Математическое моделирование применительно к литейному производству. Черный А.А. - 20 стр.

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a
1r
= e
′
o
+ e
2n
⋅ x
2n
+ e
2r
⋅ x
2r
+ e
2s
⋅ x
2s
+ e
2w
⋅ x
2w
;
y = a
′
o
+ a
1n
⋅ x
1n
+ a
1r
⋅ x
1r
+ a
1s
⋅ x
1s
,
где a
′
o
= c
′
o
⋅ x
o
+ c
2n
⋅ x
2n
+ c
2r
⋅ x
2r
+ c
2s
⋅ x
2s
+ c
2w
⋅ x
2w
;
a
1n
= d
′
o
+ d
2n
⋅ x
2n
+ d
2r
⋅ x
2r
+ d
2s
⋅ x
2s
+ d
2w
⋅ x
2w
;
a
1r
= e
′
o
+ e
2n
⋅ x
2n
+ e
2r
⋅ x
2r
+ e
2s
⋅ x
2s
+ e
2w
⋅ x
2w
;
a
1s
= f
′
o
+ f
2n
⋅ x
2n
+ f
2r
⋅ x
2r
+ f
2s
⋅ x
2s
+ f
2w
⋅ x
2w
.
После подстановки, перемножений и замены коэффициентов
получаются следующие полиномы.
Для плана 5
2
(см. табл. 3):
y = b
′
o
⋅ x
o
+ b
1n
⋅ x
1n
+ b
2n
⋅ x
2n
+ b
1n,2n
⋅ x
1n
⋅ x
2n
+ b
1r
⋅ x
1r
+ b
2r
⋅
x
2r
+ b
1n,2r
⋅ x
1n
⋅ x
2r
+ b
2n,1r
⋅ x
2n
⋅ x
1r
+ b
2r,1r
⋅ x
1r
⋅ x
2r
+ b
1s
⋅ x
1s
+ b
2s
⋅ x
2s
+
b
2s,1n
⋅ x
1r
⋅ x
2s
+ b
2n,1s
⋅ x
2n
⋅ x
1s
+ b
2s,1r
⋅ x
2s
⋅ x
1r
+ b
2r,1s
⋅ x
2r
⋅ x
1s
+ b
2s,1s
⋅ x
2s
⋅
x
1s
+ b
1w
⋅ x
1w
+ b
2w
⋅ x
2w
+ b
2w,1n
⋅ x
2w
⋅ x
1n
+ b
2n,1w
⋅ x
2n
⋅ x
1w
+ b
2w,1r
⋅ x
2r
⋅
x
2w
+ b
2r,1w
⋅ x
2r
⋅ x
1w
+ b
2w,1s
⋅ x
2s
⋅ x
2w
+ b
2s1w
⋅ x
2s
⋅ x
1w
+ b
2w,1w
⋅ x
2w
⋅ x
1w
(13)
Для плана 4
2
(см. табл. 4):
y = b
′
o
⋅ x
o
+ b
1n
⋅ x
1n
+ b
2n
⋅ x
2n
+ b
1n,2n
⋅ x
1n
⋅ x
2n
+ b
1r
⋅ x
1r
+ b
2r
⋅
x
2r
+ b
1n,2r
⋅ x
1n
⋅ x
2r
+ b
2n,1r
⋅ x
2n
⋅ x
1r
+ b
2r,1r
⋅ x
1r
⋅ x
2r
+ b
1s
⋅ x
1s
+ b
2s
⋅ x
2s
+
b
1n,2s
⋅ x
1n
⋅ x
2s
+ b
2n,1s
⋅ x
2n
⋅ x
1s
+ b
2s,1r
⋅ x
2s
⋅ x
1r
+ b
2r,1s
⋅ x
2r
⋅ x
1s
+ b
2s,1s
⋅
x
2s
⋅ x
1s
(13)
Для плана 3
2
(см. табл. 3);
y = b
′
o
⋅ x
o
+ b
1n
⋅ x
1n
+ b
2n
⋅ x
2n
+ b
1n,2n
⋅ x
1n
⋅ x
2n
+ b
1r
⋅ x
1r
+ b
2r
⋅
x
2r
+ b
1n,2r
⋅ x
1n
⋅ x
2r
+ b
2n,1r
⋅ x
2n
⋅ x
1r
+ b
2r,1r
⋅ x
1r
⋅ x
2r
