich structures are identified from measurements using modal, energetic and spatial methods. The results using the space domain definition are in very good agreement with the analytical predictions and the estimations of the modal and energetic methods for both plates for a large frequency band (up to 20 kHz), demonstrating the validity of the approach developed in this paper. ispartof: Journal Of Sound And Vibration vol:474 status: published

At low frequencies the assessment of the sound reduction index of building elements in the laboratory according to the standard ISO 10140-2:2010 is burdened by a large variation in the measurement results. This is due to the fact that at low frequencies the acoustic field is not sufficiently diffuse. This paper discusses a measurement procedure in which a diffuse field is created in the source room by means of an array of loudspeakers positioned closely to the building insulation element under test. This procedure exploits the acoustic near field of the loudspeaker array. The problems related to the breakdown of the diffuse field assumption of the receiving room are eliminated by measuring the structural response of the building insulation element under test by means of laser Doppler vibrometry and the application of the Rayleigh integral to compute the radiated sound power. The sound reduction index is determined from the ratio of the incident sound power, created by the loudspeaker array, and the radiated sound power. The measurement approach is validated by means of a measurement of the sound reduction index of a single layer glazing. Comparisons are made with an analytical model and with a standardized ISO 10140-2:2010 measurement. Although the method offers clear, strong points in terms of removing room acoustic effects from the measurements in the lower frequency range, a point of concern is the measurement effort. ispartof: APPLIED ACOUSTICS vol:140 pages:225-235 status: published

International audience; Rotating machines diagnosis is conventionally related to vibration analysis. Sensors are usually placed on the machine to gather information about its components. The recorded signals are then processed through a fault detection algorithm allowing the identification of the failing part. This paper proposes an acoustic-based diagnosis method. A microphone array is used to record the acoustic field radiated by the machine. The main advantage over vibration-based diagnosis is that the contact between the sensors and the machine is no longer required. Moreover, the application of acoustic imaging makes possible the identification of the sources of acoustic radiation on the machine surface. The display of information is then spatially continuous while the accelerometers only give it discrete. Beamforming provides the time-varying signals radiated by the machine as a function of space. Any fault detection tool can be applied to the beamforming output. Spectral kurtosis, which highlights the impulsiveness of a signal as function of frequency, is used in this study. The combination of spectral kurtosis with acoustic imaging makes possible the mapping of the impulsiveness as a function of space and frequency. The efficiency of this approach lays on the source separation in the spatial and frequency domains. These mappings make possible the localization of such impulsive sources. The faulty components of the machine have an impulsive behavior and thus will be highlighted on the mappings. The study presents experimental validations of the method on rotating machines.

International audience; Acoustical source reconstruction is a typical inverse problem, whose minimum frequency of reconstruction hinges on the size of the array and maximum frequency depends on the spacing distance between the microphones. For the sake of enlarging the frequency of reconstruction and reducing the cost of an acquisition system, Cyclic Projection (CP), a method of sequential measurements without reference, was recently investigated (JSV,2016,372:31-49). In this paper, the Propagation based Fast Iterative Shrinkage Thresholding Algorithm (Propagation-FISTA) is introduced, which improves CP in two aspects: (1) the number of acoustic sources is no longer needed and the only making assumption is that of a “weakly sparse” eigenvalue spectrum; (2) the construction of the spatial basis is much easier and adaptive to practical scenarios of acoustical measurements benefiting from the introduction of propagation based spatial basis. The proposed Propagation-FISTA is first investigated with different simulations and experimental setups and is next illustrated with an industrial case.

During the last decades, an emerging interest has been reported on modelling rotating machinery signals as cyclostationary. Several tools, such as the Spectral Correlation Density (SCD) and the Cyclic Modulation Spectrum (CMS) have been proposed, assuming constant or almost constant rotating speed. To overcome this limitation, generalizations of SCD and CMS have been proposed that display cyclic Order versus Frequency. On the other hand the estimation of the instantaneous angular speed of the rotating machine is a crucial issue that has to be tackled before any analysis or diagnosis of the machine operating under non-stationary conditions. This operation is generally carried out thanks to a tachometer, or an angle encoder, but in some cases this information can be missing for different reasons. The goal of this paper is to combine a novel approach for the analysis of cyclo-non-stationary signals based on the generalization of the indicators of cyclostationarity in order to cover the speed varying conditions, introducing a new speed-dependent angle averaging operator, with a new speed estimation method, that extracts from a vibration signal the most probable instantaneous rotation frequency without focusing on one specific order based on the a priori knowledge of the kinematics of the machine. The effectiveness of the ensemble method is evaluated on an acceleration signal captured at the wind turbine gearbox operating under speed varying conditions.

