PSI - Issue 80

Vinit Vijay Deshpande et al. / Procedia Structural Integrity 80 (2026) 327–338 Vinit V. Deshpande et al./ Structural Integrity Procedia 00 (2019) 000 – 000

334

8

∑ , ℎ

=1 =0 .

(7)

where, ℎ are the number of neighbour nodes to node . According to Ohm’s law, , = − , , (8) where, is the electric potential at node and , is the resistance between nodes and . Substituting Eq. 8 in Eq. 7, At each interior node , ∑ − , ℎ =1 =0 . (9) At the boundary node , ∑ − , ℎ =1 = . (10) where, is the current flowing through the boundary (top or bottom) edge. Note that at the boundary is defined as a boundary condition. At each node, the Eqs. 9 or 10 are assembled to form a global system of linear equations of the form, Φ = , (11) where, is the global conductivity matrix. Φ is the electric potential vector and is the current vector. Eq. 11 is solved to calculate . The total resistance of the composite specimen, is calculated as, = ( − ) ⁄ . In this model, the best available method to calculate the resistance , of each node pair is the analytical expression described in section 2.1 in Eq. 6. The total resistance of the composite specimen shown in Fig. 6a calculated using the Resistor Network method is 9428.5 Ω which shown a relative error of 28.3 %. It can be seen that approximation of the intra particle resistance leads to significant errors in the prediction of the resistance of the composite specimen as well. 3.3. Conditional Generative Adversarial Network Goodfellow et al. (2014) developed Generative Adversarial Networks that are typically used to generate synthetic image data that matches the dataset it is trained on. It learns a mapping from a random noise to output image , : → . A conditional Generative Adversarial Network (cGAN) learns a mapping from an input image and a random noise to , : { , } → (Isola et al. (2017)). A cGAN is made up of two components – a generator and a discriminator. Generator G has a U-net architecture and discriminator D has a series of convolutional layers. Fig. 8 shows the overall architecture of the conditional GAN model.