(14)
Для плана 3 ⋅ 4 (табл. 5);
y = b
′
o
⋅ x
o
+ b
1n
⋅ x
1n
+ b
2n
⋅ x
2n
+ b
1n,2n
⋅ x
1n
⋅ x
2n
+ b
1r
⋅ x
1r
+ b
2r
⋅
x
2r
+ b
1n,2r
⋅ x
1n
⋅ x
2r
+ b
2n,1r
⋅ x
2n
⋅ x
1r
+ b
2r,1r
⋅ x
1r
⋅ x
2r
+ b
2s
⋅ x
2s
+ b
2s,1n
⋅ x
1n
⋅ x
2s
+ b
2s,1r
⋅ x
1r
⋅ x
2s
(15)
Для плана 3 ⋅ 5 (см. табл. 6);
y = b
′
o
⋅ x
o
+ b
1n
⋅ x
1n
+ b
2n
⋅ x
2n
+ b
1n,2n
⋅ x
1n
⋅ x
2n
+ b
1r
⋅ x
1r
+ b
2r
⋅
x
2r
+ b
1n,2r
⋅ x
1n
⋅ x
2r
+ b
2n,1r
⋅ x
2n
⋅ x
1r
+ b
2r,1r
⋅ x
1r
⋅ x
2r
+ b
2s
⋅ x
2s
+ b
2s,1n
⋅ x
1n
⋅ x
2s
+ b
2s,1r
⋅ x
1r
⋅ x
2s
+ b
2w
⋅ x
2w
+ b
2w,1n
⋅ x
1n
⋅ x
2w
+ b
2w,1r
⋅ x
1r
⋅ x
2w
(16)
Для плана 4 ⋅ 5 (см. табл. 7) ;
y = b
′
o
⋅ x
o
+ b
1n
⋅ x
1n
+ b
2n
⋅ x
2n
+ b
1n,2n
⋅ x
1n
⋅ x
2n
+ b
1r
⋅ x
1r
+ b
2r
⋅
x
2r
+ b
1n,2r
⋅ x
1n
⋅ x
2r
+ b
2n,1r
⋅ x
2n
⋅ x
1r
+ b
2r,1r
⋅ x
1r
⋅ x
2r
+ b
1s
⋅ x
1s
+ b
2s,1n
⋅ x
1n
⋅ x
2s
+ b
1s,2n
⋅ x
2n
⋅ x
1s
+ b
1r,2s
⋅ x
1r
⋅ x
2s
+ b
2r,1s
⋅ x
2r
⋅ x
1s
+ b
2s1s
⋅ x
2s
⋅ x
1s
+
b
2w
⋅ x
2w
+ b
2w,1n
⋅ x
1n
⋅ x
2w
+ b
2w,1r
⋅ x
1r
⋅ x
2w
+ b
2w,1s
⋅ x
1s
⋅ x
2w
(17)
В уравнениях регрессии (12) - (17) y - показатель (параметр)
процесса;
x
o
= + 1; x
1n
=x
n
1
+ v
1
;
x
1r
= x
r
1
+ a
1
⋅ x
n
1
+ c
1
; x
1s
= x
s
1
+ d
1
⋅ x
r
1
+ e
1
⋅ x
n
1
+ f
1
; 
             a1r = e′o + e2n ⋅ x2n + e2r ⋅ x2r + e2s ⋅ x2s + e2w ⋅ x2w ;
             y = a′o + a1n ⋅ x1n + a1r ⋅ x1r + a1s ⋅ x1s ,
                  где a′o = c′o ⋅ xo + c2n ⋅ x2n + c2r ⋅ x2r + c2s ⋅ x2s + c2w ⋅ x2w ;
                a1n = d′o + d2n ⋅ x2n + d2r ⋅ x2r + d2s ⋅ x2s + d2w ⋅ x2w ;
             a1r = e′o + e2n ⋅ x2n + e2r ⋅ x2r + e2s ⋅ x2s + e2w ⋅ x2w ;
             a1s = f′o + f2n ⋅ x2n + f2r ⋅ x2r + f2s ⋅ x2s + f2w ⋅ x2w .
         После подстановки, перемножений и замены коэффициентов
получаются следующие полиномы.
