Ils sont fournis par O. Abraham. Toutes les descriptions de maillage, pas de calcul, impact, tests réels ... sont présentés par Abraham et al. dans la référence [4]. Les tests de validation de la transformation en ondelettes ci-après sont classés suivant deux catégories, Les signaux expérimentaux sont réalisés au LCPC Nantes ,
Thickness frequency profile for the detection of voids in tendon ducts, ACI Structural Journal, vol.99, issue.1, pp.239-247, 2002. ,
Méthode impact-´ echo basse fréquence pour la détection de vide dans les gaines de précontraite, Bulletin des laboratoires des Ponts et Chaussées, vol.239, pp.41-50, 2003. ,
Two enhanced complementary impact echo approaches for the detection of void in tendon ducts, First International Conference on Bridge Maintenance, Safety and Management, 2002. ,
Time frequency analysis of impactecho signals : Numerical modeling and experimental validation, ACI Materials journal, pp.97-73645, 2000. ,
Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1972. ,
DOI : 10.1119/1.1972842
Wave Propagation in Elastic Solids, Journal of Applied Mechanics, vol.41, issue.2, 1973. ,
DOI : 10.1115/1.3423344
IDENTIFICATION OF DAMPING: PART 1, VISCOUS DAMPING, Journal of Sound and Vibration, vol.243, issue.1, pp.43-61, 2001. ,
DOI : 10.1006/jsvi.2000.3391
IDENTIFICATION OF DAMPING: PART 2, NON-VISCOUS DAMPING, Journal of Sound and Vibration, vol.243, issue.1, pp.63-88, 2001. ,
DOI : 10.1006/jsvi.2000.3392
A UNIFIED MATRIX POLYNOMIAL APPROACH TO MODAL IDENTIFICATION, Journal of Sound and Vibration, vol.211, issue.3, pp.301-322, 1998. ,
DOI : 10.1006/jsvi.1997.1321
Time-frequency analysis of free oscillations of mechanical structures. application to the identification of the mechanical behavior of buildings under chocks. Proceeding of the COST F3 conference : System Identification and Structural Health Monitoring, pp.283-292, 2000. ,
Analyse temps-fréquence de réponses de bâtimentsbâtiments`bâtimentsà des essais de chocs, Actes du 5 e Colloque Nationale en Calcul des Structures, pp.1057-1064, 2001. ,
Instantaneous indicators of structural behavior based on the continuous cauchy wavelet analysis, Mechancal System and Signal Processing, pp.243-250, 2003. ,
Wavelet analysis of transient signals in civil engineering. Novel approaches in civil engineering, 2003. ,
Traitement numérique du signal, 1981. ,
Analysis of multi-degree of freedom strongly non-linear mechanical systems with random input, Probabilistic Engineering Mechanics, vol.14, issue.3, pp.229-244, 1999. ,
DOI : 10.1016/S0266-8920(98)00007-1
IDENTIFICATION OF COUPLED NON-LINEAR MODES FROM FREE VIBRATION USING TIME-FREQUENCY REPRESENTATIONS, Journal of Sound and Vibration, vol.243, issue.2, pp.191-213, 2001. ,
DOI : 10.1006/jsvi.2000.3407
Use of the cross Wigner-Ville distribution for estimation of instantaneous frequency, IEEE Transactions on Signal Processing, vol.41, issue.3, pp.41-1439, 1993. ,
DOI : 10.1109/78.205752
Time-Frequency and Ambiguity Function Approaches in Structural Identification, Journal of Engineering Mechanics, vol.123, issue.12, pp.1260-1267, 1997. ,
DOI : 10.1061/(ASCE)0733-9399(1997)123:12(1260)
USE OF CROSS-TIME???FREQUENCY ESTIMATORS FOR STRUCTURAL IDENTIFICATION IN NON-STATIONARY CONDITIONS AND UNDER UNKNOWN EXCITATION, Journal of Sound and Vibration, vol.237, issue.5, pp.775-791, 2000. ,
DOI : 10.1006/jsvi.2000.3097
Projet : approche de la vulnérabilité sismique par l'´ etude du comportement de bâtiments réels, 1999. ,
Parameter estimation techniques for modal analysis. SAE Technical Paper series, 1979. ,
The Impact-Echo Method: An Overview, Structures 2001, 2001. ,
DOI : 10.1061/40558(2001)15
Practical time-frequency analysis, 1998. ,
