Neural network approach to model the limit state surface for reliability analysis

Abstract

Structural reliability methods are often used to evaluate the failure performance of geotechnical structures. A common approach is to use the first-order reliability method. Its popularity results from the mathematical simplicity of the method, since only second moment information (mean and coefficient of variation) on the random variables is required. The probability of failure is then assessed by an index known commonly as the reliability index. One critical aspect in determining the reliability index is the explicit definition of the limit state surface of the system. In a problem involving multi-dimensional random variables, the limit state surface is the boundary separating the safe domain from the "failure" (or lack of serviceability) domain. In many complicated and nonlinear problems where the analyses involve the use of numerical procedures such as the finite element method, this surface may be difficult to determine explicitly in terms of the random variables, and therefore the limit state can only be expressed implicitly rather than in a closed-form solution. It is proposed in this paper to use an artificial intelligence technique known as the back-propagation neural network algorithm to model the limit state surface. First, the failure domain is found through repeated point-by-point numerical analyses with different input values. The neural network is then trained on this set of data. Using the optimal weights of the neural network connections, it is possible to develop a mathematical expression relating the input and output variables that approximates the limit state surface. Some examples are given to illustrate the application and accuracy of the proposed approach.Key words: first-order reliability method, geotechnical structures, limit state surface, neural networks, reliability.