jeanflop/post_ocr_correction2 huggingface dataset:
Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available. The eigenvalues of the propagation tensor should be numerically computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. INTRODUCTION. — The localization of sources of acoustic emission is usually realized, for isotropic media, by triangulation techniques ([2], [3]). Whether it be for the localization of earthquake epicenters or for applications in Science of Materials/Mechanics of Fracture, least squares [4], and correlation ([5], [6]) techniques are commonly used. However, anisotropy was until then absent from these treatments which motivated the introduction of the optimization procedure described in a previous Note [1]. This method of localization of point sources of acoustic emission is tested in the present Note for a fiberglass-reinforced polyester resin composite material. The material chosen for this purpose, possesses an average anisotropy, and is by the way very ordinary, lightly porous and rather inhomogeneous. Thus, we place ourselves deliberately in conditions rather unfavorable. Notably, the state of the surface of the material is rather mediocre
configurations. These developments and further experimental data will be described elsewhere [20]. INTRODUCTION. — The localization of sources of acoustic emission is usually realized, for isotropic media, by triangulation techniques ([2], [3]). Whether it be for the localization of earthquake epicenters or for applications in Science of Materials/Mechanics of Fracture, least squares [4], and correlation ([5], [6]) techniques are commonly used. However, anisotropy was until then absent from these treatments which motivated the introduction of the optimization procedure described in a previous Note [1]. This method of localization of point sources of acoustic emission is tested in the present Note for a fiberglass-reinforced polyester resin composite material. The material chosen for this purpose, possesses an average anisotropy, and is by the way very ordinary, lightly porous and rather inhomogeneous. Thus, we place ourselves deliberately in conditions rather unfavorable. Notably, the state of the surface of the material is rather mediocre and the condition of a thin plate with parallel faces required by the modeling appears at most as an approximation. For the experimental measurements, an ultrasonic system associating sources of acoustic emission point-like and a network of quasi-point-like transducers was used. Details concerning this apparatus are available elsewhere [10]. This testing bench opens interesting perspectives for experiments in mechanics of fracture ([11], [12]). The sources of acoustic emission are simulated by breaking 0.08 mm o.d. capillary glass tubes. The rise time for such acoustic emission events is typically in the range of 50 ns. The sensors used are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the
testing bench opens interesting perspectives for experiments in mechanics of fracture ([11], [12]). The sources of acoustic emission are simulated by breaking 0.08 mm o.d. capillary glass tubes. The rise time for such acoustic emission events is typically in the range of 50 ns. The sensors used are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the optimization procedure described in [1], which involves the solution of a non-linear set of equations with a Newton-Raphson numerical method [14], the location of the source is determined. The measurements were done in the near-field to limit the influence of attenuation and dispersion of the transient waves. Figure 2 shows some characteristic waveforms. Attenuation and dispersion are clearly seen on these transient waves and might be detrimental to the precision of the results. Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is
some characteristic waveforms. Attenuation and dispersion are clearly seen on these transient waves and might be detrimental to the precision of the results. Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available. The eigenvalues of the propagation tensor should be numerically computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. NOTES POUR LA CORRECTION ### Abridged English Version — An original numerical scheme has been recently introduced for locating acoustic emission sources in anisotropic media [1]. Generally, in the case of isotropic solids, such a localization process is done using triangulation techniques ([2], [3]). In principle, the approaches are similar for both acoustic emission source location as applied to fracture mechanics problems and for earthquake epicenter determinations [4]. Least-square methods are already used for such problems as well as signal processing techniques using correlation methods ([5], [6]). Furthermore, in the field of isotropic materials testing, several systems already exist ([7], [8]). To test our algorithm for anisotropic materials, an ultrasonic point-source/point-receiver materials testing system has
computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. NOTES POUR LA CORRECTION ### Abridged English Version — An original numerical scheme has been recently introduced for locating acoustic emission sources in anisotropic media [1]. Generally, in the case of isotropic solids, such a localization process is done using triangulation techniques ([2], [3]). In principle, the approaches are similar for both acoustic emission source location as applied to fracture mechanics problems and for earthquake epicenter determinations [4]. Least-square methods are already used for such problems as well as signal processing techniques using correlation methods ([5], [6]). Furthermore, in the field of isotropic materials testing, several systems already exist ([7], [8]). To test our algorithm for anisotropic materials, an ultrasonic point-source/point-receiver materials testing system has been used in this study [9]. Recently, such an approach was successful to describe experimentally various problems in fracture mechanics ([11], [12]). The acoustic emission sources were simulated by breaking 0.08 mm o.d. capillary glass tubes. The rise time for such acoustic emission events is typically in the range of 50 ns. The sensors used here are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the optimization procedure described in [1], which involves the solution of a non-linear set of equations with a Newton-Raphson numerical method [14], the location of the source is determined. The measurements were done in the near-field to limit the influence of attenuation
50 ns. The sensors used here are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the optimization procedure described in [1], which involves the solution of a non-linear set of equations with a Newton-Raphson numerical method [14], the location of the source is determined. The measurements were done in the near-field to limit the influence of attenuation and dispersion of the transient waves. Figure 2 shows some characteristic waveforms. Attenuation and dispersion are clearly seen on these transient waves and might be detrimental to the precision of the results. Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available.
