Which method can be used to optimize parameters of a model, to fit experimental data?
Concrete: Following parameters and calculation model:
P0 = 101325; Pr = 0.71; η = 1.838*10^-5; κ = 1.4; ρ0 = 1.19; c0 = (κ*P0/ρ0)^0.5; Z0 = ρ0*c0; f = Range[400, 10000]; ω = 2*Pi*f; d := 15*10^-3;
Adjustable parameters. Accuracy should be 0.01, except σ (0.1). Range/Boundary conditions are in brackets.
ϕ -> [0.5 - 1]; σ -> [5000, 140000]; α -> [1, 4]; λ -> [1*10^-6 , 1*10^-4]; λ' -> [1*10^-6 , 1*10^-4]; kop -> [1*10^-11 , 1*10^-9];
Calculation model with formulas:
H = (λ^2*σ^2*ϕ^2)/(4*α^2*η*ρ0); g = Sqrt[1 + (I*ω)/H]; nup = η/(Pr*ρ0); Mp = (8*kop)/(λ^2*ϕ); wtl = (nup*ϕ)/kop; gp = Sqrt[1 + (I*Mp*ω)/(2*wtl)]; Reff = α*(1 + (g*(σ*ϕ))/(I*α*ρ0*ω)); Keff = κ/(κ - (κ - 1)/(1 - (I*gp*wtl)/ω)); kw = ω*Sqrt[Reff/Keff]; Zc = Sqrt[Reff*Keff]; Zs = -I*Zc*Cot[kw*d]; r = (Zs - 1)/(Zs + 1); (*Target value a (absorption over frequency f *) a = 1 - Abs[r]^2;
I want to import data like this: (Must the frequency steps be the same as the setps of the range of defined variable
My target is now, to get the adjustable parameters for the best fit to a given plot/imported-data.
Please give concrete answers. Best would be a concrete solution inculdung an optimization model with implemented boundaries. Explanation or suggestions are also welcome.