URL : https://hal.archives-ouvertes.fr/hal-01302102
Identification of Chirps with Continuous Wavelet Transform, Wavelet and Statistics, issue.103, 1995. ,
DOI : 10.1007/978-1-4612-2544-7_7
URL : https://hal.archives-ouvertes.fr/hal-01304136
Characterization of signals by the ridges of their wavelet transforms, IEEE Transactions on Signal Processing, vol.45, issue.10, p.10, 1996. ,
DOI : 10.1109/78.640725
URL : https://hal.archives-ouvertes.fr/hal-01223134
Multi-ridge detection and time-frequency reconstruction, IEEE Trans. Signal Processing, issue.47, 1999. ,
URL : https://hal.archives-ouvertes.fr/hal-01223139
MODAL ANALYSIS OF A CRACKED BEAM, Journal of Sound and Vibration, vol.207, issue.2, pp.249-270, 1997. ,
DOI : 10.1006/jsvi.1997.1099
URL : https://hal.archives-ouvertes.fr/hal-01510818
A modified Lindstedt-Poincar?? method for certain strongly non-linear oscillators, International Journal of Non-Linear Mechanics, vol.26, issue.3-4, pp.376-378, 1991. ,
DOI : 10.1016/0020-7462(91)90066-3
An Introduction to Wavelets, Computers in Physics, vol.6, issue.6, 1992. ,
DOI : 10.1063/1.4823126
Dynamique des structures, tome 1 : principes fondamentaux. ´ Editions pluralis, 1980. ,
Time-frequency analysis, 1995. ,
Automated impact-echo and method improvement, Proc. Non-Destructive Testing in Civil Engineering, 2000. ,
DOI : 10.1016/B978-008043717-0/50051-9
Higher-order spectra : the bispectrum and trispectrum. Mechancal System and Signal Processing Identification modale sous excitation ambiante : ApplicationàApplication`Applicationà la surveillance des ponts, Mécanique & Industries, vol.12, pp.375-394, 1998. ,
The wavelet transform, time-frequency localisation and signal analysis, IEEE, vol.36, pp.961-1005, 1990. ,
Analysis of ambient vibration data from queensboroug bridge using cohen class time-frequency distributions, Proceedings 14 th International Modal Analysis Conference, pp.470-476, 1996. ,
Wigner transforms, Gabor coefficients, and Weyl???Heisenberg wavelets, The Journal of the Acoustical Society of America, vol.89, issue.5, pp.2355-2361, 1991. ,
DOI : 10.1121/1.400924
Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies, IEEE Transactions on Information Theory, vol.38, issue.2, pp.644-664, 1992. ,
DOI : 10.1109/18.119728
URL : https://hal.archives-ouvertes.fr/hal-01222729
-Linear theory, Elastodynamics, vol.2, 1975. ,
URL : https://hal.archives-ouvertes.fr/hal-00302294
Non-linear system vibration analysis using hilbert transform-i free vibration analysis method 'freevib'. Mechancal System and Signal Processing, pp.119-127, 1994. ,
Non-linear system vibration analysis using hilbert transform-ii forced vibration analysis method 'forcevib'. Mechancal System and Signal Processing, pp.309-318, 1994. ,
NON-LINEAR FREE VIBRATION IDENTIFICATION VIA THE HILBERT TRANSFORM, Journal of Sound and Vibration, vol.208, issue.3, pp.475-489, 1997. ,
DOI : 10.1006/jsvi.1997.1182
A method for nonlinear system classification in the time???frequency plane, Signal Processing, vol.65, issue.1, pp.147-153, 1998. ,
DOI : 10.1016/S0165-1684(98)00029-2
Théorie des vibrations. ApplicationàApplication`Applicationà la dynamique des structures, 1996. ,
On using the wavelet transform in modal analysis, Mechanics Research Communications, vol.28, issue.5, pp.561-569, 2001. ,
DOI : 10.1016/S0093-6413(01)00209-9
On the choice of parameters for time-frequency analysis, Proc. of Int. Conf. " Wavelets and Applications, pp.82-96, 1992. ,
The analysis of nonstationary signals. Sound and Vibration, pp.40-97, 1997. ,
Decomposition of hardy functions into square integrable wavelets of constant shape, Society for Industrial and Applied Mathematics, vol.15, pp.723-736, 1984. ,
