INTERPRETACION DE DATOS EN EL MODELO CROWLEY- KITZES

Tabla de datos:T= 160 C

%

0.53779.196.34.010.11

13539.2411.87.50.21

23489.262314.620.42

33449.2634.521.940.64

3.53367.8539.324.990.74

43306.7944.128.040.85

53275.354.434.721.06

63234.3164.741.141.27

73175.973.746.861.48

83096.8482.652.521.7

93099.3591.558.181.91

102993.1699.963.592.12

I. Graficas:

II. Ajuste al modelo CROWLEY-KITZES:

Modelo de Crowley Kitzes:

Parmetros:

Cambiando las variables:

El modelo resulta:

Sea los valores estimados por el modelo:

La funcin objetivo est dada por:

Reemplazando:

Derivando para cada uno de los parmetros:

Programa en Polymath:f(AL) =2*(Y1-((X1*(1.2-AL*((1+((C*X1)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X1)^0.2))^3)))))*(((X1*((1+((C*X1)^0.2))^3))/(MU*(1.2+AL*((1+((C*X1)^0.2))^3))))+(((X1*(1.2-AL*((1+((C*X1)^0.2))^3)))*((1+((C*X1)^0.2))^3))/(MU*((1.2+AL*((1+((C*X1)^0.2))^3))^2))))+2*(Y2-((X2*(1.2-AL*((1+((C*X2)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X2)^0.2))^3)))))*(((X2*((1+((C*X2)^0.2))^3))/(MU*(1.2+AL*((1+((C*X2)^0.2))^3))))+(((X2*(1.2-AL*((1+((C*X2)^0.2))^3)))*((1+((C*X2)^0.2))^3))/(MU*((1.2+AL*((1+((C*X2)^0.2))^3))^2))))+2*(Y3-((X3*(1.2-AL*((1+((C*X3)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X3)^0.2))^3)))))*(((X3*((1+((C*X3)^0.2))^3))/(MU*(1.2+AL*((1+((C*X3)^0.2))^3))))+(((X3*(1.2-AL*((1+((C*X3)^0.2))^3)))*((1+((C*X3)^0.2))^3))/(MU*((1.2+AL*((1+((C*X3)^0.2))^3))^2))))+2*(Y4-((X4*(1.2-AL*((1+((C*X4)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X4)^0.2))^3)))))*(((X4*((1+((C*X4)^0.2))^3))/(MU*(1.2+AL*((1+((C*X4)^0.2))^3))))+(((X4*(1.2-AL*((1+((C*X4)^0.2))^3)))*((1+((C*X4)^0.2))^3))/(MU*((1.2+AL*((1+((C*X4)^0.2))^3))^2))))+2*(Y5-((X5*(1.2-AL*((1+((C*X5)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X5)^0.2))^3)))))*(((X5*((1+((C*X5)^0.2))^3))/(MU*(1.2+AL*((1+((C*X5)^0.2))^3))))+(((X5*(1.2-AL*((1+((C*X5)^0.2))^3)))*((1+((C*X5)^0.2))^3))/(MU*((1.2+AL*((1+((C*X5)^0.2))^3))^2))))+2*(Y6-((X6*(1.2-AL*((1+((C*X6)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X6)^0.2))^3)))))*(((X6*((1+((C*X6)^0.2))^3))/(MU*(1.2+AL*((1+((C*X6)^0.2))^3))))+(((X6*(1.2-AL*((1+((C*X6)^0.2))^3)))*((1+((C*X6)^0.2))^3))/(MU*((1.2+AL*((1+((C*X6)^0.2))^3))^2))))+2*(Y7-((X7*(1.2-AL*((1+((C*X7)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X7)^0.2))^3)))))*(((X7*((1+((C*X7)^0.2))^3))/(MU*(1.2+AL*((1+((C*X7)^0.2))^3))))+(((X7*(1.2-AL*((1+((C*X7)^0.2))^3)))*((1+((C*X7)^0.2))^3))/(MU*((1.2+AL*((1+((C*X7)^0.2))^3))^2))))+2*(Y8-((X8*(1.2-AL*((1+((C*X8)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X8)^0.2))^3)))))*(((X8*((1+((C*X8)^0.2))^3))/(MU*(1.2+AL*((1+((C*X8)^0.2))^3))))+(((X8*(1.2-AL*((1+((C*X8)^0.2))^3)))*((1+((C*X8)^0.2))^3))/(MU*((1.2+AL*((1+((C*X8)^0.2))^3))^2))))+2*(Y9-((X9*(1.2-AL*((1+((C*X9)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X9)^0.2))^3)))))*(((X9*((1+((C*X9)^0.2))^3))/(MU*(1.2+AL*((1+((C*X9)^0.2))^3))))+(((X9*(1.2-AL*((1+((C*X9)^0.2))^3)))*((1+((C*X9)^0.2))^3))/(MU*((1.2+AL*((1+((C*X9)^0.2))^3))^2))))+2*(Y10-((X10*(1.2-AL*((1+((C*X10)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X10)^0.2))^3)))))*(((X10*((1+((C*X10)^0.2))^3))/(MU*(1.2+AL*((1+((C*X10)^0.2))^3))))+(((X10*(1.2-AL*((1+((C*X10)^0.2))^3)))*((1+((C*X10)^0.2))^3))/(MU*((1.2+AL*((1+((C*X10)^0.2))^3))^2))))+2*(Y11-((X11*(1.2-AL*((1+((C*X11)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X11)^0.2))^3)))))*(((X11*((1+((C*X11)^0.2))^3))/(MU*(1.2+AL*((1+((C*X11)^0.2))^3))))+(((X11*(1.2-AL*((1+((C*X11)^0.2))^3)))*((1+((C*X11)^0.2))^3))/(MU*((1.2+AL*((1+((C*X11)^0.2))^3))^2))))+2*(Y12-((X12*(1.2-AL*((1+((C*X12)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X12)^0.2))^3)))))*(((X12*((1+((C*X12)^0.2))^3))/(MU*(1.2+AL*((1+((C*X12)^0.2))^3))))+(((X12*(1.2-AL*((1+((C*X12)^0.2))^3)))*((1+((C*X12)^0.2))^3))/(MU*((1.2+AL*((1+((C*X12)^0.2))^3))^2))))

