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Aung

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1 years, 203 days
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least square curve fitting ...

Aung 60 Maple 2023
fitting regression optimization
September 07 2024
0 7

can someone help me curve fitting these parameeters...i only got 1 for all of this 90As4.mw

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restart
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with(Statistics)with(plots)with(Optimization)with(LinearAlgebra)
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E[1] := 126*10^9E[2] := 11*10^9G[12] := 6.6*10^9G_0__12 := 10.1*10^9nu[12] := .28E_0__2 := 15.5*10^9
> 

true_strain := [0, .406915, .710106, .989362, 1.28457, 1.53989, 1.86702, 2.21011, 2.625, 2.99202]; true_stress := [0, 46.0227*10^6, 81.8182*10^6, 109.091*10^6, 138.068*10^6, 163.636*10^6, 194.318*10^6, 219.886*10^6, 248.864*10^6, 267.614*10^6]; epsilon_dot := 10^(-4)
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sigma_t := map(proc (epsilon) options operator, arrow; E[instantaneous]*(1-lambda[90*deg]*epsilon*(sum(P[i], i = 1 .. 10)-(sum(P[i]*exp(lambda[i]*epsilon/epsilon_dot), i = 1 .. 10)))/epsilon_dot)*epsilon end proc, true_strain)
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``
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obj := sum((sigma_t[i]-true_stress[i])^2, i = 1 .. 10)
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indets(obj, name)

{E[instantaneous], P[1], P[2], P[3], P[4], P[5], P[6], P[7], P[8], P[9], P[10], lambda[1], lambda[2], lambda[3], lambda[4], lambda[5], lambda[6], lambda[7], lambda[8], lambda[9], lambda[10], lambda[90*deg]}

 (1)
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Optimization[Interactive](obj)

The solution was obtained with the following warning:
  no iterations performed as initial point satisfies first-order conditions

  

[Float(infinity), [E[instantaneous] = HFloat(1.0), P[1] = HFloat(1.0), P[2] = HFloat(1.0), P[3] = HFloat(1.0), P[4] = HFloat(1.0), P[5] = HFloat(1.0), P[6] = HFloat(1.0), P[7] = HFloat(1.0), P[8] = HFloat(1.0), P[9] = HFloat(1.0), P[10] = HFloat(1.0), lambda[1] = HFloat(1.0), lambda[2] = HFloat(1.0), lambda[3] = HFloat(1.0), lambda[4] = HFloat(1.0), lambda[5] = HFloat(1.0), lambda[6] = HFloat(1.0), lambda[7] = HFloat(1.0), lambda[8] = HFloat(1.0), lambda[9] = HFloat(1.0), lambda[10] = HFloat(1.0), lambda[90*deg] = HFloat(1.0)]]

 (2)
 

NULL

Download 90As4.mw

partial dervative of function ?...

Aung 60 Maple
differentiation
June 16 2024
1 5

using diff command to find  partial dervative of function g give zero in maple...it shouldn't be zero...how to fix itpartial_dervative.mw

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restart:
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sigma_t:= map(epsilon-> E_0[90]*epsilon_dot*((epsilon/epsilon_dot)-(sum(p[i], i = 1 .. 3)*(epsilon/epsilon_dot))+(sum(p[i]*tau[i],i=1..3))-(sum(p[i]*tau[i]*exp(-(epsilon/(epsilon_dot*tau[i]))),i=1..3))),true_strain):
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 g:= sum(( sigma[j]-sigma_t[j])^2,j=1..10):
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diff(g,p[1]);

0

 (1)
 

 

Download partial_dervative.mw

what kind of algothrim does maple used t...

Aung 60 Maple
least-squares optimization statistics
June 16 2024
1 0

if i want to solve non linear least square problem ..maple optimazation Interactive box show ..many option...but when it comes to least square default....what kind of algothrim does it used....and in maple ..NonLinear fit commad use what kind of algothrim?..Levenberg-Marquardt algorithm?

how to solve this integration using inte...

Aung 60 Maple 2023
integration sum int
May 31 2024
1 2

how to solve this using integration by parts?

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restart:
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with(IntegrationTools):
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``
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eq1:=int(1-(sum(p[i]*(1-exp(-((t-xi)/tau[i]))),i=1..n)),xi=0..t);

int(1-(sum(p[i]*(1-exp(-(t-xi)/tau[i])), i = 1 .. n)), xi = 0 .. t)

 (1)


Download 1111.mw

linear gression to get weibull parameter...

Aung 60 Maple 2023
parameters regression statistics
May 29 2024
2 1

weibull_damage.mw
i have weibull plot...and i want to get size and shpae parametr...how can i get ...parameters .i don't know how to perform linear regression to get these parameters in maple..please help

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