Structural reliability updating using experimental data

Conventional reliability analysis requires the information from an existing structure, such as a mechanical model and random distributed inputs. In many engineering problems, a state monitoring system commonly provides experimental or monitoring data, which can be used to update the initial estimation for structural reliability to reduce prediction uncertainty. A critical issue in this process is the manner in which the existing information and new data can be reasonably integrated into a reliability estimation. In this paper, Bayesian updating approach is applied to incorporate the additional data. Firstly, a theoretical model is established to predict the prior distribution of the limit state function (LSF) with the first-order reliability method. Then, the Bayesian inference theory is applied to update the probability distribution parameters of LSF using the acquired experimental or monitoring data. The analytical form of the LSF's posterior distribution is derived under the assumption that the experimental test error follows a normal distribution. To improve accuracy, a second-order reliability method is proposed based on the theory of saddlepoint approximation. Markov chain Monte Carlo simulation is used to derive a general method for updating the LSF's distribution using the experimental or monitoring data. Finally, three numerical examples are provided to illustrate the proposed framework's validity.