f(C) =2*(Y1-((X1*(1.2-AL*((1+((C*X1)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X1)^0.2))^3)))))*(((0.6*(X1^(2))*AL*((1+((C*X1)^0.2))^2))/MU*((C*X1)^(0.8))*(1.2+AL*((1+((C*X1)^0.2))^3))))+((0.6*(X1^(2))*(1.2-AL*((1+((C*X1)^0.2))^3))*AL*((1+((C*X1)^0.2))^2))/(MU*((1.2+AL*((1+((C*X1)^0.2))^3))^2)*((C*X1)^(0.8))))+2*(Y2-((X2*(1.2-AL*((1+((C*X2)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X2)^0.2))^3)))))*(((0.6*(X2^(2))*AL*((1+((C*X2)^0.2))^2))/MU*((C*X2)^(0.8))*(1.2+AL*((1+((C*X2)^0.2))^3))))+((0.6*(X2^(2))*(1.2-AL*((1+((C*X2)^0.2))^3))*AL*((1+((C*X2)^0.2))^2))/(MU*((1.2+AL*((1+((C*X2)^0.2))^3))^2)*((C*X2)^(0.8))))+2*(Y3-((X3*(1.2-AL*((1+((C*X3)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X3)^0.2))^3)))))*(((0.6*(X3^(2))*AL*((1+((C*X3)^0.2))^2))/MU*((C*X3)^(0.8))*(1.2+AL*((1+((C*X3)^0.2))^3))))+((0.6*(X3^(2))*(1.2-AL*((1+((C*X3)^0.2))^3))*AL*((1+((C*X3)^0.2))^2))/(MU*((1.2+AL*((1+((C*X3)^0.2))^3))^2)*((C*X3)^(0.8))))+2*(Y4-((X4*(1.2-AL*((1+((C*X4)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X4)^0.2))^3)))))*(((0.6*(X4^(2))*AL*((1+((C*X4)^0.2))^2))/MU*((C*X4)^(0.8))*(1.2+AL*((1+((C*X4)^0.2))^3))))+((0.6*(X4^(2))*(1.2-AL*((1+((C*X4)^0.2))^3))*AL*((1+((C*X4)^0.2))^2))/(MU*((1.2+AL*((1+((C*X4)^0.2))^3))^2)*((C*X4)^(0.8))))+2*(Y5-((X5*(1.2-AL*((1+((C*X5)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X5)^0.2))^3)))))*(((0.6*(X5^(2))*AL*((1+((C*X5)^0.2))^2))/MU*((C*X5)^(0.8))*(1.2+AL*((1+((C*X5)^0.2))^3))))+((0.6*(X5^(2))*(1.2-AL*((1+((C*X5)^0.2))^3))*AL*((1+((C*X5)^0.2))^2))/(MU*((1.2+AL*((1+((C*X5)^0.2))^3))^2)*((C*X5)^(0.8))))+2*(Y6-((X6*(1.2-AL*((1+((C*X6)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X6)^0.2))^3)))))*(((0.6*(X6^(2))*AL*((1+((C*X6)^0.2))^2))/MU*((C*X6)^(0.8))*(1.2+AL*((1+((C*X6)^0.2))^3))))+((0.6*(X6^(2))*(1.2-AL*((1+((C*X6)^0.2))^3))*AL*((1+((C*X6)^0.2))^2))/(MU*((1.2+AL*((1+((C*X6)^0.2))^3))^2)*((C*X6)^(0.8))))+2*(Y7-((X7*(1.2-AL*((1+((C*X7)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X7)^0.2))^3)))))*(((0.6*(X7^(2))*AL*((1+((C*X7)^0.2))^2))/MU*((C*X7)^(0.8))*(1.2+AL*((1+((C*X7)^0.2))^3))))+((0.6*(X7^(2))*(1.2-AL*((1+((C*X7)^0.2))^3))*AL*((1+((C*X7)^0.2))^2))/(MU*((1.2+AL*((1+((C*X7)^0.2))^3))^2)*((C*X7)^(0.8))))+2*(Y8-((X8*(1.2-AL*((1+((C*X8)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X8)^0.2))^3)))))*(((0.6*(X8^(2))*AL*((1+((C*X8)^0.2))^2))/MU*((C*X8)^(0.8))*(1.2+AL*((1+((C*X8)^0.2))^3))))+((0.6*(X8^(2))*(1.2-AL*((1+((C*X8)^0.2))^3))*AL*((1+((C*X8)^0.2))^2))/(MU*((1.2+AL*((1+((C*X8)^0.2))^3))^2)*((C*X8)^(0.8))))+2*(Y9-((X9*(1.2-AL*((1+((C*X9)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X9)^0.2))^3)))))*(((0.6*(X9^(2))*AL*((1+((C*X9)^0.2))^2))/MU*((C*X9)^(0.8))*(1.2+AL*((1+((C*X9)^0.2))^3))))+((0.6*(X9^(2))*(1.2-AL*((1+((C*X9)^0.2))^3))*AL*((1+((C*X9)^0.2))^2))/(MU*((1.2+AL*((1+((C*X9)^0.2))^3))^2)*((C*X9)^(0.8))))+2*(Y10-((X10*(1.2-AL*((1+((C*X10)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X10)^0.2))^3)))))*(((0.6*(X10^(2))*AL*((1+((C*X10)^0.2))^2))/MU*((C*X10)^(0.8))*(1.2+AL*((1+((C*X10)^0.2))^3))))+((0.6*(X10^(2))*(1.2-AL*((1+((C*X10)^0.2))^3))*AL*((1+((C*X10)^0.2))^2))/(MU*((1.2+AL*((1+((C*X10)^0.2))^3))^2)*((C*X10)^(0.8))))+2*(Y11-((X11*(1.2-AL*((1+((C*X11)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X11)^0.2))^3)))))*(((0.6*(X11^(2))*AL*((1+((C*X11)^0.2))^2))/MU*((C*X11)^(0.8))*(1.2+AL*((1+((C*X11)^0.2))^3))))+((0.6*(X11^(2))*(1.2-AL*((1+((C*X11)^0.2))^3))*AL*((1+((C*X11)^0.2))^2))/(MU*((1.2+AL*((1+((C*X11)^0.2))^3))^2)*((C*X11)^(0.8))))+2*(Y12-((X12*(1.2-AL*((1+((C*X12)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X12)^0.2))^3)))))*(((0.6*(X12^(2))*AL*((1+((C*X12)^0.2))^2))/MU*((C*X12)^(0.8))*(1.2+AL*((1+((C*X12)^0.2))^3))))+((0.6*(X12^(2))*(1.2-AL*((1+((C*X12)^0.2))^3))*AL*((1+((C*X12)^0.2))^2))/(MU*((1.2+AL*((1+((C*X12)^0.2))^3))^2)*((C*X12)^(0.8))))

