Электромпедансная томография
Download
Report
Transcript Электромпедансная томография
THE ANALYSIS OF FRACTURE
SURFACES OF POROUS METAL
MATERIALS USING AMT AND
FRACTAL GEOMETRY METHODS
Sergei Kucheryavski
Artem Govorov
Altai State University
Barnaul, Russia
Ideal life
Fractured specimen
Fracture surface picture
Image Processing
and Analysis
Possible cause of
Deformation and fracture
A priory information
about deformation
behavior
Deformation Structure of Porous Metals
Deformation stages
(Optical microscope)
Fracture surfaces
(Electronic microscope)
Known methods
Traditional methods
Classical statistics methods (i.e. Mean Absolute
Deviation)
Textural features methods
Alternative methods
Fractal analysis
The AMT technique
Fractal geometry
Fractals:
irregular, fragmented objects
self-similar objects
Fractal geometry methods
simulation complex objects like trees, clouds and so on
measure of self-similarity
quantitative description of irregular, complex structure –
fractal dimension Df
Housdorf dimension
h( ) (d )
=1–
d
M d h( )
for squares, cubes
= /4 –
for circles
= /6 –
for spheres
0, d D
M d (d ) (d ) N ( )
0
, d D
d
D – Housdorf dimension
d
Fractal dimension
N ( ) ~
1
D
N – number of cells
Fractal dimension
Advantages:
D – can be considered as the measure of roughness,
irregularity of surface
The results showed the dependencies between fractal
dimension of fracture surfaces and their porosity were
obtained
Disadvantages:
Some time there is no chance to calculate D
It works bad with surfaces that have a small D (from 2
to 2.2)
It works bad with noised images
AMT – Angle Measure Technique
Algorithm:
1.
Image is unfolded Х-Difference
into 1D digitized line.
2.
C – A – are randomly chosen along the line.
A number of points
3.
S 1A
For all scales S from
to N:
•
•
•
4.
B
Y-Difference
Find points B and C – points of intersection of circle with
radius S and line;
Angle
For each point A the Angle and Y-Difference are measured;
For all measuring the Mean Angle (MA) and Mean Y
Difference (MDY) are calculated.
The AMT-spectrum (dependencies of MA and MDY on scale S) is
plotted.
AMT-Spectra example
AMT Features
AMT transform the 2D image into 1D spectra
without losses the structure information
AMT can be used for data compression
AMT is highly sensitive
Using PCA or PLS for AMT-spectra one can
analyze and classify the structures
Fractal Analysis vs. AMT
1.
Is there any correlations between fractal
dimension of surfaces and their AMT-spectra?
2.
Is it possible to use AMT for noised images of
surfaces?
3.
Apply the AMT to analyze the fracture surfaces
of porous metals
Software
Fractal software simulation - C++ program
(Diamond-Square Algorithm)
Fractal dimension calculations – C++ program
(Box-Counting Algorithm)
AMT-analysis – MATLAB macros (Jun Huang,
Telemark University College)
PCA-analysis – The Unscrumbler®
Simulated fractal surfaces
D = 2.1
D = 2.4
D = 2.6
D = 2.9
The results of PCA of AMT spectra
225 specimen with Df from 2.1 to 2.9
The results of PCA of AMT spectra
Outliers detection and scores w/o outliers
The results of PCA of AMT spectra
The result for specimen with D=2.1 and 2.9
Conclusions
PCA-analysis of AMT-spectra of fractal surfaces
allow to make a classification depending on
fractal dimension
Scores plot shows that the “clouds” of samples
with D<2.5 are overlapped
Score plot shows that the samples with greater D
are arranged closely than others
Fractal analysis vs. AMT. Noised images
The real fracture surfaces is differ from
simulated fractal surfaces first of all with
presence of noise – because of imperfection of
devices, external influence and so on.
The task is to add the noise to simulated fractal
surfaces and to compare fractal analysis and
AMT results.
Simulated surfaces with Gauss noise
Original D:
2.1
Calculated
OriginalD:
D: 2.8 2.3
Calculated
D: D:2.7
Original
2.5
Calculated
D:D: 2.7 2.9
Original
Calculated D:
2.8
AMT results
- Noised Images
- w/o Noise
AMT-results
- Noised Images
- w/o Noise
Conclusions
Fractal analysis doesn’t allow to classify noised
images – the calculated and initial fractal
dimension are in not close agreement
PCA-results of AMT-spectra of noised images
show that “clouds” of samples with equal D are
more overlapped and stretched along PC1
In further investigations one can use the fractal
dimension of surface as an additional variable in
PCA analysis