Evaluation of MIMO Input Derivations and Their Physical Context

Multi-Input-Multi-Output (MIMO) vibration testing is considered to be more representative of the actual loads on many articles of interest. Since the derivation of MIMO inputs involve a matrix inversion process using N x M transfer functions corresponding to N input and M output locations, it is affected by both mathematical and physical parameters. The derived input loads can differ depending on the inversion and convergence algorithm used as well as on the accuracy of the underlying data. A study was conducted using data from a benchtop MIMO test. The objective of the study was to understand how the convergence criteria and the underlying data used in MIMO algorithms affect the derived inputs. Two different input derivation methods were used. Of particular interest is the influence of the Tikhonov regularization used in the matrix inversion process and the consequence thereof in achieving the desired outputs as well as the input loads. The paper will present the results of these studies with the intent of providing a better understanding of their implications in tests and analyses associated with MIMO.