Reliability calculation of time-consuming problems using a small-sample artificial neural network-based response surface method

An important step when designing and assessing the reliability of existing structures and/or structural elements is to calculate the reliability level described by failure probability or reliability index. Since calculating the structural response of complex systems such as bridges is usually a time-consuming task, the utilization of approximation methods with a view to reducing the computational effort to an acceptable level is an appropriate solution. The paper introduces a small-sample artificial neural network-based response surface method. An artificial neural network is used as an approximation (a so-called response surface) of the original limit state function. In order to be as effective as possible with respect to computational effort, a stratified Latin hypercube sampling simulation method is utilized to properly select training set elements. Subsequently, the artificial neural network-based response surface is utilized to calculate failure probability. To increase the accuracy of the determined failure probability, the response surface can be updated close to the failure region. This is performed by finding a new anchor point, which lies close to the design point of the limit state function. The new anchor point is then used to prepare the updated training set. The efficiency of the proposed method is tested for different training set sizes using a nonlinear limit state function taken from the literature, and the reliability assessment of three concrete bridges, one with explicit and two with implicit limit state functions in the form of finite element method models.