Re: Questions about de_min in octave

[denizyazgac]

EDIT
Please forget previous one

Sorry;
I try to make a back calculation with using Johnson Champoux Allard
mathematical model, which defines acoustic impedance behaviour of acoustic
foams. 
f,RRR,III vectors are measured data(frequency,real and imaginer parts) from
impedance tube (they are surface impedance), I try to obtain some critical
parameters like tortousity,char. viscous and thermal length from this data
with de_min function.

<http://octave.1599824.n4.nabble.com/file/t372543/back_calc_2.m>  


#back_calclation for porous samples 
clc
clear all
pkg load optim
gamma=1.401 # specific heat ratio 
P0=99700 #pressure
eta= 1.56E-5; #dynamic viscosity
B=0.707 # Prandtl number
fi=0.95 # porosity    
L=34.35/1000 #thickness
rho0=1.2 #air density
sigma=8197# air resistivity
c=340;# sound speed

f=[202.53
300.94
399.35
502.52
599.34
704.10
800.92
897.74
1002.50
1100.91
1204.09
1305.67
1404.09
1500.92
1604.09];

RRR=[0.731942065
0.701451715
0.641506283
0.596238299
0.580492187
0.535207505
0.504733852
0.48898774
0.473158139
0.457395329
0.471037507
0.469968842
0.468933572
0.497370082
0.496284719];

III=[-6.057454106
-4.070271408
-3.040378842
-2.422907504
-2.011571639
-1.688601017
-1.409863111
-1.219406958
-1.014356847
-0.868083316
-0.721893274
-0.590363981
-0.458884781
-0.312678041
-0.225364765];

w=2.*pi.*f(4); %f(4) can be change between f(1)....f(15) with length of f
vector.

#effective density
edn= @(x)  rho0.*x(1).*(1+ ( (fi.*sigma./(j.*w.*rho0.*x(1))).*sqrt(1+
(j.*(4.*w.*rho0.*eta.*(x(1).^2))./(sigma.^2.*fi.^2.*x(2).^2)))));
#effective bulk modulus
ebm= @(x) (gamma.*P0)./
(gamma-((gamma-1).*(1+(8.*eta./(j.*w.*B.*(x(3).^2).*rho0)).*sqrt(1+(j.*(w.*B.*rho0.*(x(3).^2))./(16.*eta)))).^(-1)));
#complex wave number
kwave= @(x) (w.*sqrt(edn(x)./ebm(x)));
#char impedance back_calc_2.m

ZC=@(x) sqrt(edn(x).*ebm(x));
#general function x(1) tortuosity,x(2) viscous characteristic length,x(3)
thermal characteristic length 
ZS=@(x) ((-j.*ZC(x).*cot(kwave(x).*L))./(fi.*rho0.*c));
optim=@(x) abs(RRR(4)+i.*III(4)-ZC(x));

ctl.XVmin = [1 0 0];
ctl.XVmax = [4 1 1];
# note to forumers: as a result of theory x(3)>x(2) but I can not define in
ctl structure
[x, obj_value, nfeval, convergence] = de_min (optim, ctl)





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