International audience; The problem of localizing and quantifying acoustic sources from a set of acoustic measurements has been addressed, in the last decades, by a huge number of scientists, from different communities (signal processing, mechanics, physics) and in various application fields (underwater, aero, or vibro acoustics). This led to the production of a substantial amount of literature on the subject, together with the development of many methods, specifically adapted and optimized for each configuration and application field, the variety and sophistication of proposed algorithms being sustained by the constant increase in computational and measurement capabilities. The counterpart of this prolific research is that it is quite tricky to get a clear global scheme of the state of the art. The aim of the present work is to make an attempt in this direction, by proposing a unified formalism for different well known imaging techniques, from identification methods (acoustic holography, equivalent sources, Bayesian focusing, Generalized inverse beamforming…) to beamforming deconvolution approaches (DAMAS, CLEAN). The hypothesis, advantages and pitfalls of each approach will be established from a theoretical point of view, with a particular effort in trying to separate differences in the problem definition (a priori information, main assumptions) and in the algorithms used to find the solution. Numerical simulations will be proposed for different source configurations (coherent/incoherent/extended/sparse distributions), and an experimental illustration on a supersonic jet will be finally discussed.

Research highlights: -Determination of material properties of thin plates from experimental vibrational fields. -Wave fitting approach projecting measurement data of plate vibrations on to an analytical image source model. -Bayesian regularization for the determination of the strengths of the image sources.; International audience; This paper presents a new wave fitting approach to estimate the frequency dependent material properties of thin isotropic plate structures from an experimentally obtained vibrational field, exciting the plate at a single point. The method projects the measurement data on to an analytical image source model, in which Hankel's functions are used for a description of the wave fields emanating from the point of excitation, including the reflected wave fields from the edges of the finite plate. By minimizing the error between the projected field and the measured field, varying the complex wave number and the source strengths of the image sources, an optimum fit is searched for. Thus the source strengths of the image sources do not need to be determined theoretically, but are estimated from the fit on to the experimental data instead (thus avoiding difficulties in theoretically assessing the reflection coefficient of the edges of the plate). The approach uses a complex wavenumber fit, enabling the determination of the dynamic stiffness of the plate structure and its damping properties as function of frequency. The method is especially suited for plates with a sufficient amount of damping, excited at high frequencies

Acoustic beamforming is a technique to measure the sound field and then achieve the localization of the sound sources. It usually works at a high frequency because the size and density of the microphone array are limited. Differing from the traditional beamforming, non-synchronous measurements beamforming can widen the working frequency bandwidth with a movable microphone array. It generates a cross-spectral matrix of all the microphones in the sequential positions of measurements, and this matrix is incomplete due to the missing phase relationships between non-synchronous measurements. Thus the non-synchronous measurements beamforming can be regarded as a cross-spectral matrix completion problem. One application of the non-synchronous measurements beamforming is that it can immediately obtain a completed noise image by scanning a large sound source; then the primary sound sources are expected to be identified by the global image. However, it is still a challenge for the current non-synchronous measurements beamforming algorithm since the computation time is long when more numbers of measurements are involved. In this paper, two algorithms based on the augmented Lagrange multiplier method and alternating direction method of multipliers are proposed for achieving fast implementation. The proposed algorithms can improve the iteration speed of the non-synchronous measurements beamforming which is proved first in the simulation, and they are further applied in the on-site measurement of the vehicle engine compartment (the data missing cross-spectral matrix of 15 non-synchronous measurements for a given frequency can be completed only in a few seconds). This industrial application has shown the potential of the proposed methods to be further applied for the sound source imaging of large mechanical systems.

International audience

International audience; An algorithm based on a hierarchical Bayesian model is introduced to separate sources highly overlapping in time and frequency and observed through correlated references. The method is applied to internal combustion (IC) engine signals with the aim of separating the contributions due to different physical origins. The results are compared to the ones provided by classical Wiener filter. The Bayesian context allows correlated references to be taken into account with no consequences on the identifiability of the sources, thanks to the possibility of providing some regularizing prior information in the form of Bayesian prior laws. Moreover, the credibility interval on the estimated sources derives directly from the adopted sampling strategy. Finally, it is shown in a simple case that the proposed algorithm can be rewritten as a weighted sum of the classical and cyclic Wiener filters proposed by Pruvost in 2009. As opposed to them, the present algorithm autonomously chooses one or the other depending on the characteristics of the analysed signals. Even if the development context is the separation of the sources in an IC engine, the presented method is general and can be applied to any source separation problem.

The paper describes an equivalent source model of acoustic sources from optical measurements using refracto-vibrometry. The acousto-optic effect is used to characterize the acoustic source in a non-invasive manner. The equivalent source model is constructed with a volumic distribution of monopole sources: its radiation should produce an acouto-optic effect which match with the measured one. The solution of this inverse problem gives the monopole strengths. This method is applied to the characterization of an acoustic pulse source. It is shown that the reconstructed pressure with the equivalent source matches the measured one within a 2 dB range. Moreover, the equivalent source dimensions, spatial location and directivity are in good accordance with expected characteristics of the real source.

