Compatibility of multi-channel reference kurtoses and correlations for non-Gaussian random vibration control

Multi-input multi-output non-Gaussian random vibration control has received increasing attention in recent years. However, there are still many related issues that remain unresolved. This work investigates the relationship and compatibility between multi-channel kurtoses and correlations for multi-dimensional non-Gaussian reference definition. The coupling mechanism between multi-channel kurtoses and correlations is first revealed that there is a compatibility constraint between them. To find this compatibility condition, an analytical expression between the multi-channel kurtoses and correlations is derived theoretically by introduction of the covariance matrix and adjunction of independent non-Gaussian signal sources from the time domain. Subsequently, a compatibility examination procedure is proposed and it is found that the nonzero-correlation channels should be manipulated in sequence while all zero-correlation channels can be adjusted simultaneously. Finally, a commonly used three-input three-output vibration case is studied and a triaxial non-Gaussian random vibration control experiment is provided. The theoretical achievements of the work can further promote the development of multi-input multi-output non-Gaussian random vibration tests.