PSI - Issue 51

Kenichi Ishihara et al. / Procedia Structural Integrity 51 (2023) 62–68 K. Ishihara and T. Meshii / Structural Integrity Procedia 00 (2022) 000–000

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3. Construction of DL model In order to regress desired parameters ( a , b ) with input parameters v , Q , W , D , an artificial neural network (ANN) that can express complex nonlinear behaviour was used for the machine learning model. The conceptual diagram of ANN was shown as Fig. 3. Here, features of the input layer are parameters v , Q , W , D and the variables of the output layer are parameters ( a , b ) in Fig. 3.

Input layer

Hidden layer Output layer

Bias

Bias

+1

+1

X 1

f ( X )

a 1

X 2

Feature ( X )

a 2

・・・

g ( X )

・・・

Output

a k

X n

Fig. 3. The conceptual diagram of ANN.

In order to prepare learning data, TDA was conducted for 648 combinations of v , Q , a , b and size of the molten shape W , D were collected as shown Fig. 4. In some cases, the temperature did not exceed the melting point temperature, thus 486 learning data set were obtained. The material properties for TDA were used as density ρ is 7820 kg/m 3 , conductivity λ is 29 W/(m ･ o C) and specific heat c p is 600 J/(kg ･ o C). Here, the maximum W and D generated from the maximum temperature distribution at each position of TDA were used as learning data.

TDA results

TDA solution

・ v [mm/s] ・ Q [W] Welding records

2 W

D

molten shape: W , D 486 learning data set

Heat source model

c f

c r

v [mm/s]

Q [W]

a [mm]

b [mm]

W [mm]

D [mm]

a

b

Density

ρ [kg/m 3 ]

7820

v 1 v i v n

Q 1 Q i Q n

a 1 a i a n

b 1 b i b n

W 1 W i W n

D 1 D i D n

648 dataset

Conductivity Specific heat

λ [W/m/ o C]

29

v [mm/s]

Q [W]

a [mm]

b [mm]

c p [J/kg/

o C]

600

6.1 ☓ 10 -6

v 1 v i v n

Q 1 Q i Q n

a 1 a i a n

b 1 b i b n

Thermal diffusivity

κ [m 2 /s]

・ v = (1, 4, 7) ・ Q = (1000, 3000, 5000, 9000, 15000, 25000) ・ a , b = (2, 4, 6, 8, 10, 12)

Fig. 4. The learning data.

There are several general-purpose program code or software for constructing machine learning models. For example, Python (Python, 2022), Mathematica (Wolfram, 2022), MATLAB (MathWorks, 2022) etc. In this work, Python (Python, 2022) which is open source and has a wide variety of packages was used. In concrete, a machine learning model was constructed using 486 learning data set. It is tradition in ML to split learning data set to train and