International audience; In a previous work, an attempt was made to give a unified view of some acoustic holographic methods within a Bayesian framework. One advantage of the so-called “Bayesian Focusing” approach is to introduce an aperture function that acts like a lens and thus significantly improves the reconstruction results in terms of spatial resolution, but also of quantification over a larger frequency interval than allowed by conventional methods. This is particularly remarkable when the aperture function is allowed to become very narrow as in the case of sparse sources. The aim of the present paper is to demonstrate that the aperture function – which was previously manually tuned by the user – can be automatically estimated, together with the source distribution, in the same inverse problem. The principle is to use the current estimate of the source distribution to update the aperture function in the next iteration. The resulting algorithm is an iterated version of Bayesian Focusing, which can be formalized as an Expectation-Maximization algorithm with proved convergence. The proof of convergence is based on modeling the aperture function as a random quantity, which assigns the source coefficients with prior probability distribution in the form of a “scale mixture of Gaussians” that enforces sparse solutions. Various types of sparsity enforcing priors can thus be constructed, in a much richer setting than the usual ℓ1 penalized approach, leading to different updating rules of the aperture function. Some immediate byproducts of iterating Bayesian Focusing are 1) to provide a technique for the automatic setting of the regularization parameter, 2) to apply on the cross-spectral matrix of the measurements, and 3) to easily allow the grouping of frequencies for the broadband analysis of sources that are stationary in space. Experimental results confirm that sparse holography improves the reconstruction of sources not only in terms of localization, but also of quantification and of directivity in a frequency range considerably enlarged as compared to classical methods. These improvements can be achieved even with regular arrays, provided that sparser priors than those leading to the standard ℓ1 penalization are used.

Phased microphone arrays have become a well-established tool for performing aeroacoustic measurements in wind tunnels (both open-jet and closed-section), flying aircraft, and engine test beds. This paper provides a review of the most well-known and state-of-the-art acoustic imaging methods and recommendations on when to use them. Several exemplary results showing the performance of most methods in aeroacoustic applications are included. This manuscript provides a general introduction to aeroacoustic measurements for non-experienced microphone-array users as well as a broad overview for general aeroacoustic experts.

International audience; EDF R&D carries out studies for many years in order to improve and quantify the performances of the ultrasonic NDT process implemented on nuclear power plants. The detection and sizing of defects in coarse grained materials is a very challenging issue related to the inspection of critical components of nuclear power plants. Indeed in coarse grained material, the scattering of the ultrasonic wave at grain boundaries is responsible for the high attenuation which highly degrades the detection performances. This unfavorable phenomenon is predominant where the mean grain size is comparable to the wavelength of the control. In this framework, EDF R&D has carried out studies on the simulation of the ultrasonic propagation in complex materials with the finite elements code ATHENA. 2D and 3D finite element modeling approaches of ultrasonic propagation have been implemented, combined with a description of the microstructure of coarse grain materials [1]. The aim of this study is to demonstrate that the integration of a relevant description of the microstructure of macroscopically isotropic grain materials in a numerical simulation is an efficient tool to predict the ultrasonic attenuation in those materials. In addition, the influence of grain morphology, size and orientation on the ultrasonic attenuation coefficient is studied. The simulation results are compared with theoretical models and experimental measurement performed on an isotropic polycrystalline material (coarse grain Ni-based alloy).

Measured acoustic data can be contaminated by noise. This typically happens when microphones are mounted in a wind tunnel wall or on the fuselage of an aircraft, where hydrodynamic pressure fluctuations of the Turbulent Boundary Layer (TBL) can mask the acoustic pressures of interest. For measurements done with an array of microphones, methods exist for denoising the acoustic data. Use is made of the fact that the noise is usually concentrated in the diagonal of the Cross-Spectral Matrix, because of the short spatial coherence of TBL noise. This paper reviews several existing denoising methods and considers the use of Conventional Beamforming, Source Power Integration and CLEAN-SC for this purpose. A comparison between the methods is made using synthesized array data., Comment: 2019 AIAA/CEAS Aeroacoustics conference, May 2019, Delft, Netherlands

The issue of acoustic source identification has been widely explored in static or quasi-static source contexts, more recently for moving sources, in a wide range of applications. In the case of a passing-by vehicle, the beamforming method is a reference having well-known limitations that deconvolution methods try to overcome. Mostly developed in static source situations at the beginning, some recent deconvolution extensions to moving sources have been proposed in the transportation field, mainly in air transportation and underwater acoustics. In the present investigation, a new approach - called CLEANT for CLEAN-Time domain - is proposed and numerically tested with parameters fitted to the road vehicle context. Inspired by the CLEAN algorithm used to solve deconvolution problems, it is performed exclusively in the time domain and takes advantage of the source signal reconstruction available from the beamforming procedure. Its performance is assessed at several different speeds, source-to-array distances and with various additional noise levels, as well as its robustness regarding an uncertainty on some input parameters. The proposed approach is compared to a reference method using performance indicators. The simulations show better localization and quantification with CLEANT as compared to the other method tested in this road transportation context. Laboratory measurements in scaled pass-by conditions have been conducted and the results are presented and confirm the improvement brought by CLEANT.