f(MU) =2*(Y1-((X1*(1.2-AL*((1+((C*X1)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X1)^0.2))^3)))))*((X1*(1.2-AL*((1+((C*X1)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X1)^0.2))^3))))+2*(Y2-((X2*(1.2-AL*((1+((C*X2)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X2)^0.2))^3)))))*((X2*(1.2-AL*((1+((C*X2)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X2)^0.2))^3))))+2*(Y3-((X3*(1.2-AL*((1+((C*X3)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X3)^0.2))^3)))))*((X3*(1.2-AL*((1+((C*X3)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X3)^0.2))^3))))+2*(Y4-((X4*(1.2-AL*((1+((C*X4)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X4)^0.2))^3)))))*((X4*(1.2-AL*((1+((C*X4)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X4)^0.2))^3))))+2*(Y5-((X5*(1.2-AL*((1+((C*X5)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X5)^0.2))^3)))))*((X5*(1.2-AL*((1+((C*X5)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X5)^0.2))^3))))+2*(Y6-((X6*(1.2-AL*((1+((C*X6)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X6)^0.2))^3)))))*((X6*(1.2-AL*((1+((C*X6)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X6)^0.2))^3))))+2*(Y7-((X7*(1.2-AL*((1+((C*X7)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X7)^0.2))^3)))))*((X7*(1.2-AL*((1+((C*X7)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X7)^0.2))^3))))+2*(Y8-((X8*(1.2-AL*((1+((C*X8)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X8)^0.2))^3)))))*((X8*(1.2-AL*((1+((C*X8)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X8)^0.2))^3))))+2*(Y9-((X9*(1.2-AL*((1+((C*X9)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X9)^0.2))^3)))))*((X9*(1.2-AL*((1+((C*X9)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X9)^0.2))^3))))+2*(Y10-((X10*(1.2-AL*((1+((C*X10)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X10)^0.2))^3)))))*((X10*(1.2-AL*((1+((C*X10)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X10)^0.2))^3))))+2*(Y11-((X11*(1.2-AL*((1+((C*X11)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X11)^0.2))^3)))))*((X11*(1.2-AL*((1+((C*X11)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X11)^0.2))^3))))+2*(Y12-((X12*(1.2-AL*((1+((C*X12)^0.2))^3)))/(MU*(1.2+AL*((1+((C*X12)^0.2))^3)))))*((X12*(1.2-AL*((1+((C*X12)^0.2))^3)))/((MU^(2))*(1.2+AL*((1+((C*X12)^0.2))^3))))

MU(0) = 2800AL(0) = 0.5C(0) = 1.5X1 = 4.01X2 = 7.5X3 = 14.62X4 = 21.94X5 = 24.99X6 = 28.04X7 = 34.72X8 = 41.14X9 = 46.86X10 = 52.52X11 = 58.18X12 = 63.59Y1 = 0.11Y2 = 0.21Y3 = 0.42Y4 = 0.64Y5 = 0.74Y6 = 0.85Y7 = 1.06Y8 = 1.27Y9 = 1.48Y10 = 1.7Y11 = 1.91Y12 = 2.12

Observacin:Las soluciones del sistema de ecuaciones no lineales no convergen.