Tomography

[Overview] [Real-time] [Fuzzy-Logic] [Parametric] [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. It is an analysis and presentation method of captured CSL data, that projects the logged results into 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:

1. 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).
    

2. 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)
    

3. 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, Parametric 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)

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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:

The (simplified) algorithm:

1. Find the most common FAT/Attenuation value X from all horizontal pulses. Since real-life piles are mostly solid, this value represents good* concrete.

2. 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)

3. break the pile into pixels, for each pixel, find all pulses crossing it

4. A pixel is good* if at least one of the pulses crossing it is good (fuzzy "or")

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CHUM is actually using a faster recursive method, using a variable pixel size:

1. Start with the whole cross-section as a single "pixel"

2. if all pulses passing through the current pixel agree*, or if the pixel is small enough then

3. this pixel is done - and painted according to the value of the pulse

4. else

5. break the pixel into to two pixels (vertically or horizontally, according to proportions) and submit each pixel to step 2

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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:

• Quick and intuitive.

• Excellent cost/benefit ratio.

• Very easy to explain.

• Easy to view the results in the field, and to get an immediate feedback.

• No special cost incurred

Cons:

• Always shows small triangular ghost shadow

• Might be sensitive to noise (Adequate filtering reduces this significantly)

Real-Time tomography:
(Unique to CHUM)

Real-time tomography allows viewing the defect shape while the logging is being performed. The operator starts with both probes at the bottom of the pile, and start pulling. 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, post-processing, using any tomography method, can be applied to the logged data.

CHUM's real-time tomography is a simplified version of the fuzzy-logic tomography, which does not require a high-end computer to enable the complex calculations in real-time.

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Pros:

• All of Fuzzy-logic  

• + 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:

• Same as for Fuzzy-Logic

• Sensitive to noise which later gets corrected in post-processing

• Non-quantifiable results

Parametric tomography
(Unique to CHUM)
 

The basic idea: Guess the location of a defect; apply a forward model to calculate what would the FAT/Attenuation be. Move/Resize the defect around until the forward model best matches the actual data.

Some simplifying assumptions in CHUM:

• The initial vertical position of a defect is calculated from the 1-D horizontal pulses

• only one defect exists at the same vertical level

• Defects are box-shape (rectangles in the cross section)

• Defects are uniform (fixed velocity)

• Calculation can be done on one defect at a time (superposition)

Under those assumptions - there are only 5 parameters for each defect (location & velocity). The depth and height will not change much from the 1D data, and it is simple to reach convergence.
 

The algorithm:
 

• Based on horizontal pulses only, assume large (Full width, generous height) defects on all locations of 1-D anomalies.

• For each defect:

•     Calculate the forward model

•     Calculate the error E = f( Actual data, Calculated data )

•     change the vector <X,Y,Width,Height,Velocity> to the direction of the biggest effect (Gradient descent)

•     Keep on changing in small steps, until no change can reduce E

•     If the defect is smaller than a threshold value (5x5cm) - drop it   

Parametric tomography can give surprisingly accurate results. The results can quantify the defects (for example: "30x30cm anomaly at 3.5m").

Pros:

• Quick and intuitive

• Not sensitive to noise

• Quantifiable, clean results
   

Cons:

• Simplistic (Real defects are never box-shaped voids - Do we really care?)

• The more realistic the forward model is, the longer it takes to calculate.

• Gradient descent solution is sensitive to local minima (Reduced by trying random leaps)

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:

• Quantifiable results (Sound velocity)

• No ghost shadows
   

Cons:

• Requires computing power and is therefore not commonly performed in the field but as post-procession in the office.

• 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:

• Clear and impressive pictures (Usually colorful)
   

Cons:

• Data not actionable: Hard to make sound engineering calls based on pictures...

• Slow, requires a lot of computing

• Higher performance comes with a higher price ( Piletest can offer some free trails for a start) 

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:
 

• Nice, impressive pictures (Usually colorful)

• Actionable: can cautiously assess the reduction of cross-section and effect on capacity

Cons:

• 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