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Estimation for accumulated damage models via approximate Bayesian computation
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Estimation for accumulated damage models via approximate Bayesian computation


Download and compile the code:

git clone
cd abc-adm/src
make all



DOLmod_MCMC number_of_samples burning thining delta data

  • The data file name should be "something_tau_c_t_c(in years).csv", e.g., constLoad_4500_1Y.csv.
  • Output files: theta.csv containing m theta vectors and accept.csv containing the acceptance rate.


generate file_of_parameters output_filename number_of_samples tau_c t_c(in hours)

  • Output file: A csv file contain generated samples from the parameters; each column contains samples form one parameter


CanADM theta_file_name phi

  • This program will give the estimated probability of failure after 30 years based on a large number of replications with given load profile. It will read, from user, the parameter vectors thetas. The thetas will then be used to solve the Canadian ADM for time-to-failure T_f and probability of failure P_f. Tf and Pf per theta will be written into files with suffix “csv”. The output file names depend on phi. Set value of phi and number of thetas will be printed along with the simulation steps.
  • Output file: probability of failure with and without DOL


cd ../example
# simulate data using parameters in true_theta.csv 
# with constant load 4500 psi and test of duration 1Y (8760 hours)
../generate true_theta.csv simuConstLoad_4500_1Y.csv 300 4500 8760
# run the abc-mcmc algorithm to obtain 500 posterior samples
../DOLmod_MCMC 100 100 10 0.3 simuConstLoad_4500_1Y.csv
# simulate the time-to-failures given theta under the residential loads
../CanADM theta_0.3_csv 1  


There are some additional parameters in CanADM (solveCanODE.cpp) that can be modified:

  • mu: constant with units ‘time’ to ensure dimensional consistency.
  • k: standard ramp-loading rate.
  • T0: with Tc = 4500psi, T0 = Tc/k
  • n_per_theta: number of replications for each draw of theta. (could be modified for better approximation)
  • t_start: 0 as start of time.
  • t_end: hours in 30 years.(should be modified based on return period)
  • dt: step of time. (could be modified for better approximation)

The current load profile in CanADM is the residential load profile. Other load profiles can be added by creating a new class.

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