Hello

There is a simpler and easier solution to compute fragility curve.

You can use Excel to compute statistical functions.

Dear Pedram Omidian,

If you have a small program on Excel I will be very grateful if you can share it with me to get inspired in programming with MATLAB!

Hello

According to Backer research group, I think bellow website will be helpful.

https://web.stanford.edu/~bakerjw/fragility_old.html

You may use the SPF Creator, available within SeismoStruct, to create the required models for the fragility curve. It is really easy to use. You may then run multiple analysis with the Batch Facility, which is also available within SeismoStruct.

Fragility1.m

clear all

% Median Ground Acceleration

Agm = 0.75;

% Log Standard Deviation for Uncertainty

Bu = 0.38;

% Log Standard Deviation for Randomness

Br = 0.37;

% Combined Log Standard Deviation

Bc = sqrt(Bu^2 + Br^2);

% Ground Acceleration Range

Ag = 0:0.01:1.6;

figure;

% MC Simulation of fragility curves based on median randomness

for i = 1:200;

% Simulate median value for ground acceleration

Agms = lognrnd(log(Agm),Bu,1,1);

subplot(1,2,1);

plot([Agms Agms],[0 lognpdf(Agms,log(Agm),Bu)],'r');hold on

% Obtain probability of failure for simulated median value

subplot(1,2,2);

Pfs(i,:) = logncdf(Ag,log(Agms),Br);

% Plot simulated probability of failure

plot(Ag,Pfs(i,:),'r');hold on

end

subplot(1,2,1);

Mpdf = lognpdf(Ag,log(Agm),Bu);

plot(Ag,Mpdf,'k-','LineWidth',2);hold on;

xlabel('Median Peak Ground Acceleration A_g','FontSize',12)

ylabel('Probability Density Function','FontSize',12)

axis([0.1 1.6 0 2])

axis square

subplot(1,2,2);

% Plot Median, Mean (best estimate) and 5th/95th percentile Probability of

% Failure obtained from theory

Pfm = logncdf(Ag,log(Agm),Br);

Pfe = logncdf(Ag,log(Agm),Bc);

Pf95 = logncdf(Ag,log(Agm*exp(-norminv(0.95)*Bu)),Br);

Pf5 = logncdf(Ag,log(Agm*exp(-norminv(0.05)*Bu)),Br);

plot(Ag,Pfm,'k-','LineWidth',2);hold on;

plot(Ag,Pfe,'k-','LineWidth',2)

plot(Ag,Pf5,'k-','LineWidth',2)

plot(Ag,Pf95,'k-','LineWidth',2)

xlabel('Peak Ground Acceleration','FontSize',12)

ylabel('Conditional Frequency of Failure P_f','FontSize',12)

axis([0.1 1.6 0 1])

axis square

Fragility.m

clear all

% Median Ground Acceleration

Agm = 0.75;

% Log Standard Deviation for Uncertainty

Bu = 0.38;

% Log Standard Deviation for Randomness

Br = 0.37;

% Combined Log Standard Deviation

Bc = sqrt(Bu^2 + Br^2);

% Ground Acceleration Range

Ag = 0:0.01:1.6;

% Plot Median, Mean (best estimate) and 5th/95th percentile Probability of

% Failure obtained from theory

Pfm = logncdf(Ag,log(Agm),Br);

Pfe = logncdf(Ag,log(Agm),Bc);

Pf95 = logncdf(Ag,log(Agm*exp(-norminv(0.95)*Bu)),Br);

Pf5 = logncdf(Ag,log(Agm*exp(-norminv(0.05)*Bu)),Br);

figure

plot(Ag,Pfm,'--','LineWidth',2);hold on;

plot(Ag,Pfe,'r--','LineWidth',2)

plot(Ag,Pf5,'g--','LineWidth',2)

plot(Ag,Pf95,'k--','LineWidth',2)

xlabel('Peak Ground Acceleration','FontSize',12)

ylabel('Conditional Frequency of Failure (P_f)','FontSize',12)

axis([0 1.6 0 1])

% MC Simulation of fragility curves based on median randomness

for i = 1:1000;

% Simulate median value for ground acceleration

Agms = lognrnd(log(Agm),Bu,1,1);

% Obtain probability of failure for simulated median value

Pfs(i,:) = logncdf(Ag,log(Agms),Br);

% Plot simulated probability of failure

%plot(Ag,Pfs(i,:),'r');

end

% Plot mean, median and 5th/95th percentile fragility curve obtained from

% simulation

plot(Ag,median(Pfs),'-','LineWidth',1)

plot(Ag,mean(Pfs),'r-','LineWidth',1)

Pf5s = prctile(Pfs,5,1);

plot(Ag,Pf5s,'g-','LineWidth',1)

Pf95s = prctile(Pfs,95,1);

plot(Ag,Pf95s,'k-','LineWidth',1)

legend('Median','Mean','5^{th}','95^{th}','Median Sim','Mean Sim','5^{th} Sim','95^{th} Sim')