Tomography
For CHUM-Cross Hole Ultrasonic Monitor
(CSL Tester) with tomography support
Tomography
[Overview] [Real-time] [Fuzzy-Logic] [Matrix inversion] [3D] [Horizontal slices] [Additional reading]
Overview:
While normal (1D) CSL can only show the depth of an anomaly, tomography can help in the visualization of the shape, size, and location of anomalies. Tomography is an analysis and presentation method of captured CSL data that projects the logged results into a two-dimensional (2D) plane or three-dimensional (3D) body.
What is calculated?
Some of the tomography techniques described herein are linear - assuming that waves travel in straight lines. Tomography usually uses velocity or energy data. To convert those into linear quantities, propagation time is used for velocity, and attenuation is used for energy.
More advanced tomography techniques use bent-ray and wavefront analysis in an iterative approach.
In CHUM (Cross Hole Ultrasonic Monitor), the operator may choose FAT-based tomography, attenuation-based tomography, or a combination.
Logging of the data:
Several methods for data logging exist:
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Single depth encoder (not used by CHUM): The cross-section is logged three times: Horizontally, +45°, and -45°. The three cross-sections are combined in a post-processing phase. The distribution of information is uniform all over the cross-section and does not concentrate on the suspected zones. (picture 1-1).
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Two depth encoders: Horizontal and diagonal readings are logged in the same cross-section. The operator collects much more information around defects, at any angle, and a normal amount of data on good pile sections, This results in a better resolution, and smaller logs (Better information distribution) (picture 1-2)
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Multiple receivers: are chained at fixed distances to the same line, and the data gathered is the same as in (1), The section needs to be logged once. This method, popular in geophysics, is hardly used in piling.
Picture 1-1
Picture 1-2
CHUM is using the following tomography algorithms: Real-Time, Fuzzy logic, and Matrix-based inversion. CHUM also supports 3D and horizontal slices tomography.
See here (downloads/TomographyDemo.exe) a demonstration animation (No setup required!) of the tomography data-collection process.
Fuzzy Logic tomography
(Unique to CHUM)
The basic idea: A pixel is as Solid*/Good* as the best* pulse that passes through it.
All terms marked with * are fuzzy values: 0.0 means false, 1.0 means absolutely true. 0.5 may be interpreted as "maybe", and 0.9 as "most probably" the following table summarizes the logic operators used:
p and q | p or q | not(p) |
|---|---|---|
The (simplified) algorithm:
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Find the most common FAT/Attenuation value X from all horizontal pulses. Since real-life piles are mostly solid, this value represents good* concrete.
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For each pulse (including diagonals), assign a value representing how good* it is. 0=bad concrete, 1=as solid as X. the value may be calculated by FAT, attenuation, or a combination of both (Operator control)
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break the pile into pixels, for each pixel, find all pulses crossing it
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A pixel is good* if at least one of the pulses crossing it is good (fuzzy "or")
CHUM is actually using a faster recursive method, using a variable pixel size:
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Start with the whole cross-section as a single "pixel"
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if all pulses passing through the current pixel agree*, or if the pixel is small enough then
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this pixel is done - and painted according to the value of the pulse
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else
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break the pixel into to two pixels (vertically or horizontally, according to proportions) and submit each pixel to step 2
The image on the right shows the pixels that have been used to produce a tomography. Most of the pile is solid, and broken into big pixels. Areas with mixed good* and bad* data are broken into smaller pixels until the pixels are small enough, or all pulses through it agree*.
Compared to fixed-size pixels, the total number of pixels is very small, and the smallest pixels are much smaller. The variable pixel size method has a considerable advantage in both calculation time and resolution.
CHUM also filters the pulses before looking at a pixel, to reduce sensitivity to noise. The details of the filter are not presented here for brevity.
Pros:
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Quick and intuitive.
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Excellent cost/benefit ratio.
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Very easy to explain.
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Easy to view the results in the field, and to get an immediate feedback.