International audience; Abstract This paper addresses the problem of in situ calibration of a pin hole-mounted microphone array for in-duct acoustic measurements. One approach is to individually measure the frequency response of each microphone, by submitting the probe to be calibrated and a reference microphone to the same pressure field. Although simple, this task may be very time consuming for large microphone arrays and eventually suffer from lack of access to microphones once they are installed on the test bench. An alternative global calibration procedure is thus proposed in this paper. The approach is based on the fact that the acoustic pressure can be expanded onto an analytically known spatial basis. A projection operator is defined allowing the projection of measurements onto the duct modal basis. The main assumption of the method is that the residual resulting from the difference between actual and projected measurements is mainly dominated by calibration errors. An iterative procedure to estimate the calibration factors of each microphone is proposed and validated through an experimental set-up. In addition, it is shown that the proposed scheme allows an optimization of physical parameters such as the sound speed and parameters associated to the test bench itself, such as the duct radius or the termination reflection coefficient.

A new measurement procedure is proposed to assess the airborne sound insulation of a partition under diffuse sound field excitation using mobility measurements combined with a numerical procedure. The advantage of this hybrid approach is that the diffuse acoustic field does not need to be physically created, thus avoiding problems related to the generation of such fields at low frequencies. Furthermore, the acoustic properties of both the source and receiving rooms will not affect the determination of the sound reduction index R. The proposed method is especially suited for frequencies below the so called Schroeder frequency of the room, and is complementary to the standardized measurement approaches as described in ISO 10140-2:2010. The measurement part of the proposed procedure involves the measurement of the mobility by forcing the partition along a grid of excitation points (e.g. by means of a shaker) and measuring its response along a grid of response points (e.g. by means of a scanning laser Doppler vibrometer). Using the resulting matrix of mobility transfer functions, the vibrational response of the partition excited by a diffuse acoustic field is numerically calculated, from which the radiated sound power is computed using the Rayleigh integral. Thus the reliance on source and receiving rooms used in standard sound insulation testing is removed entirely. The proposed method provides an estimate that only depends on the properties of the partition. The method was tested in an acoustic laboratory on a single layer glass plate of 1.35 x 1.54 m2, as well as on a funicular shell structure with dimensions of 3 x 3 m2. Comparisons with analytical models and standardized ISO10140-2:2010 measurements confirm the validity of the results. ispartof: JOURNAL OF SOUND AND VIBRATION vol:432 pages:680-698 status: published

International audience; With the aim of decreasing CO2 emissions, car producers’ efforts are focused, among others, on reducing the weight of vehicles yet preserving the overall vibrational comfort. To do so, new lightweight materials combining high stiffness and high (passive) damping are sought. For panels essentially loaded in bending, sandwich composites made of two external metallic stiff layers (skins) and an inner polymeric (i.e. absorbing) core are broadly used. Now aiming at creating materials by design with a better control of the final performance of the part, the tuning of the local material properties is pursued. To this end, the present work focuses on controlling the spatial in-plane viscoelastic properties of the polymeric core of such sandwich structures. The spatial patterning is achieved using a recently developed UV irradiation selective technique of Room Temperature Vulcanization (RTV) silicone elastomeric membrane, in which the ultraviolet (UV) irradiation dose, curing time and temperature are the process parameters controlling the viscoelastic properties of the polymeric membrane. Finally, a protocol for the realization of architected aluminum - silicone - aluminum composite sandwich panels is proposed. The influence of UV irradiation selective technique is demonstrated by Dynamic Mechanical Analysis (DMA) measurements on the silicone core itself and by the Corrected Force Analysis Technique (CFAT) to measure the equivalent Young’s modulus and damping of the sandwich structure over a large frequency band. As a first demonstration application, sandwich beams with different core patterns (homogeneous and heterogeneous) are designed and tested. Furthermore, the analytical formalism developed by Guyader et al. is used to model the vibro-acoustic performances of the homogenous sandwich beams and fair model-experiments comparisons are obtained. The spatial patterning of the polymer layer is found to successfully affect the local properties of the composite heterogeneous beam as evidenced by the CFAT method. Finally, this work permits the enunciation of guidelines for designing complex architectured systems with further control of the vibro-acoustics performances.

JTAV 2018, Journées Techniques Acoustique et Vibrations, Saint Brieuc, FRANCE, 13-/06/2018 - 14/06/2018; L'identification de sources acoustiques a été largement traitée dans le cas de sources fixes ou quasi-statiques, pour une grande variété de contextes d'application. La formation de voies est la méthode de référence dans ce cas. Les limites de cette méthode sont bien connues en matière de localisation et de quantification, et des méthodes de déconvolution sont souvent utilisées en complément pour s'en affranchir. Ces dernières, implémentées dans le domaine fréquentiel, sont mal adaptées au contexte de sources mobiles. Une approche novatrice adaptée aux conditions instationnaires des véhicules au passage est présentée. Elle opère exclusivement dans le domaine temporel, associant une formation de voies avec suivi de sources et un algorithme de nettoyage itératif.