have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available. The eigenvalues of the propagation tensor should be numerically computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. INTRODUCTION. — The localization of sources of acoustic emission is usually realized, for isotropic media, by triangulation techniques ([2], [3]). Whether it be for the localization of earthquake epicenters or for applications in Science of Materials/Mechanics of Fracture, least squares [4], and correlation ([5], [6]) techniques are commonly used. However, anisotropy was until then absent from these treatments which motivated the introduction of the optimization procedure described in a previous Note [1]. This method of localization of point sources of acoustic emission is tested in the present Note for a fiberglass-reinforced polyester resin composite material. The material chosen for this purpose, possesses an average anisotropy, and is by the way very ordinary, lightly porous and rather inhomogeneous. Thus, we place ourselves deliberately in conditions rather unfavorable. Notably, the state of the surface of the material is rather mediocre and the condition of a thin plate with parallel faces required by the modeling appears at most as
of acoustic emission is usually realized, for isotropic media, by triangulation techniques ([2], [3]). Whether it be for the localization of earthquake epicenters or for applications in Science of Materials/Mechanics of Fracture, least squares [4], and correlation ([5], [6]) techniques are commonly used. However, anisotropy was until then absent from these treatments which motivated the introduction of the optimization procedure described in a previous Note [1]. This method of localization of point sources of acoustic emission is tested in the present Note for a fiberglass-reinforced polyester resin composite material. The material chosen for this purpose, possesses an average anisotropy, and is by the way very ordinary, lightly porous and rather inhomogeneous. Thus, we place ourselves deliberately in conditions rather unfavorable. Notably, the state of the surface of the material is rather mediocre and the condition of a thin plate with parallel faces required by the modeling appears at most as an approximation. For the experimental measurements, an ultrasonic system associating sources of acoustic emission point-like and a network of quasi-point-like transducers was used. Details concerning this apparatus are available elsewhere [10]. This testing bench opens interesting perspectives for experiments in mechanics of fracture ([11], [12]). The sources of acoustic emission are simulated by breaking 0.08 mm o.d. capillary glass tubes. The rise time for such acoustic emission events is typically in the range of 50 ns. The sensors used are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the optimization procedure described in [1], which involves the solution of a non-linear set of equations with a Newton-Raphson
are simulated by breaking 0.08 mm o.d. capillary glass tubes. The rise time for such acoustic emission events is typically in the range of 50 ns. The sensors used are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the optimization procedure described in [1], which involves the solution of a non-linear set of equations with a Newton-Raphson numerical method [14], the location of the source is determined. The measurements were done in the near-field to limit the influence of attenuation and dispersion of the transient waves. Figure 2 shows some characteristic waveforms. Attenuation and dispersion are clearly seen on these transient waves and might be detrimental to the precision of the results. Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact
the precision of the results. Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available. The eigenvalues of the propagation tensor should be numerically computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. Ces résultats classiques sont : Pour déterminer les différentes vitesses de propagation entrant en jeu dans les équations (1) et (2), un certain nombre de mesures de différences des temps de transit pour une paire de transducteurs donnée sont réalisées en différentes positions repérées sur la figure 1. Une simple moyenne arithmétique est alors calculée fournissant avec précision les valeurs des vitesses nécessaires. Dès lors, une position arbitraire est retenue pour simuler l'emplacement de la source ponctuelle d'émission acoustique, et la procédure d'optimisation peut avoir lieu [14]. RÉSULTATS EXPÉRIMENTAUX. — Le déroulement des calculs est indépendant du nombre de senseurs (3 est le minimum). Pour des raisons pratiques, les mêmes senseurs furent utilisés, à la fois pour la procédure de calibration et pour celle d'optimisation, bien que nous ayons la possibilité d'utiliser jusqu'à