In a number of vibration applications, systems under study are slightly non-linear. It is thus of great importance to have a way to model and to measure these non-linearities in the frequency range of use. Cascade of Hammerstein models conveniently allows one to describe a large class of non-linearities. A simple method based on a phase property of exponential sine sweeps is proposed to identify the structural elements of such a model from only one measured response of the system. Mathematical foundations and practical implementation of the method are discussed. The method is afterwards validated on simulated and real systems. Vibrating devices such as acoustical transducers are well approximated by cascade of Hammerstein models. The harmonic distortion generated by those transducers can be predicted by the model over the entire audio frequency range for any desired input amplitude. Agreement with more time consuming classical distortion measurement methods was found to be good.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This is an author-deposited version published in: https://sam.ensam.eu Handle ID AbstractThis paper focuses on Bayesian Lamb wave-based damage localization in structural health monitoring of anisotropic composite materials. A Bayesian framework is applied to take account for uncertainties from experimental time-of-flight measurements and angular dependent group velocity within the composite material. An original parametric analytical expression of the direction dependence of group velocity is proposed and validated numerically and experimentally for anisotropic composite and sandwich plates. This expression is incorporated into time-of-arrival (ToA: ellipse-based) and time-difference-of-arrival (TDoA: hyperbola-based) Bayesian damage localization algorithms. This way, the damage location as well as the group velocity profile are estimated jointly and a priori information taken into consideration. The proposed algorithm is general as it allows to take into account for uncertainties within a Bayesian framework, and to model effects of anisotropy on group velocity. Numerical and experimental results obtained with different damage sizes or locations and for different degrees of anisotropy validate the ability of the proposed algorithm to estimate both the damage location and the group velocity profile as well as the associated confidence intervals. Results highlight the need to consider for anisotropy in order to increase localization accuracy, and to use Bayesian analysis to quantify uncertainties in damage localization.

Research highlights: - Nonlinearity characterization of a structure independently from its exciting device. - Experimental modal identification, including damping, in the mid-frequency range. - Boundary conditions, low-and high-frequency regimes clarified in the piano soundboard. - Good match between experimental observations and FEM results at low frequencies. - FEM of a non-regularly ribbed soundboard reveals high-frequency localization in piano.International audienceThe piano soundboard transforms the string vibration into sound and therefore, its vibrations are of primary importance for the sound characteristics of the instrument. An original vibro-acoustical method is presented to isolate the soundboard nonlinearity from that of the exciting device (here: a loudspeaker) and to measure it. The nonlinear part of the soundboard response to an external excitation is quantitatively estimated for the first time, at ≈ -40 dB below the linear part at the ff nuance. Given this essentially linear response, a modal identification is performed up to 3 kHz by means of a novel high resolution modal analysis technique (Ege et al., High-resolution modal analysis, JSV, 325(4-5), 2009). Modal dampings (which, so far, were unknown for the piano in this frequency range) are determined in the midfrequency domain where FFT-based methods fail to evaluate them with an acceptable precision. They turn out to be close to those imposed by wood. A finite-element modelling of the soundboard is also presented. The low-order modal shapes and the comparison between the corresponding experimental and numerical modal frequencies suggest that the boundary conditions can be considered as blocked, except at very low frequencies. The frequency-dependency of the modal density and the observation of modal shapes reveal two well-separated regimes. Below ≈ 1 kHz, the soundboard vibrates more or less like a homogeneous plate. Above that limit, the structural waves are confined by ribs, as already noticed by several authors, and localised in restricted areas (one or a few inter-rib spaces), presumably due to a slightly irregular spacing of the ribs across the soundboard

This paper presents a temperature compensation method for Lamb wave structural health monitoring. The proposed approach considers a representation of the piezo-sensor signal through its Hilbert transform that allows one to extract the amplitude factor and the phaseshift in signals caused by temperature changes. An ordinary least square (OLS) algorithm is used to estimate these unknown parameters. After estimating these parameters at each temperature in the operating range, linear functional relationships between the temperature and the estimated parameters are derived using the least squares method. A temperature compensation model is developed based on this linear relationship that allows one to reconstruct sensor signals at any arbitrary temperature. The proposed approach is validated numerically and experimentally for an anisotropic composite plate at different temperatures ranging from 16• C to 85 • C. A close match is found between the measured signals and the reconstructed ones. This approach is interesting as it needs only a limited set of piezo-sensor signals at different temperatures for model training and temperature compensation at any arbitrary temperature. Damage localization results after temperature compensation demonstrate its robustness and effectiveness.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. To cite this version :Victor BENICHOUX, Marc REBILLAT, Romain BRETTE -On the variation of interaural time differences with frequency

Structural health monitoring (SHM) processes for aeronautic composite structures are generally based on the comparison of healthy and unknown databases. The need for prior baseline signals is one of the barriers to industrial deployment and can be avoided with baseline-free SHM (BF-SHM) methods, based on the attenuations and reflections of symmetric and antisymmetric Lamb wave modes attributable to damage. A promising mode decomposition method is based on the use of dual-PZTs (concentric disc and ring electrodes lying on a single piezoelectric transducer of lead zirconate titanate). However, the performance of such methods highly depends on the Lamb wave mode properties (propagation speed and attenuation , which vary with material orientation and inter-PZT distance), the number and the sensitivity of the dual-PZT to each mode (which depends on the frequency and element size). Considering these constraints, an original three-step process able to design a full dual-PZT network and the optimal range of excitation frequencies to consider on a highly anisotropic and arbitrarily complex aeronautic structure is presented. First, the dispersion curves of Lamb waves in the investigated material together with the minimal size of the damage to detect are used to estimate the size of the dual-PZT, as well as convenient excitation frequencies. A local finite element model representative of the full-scale structure is then used to estimate the optimal distance and orientation between neighboring PZT elements. Finally, a network optimization solver applies these parameters to place dual-PZTs on the fan cowl of an aircraft nacelle and provides a candidate network covering the whole structure.

Structural health monitoring offers new approaches to interrogate the integrity of complex structures. The structural health monitoring process classically relies on four sequential steps: damage detection, localization, classification, and quantification. The most critical step of such process is the damage detection step since it is the first one and because performances of the following steps depend on it. A common method to design such a detector consists of relying on a statistical characterization of the damage indexes available in the healthy behavior of the structure. On the basis of this information, a decision threshold can then be computed in order to achieve a desired probability of false alarm. To determine the decision threshold corresponding to such desired probability of false alarm, the approach considered here is based on a model of the tail of the damage indexes distribution built using the Peaks Over Threshold method extracted from the extreme value theory. This approach of tail distribution estimation is interesting since it is not necessary to know the whole distribution of the damage indexes to develop a detector, but only its tail. This methodology is applied here in the context of a composite aircraft nacelle (where desired probability of false alarm is typically between 10 24 and 10 29 ) for different configurations of learning sample size and probability of false alarm and is compared to a more classical one which consists of modeling the entire damage indexes distribution by means of Parzen windows. Results show that given a set of data in the healthy state, the effective probability of false alarm obtained using the Peaks Over Threshold method is closer to the desired probability of false alarm than the one obtained using the Parzen-window method, which appears to be more conservative.