非负矩阵分解在地震作用下结构随机响应分析中的应用

Application of nonnegative matrix factorization in structural random response analysis under earthquake action

地震动作为一类典型的非平稳随机过程可由演变谱刻画其能量的时-频分布。然而,演变谱的时-频耦合特性却限制了经典谱表示法的模拟效率。为提高非平稳地震动模拟效率,简化非平稳地震作用下结构随机响应分析,提出了基于非负矩阵分解(nonnegative matrix factorization,NMF)的地震动演变谱解耦方案,使结构在非平稳地震作用下的响应计算简化为各项均匀调制激励下的结构随机响应叠加。分析结果表明,基于非负矩阵分解的地震动演变谱解耦具有良好的精度,快速傅里叶变换技术的引入提高了经典谱表示法的模拟效率,模拟样本自相关函数与目标值吻合良好,非平稳地震作用下结构随机响应频域分析得到简化。

Ground motion is a typical nonstationary stochastic process,and its energy time-frequency distribution can be described by evolution spectrum.However,time-frequency coupled characteristics of evolution spectrum limit the simulation efficiency of the classical spectral representation method.Here,in order to improve the efficiency of non-stationary ground motion simulation,and simplify the structural random response analysis under non-stationary earthquake,a decoupling scheme of ground motion evolution spectrum based on non-negative matrix factorization was proposed to simplify the calculation of structural response under non-stationary earthquake as superposition of structural random responses under each uniform modulated excitation.Results showed that the decoupling of the evolution spectrum of ground motion based on non-negative matrix factorization has good accuracy;introducing fast Fourier transformation(FFT)technology improves the simulation efficiency of the classical spectral representation method,the auto-correlation function of simulation samples agrees well with the target value,and the frequency domain analysis of structure random responses under the action of nonstationary earthquake is simplified.