Detection, monitoring, and determination of location of changes in metallic structures using multimode acoustic signals
Acoustic transducers generate and receive acoustic signals at multiple locations along a surface of rigid structure, wherein longitudinal spacing between transducer locations define measurement zones. Acoustic signals with chosen amplitude-time-frequency characteristics excite multiple vibration modes in the structure within each zone. Small mechanical changes in inspection zones lead to scattering and attenuation of broadband acoustic signals, which are detectable as changes in received signal characteristics as part of a through-transmission technique. Additional use of short, narrowband pulse acoustic signals as part of a pulse-echo technique allows determination of the relative location of the mechanical change within each zone based on the differential delay profiles. For accurate acoustic modeling and simulation, the mesh size, time step, time delay, and time-window size are optimized. Frequency normalization of the Short-Time Fourier Transform of acoustic response output improves experiment-simulation cross-validation. Applications of the method to structures with arbitrarily complex geometries are also demonstrated.
1. A method for detecting and monitoring a mechanical change in an elongated rigid structure, the method comprising:
locating a first acoustic transducer at a first location along a surface of the rigid structure;
locating a second acoustic transducer at a second location along the surface of the rigid structure;
locating a third acoustic transducer at a third location along the surface of the rigid structure, wherein the second location is between the first location and the third location, a longitudinal spacing between the first location and the second location define a first zone, and a longitudinal spacing between the second location and the third location define a second zone;
generating, with the second acoustic transducer, a baseline broadband acoustic signal along the rigid elongated structure;
obtaining, with the first acoustic transducer, a first baseline transmission signal responsive to the baseline broadband acoustic signal in the first zone and obtaining, with the third acoustic transducer, a second baseline transmission signal responsive to the baseline broadband acoustic signal in the second zone;
generating, with the second acoustic transducer, a monitoring broadband acoustic signal along the rigid elongated structure;
obtaining, with the first acoustic transducer, a first monitoring transmission signal responsive to the monitoring broadband acoustic signal in the first zone and obtaining, with the third acoustic transducer, a second monitoring transmission signal responsive to the monitoring transmission signal in the second zone;
determining a first differential transmission signal as a difference between the first monitoring transmission signal and the first baseline transmission signal;
determining a second differential transmission signal as a difference between the second monitoring transmission signal and the second baseline transmission signal; and
determining if the mechanical change occurred in the first zone of the elongated rigid structure based on the first differential transmission signal or if the mechanical change occurred in the second zone of the elongated rigid structure based on the second differential transmission signal;
wherein determination of if the mechanical change occurred in the first zone of the elongated rigid structure based on the first differential transmission signal or if the mechanical change occurred in the second zone of the elongated rigid structure based on the second differential transmission signal is validated based on an acoustic modeling and numerical simulation of the mechanical change in the elongated rigid structure.
2. The method of claim 1 , further comprising:
generating, with the second acoustic transducer, a baseline narrow-band pulse acoustic signal along the elongated rigid structure;
obtaining, with the first acoustic transducer, a first baseline response signal responsive to the baseline narrow-band pulse acoustic signal in the first and second zones and obtaining, with the third acoustic transducer, a second baseline response signal responsive to the baseline narrow-band pulse acoustic signal in the second and first zones;
generating, with the second acoustic transducer, a monitoring narrow-band pulse acoustic signal along the elongated rigid structure;
obtaining, with the first acoustic transducer, a first monitoring response signal responsive to the monitoring narrow-band pulse acoustic signal in the first and second zones and obtaining, with the third acoustic transducer, a second monitoring response signal responsive to the monitoring narrow-band pulse acoustic signal in the second and first zones;
determining a first differential response signal as a difference between the first monitoring response signal and the first baseline response signal;
determining a second differential response signal as a difference between the second monitoring response signal and the second baseline response signal;
generating a first differential delay profile as a function of the first differential response signal as compared with the second differential response signal;
generating a second differential delay profile as a function of the second differential response signal as compared with the first differential response signal; and
determining the relative location of the mechanical change within the first zone or the second zone based on the first differential delay profile and the second differential delay profile;
wherein determination of the relative location of the mechanical change within the first zone or the second zone based on the first differential delay profile and the second differential delay profile is validated based on the acoustic modeling and numerical simulation of the mechanical change in the elongated rigid structure.