DAMPING IDENTIFICATION IN MULTI-DEGREE-OF-FREEDOM SYSTEM VIA A WAVELET-LOGARITHMIC DECREMENT???PART 2: STUDY OF A CIVIL ENGINEERING BUILDING, Journal of Sound and Vibration, vol.235, issue.3, pp.375-403, 2000. ,
DOI : 10.1006/jsvi.1999.2927
URL : https://hal.archives-ouvertes.fr/hal-00814693
Modal analysis theory and testing, 1997. ,
Nondestructive evaluation of concrete quality and integrity in composite columns, NDT & E International, vol.32, issue.7, pp.375-382, 1999. ,
DOI : 10.1016/S0963-8695(99)00002-X
Phase error in fast fourier transform analysis, Mechanical Systems and Signal Processing, vol.9, pp.113-118, 1995. ,
A wavelet-based algorithme for the hilbert transform, Mechanical Systems and Signal Processing, vol.10, pp.125-134, 1996. ,
A method for the direct identification of vibration parameters from the free response. The Shock and Vibration Bulletin, pp.183-198, 1977. ,
Identification of non-proportional modal damping matrix and real normal modes. Mechancal System and Signal Processing, pp.921-934, 2002. ,
THEORETICAL AND EXPERIMENTAL IDENTIFICATION OF A NON-LINEAR BEAM, Journal of Sound and Vibration, vol.244, issue.4, pp.597-613, 2001. ,
DOI : 10.1006/jsvi.2000.3490
PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION, Journal of Sound and Vibration, vol.249, issue.5, pp.849-865, 2002. ,
DOI : 10.1006/jsvi.2001.3930
Identification of a continuous structure with a geometrical non-linearity. Part I: Conditioned reverse path method, Journal of Sound and Vibration, vol.262, issue.4, pp.889-906, 2003. ,
DOI : 10.1016/S0022-460X(02)01151-3
Non-linearity identification and quantification using an inverse fourier transform, Mechanical Systems and Signal Processing, vol.7, issue.3, pp.239-255, 1993. ,
DOI : 10.1006/mssp.1993.1011
Asymptotic analysis of nonlinear mode localization in a class of coupled continuous structures, International Journal of Solids and Structures, vol.32, issue.8-9, pp.1161-1177, 1995. ,
DOI : 10.1016/0020-7683(94)00180-5
DAMPING IDENTIFICATION IN MULTI-DEGREE-OF-FREEDOM SYSTEMS VIA A WAVELET-LOGARITHMIC DECREMENT???PART 1: THEORY, Journal of Sound and Vibration, vol.235, issue.3, pp.361-374, 2000. ,
DOI : 10.1006/jsvi.1999.2928
URL : https://hal.archives-ouvertes.fr/hal-00814669
Identification of modal parameters using the wavelet transform, International Journal of Mechanical Sciences, vol.44, issue.11, pp.2263-2283, 2002. ,
DOI : 10.1016/S0020-7403(02)00175-3
URL : https://hal.archives-ouvertes.fr/hal-00079408
Continuous wavelet transform for modal identification using free decay response, Accepté pour publication, 2003. ,
DOI : 10.1016/j.jsv.2003.08.049
Utilisation de la transformation en ondelettes pour l'identification des systèmes mécaniques non-linéaires en vibration. 16 e Congrès Français de Mécanique, 2003. ,
Identification des modèles structuraux en dynamique non linéaire, 2002. ,
PROPER ORTHOGONAL DECOMPOSITION FOR MODEL UPDATING OF NON-LINEAR MECHANICAL SYSTEMS, Mechanical Systems and Signal Processing, vol.15, issue.1, pp.31-43, 2001. ,
DOI : 10.1006/mssp.2000.1350
Identification of a continuous structure with a geometrical non-linearity. Part II: Proper orthogonal decomposition, Journal of Sound and Vibration, vol.262, issue.4, pp.907-919, 2003. ,
DOI : 10.1016/S0022-460X(02)01132-X
Detection of the corrosion damage of rebar in concrete using impactecho method. Cement and Concrete research, pp.31-1427, 2001. ,
Detection of small voids by impact-echo and signal processing. Construction materials serviability/durability, pp.1223-1232 ,
Improved Impact-Echo Technique by Signal Processing, Research in Nondestructive Evaluation, vol.83, issue.1, pp.45-56, 1990. ,
DOI : 10.1121/1.387763
