Research On Structural Reliability Analysis Based On Radial Basis Function

An important problem in metamodel-based structural reliability analysis is how to reduce the computation time. The objective of this dissertation is to develop the efficient and accurate reliability analysis techniques to support metamodel-based reliability analysis. Therefore, there are basically four tasks to be carried out:First, the first-order reliability method (FORM) is one of the most widely used structural reliability analysis techniques due to its simplicity and efficiency. However, direct using FORM seems disability to work well for complex problems, especially related to high-dimensional variables and computation intensive numerical models. To expand the applicability of the FORM for more practical engineering problems, a response surface approach based FORM is proposed for structural reliability analysis. The radial basis function (RBF) is employed to approximate the implicit limit-state functions combined with Latin Hypercube Sampling strategy. To guarantee the numerical stability, the improved HL-RF (zHL-RF) algorithm is used to assess the reliability index and corresponding probability of failure based on the constructed response surfac model.Second, the performance measure approach (PMA) is widely adopted for reliability analysis and reliability-based design optimization because of its robustness and efficiency compared to reliability analysis approach. However, it has been reported that PMA involves repeat evaluations of probabilistic constraints therefore it is prohibitively expensive for many large-scale applications. In order to overcome these disadvantages, this study proposes an efficient PMA-based reliability analysis technique using radial basis function. The RBF is adopted to approximate the implicit limit state functions in combination with Latin Hypercube Sampling strategy. The advanced mean value method is applied to obtain the most probable point with the prescribed target reliability and corresponding probabilistic performance measure to improve analysis accuracy. A sequential framework is proposed to relocate the sampling center to the obtained most probable point and reconstruct RBF until a criteria is satisfied.Third, the Monte Carlo method and the finite element method for the structural reliability analysis lead often to a prohibitive computational cost. In the reliability estimation of complex structures, a response surface based on RBF has been suggested as a way to estimate the implicit limit state function. However, the parameters and basis functions of the RBF effects to the structural reliability analysis results but, there is no guidance how to select appropriate values for the parameters and basis functions. Therefore, this study researches effect of parameters and basis functions on RIA-based structural reliability estimates using the radial basis functions such as Gaussian, Multi-Quadric, Inverse Multi-Quadric, Thin Plate Spline, Cubic and Linear. The RBFs is adopted to approximate the limit state functions in combination with Latin Hypercube Sampling strategy. The HL-RF algorithm is applied to obtain the reliability index and probability of failure based on the constructed response surface model.Fourth, the response surface method is a powerful structural reliability method using the values of the function at specific points that approximates the limit state function with a polynomial expression. The analytical function replaces the exact limit state function which the computational time required for the assessment of the reliability of structural systems can be reduced significantly. However, the location of the sample points has been investigated by several authors and the performance of the response surface method is still under discussion. Therefore, this study proposes a new response surface method for sensitivity estimation of parameters in structural reliability analysis. A first order polynomial without cross terms is adopted to approximate the limit-state function, and the sensitivity vector of the limit state function can be obtained. An experimental design with4n+1sampling points includes2n+l sampling points are chosen along the coordinate axes of the U-space of standard normal random variables and2n sampling points is rotated according to the sensitivity vector of the limit state function is built. A quadratic polynomial is adopted to approximate the limit-state function, and the most probable point can be obtained by conducting HL-RF algorithm based on the created response surface.