Bayesian neural network based probability density evolution approach for efficient structural reliability analysis

This study presents a unique proposal for the estimation of structural reliability using a Bayesian neural network (BNN)-based probability density evolution of the structural response. The advantage of this approach is that the probability space is decoupled from the physical space, which helps in reliability estimation for both static and dynamic cases. The problem is more prominent for dynamic systems where the traditional Fokker–Planck–Kolmogorov equation is coupled with the physical space, making it difficult to solve. Thus, a significant number of representative points are required for the numerical solution of the probability density function to achieve adequate accuracy, which is often computationally expensive for complex systems. This issue is addressed using a Bayesian neural network, which has an inherent ability to model aleatoric as well as epistemic uncertainty. To illustrate the proposed BNN-based probability density evaluation, six different problems are presented, which are a one-dimensional nonlinear oscillator, a Duffing oscillator, a composite beam, a portal frame, a planar truss, and a space truss. The first two examples are utilized to show the accuracy of the proposed method by comparing the results with the Fokker–Planck–Kolmogorov equation, the Euler–Maruyama-based solution, and Monte Carlo simulation. The numerical results of this study show that the proposed BNN-based probability density evaluation can predict the likelihood of failure using relatively few representative points without sacrificing accuracy, leading to a reduction in computational costs when compared to simulation or other traditional approaches. This approach is more generic for reliability estimation through a complete description of pdf as opposed to solving an optimization problem involving random variables.