Bayesian fatigue damage and reliability analysis using Laplace approximation and inverse reliability method

This paper presents an efficient analytical Bayesian method for reliability and system response estimate and update. The method includes additional data such as measurements to reduce estimation uncertainties. Laplace approximation is proposed to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability level. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A numerical example and a practical fatigue crack propagation problem with experimental data are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method is compared with simulation-based methods.