Математическое моделирование при планировании экспериментов на трех уровнях факторов. Черный А.А. - 16 стр.

UptoLike

ВУЗ: 

ПГУ | Пенза

Составители: 

Рубрика: 

16
мо друг от друга. Для уравнения (12), соответствующего плану 3
3
(см.табл.3), расчет коэффициентов регрессии производится по сле-
дующим формулам:
;
N
y
x
yx
b
N
u
u
N
u
u,o
u
N
u
u,o
'
∑
∑
∑
=
=
=
=
⋅
=
1
1
2
1
0
;
x
yx
b
N
u
u,n
u
N
u
u,n
n
∑
∑
=
=
⋅
=
1
2
1
1
1
1
;
x
yx
b
N
u
u,n
u
N
u
u,n
n
∑
∑
=
=
⋅
=
1
2
2
1
2
2
;
x
yx
b
N
u
u,n
u
N
u
u,n
n
∑
∑
=
=
⋅
=
1
2
3
1
3
3
;
)xx(
yxx
b
N
u
u,nu,n
uu,n
N
u
u,n
n,n
∑
∑
=
=
⋅
⋅⋅
=
1
2
21
2
1
1
21
;
)xx(
yxx
b
N
u
u,nu,n
uu,n
N
u
u,n
n,n
∑
∑
=
=
⋅
⋅⋅
=
1
2
31
3
1
1
31
;
)(
,
,
,,
,
∑
∑
=
=
⋅
⋅⋅
=
N
u
un
un
uun
N
u
un
nn
xx
yxx
b
1
2
3
2
3
1
2
32
;
)xxx(
yxxx
b
N
u
u,nu,nu,n
uu,nu,n
N
u
u,n
n,n,n
∑
∑
=
=
⋅⋅
⋅⋅⋅
=
1
2
321
32
1
1
321
;
x
yx
b
N
u
u,r
u
N
u
u,r
r
∑
∑
=
=
⋅
=
1
2
1
1
1
1
;
x
yx
b
N
u
u,r
u
N
u
u,r
r
∑
∑
=
=
⋅
=
1
2
2
1
2
2
;
x
yx
b
N
u
u,r
u
N
u
u,r
r
∑
∑
=
=
⋅
=
1
2
3
1
3
3
;
)xx(
yxx
b
N
u
u,ru,n
u
N
u
u,ru,n
r,n
∑
∑
=
=
⋅
⋅⋅
=
1
2
21
1
21
21
;
)xx(
yxx
b
N
u
u,ru,n
u
N
u
u,ru,n
r,n
∑
∑
=
=
⋅
⋅⋅
=
1
2
31
1
31
31
;
)xx(
yxx
b
N
u
u,ru,n
u
N
u
u,ru,n
r,n
∑
∑
=
=
⋅
⋅⋅
=
1
2
12
1
12
12
мо друг от друга. Для уравнения (12), соответствующего плану 33
(см.табл.3), расчет коэффициентов регрессии производится по сле-
дующим формулам:


                           N                                N                        N
                        ∑ xo ,u ⋅ yu                    ∑ yu                      ∑ x1n ,u ⋅ yu
                        u =1                            u =1                      u =1
          b0'    =              N
                                                    =                ; b1n =              N
                                                                                                             ;
                                                                N
                               ∑      xo2,u                                              ∑      x12n ,u
                               u =1                                                      u =1


                            N                                                        N
                           ∑ x 2 n ,u ⋅ yu                                        ∑ x3n ,u ⋅ yu
                           u =1                                                   u =1
          b2 n =                  N
                                                        ;                b3n =            N
                                                                                                             ;
                                 ∑       x 22n ,u                                        ∑        x32n ,u
                                u =1                                                     u =1


                       N                                                                      N
                    ∑ x1n ,u ⋅ x2n ,u ⋅ yu                                                 ∑ x1n ,u ⋅ x3n ,u ⋅ yu
                    u =1                                                                   u =1
     b1n ,2 n =      N
                                                                ;           b1n ,3n =       N
                                                                                                                         ;
                     ∑ ( x1n ,u ⋅ x2 n ,u )                 2
                                                                                           ∑ ( x1n ,u ⋅ x3n ,u )     2

                     u =1                                                                  u =1
                        N                                                                 N
                        ∑ x2n,u ⋅ x3n,u ⋅ yu                                             ∑ x1n ,u ⋅ x2 n ,u ⋅ x3n ,u ⋅ yu
                        u =1                                                             u =1
     b2n,3n =             N
                                                                    ; b1n ,2 n ,3n =      N
                                                                                                                                 ;
                        ∑ ( x2n,u ⋅ x3n,u )                     2
                                                                                          ∑ ( x1n ,u ⋅ x2 n ,u ⋅ x3n ,u )    2

                        u =1                                                              u =1
             N                                                                           N
             ∑ x1r ,u ⋅ yu                                                           ∑ x2r ,u ⋅ yu
             u =1                                                                    u =1
     b1r =          N
                                            ;                               b2 r =            N
                                                                                                                 ;
                 ∑         x12r ,u                                                         ∑       x22r ,u
                 u =1                                                                      u =1


                N                                                                             N
                ∑ x3r ,u ⋅ yu                                                              ∑ x1n ,u ⋅ x2r ,u ⋅ yu
                u =1                                                                       u =1
     b3r =             N
                                                ;                           b1n ,2 r =      N
                                                                                                                         ;
                    ∑          x32r ,u                                                     ∑ ( x1n ,u ⋅ x2r ,u )     2

                    u =1                                                                   u =1
                     N                                                                     N
                    ∑ x1n ,u ⋅ x3r ,u ⋅ yu                                                 ∑ x2 n ,u ⋅ x1r ,u ⋅ yu
                    u =1                                                                   u =1
     b1n ,3r =       N
                                                                ;           b2 n ,1r =      N
                                                                                                                         ;
                    ∑ ( x1n ,u ⋅ x3r ,u )                   2
                                                                                           ∑ ( x2 n ,u ⋅ x1r ,u )    2

                    u =1                                                                   u =1




                                                                       16

Страницы