Une Exploration des Signaux en Ondelettes, LesÉditionsLes´LesÉditions de L'´ ecole Polytechniques, 2000. ,
Accuracy of nde in bridge assessment Engineering structures Influence of concrete properties on impulse hammer spectrum and compression wave velocity. Construction and building materials, pp.979-984245, 1995. ,
DIRECT AND INVERSE PROBLEMS ENCOUNTERED IN VIBRO-IMPACT OSCILLATIONS OF A DISCRETE SYSTEM, Journal of Sound and Vibration, vol.216, issue.2, pp.227-250, 1998. ,
DOI : 10.1006/jsvi.1998.1613
URL : https://hal.archives-ouvertes.fr/hal-01352131
Spectral Response of a Bilinear Oscillator, Journal of Sound and Vibration, vol.163, issue.2, pp.319-326, 1993. ,
DOI : 10.1006/jsvi.1993.1168
The Fourier transform and Its applications. International student edition, 1978. ,
Wavelet Analysis of Vibration: Part 1???Theory, Journal of Vibration and Acoustics, vol.116, issue.4, pp.409-416, 1994. ,
DOI : 10.1115/1.2930443
Wavelet Analysis of Vibration: Part 2???Wavelet Maps, Journal of Vibration and Acoustics, vol.116, issue.4, pp.417-425, 1994. ,
DOI : 10.1115/1.2930444
Ridge and Phase Identification in the Frequency Analysis of Transient Signals by Harmonic Wavelets, Journal of Vibration and Acoustics, vol.121, issue.2, pp.149-155, 1999. ,
DOI : 10.1115/1.2893957
Comportement dynamque de structures non-linéaires soumisesàsoumises`soumisesà des charges mobiles, 2002. ,
Stack imaging of spectral amplitudes based on impact-echo for flaw detection, NDT & E International, vol.35, issue.3, pp.189-196, 2002. ,
DOI : 10.1016/S0963-8695(01)00045-7
Instantaneous frequency estimation using the cross wigner-ville distribution with application to non-stationary transient detection, IEEE, vol.2, pp.2887-2890, 1990. ,
Identification of structural dynamique models using waveletgenerated impulse response data, Journal of Vibration and Acoustics, vol.120, pp.261-266, 1998. ,
Ondelettes et Mécanique Quantique, 1986. ,
Méthodes ondelettes pour l'´ etude des vibrations et de la stabilité des systèmes dynamiques, 2000. ,
Influence of steel reinforcing bars on the evaluation of the early-age concrete strength using the impact-echo method, ACI Materials Journal, vol.94, pp.378-388, 1997. ,
Modelling and identification of the dynamique response of a supported bridge, Mechancal System and Signal Processing, pp.75-89, 2000. ,
The wavelet tutorial ,
Effects of Poisson's Ratio on Impact-Echo Test Analysis, Journal of Engineering Mechanics, vol.123, issue.8, pp.843-851, 1997. ,
DOI : 10.1061/(ASCE)0733-9399(1997)123:8(843)
The use of a neural network for automating impact-echo signal interpretation, NDT & E International, vol.25, issue.1, p.10, 1991. ,
DOI : 10.1016/0963-8695(92)90014-8
Parameter estimation from frequency response measurements using rational fraction polynomials, Proceedings of the 1 st International Modal Analysis Conference (IMAC I), pp.167-181, 1982. ,
Distributions et Transformation de Fourier, 1981. ,
The Normal Modes of Nonlinear n-Degree-of-Freedom Systems, Journal of Applied Mechanics, vol.29, issue.1, pp.7-14, 1962. ,
DOI : 10.1115/1.3636501
URL : https://hal.archives-ouvertes.fr/hal-01344457
NATURAL FREQUENCIES AND DAMPINGS IDENTIFICATION USING WAVELET TRANSFORM: APPLICATION TO REAL DATA, Mechanical Systems and Signal Processing, vol.11, issue.2, pp.207-218, 1997. ,
DOI : 10.1006/mssp.1996.0078
Advanced NDT methods for evaluating concrete bridges and other structures, NDT & E International, vol.28, issue.6, pp.349-357, 1995. ,
DOI : 10.1016/0963-8695(95)00045-3
Impact-echo : Nondestructive testing of concrete and masonery, 1997. ,
DOI : 10.6028/NBS.IR.86-3452
A procedure for determining p-wave speed in concrete for use in impact-echo testing using a p-wave speed measurement technique, ACI Materials Journal, vol.94, pp.531-539, 1997. ,
