Narrow Results

Stochastic dynamic analysis of structures with random parameters continues to be an open question in the field of civil engineering. As a newly developed method, the probability density evolution method (PDEM) can provide the probability density function (PDF) of the dynamic responses of highly nonlinear structures. In this paper, a new method based on PDEM and the kriging surrogate model, named the K-PDEM, is proposed to study the stochastic response of a structure. Being an exact interpolation method, the Gaussian process regression or the so-called kriging method is capable of producing highly accurate results. Unlike the traditional PDEM numerical method whose numerical precision is strongly influenced by the number of representative points, the K-PDEM employs the kriging method at each instant to generate additional time histories. Then, the PDEM, which is capable of capturing the instantaneous PDF of a dynamic response and its evolution, is employed in nonlinear stochastic dynamic systems. Because of the decoupling properties of the K-PDEM, the numerical precision of the result is improved by the enrichment of the generalized density evolution equations without increasing the computation time. The result shows that the new method is capable of calculating the stochastic response of structures with efficiency and accuracy.

Point interpolation method based on radial basis function, or RPIM, has been successfully developed and applied in meshfree method. Recently, a new meshfree method is proposed based on the general moving Kriging method. In this paper, both the two methods are formulated in detail to construct their shape functions. It can be found that their shape functions are identical if the same basis function or semivariogram is adopted. Despite of this, the theorems used in Kriging may provide an alternative theoretical support for RPIM that is the simplest in formulation ensuring the minimum error of approximation.