PSI - Issue 52

Yuhang Pan et al. / Procedia Structural Integrity 52 (2024) 699–708 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

702 4

1 = − = −  1 n 

T

c 

b  n

0 [ ( ) n c t

][ ( ) b t

]

−

−

n n

(1)

(1)

DI

t

=

n

c b n n  

max () max[ () r t

( )]

c t b t

n b t −

(2)

DI

=

=

n

n

n

(2)

n

max ( ) b t

max ( )

n

2

= 

T

[ ( ) c t b t −

( )]

(3)

n

n

(3)

DI

0

t

=

n



T t

2

( )

n b t

0

=

The first damage index expressed in Eq. (1) describes the correlation between the current signal and its baseline, where ρ n is the correlation coefficient between the baseline signal b n (t) and the current signal c n (t), μ n and σ n represent the mean value and the standard deviation of the signal, and T is the time window of the signal used for comparison. The second damage index is defined as the ratio of the maximum value of residue signal and the maximum value of baseline signal, as shown in Eq. (2). Eq. (3) shows the third damage index, which is defined normalized squared difference between the signal and its baseline. These damage indices are capable of describing the change of the signal ’s phase and amplitude under the same environmental condition. For the vibration-based method, the frequency response function (FRF) is used to describe the change of the modal properties before and after damage since some modal properties such as damping ratio and resonance frequency can be analysed from it. The FRF is defined as:

( ) ( )

ik x w F w

( )

ik H w

=

(4)

k

H ik ( w ) is the FRF obtained by the excitation force and the corresponding response at one point. F k ( w ) is the exaction force in the frequency domain, and X ik ( w ) is the vibration response received by the accelerometer. The FRFs between 5Hz to 2000Hz obtained by pristine and damaged conditions are plotted in Fig.3(a). The figure reveals that the primary frequency components of the plate are concentrated within the 500-2000 Hz range. Consequently, this frequency band was chosen as the fundamental information for the VSHM method. The comparison between pristine and damage in this frequency band is showed in Fig.3(b).

Fig. 3. Frequency response function (FRF) obtained from pristine and damage condition with frequency range: (a) 5-2000Hz, (b)500-2000Hz

The FRF in the range of 500-2000Hz comprises a total of 237 data points. Inputting all these points into the neural network would increase both the efficiency and complexity of model learning. Therefore, the principal component analysis (PCA) method is used to reduce the number of input points. The eigenvalue and the cumulative percentage of FRF are summarized in Fig.4.