Normal Modes for Non-Linear Vibratory Systems, Journal of Sound and Vibration, vol.164, issue.1, pp.85-124, 1993. ,
DOI : 10.1006/jsvi.1993.1198
Normal Modes of Vibration for Non-Linear Continuous Systems, Journal of Sound and Vibration, vol.169, issue.3, pp.319-347, 1994. ,
DOI : 10.1006/jsvi.1994.1021
URL : https://hal.archives-ouvertes.fr/hal-01471098
Analyse Numérique, 1987. ,
Improving impact-echo method by wavelet transform for infrastructure inspection, Proc of 11 th Pacific Basin Nuclear Conference Banff, Canada, pp.1649-1654, 1998. ,
La méthode du recuit simulé : théorie et application, I.D.S.E.T, 1988. ,
Damping identification using a continuous wavelet transform: application to real data, Journal of Sound and Vibration, vol.262, issue.2, pp.291-307, 2003. ,
DOI : 10.1016/S0022-460X(02)01032-5
Application of the wavelet transform to fault detection in a spur gear, Mechancal System and Signal Processing, pp.289-307, 1994. ,
DOI : 10.1006/mssp.1994.1022
IDENTIFICATION OF DAMPING IN MDOF SYSTEMS USING TIME-SCALE DECOMPOSITION, Journal of Sound and Vibration, vol.203, issue.2, pp.283-305, 1996. ,
DOI : 10.1006/jsvi.1996.0864
IDENTIFICATION OF NON-LINEAR SYSTEMS USING MULTI-SCALE RIDGES AND SKELETONS OF THE WAVELET TRANSFORM, Journal of Sound and Vibration, vol.214, issue.4, pp.639-658, 1998. ,
DOI : 10.1006/jsvi.1998.1616
LOCAL TOOTH FAULT DETECTION IN GEARBOXES USING A MOVING WINDOW PROCEDURE, Mechanical Systems and Signal Processing, vol.11, issue.3, pp.331-350, 1997. ,
DOI : 10.1006/mssp.1996.0087
TIME???FREQUENCY ANALYSIS IN GEARBOX FAULT DETECTION USING THE WIGNER???VILLE DISTRIBUTION AND PATTERN RECOGNITION, Mechanical Systems and Signal Processing, vol.11, issue.5, pp.673-692, 1997. ,
DOI : 10.1006/mssp.1997.0102
Impact-echo from a unilateral interlayer crack. lcp-bem modelling and neural identification. Engineering fracture machanics, pp.165-184, 1999. ,
ON THE TIME???FREQUENCY ANALYSIS OF SIGNALS THAT DECAY EXPONENTIALLY WITH TIME, Journal of Sound and Vibration, vol.234, issue.2, pp.241-258, 1999. ,
DOI : 10.1006/jsvi.1999.2876
Theoretical and Experimental Modal Analysis. Research studies press Ltd, 1986. ,
Contrôle non destructif des matériaux et des structures par analyse dynamique non linéaire, 1995. ,
Analyse continue par ondelettes. InterÉditionInter´InterÉdition/CNRSÉditionCNRS´CNRSÉdition, 1995. ,
Time-frequency and time-scale analysis, Signal Processing for Multimedia, 1999. ,
Ondelettes pour le signal numérique, HERMES, 1998. ,
NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW, Mechanical Systems and Signal Processing, vol.11, issue.1, pp.3-22, 1997. ,
DOI : 10.1006/mssp.1996.9999
URL : https://hal.archives-ouvertes.fr/hal-01354037
Periodic Response Of Piecewise-Linear Oscillators Using Trigonometric Collocation, Journal of Sound and Vibration, vol.177, issue.4, pp.573-576, 1994. ,
DOI : 10.1006/jsvi.1994.1453
LINEAR DAMPING MODELS FOR STRUCTURAL VIBRATION, Journal of Sound and Vibration, vol.215, issue.3, pp.547-569, 1998. ,
DOI : 10.1006/jsvi.1998.1709
Detection and classification of flaws in concrete structure using bispectra and neural networks, NDT & E International, vol.35, issue.1, pp.19-27, 2002. ,
DOI : 10.1016/S0963-8695(01)00018-4
Les Ondelettes, algorithmes et applications, Armand COLIN, 1992. ,
Transformations int??grales et identification modale, Comptes Rendus de l'Acad??mie des Sciences - Series IIB - Mechanics-Physics-Astronomy, vol.327, issue.8, pp.777-783, 1999. ,
DOI : 10.1016/S1287-4620(99)80135-5
Optimal frequency-to-bandwidth ratio of wavelet in ultrasonic non-destructive evaluation, Ultrasonics, vol.39, issue.1, pp.13-17, 2001. ,
DOI : 10.1016/S0041-624X(00)00043-3