Issue 66

A. Anjum et alii, Frattura ed Integrità Strutturale, 66 (2023) 112-126; DOI: 10.3221/IGF-ESIS.66.06

The performance of regression models is evaluated using various evaluation metrics such as root means square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and coefficient of determination (R 2 ). The mathematical formulations, characteristics, applications, advantages, disadvantages, and limitations of these metrics can be found in [43].

Type of SVM

Mercer Kernel

Description

Gaussian or Radial Basis Function (RBF)

One class learning.  is the width of the kernel

 

  2

 2 x x 1 2





2

   exp

, k x x

 

1 2

Two class learning.

Linear

   , T k x x x x 1 2 1 2

 is the order of the polynomial

Polynomial

   tanh

 



1 2 T k x x x x 1 2 ,



1





Sigmoid

 0 , and  1 are constants for which it becomes a mercer kernel function.





0 1 2 x x T







 1

, k x x

1 2

Table 4. Types of SVM and Kernel Functions [41].

F INITE ELEMENT RESULTS AND DISCUSSION

Grid independence test o evaluate the influence of mesh size on computational results, three mesh sizes were chosen and presented in Fig. 4. The adhesive bond and piezoelectric actuator were meshed using the grid-structured mesh with component size based on the mesh type. The elements were separated for the damaged plate by choosing each line, resulting in an unstructured type of mesh. As shown in Fig. 4, refining the mesh from medium to fine led to a slight improvement in the accuracy of the SIF value solution, with a maximum relative difference of 14 percent. However, the medium mesh provided adequate resolution and accuracy while requiring only half the computation time, making it the preferred option for the remaining simulations. T

0.12

0.10

0.08

No. of Elements : 11,832 No. of Nodes : 28,692 CPU run : 309 sec

0.06

No. of Elements : 33,452 No. of Nodes : 73,633 CPU run : 600 sec

No. of Elements : 68,920 No. of Nodes : 133,633 CPU run : 1522 sec

SIF (MPa)

0.04

0.02

0.00

Coarse

Medium

Fine

Mesh Type

Figure 4: Mesh independence results.

Validation of the numerical model Fig. 5 provides visual evidence of the strong agreement between the two results, indicating that the computational model is a reliable and accurate representation of the physical experiment. The maximum relative error of about 10% suggests that the differences between the simulation and experimental results are relatively small, considering the complexities involved in conducting physical experiments. Despite the small differences, it is important to note that the accuracy of the experimental results may have been affected by various factors, such as human error in situating and aligning the

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