3. The method of claim 1 , wherein the acoustic modeling and numerical simulation of the mechanical change in the elongated rigid structure is defined by a mesh size, a time step, a time delay, and a time window, the mesh size defining a spatial resolution of the acoustic modeling and numerical simulation, the time step defining a temporal resolution of the acoustic modeling and numerical simulation, the time delay defining the difference in time between acoustic excitation and start of acoustic response acquisition, and the time window defining a response acquisition duration for simulated excitation of the elongated rigid structure.
4. The method of claim 3 , wherein the mesh size is determined based on:
a first trial numerical simulation of the elongated rigid structure without the mechanical change, the first trial numerical simulation run using a trial mesh size;
generation of a Short-Time-Fourier-Transform map based on the first trial numerical simulation;
determination of active modes based on the Short-Time-Fourier-Transform map, the active modes associated with wavelengths; and
determination of the mesh size based on the wavelengths.
5. The method of claim 4 , wherein the trial mesh size is determined based on a highest frequency of interest.
6. The method of claim 4 , wherein the determination of the mesh size based on the wavelengths includes:
determination of a maximum mesh size based on a shortest wavelength among the wavelengths from the first trial numerical simulation of the elongated rigid structure;
a second trial numerical simulation of the elongated rigid structure, the second trial numerical simulation run using the maximum mesh element size;
identification of wavelengths of interest based on the second trial numerical simulation of the elongated rigid structure; and
determination of the mesh size based on shorter of the shortest wavelength from the first trial numerical simulation of the elongated rigid structure and a shortest wavelength of interest from the second trial numerical simulation of the elongated rigid structure.
7. The method of claim 6 , wherein:
responsive to the shortest wavelength of interest being longer than the shortest wavelength from the first trial numerical simulation of the elongated rigid structure, the mesh size is determined to be the maximum mesh size; and
responsive to the shortest wavelength of interest being shorter than the shortest wavelength from the first trial numerical simulation of the elongated rigid structure, the mesh size is determined based on the shortest wavelength of interest from the second trial numerical simulation of the elongated rigid structure.
8. The method of claim 7 , wherein the time step is determined based on the mesh size and a fastest wave velocity among wave velocities associated with the active modes.
9. The method of claim 8 , wherein the window size is limited by the mesh size.
10. The method of claim 1 , wherein numerical simulation output and experiment output of the mechanical change in the elongated rigid structure in a frequency-time domain are normalized by a local maximum across frequencies to facilitate cross-validation of the numerical simulation output and the experiment output.
11. A system that detects and monitors a mechanical change in an elongated rigid structure, the system comprising:
a first acoustic transducer located at a first location along a surface of the rigid structure;
a second acoustic transducer located at a second location along the surface of the rigid structure; and
a third acoustic transducer located at a third location along the surface of the rigid structure, wherein the second location is between the first location and the third location, a longitudinal spacing between the first location and the second location define a first zone, and a longitudinal spacing between the second location and the third location define a second zone;
wherein:
the second acoustic transducer is configured to generate a baseline broadband acoustic signal along the rigid elongated structure;
the first acoustic transducer is configured to obtain a first baseline transmission signal responsive to the baseline broadband acoustic signal in the first zone;
the third acoustic transducer is configured to obtain a second baseline transmission signal responsive to the baseline broadband acoustic signal in the second zone;
the second acoustic transducer is configured to generate a monitoring broadband acoustic signal along the rigid elongated structure;
the first acoustic transducer is configured to obtain a first monitoring transmission signal responsive to the monitoring broadband acoustic signal in the first zone;
the third acoustic transducer is configured to obtain a second monitoring transmission signal responsive to the monitoring transmission signal in the second zone;
a first differential transmission signal is determined as a difference between the first monitoring transmission signal and the first baseline transmission signal;
a second differential transmission signal is determined as a difference between the second monitoring transmission signal and the second baseline transmission signal;
if the mechanical change occurred in the first zone of the elongated rigid structure is determined based on the first differential transmission signal or if the mechanical change occurred in the second zone of the elongated rigid structure based on the second differential transmission signal; and
determination of if the mechanical change occurred in the first zone of the elongated rigid structure based on the first differential transmission signal or if the mechanical change occurred in the second zone of the elongated rigid structure based on the second differential transmission signal is validated based on an acoustic modeling and numerical simulation of the mechanical change in the elongated rigid structure.
