环境激励下Karhunen-Loève变换与模态分解间的关系

Relationship Between Karhunen-Loève Transformation and Modal Decomposition Under Ambient Excitations

Karhunen-Loève(KL)变换作为一种基于相关函数的最佳变换,在振动分析领域已经受到广泛关注。然而,该方法还缺乏清晰完整的模态解释。在空间几何上,振动分析中模态分解是振动响应信号在由振型构成的基底上的展开,KL变换是信号在由一组正交KL特征向量构成的空间中的投影过程。对环境激励下响应的KL变换与模态分解进行类比,探讨两者间的关系。结果表明:KL特征向量收敛于质量信息加权后的振型;KL特征值表征各阶模态的能量参与度;KL变换系数收敛于模态坐标。最后,通过仿真计算验证分析结论的正确性。

As a best transformation based on the correlation function,Karhunen-Loève transformation(KLT)has been paid a wide attention in vibration analysis.However,this method lacks a clear and complete modal interpretation.In view of spatial geometry,the modal decomposition in vibration analysis is a procedure of expanding response signals on the bases of modal shapes,while KLT is a projection procedure of the signals in the space composed by orthogonal KL eigenvectors.This paper discusses the relationship between the KLT and the modal decomposition under ambient excitation.The results show that the KL eigenvectors are approximated to the weighted modal shapes,the KL eigenvalues represent the energy contribution of the corresponding modes,and the KL coefficients converge to the modal coordinate.Finally,conclusion of the analysis is verified by numerical simulation.