Теория и практика эффективного математического моделирования. Черный А.А. - 31 стр.

       y = b0′ ⋅ x0 + b1n ⋅ x1n + b2 n ⋅ x2 n + b1n , 2 n ⋅ x1n ⋅ x2 n + b3n ⋅ x3n + b1n ,3n ⋅ x1n ⋅ x3n + b2 n ,3n ⋅ x2 n ⋅ x3n +
       + b1n , 2 n ,3n ⋅ x1n ⋅ x2 n ⋅ x3n ,
для плана 24 (табл. 13):
     y = b0′ ⋅ x0 + b1n ⋅ x1n + b2 n ⋅ x2 n + b1n , 2 n ⋅ x1n ⋅ x2 n + b3n ⋅ x3n + b1n ,3n ⋅ x1n ⋅ x3n + b2 n ,3n ⋅ x2 n ⋅ x3n +
    + b1n , 2 n ,3n ⋅ x1n ⋅ x2 n ⋅ x3n + b4 n ⋅ x4 n + b1n , 4 n ⋅ x1n ⋅ x4 n + b2 n , 4 n ⋅ x2 n ⋅ x4 n + b1n , 2 n , 4 n ⋅ x1n ⋅ x2 n ⋅ x4 n +
    + b3n , 4 n ⋅ x3n ⋅ x4 n + b1n ,3n , 4 n ⋅ x1n ⋅ x3n ⋅ x4 n + b2 n ,3n , 4 n ⋅ x2 n ⋅ x3n ⋅ x4 n + b1n , 2 n ,3n , 4 n ⋅ x1n ⋅ x2 n ⋅ x3n ⋅ x4 n ,
для плана 25 (табл. 14):
y = b0′ ⋅ x0 + b1n ⋅ x1n + b2 n ⋅ x2 n + b1n , 2 n ⋅ x1n ⋅ x2 n + b3n ⋅ x3n + b1n ,3n ⋅ x1n ⋅ x3n + b2 n ,3n ⋅ x2 n ⋅ x3n +
+ b1n , 2 n ,3n ⋅ x1n ⋅ x2 n ⋅ x3n + b4 n ⋅ x4 n + b1n , 4 n ⋅ x1n ⋅ x4 n + b2 n , 4 n ⋅ x2 n ⋅ x4 n + b1n , 2 n , 4 n ⋅ x1n ⋅ x2 n ⋅ x4 n +
+ b3n , 4 n ⋅ x3n ⋅ x4 n + b1n ,3n , 4 n ⋅ x1n ⋅ x3n ⋅ x4 n + b2 n ,3n , 4 n ⋅ x2 n ⋅ x3n ⋅ x4 n + b1n , 2 n ,3n , 4 n ⋅ x1n ⋅ x2 n ⋅ x3n ⋅ x4 n +
+ b5 n ⋅ x5 n + b1n ,5 n ⋅ x1n ⋅ x5 n + b2 n ,5 n ⋅ x2 n ⋅ x5 n + b1n , 2 n ,5 n ⋅ x1n ⋅ x2 n ⋅ x5 n + b3n ,5 n ⋅ x3n ⋅ x5 n +
+ b1n ,3n ,5 n ⋅ x1n ⋅ x3n ⋅ x5 n + b2 n ,3n ,5 n ⋅ x2 n ⋅ x3n ⋅ x5 n + b1n , 2 n ,3n ,5 n ⋅ x1n ⋅ x2 n ⋅ x3n ⋅ x5 n + b4 n ,5 n ⋅ x4 n ⋅ x5 n +
+ b1n , 4 n ,5 n ⋅ x1n ⋅ x4 n ⋅ x5 n + b2 n , 4 n ,5 n ⋅ x2 n ⋅ x4 n ⋅ x5 n + b1n , 2 n , 4 n ,5 n ⋅ x1n ⋅ x2 n ⋅ x4 n ⋅ x5 n +
+ b3n , 4 n ,5 n ⋅ x3n ⋅ x4 n ⋅ x5 n + b1n ,3n , 4 n ,5 n ⋅ x1n ⋅ x3n ⋅ x4 n ⋅ x5 n + b2 n ,3n , 4 n ,5 n ⋅ x2 n ⋅ x3n ⋅ x4 n ⋅ x5 n +
+ b1n , 2 n ,3n , 4 n ,5 n ⋅ x1n ⋅ x2 n ⋅ x3n ⋅ x4 n ⋅ x5 n ,
в которых у – показатель (параметр) процесса;
x0 = +1 ; x1n = x1n + v1 ; x2 n = x2n + v2 ; x3n = x3n + v3 ; x4 n = x4n + v4 ; x5 n = x5n + v5 ;
х1, х2. х3. х4, х5 – 1, 2, 3, 4, 5-й факторы (независимые переменные);
n – изменяемое число показателя степени каждого фактора (n может рав-
няться единице, быть больше или меньше 1);
v1, v2. v3. v4, v5 – коэффициенты ортогонализации, определяемые при двух
уровнях каждого m-го фактора по формуле (15).
        Так как планирование ортогональное, то все коэффициенты регрес-
сии и дисперсии в их определении рассчитываются независимо друг от
друга.
         Следующими, более сложным математическим моделированием
может быть моделирование на основе планирования экспериментов на
трех уровнях факторов.
        При планировании экспериментов на трех уровнях независимых пе-
ременных предложено универсальное уравнение регрессии, в общем виде
представляющее трехчлен
        y= b′о⋅хо+bmn⋅xmn+bmr⋅xmr;                                                        (18)
        в котором y – показатель (параметр) процесса; хо= +1;
                            хmn = xnm+vm;               xmr=xrm+am··xnm+cm;
         m – порядковый номер фактора; xm-m –й фактор (независимое пе-
ременное);n, r, – изменяемые числа показателей степени факторов; vm, am,
cm – коэффициенты ортогонализации; b′o, bmn, bmr – коэффициенты регрес-
сии.




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