The paper presents a new method for vibration testing of articles such as satellites, aerospace subsystems, transportation subsystems, civil structures, or articles whose reliability in operation may be evaluated using either mechanical or acoustic vibration testing. The method can be used for direct field or reverberant acoustic test facility testing (acoustic) systems or multiple-exciter (mechanical) testing systems to perform vibration testing. The method improves the ability of Multiple-Input-Multiple-Output (MIMO) acoustic testing systems to create diffuse or other types of acoustic fields and MIMO mechanical testing systems to produce vibration responses conforming to an initial reference Spectral Density Matrix (SDM) specification in the least mean-square error (LMSE) sense. It provides an updated positive definite or semi-definite reference SDM that enables such tests to run with less error, using minimum required drive power, as a function of the initial definition of the reference SDM, by modifying its coherence and phase off-diagonal terms, to approximate initially defined off-diagonal terms in the LMSE sense, but maintaining its initially defined diagonal terms exactly, while accounting for physical limitations existing in the overall MIMO testing system.

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