In the structural reliability analysis,the first-order reliability method(FORM)often yields significant errors when addressing nonlinear problems.Although the second-order reliability method(SORM)can provide higher ac...In the structural reliability analysis,the first-order reliability method(FORM)often yields significant errors when addressing nonlinear problems.Although the second-order reliability method(SORM)can provide higher accuracy,the additional computation of the Hessian matrix leads to lower computational efficiency.Additionally,when the dimensionality of the random variables is high,the approximation formula of SORM can result in larger errors.To address these issues,a structural reliability analysis method based on Kriging and spherical cap area integral is proposed.Firstly,this method integrates FORM with the quasi-Newton algorithm Broyden-Fletcher-Goldfarb-Shanno(BFGS),trains the Kriging model by using sample points from the algorithm’s iteration process,and combines the Kriging model with gradient information to approximate the Hessian matrix.Then,the failure surface is approximated as a rotating paraboloid,utilizing the spherical cap to replace the complex surface.For the n-dimensional case,the hyperspherical cap area expression is combined with the integral method to calculate the failure probability.Finally,the method is validated through three examples,demonstrating improved computational accuracy and efficiency compared to traditional methods.展开更多
In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
The study of marine data visualization is of great value. Marine data, due to its large scale, random variation and multiresolution in nature, are hard to be visualized and analyzed. Nowadays, constructing an ocean mo...The study of marine data visualization is of great value. Marine data, due to its large scale, random variation and multiresolution in nature, are hard to be visualized and analyzed. Nowadays, constructing an ocean model and visualizing model results have become some of the most important research topics of ‘Digital Ocean'. In this paper, a spherical ray casting method is developed to improve the traditional ray-casting algorithm and to make efficient use of GPUs. Aiming at the ocean current data, a 3D view-dependent line integral convolution method is used, in which the spatial frequency is adapted according to the distance from a camera. The study is based on a 3D virtual reality and visualization engine, namely the VV-Ocean. Some interactive operations are also provided to highlight the interesting structures and the characteristics of volumetric data. Finally, the marine data gathered in the East China Sea are displayed and analyzed. The results show that the method meets the requirements of real-time and interactive rendering.展开更多
he Rectangular Top Horn Offset Coaxial Transmission line (RTHOCT) is an expanded structure inwhich the spherical wave is guided. It is applied to manufacture a test cell called GTEM CELL in a broad band-width. In this...he Rectangular Top Horn Offset Coaxial Transmission line (RTHOCT) is an expanded structure inwhich the spherical wave is guided. It is applied to manufacture a test cell called GTEM CELL in a broad band-width. In this paper, we give the propagation constant of the first six higher order modes by the basic characteris-tics of the spherical Bessel functions of the third kind. The potential distribution of the sphere-TEM mode is alsocomputed ty boundary integral equation and multi-local expansion method. We find, in the far zone away fromthe top point of RTHOCT the propagation constant of all higher order modes is the same as that of the sphere-TEM mode.展开更多
基金National Natural Science Foundation of China(No.52375236)Fundamental Research Funds for the Central Universities,China(No.23D110316)。
文摘In the structural reliability analysis,the first-order reliability method(FORM)often yields significant errors when addressing nonlinear problems.Although the second-order reliability method(SORM)can provide higher accuracy,the additional computation of the Hessian matrix leads to lower computational efficiency.Additionally,when the dimensionality of the random variables is high,the approximation formula of SORM can result in larger errors.To address these issues,a structural reliability analysis method based on Kriging and spherical cap area integral is proposed.Firstly,this method integrates FORM with the quasi-Newton algorithm Broyden-Fletcher-Goldfarb-Shanno(BFGS),trains the Kriging model by using sample points from the algorithm’s iteration process,and combines the Kriging model with gradient information to approximate the Hessian matrix.Then,the failure surface is approximated as a rotating paraboloid,utilizing the spherical cap to replace the complex surface.For the n-dimensional case,the hyperspherical cap area expression is combined with the integral method to calculate the failure probability.Finally,the method is validated through three examples,demonstrating improved computational accuracy and efficiency compared to traditional methods.
文摘In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
基金supported by the Natural Science Foundation of China under Project 41076115the Global Change Research Program of China under project 2012CB955603the Public Science and Technology Research Funds of the Ocean under project 201005019
文摘The study of marine data visualization is of great value. Marine data, due to its large scale, random variation and multiresolution in nature, are hard to be visualized and analyzed. Nowadays, constructing an ocean model and visualizing model results have become some of the most important research topics of ‘Digital Ocean'. In this paper, a spherical ray casting method is developed to improve the traditional ray-casting algorithm and to make efficient use of GPUs. Aiming at the ocean current data, a 3D view-dependent line integral convolution method is used, in which the spatial frequency is adapted according to the distance from a camera. The study is based on a 3D virtual reality and visualization engine, namely the VV-Ocean. Some interactive operations are also provided to highlight the interesting structures and the characteristics of volumetric data. Finally, the marine data gathered in the East China Sea are displayed and analyzed. The results show that the method meets the requirements of real-time and interactive rendering.
文摘he Rectangular Top Horn Offset Coaxial Transmission line (RTHOCT) is an expanded structure inwhich the spherical wave is guided. It is applied to manufacture a test cell called GTEM CELL in a broad band-width. In this paper, we give the propagation constant of the first six higher order modes by the basic characteris-tics of the spherical Bessel functions of the third kind. The potential distribution of the sphere-TEM mode is alsocomputed ty boundary integral equation and multi-local expansion method. We find, in the far zone away fromthe top point of RTHOCT the propagation constant of all higher order modes is the same as that of the sphere-TEM mode.