International audience; In the literature, several papers deal with the localisation and quantification of forces on a structure.One of them, the FAT (Force Analysis Technique) method, which was recently extended tomaterial characterisation, was initially created for vibration source identification. This methodwas developed for beams, isotropic plates or shells and recently orthotropic plates. FAT identifiesthe equation of motion of the structure with a finite difference scheme applied on a measureddisplacement field. This scheme gives an approximation of the partial derivatives. By introducingcorrecting factors, the CFAT (Corrected FAT) methodology corrects the approximation made byfinite difference scheme and attenuates the singularities of the filter. This paper presents the extensionof this last method for laminated plates. This type of plate is different from an orthotopicplate because it presents a flexural-torsion interaction and has a complex equation of motion with5 flexural rigidities (against 3 in the orthotropic case and 1 in the isotropic case). The correctionof the finite difference scheme is now composed of 5 correcting factors estimated in this paper analyticallyand numerically. Finally, a validation of the extension of CFAT is presented on numericaldisplacement field (FEM Nastran) for laminated plates.

The workshop is partly supported by the LMAc institute, Le Mans Acoustique. This symposium is an action of the "METAPLAQ" research project funded over the period 2016-2019.; International audience; Since 2014 several collaborations between two laboratories of INSA Lyon - Mateis (materials science) and LVA (vibroacoustics) - have been focused on the modeling, designing and measuring hybrid sandwich composites structures with optimized damping properties for given frequency domains. The proposed contribution gives an overview of these modeling and experimental efforts, by presenting some results on several application cases.In a first study ([1-4]), a three layer steel/polymer/steel plate sandwich system is considered. Several aspects are studied by comparing four measurement techniques and three analytical models predictions. High resolution modal analysis coupled to contactless measurement of the velocity field of plates (CFAT) leads to the estimation of the equivalent single layer complex rigidity (frequency dependent “apparent bending stiffness” and “apparent damping”) for the whole [40Hz-20kHz] frequency band. Compared to the analytical modelling of Guyader based on wave propagation analysis, the results are in very good agreement. The comparison with this theoretical approach allows identifying the frequency dependent complex modulus of the polymer core layer through inverse resolution. The predicted properties turned out to match DMA measurements performed on the polymer material alone and the associated high frequency predictions (using the time-temperature equivalence principle). With this approach, the design of multilayer plates for vibroacoustics applications with optimized damping properties for given frequency domains may be performed.The second study ([5,6]) focuses on controlling the spatial in-plane viscoelastic properties of the polymeric core of sandwich structures. Aiming at creating materials by design, the tuning of the in-plane local material properties is pursued. The spatial patterning is achieved using a recently developed UV irradiation selective technique of Room Temperature Vulcanization silicone elastomeric membrane. “Structured” three-layer beams (aluminum/silicon/aluminum) with different core patterns (homogeneous and heterogeneous) are designed and tested. Fair model-experiments comparisons are obtained. This work permits the enunciation of guidelines for designing complex architectured systems with further control of the vibro-acoustics performances. In particular the effect of the viscoelastic patterning on the “optimum shearing zone” (position and width) will be discussed. The explored material solutions could be dedicated from low to very low frequency ranges where meta-material-based solutions are often inefficient.1.Ege et al., Inter-Noise 2015, San Francisco2.Roozen et al., JSV 2017, 390, pp.257-271. 3.Roozen et al., JSV 2017, 395, pp.90-101.4.Ege et al., JSV 2018, 426, pp.129-149.5.Gallo et al., Acoustics'2017, Boston.6.Gallo et al., ISNVH 2018, Graz.

National audience; Respecter les normes pour la lutte contre la pollution des véhicules et leurs nuisances sonores est l’un des enjeux majeurs de ces dernières années pour l’industrie du transport. Cette problématique a poussé à alléger les véhicules en remplaçant les matériaux métalliques par de nouveaux matériaux conservant de bonnes performances de résistance mécanique et d’isolation vibroacoustique. Dans cette optique, un nouveau procédé de matériaux multicouches a été développé. L’assemblage est constitué d’une âme en polymère (silicone) placée entre deux peaux métalliques. Les propriétés mécaniques du silicone sont contrôlées par irradiation UV à l’aide de masque intercalés entre la source UV et le matériau silicone permettant de contrôler localement les propriétés du polymère (module d’Young et facteur de perte) et de créer ainsi un matériau multicouches architecturé.Nous abordons dans la première partie de cet article une étude analytique (modèle de Guyader, JSV 1978) qui porte sur les différences de propriétés mécaniques qui existent entre deux poutres multicouches spatialement homogènes irradiée et non irradiée et nous en présentons la validation expérimentale. Pour cela, la méthode RIFF (Résolution Inverse Filtrée Fenêtrée) est utilisée. Elle permet d’identifier les propriétés mécaniques du matériau spatialement et en fonction de la fréquence. Pour vérifier le contrôle local du module d’Young grâce au procédé d’irradiation, une troisième poutre multicouches similaire aux précédentes, mais dont l’âme est composée d’un silicone dont l’irradiation varie sur sa longueur, est ensuite étudiée. Enfin, quelques exemples d’architecturation des propriétés du multicouches sont présentées à l’aide de modèles éléments finis.

