PSI - Issue 59

Victor Aulin et al. / Procedia Structural Integrity 59 (2024) 444–451 Victor Aulin et al. / Structural Integrity Procedia 00 (2019) 000 – 000 5

448

Step1. Introduction of output data regarding types of defects in the parts of assemblies, systems, and units of automobiles

Step2. Determining the output data range for the combination of defects in the parts of assemblies, systems, and units of automobiles

Step3. Linear normalization within the working interval x i Î [0;1] of activation function:

x x 

x

min

i

i



nor

x

x



max

min

i

i

Step4. Artificial neural network method training based on informative data using the algorithm of defect reverse propagation

Step5. Reverse normalization of the combination of defects data within the output interval

Step6. Data derivation on combinations of defects in the parts of units, systems and assemblies of vehicles

Fig.2. The block diagram of the artificial neural network method algorithm within the working range of the activation function during linear normalization.

According to the Arnold-Kolmogorov-Hecht-Nielsen theorems (Kolmogorov-Arnold-Hecht-Nielsen Theorem, 2015), one can calculate the necessary number of neurons for the hidden layer. However, the specific weight of the synaptic connection should be determined first:

N Q 

  

 

Q

1 log y 

1 ( 

1) N N N   

w y    N N

 

x

y

y

Q

N

,

(8)

2

x

where y N – is the number of neurons of the output layer; Q – is the number of values of training sampling; w N – is the necessary amount of synaptic specific weight; x N – isthenumberofneuronsoftheinputlayer. After that the number of neurons for the hidden layerwill be found by the formula:

N

L



w

N N 

x (9) The consequence derived from the Arnold-Kolmogorov-Hecht-Nielsen theorem is only used to determine the upper bound R of the number of neurons in the hidden layer. By discarding the lower bound of the interval in formula (8), equating w N to the remaining upper bound R , and substituting formula (9) into (7), we have obtained: y .

  

  

Q

1 ( 

1) N N N   

N

y

x

y

y

N



.

(10)

x

R



N N 

x

y

Theexpression (10) isusedasanupper bound, up to which the number of neurons will increase until it reaches the