From b1e82eb2c97daadecae5bf147cd514f3ee63aa8e Mon Sep 17 00:00:00 2001 From: "E. Cheynet" Date: Mon, 23 Mar 2020 09:53:53 +0100 Subject: [PATCH] Add files via upload --- Example.mlx | Bin 0 -> 84442 bytes fitKT.m | 148 ++++++++++++++++++++++++++++++++++++++++++++++++++++ seismSim.m | 85 ++++++++++++++++++++++++++++++ 3 files changed, 233 insertions(+) create mode 100644 Example.mlx create mode 100644 fitKT.m create mode 100644 seismSim.m diff --git a/Example.mlx b/Example.mlx new file mode 100644 index 0000000000000000000000000000000000000000..5a09b89fb22ef1f517f0f4daf2fd222a34bf68c4 GIT binary patch literal 84442 zcmV)bK&ih_O9KQH000080J}|hP&n;!#V-K>0F?s(022TJ09!+EZggdCbYE0?aAk8{ zE_iKhwUf(E!!Qsr4Yal+xwF;m&uts$;nOrLE9igL)T85lWZ*c{UC2`Z=x9CDb z2-avI&ZV}l`~uC6z&xVudQxRVI^zZ@?)FUS=izFSYNP{mtDTRV)P7lb&3O%&mtHqD zYre7DGozn)dC`>knN7GS)hQMb=@DwaQ$1GshC)O6kNT0*YacNSk*kpm9_K%GM1m3s zRNJ^1`hMsAv6oZZ#R%7W_n*GQTZ|7dNd7j-Gg^d%4{qhhXE_nQr%~NsHG2b4O9KQH z000080J}|hP+gbNFd_i}00{&D01E&B0AF%tY;!Lza%F6Dt&`tQ!Y~wvU#00i>o$<6 zp>UQlX%&jp6~bd&snVYZ9_iLx>_qvvm~VimC&+Q 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Termination tolerance on the estimated coefficients +% BETA. Defaults to 1e-8. +% 'dataPlot' - 'yes': shows the results of the fitting process +% +% OUTPUTS +% +% sigma: [1 x 1 ]: Fitted standard deviation of the excitation. +% fn: [1 x 1 ]: Fitted dominant frequency of the earthquake excitation (Hz). +% zeta: [1 x 1 ]: Fitted bandwidth of the earthquake excitation. +% f: [ 1 x M ]: Fitted frequency vector for the Kanai-tajimi spectrum. +% T90: [1 x 1 ]: Fitted value at 90 percent of the duration. +% eps: [1 x 1 ]: Fitted normalized duration time when ground motion achieves peak. +% tn: [1 x 1 ]: Fitted duration of ground motion. +% +% +% EXAMPLE: this requires the function seismSim.m +% +% f = linspace(0,40,2048); +% zeta = 0.3; +% sigma = 0.3; +% fn =5; +% eta = 0.3; +% eps = 0.4; +% tn = 30; +% [y,t] = seismSim(sigma,fn,zeta,f,eta,eps,tn); +% guessEnvelop=[0.33,0.43,50]; +% guessKT = [1,1,5]; +% [eta,eps,tn,zeta,sigma,fn] = fitKT(t,y,guessEnvelop,guessKT,... +% 'dataPlot','yes'); +% +% see also seismSim.m +% Author: Etienne Cheynet - modified: 23/04/2016 + +%% inputParser +p = inputParser(); +p.CaseSensitive = false; +p.addOptional('f3DB',0.05); +p.addOptional('tolX',1e-8); +p.addOptional('tolFun',1e-8); +p.addOptional('dataPlot','no'); +p.parse(varargin{:}); +tolX = p.Results.tolX ; +tolFun = p.Results.tolFun ; +f3DB = p.Results.f3DB ; +dataPlot = p.Results.dataPlot ; +% check number of input +narginchk(4,8) + +%% Get envelop parameters +dt = median(diff(t)); + +h1=fdesign.lowpass('N,F3dB',8,f3DB,1/dt); +d1 = design(h1,'butter'); +Y = filtfilt(d1.sosMatrix,d1.ScaleValues, abs(hilbert(y))); +Y = Y./max(abs(Y)); + +options=optimset('Display','off','TolX',tolX,'TolFun',tolFun); +coeff1 = lsqcurvefit(@(para,t) Envelop(para,t),guessEnvelop,t,Y,[0.01,0.01,0.1],[3,3,100],options); + +eps = coeff1(1); +T90 = coeff1(2); +tn = coeff1(3); + + + + + +%% Get stationnary perameters for the spectrum +E =Envelop(coeff1,t); +x = y./E; % there may be better solution than this one, but I don't have better idea right now. +x(1)=0; + +% calculate the PSD +[PSD,freq]=pmtm(x,7/2,numel(t),1/median(diff(t)));%% +coeff2 = lsqcurvefit(@(para,t) KT(para,freq),guessKT,freq,PSD,[0.01,0.01,1],[5,5,100],options); +zeta = coeff2(1); +sigma = coeff2(2); +fn = coeff2(3); + + + +%% dataPLot (optional) +if strcmpi(dataPlot,'yes'), + spectra = KT(coeff2,freq); + + figure + subplot(211) + plot(t,y./max(abs(y)),'k',t,Envelop(coeff1,t),'b',t,Y,'r') + legend('original data','Fitted envelop','measured envelop') + title([' T_{90} = ',num2str(coeff1(2),3),'; \epsilon = ',... + num2str(coeff1(1),3),'; t_{n} = ',num2str(coeff1(3),3)]); + xlabel('time (s)') + ylabel('ground acceleration (m/s^2)') + axis tight + + subplot(212) + plot(freq,PSD,'b',freq,spectra,'r') + legend('Measured','Fitted envelop') + legend('original data','Fitted Kanai-Tajimi spectrum') + title([' \zeta = ',num2str(coeff2(1),3),'; \sigma = ',... + num2str(coeff2(2),3),'; f_{n} = ',num2str(coeff2(3),3)]); + xlabel('freq (Hz)') + ylabel('Acceleration spectrum (m^2/s)') + axis tight + set(gcf,'color','w') +end + +% +%% NESTED FUNCTIONS +% + + function E = Envelop(para,t) + eps0 = para(1); + eta0 = para(2); + tn0 = para(3); + b = -eps0.