International audience

International audience; In this paper, the Scanning Laser Doppler Vibrometer (SLDV) is used to measure acoustic pressure in small regions of cavities for the study of acoustical localization. It is shown that this optical method leads to interesting information on localized acoustical modes inside irregular cavities, which are very difficult to observe using conventional microphone measurements. Indeed, localization regions are often of comparable size or even smaller than a typical microphone which can make this type of sensor intrusive. The SLDV is used to measure sound pressure after deriving the refracto-vibrometry method from its standard use. Data are obtained in a large area with a high spatial resolution and the method is validated on some cavities. On irregular cavities, localized modes have been measured and visualized precisely, showing a good agreement to numerical simulations. Owing to this tool, the increase of damping induced by irregularities is experimentally demonstrated through the study of the quality factor. The method is also used to estimate the sound absorption coefficient of quarter-wave resonators. The expected application of this work is the use of irregular geometries to dissipate acoustical energy, especially at frequencies at which porous materials are not efficient.

International audience

International audience; Acoustic beamforming consists in measuring the sound field by the microphone array and infers the source strength in conjunction with the propagation model. A fundamental limitation of acoustic beamforming is determined by the aperture size of the array and the microphone density. In order to extend the working frequency range of conventional phased array beamforming, the sound sources are scanned by moving sequentially a small prototype array, resulting in a large array and high microphone density measurements, which is referred to as non-synchronous measurements beamforming. The main issue of nonsynchronous measurements beamforming is that the phase relationships between consecutivesnapshots of non-synchronous measurements are missing and result in missing entries in the spectral matrix, however, complete spectral matrix information is crucial for high quality image of beamforming. Thus, non-synchronous measurements beamforming boils down to a spectral matrix completion problem which is modeled by a structured low rank model and solved by designed fast iteration algorithm. In particular, the structured low rank model is constructed by two ingredients: (1) the low rank property of the spectral matrix and (2) the continuity of the acoustic field. The simulation results show the nonsynchronous measurements beamforming extended the working frequency range of given small phased array from 2−2.8 kHz to 1.6−4.5 kHz with only 9 times non-synchronous measurements.

Research highlights : -Determination of material properties of sandwich plates from experimental vibrational fields. -Frequency dependent apparent stiffness and apparent damping of three-layered sandwich plates. -Comparisons of measured/predicted frequency dependent equivalent complex modulus. -Inverse vibrational method to identify polymer characteristics up to 20 kHz. -Comparisons with Dynamic Mechanical Analysis measurements; International audience; In the context of aeronautics, automotive and construction applications, the design of light multilayer plates with optimized vibroacoustical damping and isolation performances remains a major industrial challenge and a hot topic of research. This paper focuses on the vibrational behavior of three-layered sandwich composite plates in a broad-band frequency range. Several aspects are studied through measurement techniques and analytical modelling of a steel/polymer/steel plate sandwich system. A contactless measurement of the velocity field of plates using a scanning laser vibrometer is performed, from which the equivalent single layer complex rigidity (apparent bending stiffness and apparent damping) in the mid/high frequency ranges is estimated. The results are combined with low/mid frequency estimations obtained with a high-resolution modal analysis method so that the frequency dependent equivalent Young's modulus and equivalent loss factor of the composite plate are identified for the whole [40 Hz-20 kHz] frequency band. The results are in very good agreement with an equivalent single layer analytical modelling based on wave propagation analysis (model of Guyader). The comparison with this model allows identifying the frequency dependent complex modulus of the polymer core layer through inverse resolution. Dynamical mechanical analysis measurements are also performed on the polymer layer alone and compared with the values obtained through the inverse method. Again, a good agreement between these two estimations over the broad-band frequency range demonstrates the validity of the approach.

International audience; The aim of this paper is to propose a methodology to localize acoustic sources from the measurement of airborne induced vibrations of a thin structure. Targeted applications are the identification of acoustic sources through a thin wall , with a potential filtration of the incident field , which may be of practical interest for instance when identifying exterior acoustic sources from the inside of a moving vehicle. Two methods are coupled here to achieve this purpose : the Force Analysis Technique (FAT) , used to identify the parietal pressure field exciting the thin structure from vibration measurements , and beamforming , used for the localization of acoustic sources from the (FAT-) identified parietal pressure. The coupling of the two methods is studied first from a theoretical point of view , and an experimental proof of concept is then presented , showing the feasibility and relevance of the proposed approach .

