PSI - Issue 40

Aleksandr Zalazinskiy et al. / Procedia Structural Integrity 40 (2022) 461–469 Aleksandr Zalazinskiy at al. / Structural Integrity Procedia 00 (2022) 000 – 000

467 7

results of the computational experiment are shown in Table 1 (normalized values are indicated in parentheses). The data given in the table were processed using an expert system (Zalazinskiy, 2019, 2020). In it, the quality criteria are reduced to the normalized form (Titov, 2019) p ,  ,  in the range of [0; 1] under the conditions ; max 0.039   ; max 1.869   ; min min min 0 p      . The regression analysis method (Draper, 1998, Titov, 2019) determines the dependence of the factors p ,  ,  on the variable parameters ( λ , α , f) of the system (10) – (12) (the coefficient of determination R 2 = 0.978 ÷ 0.996): ~ 5 2 4 2 2 0.012 0.028 1.878 8 10 2.883 10 7.436 p f f               (10) min 6.676 p 

~

3

4 2 

2





(11)

6.833 10

0.056 6.336 5.812 10 f    

15.677

f

 









~

4 2

4 2 

2





(12)

0.013 0.064 6.931 2.08 10 f         

6.14 10

17.197

f

 





A generalized criterion for the quality of the technological process is introduced

2

2

2

~

~ ~ k   

(13)

F k p k  

1

2

3

where 1 , 2 , 3 are the weight coefficients. The procedure for finding the minimum value of the quality criterion of the technological process is based on the "ideal point" method (Odu, 2013, Titov, 2019) using a genetic algorithm   min , , Z F f    (14)

Table 1. Results of computational experiments for the Nb-Ti+Cu composite HMP process.

Extrusion ratio

Die cone angle, deg.

Friction factor

Extrusion load

Damage factor

Strain inhomogeneity

№

1

10

30

0.3

5.314 (0.796)

0.029 (0.744)

1.290 (0.690)

2 3 4 5 6 7 8 9

10 10 20 20 20 30 30 30

45 60 30 45 60 30 45 60

0.2 0.1 0.1 0.2 0.3 0.3 0.2 0.1

4.757 (0.713) 4.388 (0.657) 4.536 (0.679) 5.514 (0.826) 6.418 (0.961) 6.676 (1.000) 5.957 (0.892) 5.516 (0.826)

0.030 (0.769) 0.034 (0.872) 0.032 (0.821) 0.033 (0.846) 0.036 (0.923) 0.034 (0.872) 0.036 (0.923) 0.039 (1.000)

1.502 (0.804) 1.869 (1.000) 1.223 (0.654) 1.385 (0.741) 1.668 (0.893) 1.196 (0.640) 1.340 (0.717) 1.588 (0.850)

Genetic algorithms (Rutkovskaya, 2008, Wirsansky, 2020) are among the most common evolutionary computing methods, which, in comparison with deterministic methods, have a number of advantages in global optimization problems, including a significant reduction in computational time (number of cycles) and the absence of premature convergence (overcoming local extremes). Initially, an initial population is created (N=9, Table 1) from potential solutions (chromosomes) represented by a set of analyzed factors λ , α , f (genes) in the range given in Table 1. Next, the generalized criterion F (13) (fitness function) is calculated, after which the best (accepted N=4) of them are