         Для плана 52 (см. табл. 3):
             y = b′o ⋅ xo + b1n ⋅ x1n + b2n ⋅ x2n + b1n,2n ⋅ x1n ⋅ x2n + b1r ⋅ x1r + b2r ⋅
x2r + b1n,2r ⋅ x1n ⋅ x2r + b2n,1r ⋅ x2n ⋅ x1r + b2r,1r ⋅ x1r ⋅ x2r + b1s ⋅ x1s + b2s ⋅ x2s +
b2s,1n ⋅ x1r ⋅ x2s + b2n,1s ⋅ x2n ⋅ x1s + b2s,1r ⋅ x2s⋅ x1r + b2r,1s ⋅ x2r⋅ x1s + b2s,1s ⋅ x2s⋅
x1s + b1w ⋅ x1w + b2w ⋅ x2w + b2w,1n ⋅ x2w⋅ x1n + b2n,1w ⋅ x2n⋅ x1w + b2w,1r ⋅ x2r⋅
x2w + b2r,1w ⋅ x2r⋅ x1w + b2w,1s ⋅ x2s ⋅ x2w + b2s1w ⋅ x2s ⋅ x1w + b2w,1w ⋅ x2w ⋅ x1w
(13)
         Для плана 42 (см. табл. 4):
             y = b′o ⋅ xo + b1n ⋅ x1n + b2n ⋅ x2n + b1n,2n ⋅ x1n ⋅ x2n + b1r ⋅ x1r + b2r ⋅
x2r + b1n,2r ⋅ x1n ⋅ x2r + b2n,1r ⋅ x2n ⋅ x1r + b2r,1r ⋅ x1r ⋅ x2r + b1s ⋅ x1s + b2s ⋅ x2s +
b1n,2s ⋅ x1n ⋅ x2s + b2n,1s ⋅ x2n ⋅ x1s + b2s,1r ⋅ x2s⋅ x1r + b2r,1s ⋅ x2r⋅ x1s + b2s,1s ⋅
x2s ⋅ x1s                                                                            (13)
                         2
         Для плана 3 (см. табл. 3);
             y = b′o ⋅ xo + b1n ⋅ x1n + b2n ⋅ x2n + b1n,2n ⋅ x1n ⋅ x2n + b1r ⋅ x1r + b2r ⋅
x2r + b1n,2r ⋅ x1n ⋅ x2r + b2n,1r ⋅ x2n ⋅ x1r + b2r,1r ⋅ x1r ⋅ x2r                  (14)
         Для плана 3 ⋅ 4 (табл. 5);
             y = b′o ⋅ xo + b1n ⋅ x1n + b2n ⋅ x2n + b1n,2n ⋅ x1n ⋅ x2n + b1r ⋅ x1r + b2r ⋅
x2r + b1n,2r ⋅ x1n ⋅ x2r + b2n,1r ⋅ x2n ⋅ x1r + b2r,1r ⋅ x1r ⋅ x2r + b2s ⋅ x2s + b2s,1n ⋅ x1n
⋅ x2s + b2s,1r ⋅ x1r ⋅ x2s                                                            (15)
         Для плана 3 ⋅ 5 (см. табл. 6);
             y = b′o ⋅ xo + b1n ⋅ x1n + b2n ⋅ x2n + b1n,2n ⋅ x1n ⋅ x2n + b1r ⋅ x1r + b2r ⋅
x2r + b1n,2r ⋅ x1n ⋅ x2r + b2n,1r ⋅ x2n ⋅ x1r + b2r,1r ⋅ x1r ⋅ x2r + b2s ⋅ x2s + b2s,1n ⋅ x1n
⋅ x2s + b2s,1r ⋅ x1r ⋅ x2s + b2w ⋅ x2w + b2w,1n ⋅ x1n ⋅ x2w + b2w,1r ⋅ x1r ⋅ x2w (16)
         Для плана 4 ⋅ 5 (см. табл. 7) ;
             y = b′o ⋅ xo + b1n ⋅ x1n + b2n ⋅ x2n + b1n,2n ⋅ x1n ⋅ x2n + b1r ⋅ x1r + b2r ⋅
x2r + b1n,2r ⋅ x1n ⋅ x2r + b2n,1r ⋅ x2n ⋅ x1r + b2r,1r ⋅ x1r ⋅ x2r + b1s ⋅ x1s + b2s,1n ⋅ x1n
⋅ x2s + b1s,2n ⋅ x2n ⋅ x1s + b1r,2s ⋅ x1r ⋅ x2s + b2r,1s ⋅ x2r ⋅ x1s + b2s1s ⋅ x2s ⋅ x1s +
b2w ⋅ x2w + b2w,1n ⋅ x1n ⋅ x2w + b2w,1r ⋅ x1r ⋅ x2w + b2w,1s ⋅ x1s ⋅ x2w
(17)
         В уравнениях регрессии (12) - (17) y - показатель (параметр)
процесса;
             xo = + 1; x1n =xn1 + v1 ;
             x1r = xr1 + a1⋅ xn1 + c1; x1s = xs1 + d1⋅ xr1 + e1⋅ xn1 + f1;

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