International audience; Nowadays, the need of source identification methods is still growing and application cases are more and more complex. As a consequence, it is necessary to develop methods allowing us to reconstruct sound fields on irregularly shaped sources in reverberant or confined acoustic environment. The inverse Patch Transfer Functions (iPTF) method is suitable to achieve these objectives. Indeed, as the iPTF method is based on Green's identity and double measurements of pressure and particle velocity on a surface surrounding the source, it is independent of the acoustic environment. In addition, the finite element solver used to compute the patch transfer functions permits us to handle sources with 3D irregular shapes. In the present paper, two experimental applications on a flat plate and an oil pan have been carried out to show the performances of the method on real applications. As for all ill-posed problem, it is shown that the crucial point of this method is the choice of the parameter of the Tikhonov regularization, one of the most widely used in the literature. The classical L-curve strategy sometimes fails to choose the best solution. This issue is clearly explained and an adapted strategy combining L-curve and acoustic power conservation is proposed. The efficiency of this strategy is demonstrated on both applications and compared to results obtained with Generalized Cross Validation (GCV) technique.

A global estimator of the uncertainty of the average frequency response function in multi-channel spectral analysis measurements is proposed. The proposed global estimator is a generalization of the random error estimator of the frequency response function magnitude of a single-input-single-output system. In principle, the signal-to-noise ratio (and thus the quality of the frequency response function estimation) is increasing with increasing number of averages $M$, according to $\sqrt{M}$. However, in the situation that, for practical reasons, there is a maximum imposed upon the total measurement time $T_{max}$, it is clear that there is a trade-off between the number of averages $M$ and the record length $T$ [s] that is used to obtain an estimate of a single-average-frequency-response-function. There is a choice between a few long records or many short records, with the requirement that, assuming zero overlap, the number of averages $M$ times the record length $T$ may not exceed the total available measurement time, i.e. $M \times T \leq T_{max}$. In addition to the existence of such an optimum, a minimum record length is required as well which is related to the reverberation time of the system. The newly proposed global estimator is used to determine the optimal record length of a multi-channel system, such that a minimum error of the average frequency response function is obtained. It is also shown by experimental results that indeed the minimum allowable record length is related to the reverberation time of the system being measured. publisher: Elsevier articletitle: A global error estimator for the uncertainty of a multi-channel spectral analysis journaltitle: Applied Acoustics articlelink: http://dx.doi.org/10.1016/j.apacoust.2014.06.007 content_type: article copyright: Copyright © 2014 Elsevier Ltd. All rights reserved. ispartof: Applied Acoustics vol:87 issue:1 pages:57-63 status: published

International audience; This paper presents the content and outcomes of the Safran contest organized during the International Conference Surveillance 8, October 20–21, 2015, at the Roanne Institute of Technology, France. The contest dealt with the diagnosis of a civil aircraft engine based on vibration data measured in a transient operating mode and provided by Safran. Based on two independent exercises, the contest offered the possibility to benchmark current diagnostic methods on real data supplemented with several challenges. Outcomes of seven competing teams are reported and discussed. The object of the paper is twofold. It first aims at giving a picture of the current state-of-the-art in vibration-based diagnosis of rolling-element bearings in nonstationary operating conditions. Second, it aims at providing the scientific community with a benchmark and some baseline solutions. In this respect, the data used in the contest are made available as supplementary material.

Colloque avec actes et comité de lecture. Internationale.; International audience; La caractérisation de matériaux complexes comme les multicouches a déjà fait preuve de nombreux travaux. Différentes approches existent, et en particulier, celles basées sur la recherche d'une plaque équivalente homogène (Equivalent Single Layer Model). Ces dernières comparent le multicouche à une plaque mince dont les paramètres simulent le comportement dynamique du multicouche à une fréquence donnée. La caractérisation du multicouche se fait donc par l'obtention de ces paramètres « équivalents ». En particulier, le modèle développé par J.L. Guyader [Internoise 2007] est de type plaque mince, se limitant à la caractérisation d'un multicouche isotrope, indépendant du nombre de couche et permettant d'obtenir comme paramètres équivalents, un module d'Young et un amortissement dynamique. A une fréquence donnée, la plaque équivalente présente le même nombre d'onde naturel que le multicouche. En reprenant une méthodologie similaire, nous proposons d'étendre le modèle de Guyader au cas des multicouches orthotropes, par le calcul des différentes rigidités de flexion D1, D2, D3 et D4 solutions de l'équation de dispersion de la plaque mince équivalente orthotrope. Cette méthode permet d'obtenir une représentation des caractéristiques du multicouche sur le plan d'onde kx ? ky. Des comparaisons expérimentales (vibrométrie laser) / analytiques seront présentées entre 2 et 8 kHz pour différents cas d'orthotropie sur des plaques en fibre de carbone afin d'illustrer les performances de la méthode.

