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.

2

m

k1 1

2n

kf

m

Single Degree of Freedom object Fundamental Resonant Mode of Object

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Acoustic Response

3

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:corporate@natesan.co.in

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