Research on surrogate model based on local radial point interpolation method

In order to increase the accuracy of surrogate models in structural reliability analysis, we put forward a kind of surrogate model based on local radial point interpolation method (LRPIM). Three kinds of radial basis function (RBF) are employed for the shape function construction to form different kinds of LRPIM model. In order to illustrate the approximating ability of each surrogate model, we build up a nonlinear function model and carry out a numerical experiment on gas turbine disk's estimated life-span. Compared with polynomial model, Chebyshev orthogonal polynomial model, Kriging model and RBF neural network model, LRPIM model has a demonstrable difference in terms of accuracy. For different polynomial basis order with constant sampling nodes amount, we conclude that fluctuant accuracy can be described by the balance between the describing improvement brought by polynomial basis order increase and the local impairment brought by support domain expansion. For sampling nodes amount with constant polynomial basis order, we conclude that accuracy of LRPIM model improves when sampling nodes amount increases. In order to illustrate the potential in reliability analysis, we apply the best performing LRPIM model to a set of widely used test problems, which certifies the accuracy and robustness of this kind of surrogate model. In a word, LRPIM model is one of the most promising surrogate models compared with other models on nonlinear approximating problems and reliability analysis.