Abstract
Goal of PRONY`s method is to identify a sampling of N signal`s values with a finite linear development of p complex exponentials. This was done to use this method for the identification of a signal obtained by ``insonification`` (i.e. by interacting with an ultrasonic impulsion) of a target. Identified complex exponentials give constitutive amplitudes, dampings, frequencies and phases of the signal, these values characterize geometry and size of unknown targets. Mathematics involve that the solution of 3D-elastodynamic equations is given asymptotically in time by an infinite summation of complex exponentials. Signal obtained by ``insonification`` is characteristic of this solution: it means that PRONY`s method can be well suited for this identification. For that it was necessary to understand this method in all its aspects. We expose its principle and algorithm. We prove, it is one of its advantages, that PRONY is an interpolation method if N = 2p. If N > 2p the method is working like a least square method. We study how the two essentials parameters N and p of the method interact one with the other. Influence of the noise is observed. And then we approach the practice of the method, in order to verify its quality
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Citation Formats
Roux, J.
Study of a method for the defect detection by ultrasonic`s technic: Prony`s method, theory and practice; Etude d`une methode en vue de la detection de defaut par ultrasons: methode de Prony, theorie et pratique.
France: N. p.,
1993.
Web.
Roux, J.
Study of a method for the defect detection by ultrasonic`s technic: Prony`s method, theory and practice; Etude d`une methode en vue de la detection de defaut par ultrasons: methode de Prony, theorie et pratique.
France.
Roux, J.
1993.
"Study of a method for the defect detection by ultrasonic`s technic: Prony`s method, theory and practice; Etude d`une methode en vue de la detection de defaut par ultrasons: methode de Prony, theorie et pratique."
France.
@misc{etde_10140975,
title = {Study of a method for the defect detection by ultrasonic`s technic: Prony`s method, theory and practice; Etude d`une methode en vue de la detection de defaut par ultrasons: methode de Prony, theorie et pratique}
author = {Roux, J}
abstractNote = {Goal of PRONY`s method is to identify a sampling of N signal`s values with a finite linear development of p complex exponentials. This was done to use this method for the identification of a signal obtained by ``insonification`` (i.e. by interacting with an ultrasonic impulsion) of a target. Identified complex exponentials give constitutive amplitudes, dampings, frequencies and phases of the signal, these values characterize geometry and size of unknown targets. Mathematics involve that the solution of 3D-elastodynamic equations is given asymptotically in time by an infinite summation of complex exponentials. Signal obtained by ``insonification`` is characteristic of this solution: it means that PRONY`s method can be well suited for this identification. For that it was necessary to understand this method in all its aspects. We expose its principle and algorithm. We prove, it is one of its advantages, that PRONY is an interpolation method if N = 2p. If N > 2p the method is working like a least square method. We study how the two essentials parameters N and p of the method interact one with the other. Influence of the noise is observed. And then we approach the practice of the method, in order to verify its quality for identified tests problems. Successively we analyze a damping signal, an electric signal with damping, a pure periodic signal. Behaviour of PRONY is excellent with a few precautions that we specify. Finally we are interested with a ``realistic`` seismic signal. The ultrasonic wave iteration with defect is then observed in paragraph 4. Physical and experimental device are briefly described. The identification`s problem of a target, in practice the identification of a defect, is still widely opened if we use PRONY. Is it necessary to give up. Certainly not, the conclusions of the paragraph 5 offers rather stimulating challenges for the (Abstract Truncated)}
place = {France}
year = {1993}
month = {May}
}
title = {Study of a method for the defect detection by ultrasonic`s technic: Prony`s method, theory and practice; Etude d`une methode en vue de la detection de defaut par ultrasons: methode de Prony, theorie et pratique}
author = {Roux, J}
abstractNote = {Goal of PRONY`s method is to identify a sampling of N signal`s values with a finite linear development of p complex exponentials. This was done to use this method for the identification of a signal obtained by ``insonification`` (i.e. by interacting with an ultrasonic impulsion) of a target. Identified complex exponentials give constitutive amplitudes, dampings, frequencies and phases of the signal, these values characterize geometry and size of unknown targets. Mathematics involve that the solution of 3D-elastodynamic equations is given asymptotically in time by an infinite summation of complex exponentials. Signal obtained by ``insonification`` is characteristic of this solution: it means that PRONY`s method can be well suited for this identification. For that it was necessary to understand this method in all its aspects. We expose its principle and algorithm. We prove, it is one of its advantages, that PRONY is an interpolation method if N = 2p. If N > 2p the method is working like a least square method. We study how the two essentials parameters N and p of the method interact one with the other. Influence of the noise is observed. And then we approach the practice of the method, in order to verify its quality for identified tests problems. Successively we analyze a damping signal, an electric signal with damping, a pure periodic signal. Behaviour of PRONY is excellent with a few precautions that we specify. Finally we are interested with a ``realistic`` seismic signal. The ultrasonic wave iteration with defect is then observed in paragraph 4. Physical and experimental device are briefly described. The identification`s problem of a target, in practice the identification of a defect, is still widely opened if we use PRONY. Is it necessary to give up. Certainly not, the conclusions of the paragraph 5 offers rather stimulating challenges for the (Abstract Truncated)}
place = {France}
year = {1993}
month = {May}
}