International audience; In this work, various microphone phased array data processing techniques are applied to two existing datasets from aeroacoustic wind tunnel tests. The first of these is from a large closed-wall facility, DLR's Kryo-Kanal Köln (DNW-KKK), and is a measurement of the high-lift noise of a semispan model. The second is from a small-scale open-jet facility, the NASA Langley Quiet Flow Facility (QFF), and is a measurement of a clean airfoil self-noise. The data had been made publicly available in 2015, and were analyzed by several research groups using multiple analysis techniques. This procedure allows the assessment of the variability of individual methods across various organizational implementations, as well as the variability of results produced by different array analysis methods. This paper summarizes the results presented at panel sessions held at AIAA conferences in 2015 and 2016. Results show that with appropriate handling of background noise, all advanced methods can identify dominant acoustic sources for a broad range of frequencies. Lower-level sources may be masked or underpredicted. Integrated levels are more robust and in closer agreement between methods than narrowband maps for individual frequencies. Overall there is no obvious best method, though multiple methods may be used to bound expected behavior. i Research Engineer, Aeroacoustics Branch, Senior Member AIAA, christopher.j.bahr@nasa.gov ii Research Engineer, Adv. Measurements and Data Systems Branch, Associate Fellow AIAA, william.m.humphreys@nasa.gov

This paper concerns the assessment of the dynamic stiffness of plates using non-contact excitation and non-contact measurements. In particular, a constrained-layer damping sandwich plate is considered, of which the apparent dynamic stiffness as function of frequency is determined. The experimental results compare very well with an analytical model that computes the frequency dependent apparent bending stiffness of the constrained-layer damping sandwich plate. A Nd:YAG laser is used for excitation of the plate and a laser Doppler vibrometer is used to measure its dynamic response along a line on the plate, thus reducing the measurement effort. Using advanced data acquisition and data processing techniques, a signal-to-noise ratio of up to 100 dB was obtained, yielding estimates of the flexural wavenumber and dynamic stiffness of the plate up to a frequency of 50 kHz. It is shown that the Prony method and the wavenumber fit method yield a much improved wavenumber resolution as compared to the spatial Fourier transform method. An additional advantage of the wavenumber fit approach is that it allows the accuracy of the fit to be determined. The accuracy was estimated at 1 rad/m (best relative wavenumber resolution 2 perthousand). publisher: Elsevier articletitle: Non-contact experimental assessment of apparent dynamic stiffness of constrained-layer damping sandwich plates in a broad frequency range using a Nd:YAG pump laser and a laser Doppler vibrometer journaltitle: Journal of Sound and Vibration articlelink: http://dx.doi.org/10.1016/j.jsv.2017.02.012 content_type: article copyright: © 2017 Elsevier Ltd. All rights reserved. ispartof: Journal of Sound and Vibration vol:395 pages:90-101 status: published

International audience; Beamforming with a spherical microphone array has become an attractive tool for sound source localization in cabin environments. To provide a reliable localization solution with high performance , the first step is to optimize the array design. In this paper, the spatial resolution and dynamic range of an open spherical array with various microphone arrangements are evaluated, which are used as metrics for optimal array design. Several popular approaches for evenly distributing points on a sphere are investigated such that the array response is as isotropic as possible. In addition to the conventional beamforming, a state-of-the-art algorithm called functional beam-forming is also implemented. The objective is twofold: first is to improve spatial resolution and dynamic range significantly; and second is to verify that array configurations have a consistent effect on localization performance, regardless of beamforming algorithms.

173rd Meeting of Acoustical Society of America, BOSTON, ETATS-UNIS, 25-/06/2017 - 29/06/2017; The problem of the acoustic sources identification has been widely treated in static or quasi-static source contexts, more recently for moving sources, in a wide range of applications. In the context of source identification from a passing-by vehicle, the beamforming method is a reference that has well-known limitations. Deconvolution methods are used to overcome them. Mostly developed in static contexts at the beginning, extensions to moving sources have been proposed in the transportation field, mainly in air transportation and underwater acoustics. In the present investigation, the method proposed by Fleury and Bulté is numerically tested with parameters fitted to the road vehicle context. Its performance is assessed at different speeds, source-to-array distances and with various additional noise levels, as well as its robustness regarding an error on some parameter inputs. Beamforming -- as the reference method -- and this moving source deconvolution method (here called MSA-PSF) are compared using performance indicators. The simulations showed better localization, quantification and separation results with MSA-PSF compared to beamforming in this road transportation context. An experiment involving an academic pendulum setup is presented and confirms the improvement brought by MSA-PSF.

International audience

International audience; 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. Cyclostationarity is 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. In these conditions, the synchronous average depends on the 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 as a 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 frequency representation of the moving synchronous average can be computed, and the synchronization angle maximizing each point of the time frequency map 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. The analysis of the moving synchronous average leads also to the estimation of the energy loss of the synchronous average processed in angle caused by cycle-to-cycle speed fluctuations.