Acoustic Resonance Testing using Transform
Decomposition and Support Vector Machines for
efficient and accurate Detection of Defects in
Forged Components
Vivek Hari Sankaran
16th April 2012
Natesan Synchrocones P. Ltd, Chennai, India
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Acoustic Resonance Testing -Basic Principle
• Every object resonates in its natural modes when impacted
• Single degree of freedom object
• Multiple degree of freedom: multiple resonant modes each with a
resonant frequency and resonant shapes
• Defects shift the resonant frequencies.
– e.g Crack – decreases k; Porosity- changes m etc.
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m
k1 1
2n
kf
m
Single Degree of Freedom object Fundamental Resonant Mode of Object
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Acoustic Response
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Feature Extraction
• Peak
• Amplitude
• etc
Classifier
OK Not OK
Part specific unique response
Cracked parts show a shift in frequency
Fourier
Transform
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Limitations of existing ART Systems
1. Fourier Transform:
– Uses FFT which is computationally intensive when only a small subset of
output points are required
2. Classification System:
– Uses a “condition based “classification system
– Effective for major defects only
– Large amount of manual input required to identify and set thresholds
– Variation based on impact position and part positioning
– Lower accuracy
3. High Cost of System
– Existing systems use a high cost DAQ card and processors making the
entire setup expensive
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Comparison of Existing and Proposed ART System
Existing System Proposed System
Fourier Transform
Method
Fast Fourier
Transform
Transform
Decomposition
Classification
System
Condition Based
Classifier
Support Vector
Machine
Cost of System Use of expensive
DAQ cards
Low Cost using PC
and its Sound Card
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Fourier Transform- Transform Decomposition Method
• The FFT algorithm is replaced by the Transform Decomposition DFT**
• More efficient than FFT algorithm when only small subset of output
points are required.
• In ART, the frequency range of interest is narrow and hence
Transform Decomposition is more efficient
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**Transform Decomposition developed by Sorensen et al is a combination of Cooley-Tukey and Goertzel’s algorithm
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Intelligent Classification Systems
• Condition based classifiers failed to detect minor defects
• Artificial Neural Networks initially used in previous work by the author
– Accurate in detecting major crack
– Able to detect minor defects but with lower accuracy
• Support Vector Machines (SVM) used in this paper
– Able to detect both major cracks and minor defects accurately
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Application of Support Vector Mechanism to ART
• In ART generally frequency and amplitude of peak are used as features
• These were insufficient to detect minor defects as peak detection
algorithms are in accurate and fail in regions of double peaks
• Different product specific features identified
• A large number of training samples used with a good mix of OK and
Not OK parts
• Parts from different batches used to account for production variation
• The training is carried out using different Kernel Functions
• Most accurate Kernel function is chosen
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Advantages of Support Vector Machine
• SVM able to learn relationships between magnitude and frequency of
peaks in the spectrum which is impossible for human to identify.
• Automates the process of threshold identification
• Easy and quick to train new products
• Takes into account batch to batch variation
• Accurately detect internal flaws which have not yet propagated.
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Samples Tested and Defects
• Testing was carried out on a brass Synchronizer Ring
• 3D model of the component using SolidWorks
• Modal analysis to identify the resonant modes
• Modes were used as reference to
narrow down the region of interest
• The Defects tested include
– Major and Minor Cracks
– Minor defects : Internal flaws that had not yet propagated
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Modal Analysis results overlaid on frequency
response
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Experimental Setup
• A low cost Desktop computer was used to process the data
• An off the shelf Microphone was used along with the sound card of
the PC to ensure low cost of system
• A suitable pneumatic impact device was setup
• The entire processing was done using Matlab
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Results-Transform Decomposition
Nature
of
Defect
No of
Output
Points
No of
Addn. in
Real
FFT
No of Mult.
In Real
FFT
Percentage
Reduction in
Addn. (%)
Percentage
Reduction
in Mult.
(%)
Total
Computation
Reduction
(%)
Major
and
Minor
Cracks
633 655362 196610 24.98 16.08 22.92
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Results-Support Vector Machine
Method Used Accuracy in
Detecting Major
and Minor Cracks
(%)
Accuracy in
Detecting Internal
Flaws that have
not yet
propagated
(%)
Accuracy in
Detecting Ok
Parts
(%)
Condition based
Classifier
92 Not Applicable 90
Artificial Neural
Network
100 87 93
Support Vector
Machine
(using optimal
Kernel)
100 95 98
Support Vector
Machine (improved)
100 97.89 99.21
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Conclusions and Future Work
• Very robust and provided high accuracy
• Detect the internal flaw which had not yet propagated which was not
possible using existing systems
• Testing time per part around a second
• The cost of the system very low
• Future Work
– Optimize the feature vectors further to improve accuracy
– Identify more efficient Fourier Transform Methods to increase speed
– Detection of minor defects such as teeth lap and underfillings
– Dimension variation measurement
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References
[1] I. Hertlin and D.Schultze, ‘Acoustic Resonance Testing: the upcoming volume-oriented NDT
Method’, PANNDT (2003)
[2] Timoshenko, W. Weaver Jr., D.H. Young, ‘Vibration Problems in Engineering’, Fifth Edition,
John Wiley and Sons (1990)
[3] J . D. Markel, ‘FFT pruning’, IEEE Trans. Audio Electroacoust., vol. AU-19, no. 4, pp.. 305-
311, Dec. 1971.
[4] H. V. Sorensen and C. S. Burrus, ‘Efficient computation of the DFT with only a subset of input
or output points,’ IEEE Trans. Signal Processing, vol. 41, pp. 1184–1200, Mar. 1993.
[5] J W. Cooley and J. W Tukey, ‘An algorithm for the machine calculation of complex Fourier
series,’ Math Comput., vol 19, no 90, pp 297-301, Apr 1965.
[6] G. Goertzel, ‘An algorithm for the evaluation of finite trigonometric series’, Amer. Math.
Monthly, vol. 65, no. 1, pp. 34-35, Jan. 1958
[7] N Cristianini and J S Taylor, ‘An introduction to Support Vector Machines and other Kernel-
Based Learning Methods’, Cambridge University Press (2000)
[8] V H Sankaran, ‘Low cost inline NDT system for internal defect detection in automotive
components using Acoustic Resonance Testing’, Proceedings of the National Seminar &
Exhibition on Non Destructive Evaluation, NDE 2011, pp. 237-239, Dec. 2011
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THANK YOU
Natesan Synchrocones P. Ltd
No 54/4 Paul Wels Road,
St Thomas Mount,
Chennai 600 016
Email:[email protected]
Ph: +91 44 423450823/24
Fax:+91 44 2233 0354
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Transform Decomposition
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2# log 2 22 2
TD FILT REAL
N N NMUL P P
P
2
3 3# log 2
2 2TD FILT REAL
N N NADD P
P