Non-linear partial least squares response surface method for structural reliability analysis

An important challenge in structural reliability is to minimize the number of calls to the numerical models, so the current structural reliability analysis of multidimensional variable, the surrogate model with the uniform design are widely used because of fewest sample points used in the construction of the surrogate model. However, fewer points may lead to correlation exiting between the samples. The surrogate model, obtained by the original Least Squares (LS) regression using these samples, is not accurate, which leads to inaccuracies in the structural reliability analysis. To deal with the limitation of fitting the models in the original LS regression, an effective technique is introduced to the reliability analysis, and a new approach based on this technique has been proposed. The aim of this paper is to establish a new surrogate model based on the theory of Partial Least Squares (PLS) under the condition of multi-dimensional small samples data with correlation, to assess the reliability of structures in a more efficient way. The method is called the UD-BP-PLS surrogate model method, combining uniform design, non-linearity B-spline function and PLS technique. It is shown to be efficient as the probability of failure obtained by UD-BP-PLS surrogate model method is very accurate, which only needs a small number of calls to the performance function. Several examples from literature are used to illustrate the methodology and to prove its efficiency, particularly for problems dealing with high non-linearity and high dimensionality.