结构动力可靠度计算的基于反应功率谱的重要抽样法

IMPORTANCE SAMPLING METHOD BASED ON RESPONSE POWER SPECTRUM FOR STRUCTURAL DYNAMIC RELIABILITY ESTIMATIONS

提出了受随机地震作用的结构动力可靠度计算的基于反应功率谱的重要抽样法。为了提高动力可靠度计算的效率,利用反应功率谱峰值点对应频率处输入激励幅值的变化对失效概率的影响,提出了利用反应功率谱增大输入激励幅值的方差,达到重要抽样的目的;根据随机振动理论,平稳随机反应功率谱曲线与频域内反应绝对值平方曲线的期望值是相似形,而频域内反应绝对值平方曲线的期望值可以通过Fourier变换很方便的求出,所以也可利用频域内反应绝对值平方曲线的期望值增大输入激励幅值的方差;重要抽样密度函数可表示为幅值分量概率密度函数连乘的形式,其所采用的输入激励幅值的方差可通过少量的结构分析次数得出。通过对三自由度线性结构及十自由度随机结构的计算,表明该文算法是提高动力可靠度计算效率的有效途径,也是求解随机结构动力可靠度的有效途径。

Based on response spectrum,the paper proposed importance sampling method for structural dynamic reliability estimation under random earthquake excitations.In order to improve the calculation efficiency of dynamic reliability estimations,the paper uses power spectrum with importance sampling method to increase the variances of input random excitation amplitudes.The power spectral density of the response usually has some significant peaks which indicate the corresponding frequency ranges with the most contribution to the total variance of the response.Hence,the importance sampling density should be adapted for those amplitudes assigned to frequencies near the peaks of the spectrum.According to random vibration theory,the power spectral density of stationary random response is similar to the expectation of square of the absolute value of response in frequency domain,which can be easily calculated by Fourier transform and can also be used to increase the variances of input random excitation amplitudes.The importance sampling density function can be expressed as multiplications of elements of excitation amplitudes,and the variances of input random excitation amplitudes in importance sampling density function can be obtained by structural analysis for several times.Calculations of a three degree-of-freedom linear structure and a ten degree-of-freedom random structure indicate that the proposed method is an effective method for improving the dynamic reliability calculation efficiency and for estimating dynamic reliability of random structures.