Guided Wave based Quantitative Identification of Damage in ......Longitudinal wave Flexural wave...

seek LIGHT | The University of Adelaide

Guided Wave based Quantitative Identification of Damage in Beams Using a Bayesian Approach

Dr. (Alex) Ching-Tai Ng

Australian Network of Structural Health Monitoring (ANSHM) 2013 Annual Workshop 19th November 2013, Melbourne, Australia

seek LIGHT | The University of Adelaide Slide 1

Hanning windowed sinusoidal tone burst

pulse Giurgiutiu & Bao (2004) Struct. Health. Monitor. Animation from [www.me.sc.edu/Research/lamss/]

Piezoceramic transducer

•  Guided Wave §  Sensitive to small and different types of damages §  Long travel distance

Introduction and Background

Fundamental symmetric mode (S0) +

+

Fundamental anti-symmetric mode (A0) +

-


Introduction and Background

Challenges: •  Requirement of baseline data

•  Temperature variation & effect of external loading conditions •  Difficult to achieve quantitative identification of damages

Excitation

Sensor Damage

Incident pulse reflected from beam end

Excitation


•  To quantitatively identify the location and size of the damage

•  To improve the computational efficiency of the proposed damage identification method using frequency domain spectral finite element simulation

•  To quantify the uncertainties associated with the damage identification results using a Bayesian approach

•  To provide an experimental verification of the proposed method

Objectives


Frequency-domain Spectral Finite Element Method

§  Mindlin-Herrmann theory §  Describes the longitudinal wave using two coupled partial differential

equations**

§  Each element has 2 nodes & each node has 2 DoFs §  Account the axial displacement & lateral contraction effect

Spectral finite element

** Krawczuk M, Grabowska J and Palacz M, J Sound Vib 2006, 295:461-478



§  The governing equations are reduced to two ordinary differential equations and assumes the solutions in the forms

§  Formulate the dynamic stiffness matrix in frequency domain (at frequency ) by considering the boundary conditions


Excitation signal in time domain, f(t)

Excitation signal in frequency domain, f(ωn) for n = 1,…,N

FFT

Dynamic stiffness matrix K(ωn)

Calculate displacement in frequency domain

n = n+1

Excitation signal in time domain, f(t) iFFT


n = N


f(t)

Damage location, L1

L1

Damage depth, d

L2

L3

EL1 EL2 EL3

E, A1

E, A1

E, A2

Node 2 Node 3 Node 4Node 1

f(t)

Damage length, L2

EL0

Free end

Spectral finite element model of a beam with step damage

f(t)

Damage length (dL)

Damage depth (dd)

Damage length

Damage location (Ld)

Free end Infinite beam end Measurement point



§  Using the Bayes’ theorem, the probability of the set of uncertain damage parameters (θ) with a given set of dynamic data is **:

Bayesian Approach

( ) ( ) ( ), , |p D M cp D M p M=θ | |θ θ

( ) ( ) ( )22, 2o

oNNNN J

p D M e σπσ− −

=θ

|θ

( ) ( ) ( ) 21

1 ;N

oko

J k kNN =

= −∑θ q S y θ

where c is normalisation constant.

where J(θ) is:

Likelihood Prior distribution

(Allow the inclusion of engineering judgment about the possible damage)

Simulated signal Measured signal

** Beck JL and Katafygiotis LS, J. Eng. Mech. ASCE. 1998, 124(4), 455-461

The minimisation problem is solved by Hybrid Particle Swarm Algorithm


§  The updated (posterior) PDF of damage parameters for given data and model class can be approximated as a weighted sum of Gaussian distributions:

§  The weightings are given by:

( ) ( ) ( )( )( )1

1

ˆ ˆ| ,I i i

ii

p D w N −

=≈ ∑θ θ A θ

( )( ) ( )( )12ˆ ˆi i

i Nw π−

= θ A θ

Bayesian Approach


Experimental Verification

Backing mass

Piezoceramic transducer

Longitudinal guided waveStep damage

Laser head

Aluminum beam Beam cross-section: 12x6 mm2

Beam length: 2 m Excitation frequency: 80 kHz



Preliminary study of measurement location using 3D finite element method (LS-DYNA)

Scaled contour plot of displacements



Preliminary study of measurement location using 3D finite element method (LS-DYNA)

Reflected longitudinal wave propagates toward the beam end

Flexural waves propagate toward the beam end


-1 -0.5 0 0.5 1-1

-0.83-0.67

-0.5-0.33-0.17

00.170.33

0.50.670.83

1

Normalized AmplitudeNor

mal

ized

Thr

ough

-thic

knes

s Lo

catio

n

S0 guided wave

•  Modeshapes

-1 -0.5 0 0.5 1-1

-0.83-0.67

-0.5-0.33-0.17

00.170.33

0.50.670.83

1

Normalized AmplitudeNor

mal

ized

Thr

ough

-thic

knes

s Lo

catio

n A0 guided wave


Longitudinal wave

Flexural wave



0 100 200 300 400 500 600

-1.5-1

-0.50

0.51

1.5

Time (µs)

Norm

alize

d Am

plitu

de

Flexural wave reflected from damage

0 100 200 300 400 500 600

-1.5-1

-0.50

0.5

11.5

Time (µs)

Norm

alize

d Am

plitu

de

Flexural wave reflected from damage

0 100 200 300 400 500 600 -1.5

-1 -0.5

0 0.5

1 1.5

Time ( m s)

Nor

mal

ized

Am

plitu

de Incident longitudinal wave

Longtitudinal wave rebounded from left beam end

Longtitudinal wave reflected from damage



Amplifier Function generator

Oscilloscope

Computer

Positioning system

Laser head

Piezoceramictransducer

Beam

Backing mass

Step damage

Ld

LLdd

(Left end)

(Right end)


0 1 2 3 4 5 6 7x 10-4

-1

-0.5

0

0.5

1

Time (sec)

Nor

mal

ized

am

plitu

de

b)

0 1 2 3 4 5 6 7x 10-4

-1

-0.5

0

0.5

1

Time (sec)

Nor

mal

ized

am

plitu

de

a)

Incident wave Waves reflected from damage

Incident wave

Reflected wave rebounded from beam end

Waves reflected from damage



Case C1

Case C2

0 1 2 3 4 5 6 7x 10-4

-1

-0.5

0

0.5

1

Time (sec)

Nor

mal

ized

am

plitu

de

b)

0 1 2 3 4 5 6 7x 10-4

-1

-0.5

0

0.5

1

Time (sec)

Nor

mal

ized

am

plitu

de

a)

Incident wave Waves reflected from damage

Incident wave


Waves reflected from damage


Blue line: Experimental data Red line: Spectral finite element simulation with identified damage parameters


Normalized marginal PDF of the identified damage length and depth for a) Case C1 and b) C2



•  A method has been proposed to provide quantitative identification of damage in beams using longitudinal guided wave

•  The method is able to identify damage location and size •  Frequency-domain spectral finite element has been

employed to improve the computational efficiency •  The proposed method is also able to quantify the

uncertainties associated with the damage identification results

•  The proposed method has been experimentally verified •  The proposed method is currently extending to address

the multiple damages situation and structures with complicated configurations

Conclusions


Thank You!

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Guided Wave based Quantitative Identification of Damage in ......Longitudinal wave Flexural wave...

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