Spectral decoupled correction algorithm for multi-input multi-output random vibration control

Abstract

The multi-output response spectral replication correction algorithms for the multi-shaker random vibration test are investigated. In the existing matrix power correction algorithm, the control of auto and cross spectral densities is coupled which may bring some unexpected errors. The ideal spectral correction mode is that the control of auto and cross spectral densities should be independent of each other. For this purpose, a novel spectral decoupled correction algorithm is proposed with a spectral decoupling decomposition method in this work. Two lower triangular matrices are introduced to modify the auto and cross spectral densities separately during equalization procedure. Due to the positive definite constraint for the power spectral matrix, the coherence coefficient and phase difference in the cross spectral densities cannot be controlled independently when the number of the control channels is more than two. A simulation example is provided and the control results with the matrix power correction algorithm and proposed spectral decoupled correction algorithm are compared. Finally, a tri-axial shaker random vibration test is carried out and the results prove the effectiveness and feasibility of the proposed method.