12. The system of claim 11 , wherein:
the second acoustic transducer is configured to generate a baseline narrow-band pulse acoustic signal along the elongated rigid structure;
the first acoustic transducer is configured to obtain a first baseline response signal responsive to the baseline narrow-band pulse acoustic signal in the first and second zones;
the third acoustic transducer is configured to obtain a second baseline response signal responsive to the baseline narrow-band pulse acoustic signal in the second and first zones;
the second acoustic transducer is configured to generate a monitoring narrow-band pulse acoustic signal along the elongated rigid structure;
the first acoustic transducer is configured to obtain a first monitoring response signal responsive to the monitoring narrow-band pulse acoustic signal in the first and second zones;
the third acoustic transducer is configured to obtain a second monitoring response signal responsive to the monitoring narrow-band pulse acoustic signal in the second and first zones;
a first differential response signal is determined as a difference between the first monitoring response signal and the first baseline response signal;
a second differential response signal is determined as a difference between the second monitoring response signal and the second baseline response signal;
a first differential delay profile is generated as a function of the first differential response signal as compared with the second differential response signal;
a second differential delay profile is generated as a function of the second differential response signal as compared with the first differential response signal; and
the relative location of the mechanical change within the first zone or the second zone is determined based on the first differential delay profile and the second differential delay profile; and
determination of the relative location of the mechanical change within the first zone or the second zone based on the first differential delay profile and the second differential delay profile is validated based on the acoustic modeling and numerical simulation of the mechanical change in the elongated rigid structure.
13. The system of claim 11 , wherein the acoustic modeling and numerical simulation of the mechanical change in the elongated rigid structure is defined by a mesh size, a time step, a time delay, and a time window, the mesh size defining a spatial resolution of the acoustic modeling and numerical simulation, the time step defining a temporal resolution of the acoustic modeling and numerical simulation, the time delay defining the difference in time between acoustic excitation and start of acoustic response acquisition, and the time window defining a response acquisition duration for simulated excitation of the elongated rigid structure.
14. The system of claim 13 , wherein the mesh size is determined based on:
a first trial numerical simulation of the elongated rigid structure without the mechanical change, the first trial numerical simulation run using a trial mesh size;
generation of a Short-Time-Fourier-Transform map based on the first trial numerical simulation;
determination of active modes based on the Short-Time-Fourier-Transform map, the active modes associated with wavelengths; and
determination of the mesh size based on the wavelengths.
15. The system of claim 14 , wherein the trial mesh size is determined based on a highest frequency of interest.
16. The system of claim 14 , wherein the determination of the mesh size based on the wavelengths includes:
determination of a maximum mesh size based on a shortest wavelength among the wavelengths from the first trial numerical simulation of the elongated rigid structure;
a second trial numerical simulation of the elongated rigid structure, the second trial numerical simulation run using the maximum mesh element size;
identification of wavelengths of interest based on the second trial numerical simulation of the elongated rigid structure; and
determination of the mesh size based on shorter of the shortest wavelength from the first trial numerical simulation of the elongated rigid structure and a shortest wavelength of interest from the second trial numerical simulation of the elongated rigid structure.
17. The system of claim 16 , wherein:
responsive to the shortest wavelength of interest being longer than the shortest wavelength from the first trial numerical simulation of the elongated rigid structure, the mesh size is determined to be the maximum mesh size; and
responsive to the shortest wavelength of interest being shorter than the shortest wavelength from the first trial numerical simulation of the elongated rigid structure, the mesh size is determined based on the shortest wavelength of interest from the second trial numerical simulation of the elongated rigid structure.
18. The system of claim 17 , wherein the time step is determined based on the mesh size and a fastest wave velocity among wave velocities associated with the active modes.
19. The system of claim 18 , wherein the window size is limited by the mesh size.
20. The system of claim 11 , wherein numerical simulation output and experiment output of the mechanical change in the elongated rigid structure in a frequency-time domain are normalized by a local maximum across frequencies to facilitate cross-validation of the numerical simulation output and the experiment output.