Математическое моделирование применительно к литейному производству. Черный А.А. - 4 стр.

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В матрице планирования экспериментов (табл.1):
x
mna
= x
n
ma +
v
m
; x
mnb
= x
n
mb
+ v
m
;
x
mnc
= x
n
mc
+ v
m
; x
mnd
= x
n
md
+ v
m
;
x
mne
= x
n
me
+ v
m
; x
mra
= x
r
ma
+ a
m
· x
n
ma
+ c
m
;
x
mrb
= x
r
mb
+ a
m
· x
n
mb
+ c
m
; x
mrc
= x
r
mc
+ a
m
· x
n
mc
+ c
m
;
x
mrd
= x
r
md
+ a
m
· x
n
md
+ c
m
; x
mre
= x
r
me
+ a
m
· x
n
me
+ c
m
;
x
msa
= x
s
ma
+ d
m
· x
r
ma
+ e
m
⋅ x
n
ma
+ f
m ;
x
msb
= x
s
mb
+ d
m
· x
r
mb
+ e
m
⋅ x
n
mb
+ f
m
;
x
msc
= x
s
mc
+ d
m
· x
r
mc
+ e
m
⋅ x
n
mc
+ f
m
;
x
msd
= x
s
md
+ d
m
· x
r
md
+ e
m
⋅ x
n
md
+ f
m
;
x
mse
= x
s
me
+ d
m
· x
r
me
+ e
m
⋅ x
n
me
+ f
m
;
x
mwa
= x
w
ma
+ g
m
· x
s
ma
+ h
m
⋅ x
r
ma
+ k
m
⋅ x
n
ma
+ l
m
;
x
mwb
= x
w
mb
+ g
m
· x
s
mb
+ h
m
⋅ x
r
mb
+ k
m
⋅ x
n
mb
+ l
m
;
x
mwc
= x
w
mc
+ g
m
· x
s
mc
+ h
m
⋅ x
r
mc
+ k
m
⋅ x
n
mc
+ l
m
;
x
mwd
= x
w
md
+ g
m
· x
s
md
+ h
m
⋅ x
r
md
+ k
m
⋅ x
n
md
+ l
m
;
x
mwe
= x
w
me
+ g
m
· x
s
me
+ h
m
⋅ x
r
me
+ k
m
⋅ x
n
me
+ l
m
.
Для сокращения дальнейших записей введены следующие
обозначения средних арифметических величин:
(
)
n
me
n
md
n
mc
n
mb
n
ma
n
m
xxxxx
N
x ++++=
1
;
()
r
me
r
md
r
mc
r
mb
r
ma
r
m
xxxxx
N
x ++++=
1
;
()
s
me
s
md
s
mc
s
mb
s
ma
s
m
xxxxx
N
x ++++=
1
;
()
w
me
w
md
w
mc
w
mb
w
ma
w
m
xxxxx
N
x ++++=
1
;
()
n
me
n
md
n
mc
n
mb
n
ma
n
m
xxxxx
N
x
222222
1
++++=
;
()
r
me
r
md
r
mc
r
mb
r
ma
r
m
xxxxx
N
x
222222
1
++++=
;
()
s
me
s
md
s
mc
s
mb
s
ma
s
m
xxxxx
N
x
222222
1
++++=
;
()
rn
me
rn
md
rn
mc
rn
mb
rn
ma
rn
m
xxxxx
N
x
++++++
++++=
1
; 
       В матрице планирования экспериментов (табл.1):
xmna = xnma + vm ;          xmnb = xnmb + vm ;
xmnc = xnmc + vm ;                              xmnd = xnmd + vm;
xmne = xnme + vm ;                               xmra = xrma + am· xnma + cm;
xmrb = xrmb + am· xnmb + cm ;      xmrc = xrmc + am· xnmc + cm;
xmrd = xrmd + am· xnmd + cm;        xmre = xrme + am· xnme + cm;
xmsa = xsma + dm· xrma + em ⋅ xnma + fm ;
xmsb = xsmb + dm· xrmb + em ⋅ xnmb + fm;
xmsc = xsmc + dm· xrmc + em ⋅ xnmc + fm;
xmsd = xsmd + dm· xrmd + em ⋅ xnmd + fm;
xmse = xsme + dm· xrme + em ⋅ xnme + fm;
xmwa = xwma + gm· xsma + hm ⋅ xrma + km⋅ xnma + lm;
xmwb = xwmb + gm· xsmb + hm ⋅ xrmb + km⋅ xnmb + lm;
xmwc = xwmc + gm· xsmc + hm ⋅ xrmc + km⋅ xnmc + lm;
xmwd = xwmd + gm· xsmd + hm ⋅ xrmd + km⋅ xnmd + lm;
xmwe = xwme + gm· xsme + hm ⋅ xrme + km⋅ xnme + lm.
       Для сокращения дальнейших записей введены следующие
обозначения средних арифметических величин:

                        x mn =
                                    1 n
                                    N
                                            (  n
                                      x ma + x mb     n
                                                  + x mc     n
                                                         + x md     n
                                                                + x me ;        )
                     x mr =
                               1 r
                               N
                                    (     r
                                 x ma + x mb     r
                                             + x mc     r
                                                    + x md     r
                                                           + x me ;     )
                      x ms =
                               1 s
                               N
                                        ( s
                                 x ma + x mb     s
                                             + x mc     s
                                                    + x md     s
                                                           + x me ;         )
                     x mw =
                             1 w
                             N
                                    (    w
                                x ma + x mb       w
                                              + x mc      w
                                                      + x md      w
                                                              + x me  ;)
                    x m2 n =
                             N
                              1 2n
                                    (     2n
                                 x ma + x mb      2n
                                              + x mc       2n
                                                       + x md      2n
                                                               + x me  ;)
                    x m2 r =
                             1 2r
                             N
                                    (     2r
                                 x ma + x mb      2r
                                              + x mc       2r
                                                      + x md       2r
                                                               + x me  ;)
                    x m2 s =
                             1 2s
                             N
                                    (     2s
                                 x ma + x mb      2s
                                              + x mc       2s
                                                      + x md       2s
                                                               + x me  ;)
                x mn+ r =
                            N
                                (
                            1 n+ r       n+ r
                               x ma + x mb        n+ r
                                              + x mc        n+ r
                                                        + x md       n+r
                                                                 + x me  ;      )

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