A comparison of approximate response functions in structural reliability analysis

In order to reduce computational costs in structural reliability analysis, it has been suggested to utilize approximate response functions for reliability assessment. One well-established class of methods to deal with suitable approximations is the Response Surface Method. The basic idea in utilizing the response surface method is to replace the true limit state function by an approximation, the so-called response surface, whose function values can be computed more easily. The functions are typically chosen to be first- or second-order polynomials. Higher-order polynomials on the one hand tend to show severe oscillations, and on the other hand they require too many support points. This may be overcome by applying smoothing techniques such as the moving least-squares method. An alternative approach is given by Artificial Neural Networks. In this approach, the input and output parameters are related by means of relatively simple yet flexible functions, such as linear, step, or sigmoid functions which are combined by adjustable weights. The main feature of this approach lies in the possibility of adapting the input–output relations very efficiently. A further possibility lies in the utilization of radial basis functions. This method also allows for a flexible adjustment of the interpolation scheme. In all approaches as presented it is essential to achieve high quality of approximation primarily in the region of the random variable space which contributes most significantly to the probability of failure. The paper presents an overview of these approximation methods and demonstrates their potential by application to several examples of nonlinear structural analysis.