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No special cost incurred
Cons:
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Always shows small triangular ghost shadow
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Might be sensitive to noise (Adequate filtering reduces this significantly)
Real-Time tomography:
(Unique to CHUM)
Real-time tomography allows the defect shape to be viewed while the logging is being performed. The operator starts pulling the cables when both probes are at the bottom of the pile. When encountering a defect, it will appear as a full-width void. At this point, the operator starts lowering and raising one or both of the cables to log diagonally. While doing this, the defect shape is formed on-screen. When done, the logged data is processed for 3D tomography view using any tomography method.
CHUM's real-time tomography is a simplified version of fuzzy-logic tomography, which does not require a high-end computer to enable complex calculations in real-time.
Pros:
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All of Fuzzy-logic
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+ Makes sure that the correct amount of data is logged: Sparse on the good portion of the pile, dense around the defects. Quality data is the most important factor for the success of any post-processing method.
Cons:
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Same as for Fuzzy-Logic
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Sensitive to noise, which later gets corrected in post-processing
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Non-quantifiable results
Matrix-based inversion
(Fully supported by CHUM)
Commonly-used tomography methods based on matrix pseudo-inversion. Both are traditionally used only on FAT/Velocity, never on attenuation (for no reason other than tradition)
Pros:
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Quantifiable results (Sound velocity)
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No ghost shadows
Cons:
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Requires computing power and is therefore not commonly performed in the field but as post-procession in the office.
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Over-interpretation: Inversion problems have many possible solutions. Matrix-inversion based tomography tends to ignore this fact, and presents the results with high resolution and high confidence, leading the viewer to ignore the fact that the solution is NOT unique.
3D tomography
(Fully supported by CHUM)
After taking several (3 or more) cross sections from different test-tube pairs, the data may be combined to plot a three-dimensional picture of the pile, assessing defects volume and 3D shape.
3D tomography can be based on any of the tomography methods described above (Not including real-time)
Pros:
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Clear and impressive pictures (Usually colorful)
Cons:
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Data not actionable: Hard to make sound engineering calls based on pictures...
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Slow, requires a lot of computing
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Higher performance comes with a higher price ( Piletest can offer some free trails for a start)
CHUM 3DT is our 3D engine and viewer
3D View: Rotate, Tilt, Pane, Zoom, etc
slice: vertically & horizontal
Peel: hide high velocities by clicking on the palette
plus much more.
Horizontal slices tomography
(Fully supported by CHUM)
A method in which the 1D and 2D cross sections from the whole pile are combined to plot a horizontal cross section of the pile at a specified depth.
Pros:
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Nice, impressive pictures (Usually colorful)
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Actionable: can cautiously assess the reduction of cross-section and effect on capacity
Cons:
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Gives the wrong impression that the whole cross section is covered. We have little understanding on the width of the ultrasonic wave front.
Animated 3d tomography
Using existing "gaming" 3D techniques to interactively pane, rotate and zoom into a pile. The user can "fly" into defects, and assess their size and shape
Additional reading
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Aki, K., et al. (1974): Three-dimensional seismic-velocity anomalies in the crust and upper-mantle under the U.S.G.S. California seismic array (abstract), Eos Trans. AGU, 56, 1145.
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Amir, E.I & Amir J.M. (1998): Recent Advances In Ultrasonic Pile Testing, Proc. 3rd Intl Geotechnical Seminar On Deep Foundation On Bored And Auger Piles, Ghent 1998
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Khamis Y. Haramy and Natasa Mekic-Stall (2000): Cross-hole sonic logging and tomographic imaging survey to evaluate the integrity of deep foundations-case studies. Federal Highway Administration, Central Federal Lands Highway Division, Lakewood, CO.
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Robert E. Sheriff and Lloyd P. Geldart (1995): Exploration Seismology, second edition. Cambridge University Press 1982, 1995.
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Santamarina, J.C. and Fratta, D. (1998): Introduction to Discrete Signals and Inverse Problems in Civil Engineering, ASCE Press, Reston, VA., 327 pages.
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Stain, R. T., 1982, "Integrity testing", Civil Engineering, pp. 53-72.