*log(eta0)./(1+eps0.*(log(eta0)-1)); + c = b./eps0; + a = (exp(1)./eps0).^b; + E = a.*(t./tn0).^b.*exp(-c.*t./tn0); + end + function S = KT(para,freq) + zeta0 = para(1); + sigma0 = para(2); + omega0 = 2*pi.*para(3); + w =2*pi*freq; + s0 = 2*zeta0*sigma0.^2./(pi.*omega0.*(4*zeta0.^2+1)); + A = omega0.^4+(2*zeta0*omega0*w).^2; + B = (omega0.^2-w.^2).^2+(2*zeta0*omega0.*w).^2; + S = s0.*A./B; % single sided PSD + end +end + diff --git a/seismSim.m b/seismSim.m new file mode 100644 index 0000000..fcf4fed --- /dev/null +++ b/seismSim.m @@ -0,0 +1,85 @@ +function [y,t] = seismSim(sigma,fn,zeta,f,T90,eps,tn) +% [y,t] = seismSim(sigma,fn,zeta,f,T90,eps,tn) generate one time series +% corresponding to acceleration record from a seismometer. +% The function requires 7 inputs, and gives 2 outputs. The time series is +% generated in two steps: First, a stationary process is created based on +% the Kanai-Tajimi spectrum, then an envelope function is used to transform +% this stationary time series into a non-stationary record. For more +% information, see [1-3]. +% +% References +% +% [1] Lin, Y. K., & Yong, Y. (1987). Evolutionary Kanai-Tajimi earthquake models. Journal of engineering mechanics, 113(8), 1119-1137. +% [2] Rofooei, F. R., Mobarake, A., & Ahmadi, G. (2001). +% Generation of artificial earthquake records with a nonstationary +% Kanai-Tajimi model. Engineering Structures, 23(7), 827-837. +% [3] Guo, Y., & Kareem, A. (2016). +% System identification through nonstationary data using Time-requency Blind +% Source Separation. Journal of Sound and Vibration, 371, 110-131. +% +% +% INPUTS +% +% sigma: [1 x 1 ]: standard deviation of the excitation. +% fn: [1 x 1 ]: dominant frequency of the earthquake excitation (Hz). +% zeta: [1 x 1 ]: bandwidth of the earthquake excitation. +% f: [ 1 x M ]: frequency vector for the Kanai-tajimi spectrum. +% T90: [1 x 1 ]: value at 90 percent of the duration. +% eps: [1 x 1 ]: normalized duration time when ground motion achieves peak. +% tn: [1 x 1 ]: duration of ground motion. +% +% +% OUTPUTS +% +% y: size: [ 1 x N ] : Simulated aceleration record +% t: size: [ 1 x N ] : time +% +% +% EXAMPLE: +% +% f = linspace(0,40,2048); +% zeta = 0.3; +% sigma = 0.9; +% fn =5; +% T90 = 0.3; +% eps = 0.4; +% tn = 30; +% [y,t] = seismSim(sigma,fn,zeta,f,T90,eps,tn); +% figure +% plot(t,y);axis tight +% xlabel('time(s)'); +% ylabel('ground acceleration (m/s^2)') +% +% see also fitKT.m +% Author: Etienne Cheynet - modified: 23/04/2016 + +%% Initialisation +w = 2*pi.*f; +fs = f(end); dt = 1/fs; +f0= median(diff(f)); +Nfreq = numel(f); +t = 0:dt:dt*(Nfreq-1); + +%% Generation of the spectrum S +fn = fn *2*pi; % transformation in rad; +s0 = 2*zeta*sigma.^2./(pi.*fn.*(4*zeta.^2+1)); +A = fn.^4+(2*zeta*fn*w).^2; +B = (fn.^2-w.^2).^2+(2*zeta*fn.*w).^2; +S = s0.*A./B; % single sided PSD + + +%% Time series generation - Monte Carlo simulation +A = sqrt(2.*S.*f0); +B =cos(w'*t + 2*pi.*repmat(rand(Nfreq,1),[1,Nfreq])); +x = A*B; % stationary process + +%% Envelop function E +b = -eps.*log(T90)./(1+eps.*(log(T90)-1)); +c = b./eps; +a = (exp(1)./eps).^b; +E = a.*(t./tn).^b.*exp(-c.*t./tn); + +%% Envelop multiplied with stationary process to get y +y = x.*E; + +end \ No newline at end of file