PSI - Issue 52

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

704

6

The developed model, shown in Fig.5, comprises of two parts. The first part focuses on damage detection and localization by utilizing vibration and guided wave inputs individually. In the second part, all the features extracted from vibration and guided waves are combined for comparative analysis. Specifically, neural pattern recognition techniques are employed for damage detection (Pan et al. 2023). As the output is limited to damage and health condition, the SoftMax is utilized for the activation function of the output layer. In terms of the model for damage localization, the output layer employs the Pureline activation function. Additionally, this study investigates the performance of two commonly used activation functions (Logsig and Tansig) for the hidden layer, and the expression is showed in Eq. (5) and (6), aiming to developing a high-performance model.

1

F

=

(5)

1

x

1

e −

+

x e e e e − + x

x

−

(6)

F

=

2

x

−

3.3. Model evaluation and validation The confusion matrix, which comprises true position rate and false positive rate, is used to evaluate the performance of damage detection, Table 1 shows the confusion matrix for the binary classification (Yue et al. 2020).

Table 1. Confusion matrix d=0

d=0

d’=0 d’=1

Ture Negative (TN) False Position (FP)

False Negative (FN)

Ture Position (TP) Based on the confusion matrix, the probability of detection (POD) and probability of false alarm (PFA) are defined as: TP POD TP FP = + (7)

TP

(8)

PFA

=

TP FN +

Then the Accuracy is proposed to measure the classification reliability of the proposed method, which is defined as:

TP TN TP TN FP FN + + + +

Accuracy

=

(9) In terms of damage localization, the normalized Mean normalized distance (MND), as shown in Eq. (10), is used to evaluate the difference between the true value and the predicted value. (10) x ( n ) and y ( n ) are the predicted value by BPNN, 0 ( ) , 0 ( ) are the true value obtained by the experiment, and N the number of the points. The accuracy of the model’s prediction is considered higher when the MND value is smaller. ( ) n x x ( ) 2 n − + − ( ) n y y ( ) 2 n 0 0 1 ( ) ( ) N n MND N = = 