Integral Length Scales using the autocorrelation Function

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Mirian Cae
Mirian Cae 2021-11-23
I found these two methods to compute the Integral Length Scales using the autocorrelation Function. But both gave me very different results. I'm not sure about what is appening in the trapzoid function, if anyone can explain it to me or know what is the right approach is I would appreciate it.
u_HW = U_inst-mean(U_inst);
[Ruu_simm, TM_simm] = xcorr(u_HW,'coeff');
TM_simm = TM_simm./Fs;
Ruu = Ruu_simm(TM_simm>=0 & TM_simm<=0.5);
TM = TM_simm(TM_simm>=0 & TM_simm<=0.5);
fitresult_corr = fit(TM.',Ruu.','gauss8');
TM_fit = TM_simm(floor(length(TM_simm)/2)-100:end);
Ruu_fit = fitresult_corr(TM_fit);
TM_fit = TM_fit(Ruu_fit<=1);
Ruu_fit = Ruu_fit(Ruu_fit<=1);
Lags_t_domain = TM_fit(Ruu_fit >= 1e-5);
ACF_fit_domain = Ruu_fit(Ruu_fit >= 1e-5);
1-approach
Int_LS_AC = trapz(TM_fit,Ruu_fit);
2-approach
LS = trapz(TM(Ruu>=0),Ruu(Ruu>=0))+abs(trapz(TM(Ruu<0),Ruu(Ruu<0)));

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