摘要
建立了一种基于快速傅立叶变换的二阶可靠度分析方法 .状态函数在利用两点近似技术近似为二阶多项式后 ,进一步变换为统计上独立的中间变量之和 .对于中间变量的线性形式表示的状态函数 ,其概率密度的傅立叶变换是各中间变量的概率密度的傅立叶变换之积 .因此 ,状态函数的概率密度可由其傅立叶变换函数的逆变换求得 .文中的傅立叶变换和相应的逆变换均由高效的快速傅立叶变换技术完成 .该方法可应用于正态和非正态分布问题 .由于在构造二阶近似中采用了近似技术 ,因而具有很好的计算效率 .数值算例验证了该方法的应用、效率和精度 .
A fast Fourier transformation based second order reliability method (FFT SORM) is proposed. By using a two point adaptive nonlinear approximation method, the performance function of the problem is approximated as a second order polynomial function which is then transformed into a sum of statically independent intervening random variables through a series of transformations. The probability density function (PDF) of this linear form of performance function is computed by inverse transforming its PDFs Fourier transformation which is given by the product of the Fourier transformations of the PDF of every intervening random variable. All the Fourier transformations and their corresponding inverse transformations are implemented by the use of efficient fast Fourier transformation (FFT) technique. This method is applicable to both normal and non normal distribution problems and is computationally efficient due to the second order approximate performance function which is constructed by using a two point approximation method. The applicability, efficiency, and accuracy of the method are verified by numerical examples.
出处
《固体力学学报》
CAS
CSCD
北大核心
2001年第4期387-393,共7页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金重大项目 (5 9895 410 )
青年基金项目 (196 0 2 0 0 7)
教育部骨干教师资助计划项目资助
