Analyses of target definition processes for MIMO Random Vibration Control tests

In Random Vibration environmental testing, it is a common practice to specify the requirements as acceleration power spectral densities (PSDs) that need to be reproduced at user-defined control channels. Such a test is typically performed in a single-axis setting, where the test article is subjected to vibrations in one direction only. If more than one direction is of interest sequential single-axis tests are performed after rotating the test article or using a slip table configuration. This way to perform multi-axial Random Vibration tests is out of date: there is definitely some lack of realism in sequential single-axis testing, as the stress loading and boundary conditions will significantly differ from the true three-dimensional environment. For very heavy structures, often the excitation level safely reachable by a single shaker is not even sufficient, the limitation being the risk of damaging the sometimes very expensive and fragile test articles due to high concentrated stresses. All these limitations are overcome if a Multiple-Input-Multiple-Output (MIMO) Random Vibration Control test is performed. Even though the benefits of MIMO tests are clear and accepted by the environmental engineering community, their practice still needs to grow. This is mainly due to the high degree of expertise needed to perform these tests. The challenges of MIMO Random Control start even before the actual test, in the test definition phase. The target that needs to be reached during the test is a full Spectral Density Matrix where the cross terms are as important as the diagonal ones. Defining this matrix with no a-priori knowledge of the cross-correlation between control channels is very challenging: filling in the off-diagonal terms, in fact, must guarantee that the target has a physical meaning. This is translated in the algebraic constraint that the target matrix needs to be positive (semi)-definite. On the other end the pushing driver of any Random Vibration Control test is to be able to replicate specific PSDs, given, for instance, by qualification specifications or optimal profiles (in terms of fatigue damage or comfort requirements). In defining the target matrix the main challenge is to guarantee a physically realizable full target spectral density matrix that has fixed PSD terms. Several authors tackled the problem of defining the best target possible (in terms of minimum drives energy, in terms of control performances,) even though few works can be addressed that tackle the problem of defining a realizable target first. This leads to a gap in the standards about a generally accepted and robust procedure to define the MIMO Random target matrix. The purpose of this work is to investigate different target generation procedures pointing out the advantages and the challenges in terms of physical meaning and their impact on the random control strategy. Alternative solutions based on on-going research topics will also be considered to propose alternative robust target definition routines in order to aim to a well-defined automatic procedure to include in the standard practice.