多点随机振动控制中的互谱矩阵研究

Cross-Spectra in Multiple Shaker Random Vibration Test

多振动台随机振动实验中必须设置完整的参考谱矩阵。针对控制点之间互谱和自谱的关系 ,本文提出了将参考谱矩阵的正定性作为其能否物理可实现的判定条件 ,并为具有控制点之间完全相干要求的谱矩阵建立了类似 Cholesky分解的方法。利用优化逆系统求解驱动信号 ,避开了传统控制方法中直接对频响函数矩阵求逆的过程。仿真算例表明对控制点之间互谱的控制效果令人满意。

A whole reference spectral density matrix is established in multiple shaker random vibration test. Using the relation between cross-spectra and auto-spectra at reference point, a criterion is presented to examine whether the whole reference spectral matrix is rational by calculating its positive definite. A method similar to Cholesky factorization algorithm is also presented to deal with the cross-spectral density matrix in which reference points are fully coherent. The optimal inverse system method is used for generating the driving signals instead of inverse calculation to the system transfer matrix directly. Simulation example shows that the effect of the cross-spectra control results is satisfied.