Wenyi Du

This work presents a robust non-deterministic free vibration analysis for engineering structures with random field parameters in the frame of stochastic finite element method. For this, considering the randomness and spatial correlation of structural physical parameters, a parameter setting model based on random field theory is proposed to represent the random uncertainty of parameters, and the stochastic dynamic characteristics of different structural systems are then analyzed by incorporating the presented parameter setting model with finite element method. First, Gauss random field theory is used to describe the uncertainty of structural material parameters, the random parameters are then characterized as the standard deviation and correlation length of the random field, and the random field parameters are then discretized with the Karhunen–Loeve expansion method. Moreover, based on the discretized random parameters and finite element method, structural dynamic characteristics analysis is addressed, and the probability distribution density function of the random natural frequency is estimated based on multi-dimensional kernel density estimation method. Finally, the random field parameters of the structures are quantified by using the maximum likelihood estimation method to verify the effectiveness of the proposed method and the applicability of the constructed model. The results indicate that (1) for the perspective of maximum likelihood estimation, the parameter setting at the maximum value point is highly similar to the input parameters; (2) the random field considering more parameters reflects a more realistic structure.

Structural reliability analysis has an inherent contradiction between efficiency and accuracy. The metamodel can significantly reduce the computational cost of reliability analysis by a simpler approximation. Therefore, it is crucial to build a metamodel, which achieves the minimum simulations and accurate estimation for reliability analysis. Aiming at this, an effective adaptive metamodel based on the combination of radial basis function (RBF) model and Monte Carlo simulation (MCS) is proposed. Different shape parameters are first used to generate the weighted prediction variance, and the search for new training samples is guided by the active learning function that achieves a tradeoff of (1) being close enough to limit state function (LSF) to have a high reliability sensitivity; (2) keeping enough distance between the existing samples to avoid a clustering problem; and (3) being in the sensitive region to ensure the effectiveness of the information obtained. The performance of the proposed method for a nonlinear, non-convex, and high dimensional reliability analysis is validated by three numerical cases. The results indicate the high efficiency and accuracy of the proposed method.

Fatigue analysis is of great significance for thin-walled structures in the spacecraft industry to ensure their service reliability during operation. Due to the complex loadings of thin-walled structures under thermal–structural–acoustic coupling conditions, the calculation cost of finite element (FE) simulations is relatively expensive. To improve the computational efficiency of dynamic reliability analysis on thin-walled structures to within acceptable accuracy, a novel probabilistic approach named DC-ILSSVR was developed, in which the rotation matrix optimization (RMO) method was used to initially search for the model parameters of least squares support vector regression (LS-SVR). The distributed collaborative (DC) strategy was then introduced to enhance the efficiency of a component suffering from multiple failure modes. Moreover, a numerical example with respect to thin-walled structures was used to validate the proposed method. The results showed that RMO performed on LS-SVR model parameters provided competitive prediction accuracy, and hence the reliability analysis efficiency of thin-walled pipe was significantly improved.