High Order Moment Method For Reliability And Its Application

The moment method, based on the statistical moments of the response of stochastic systems. The reliability analysis based on moment method is to get the structure failure probability through the integral of the probability density function of performance function which can be obtained via the moments, determined by the distribution of the input random variables. Because the moment method is simple and easy to implement, it is widely applied to analyzing the reliability of structure without complex iterative calculation and partial derivative calculation. In this paper, researcher aims at how to calculate the statistical moment of functions and how to obtain the probability density function and calculation of reliability by statistical moment, and try to propose a more accurate and efficient method of reliability analysis based on the in-depth study of the existing analysis method.Firstly, the point estimation method is a simple and effective method in the calculation of statistical moments and is widely used. Precision and efficiency are two important indexes of evaluation the point estimation method and dimension reduction approximation provides a theoretical basis for the computational accuracy and efficiency. Currently, the adaptive estimation method based on multivariate dimension reduction approximation is accurate and efficient through introducing the delineation of the cross terms. However, the method above needs nonnormal to normal transformation which is nonlinear and may lead to the change of property for the function, because of this, the accuracy is reduced. The point estimation method based on the linear transformation of the reference variable just involving the linear transformation from the original variable to the reference variable, which makes is more accurate. Therefore, in this paper, an new the point estimation method combing the liner transformation method with the adaptive dimension reduction approximation method is proposed, taking into account the advantages of the two methods.Secondly, this paper introduces the some common method which is to fit the probability density function through the known information of statistical moment, such as Pearson system method, Saddle point approximation,Orthogonal polynomial method,The generalized Lambda distribution,The cubic normal distribution. And then via the simulation for the common distribution function which is used in engineering, the advantages and disadvantages of different methods for fitting the probability density function are analyzed. Furthermore, combined with developed based on the adaptive dimension approximate statistical moments and high order moment method and linear transformation, the probability density function fitting method is analyzed to compare the advantages and disadvantages when analyzing structure reality.Finally, for a practical engineering of a double column suspension cable tower structure, established the finite element model through general finite element software ANSYS, and calculated the statistical moments according to the proposed which combines the liner transformation method with the adaptive dimension reduction approximation, then fit the probability density function and calculate the reliability index according to the fourth-moment method based on the cubic normal transformation. Results indicates each element of the structure can meet the requirement of code for reliability index of primary structure component which fail bearing capacity.