What is a MIMO (Multi-Input Multi-Output) Model?

NOTE:  The commands in this tutorial are only available if the VES-3600 Advanced Signal Processing option is authorized by your ME'scope license. Check Help | About to verify authorization of this option.

Calculation of Transfer Functions, Outputs, and Inputs are all based upon use of a MIMO (Multi-Input Multi-Output) model of the dynamics of a structure. A MIMO model is a frequency domain model where Fourier spectra of multiple Inputs are multiplied by elements of a Transfer Function matrix to yield the Fourier Spectra of multiple Outputs.

The MIMO model is expressed with the equation:

{X(w)} = [H(w)] {F(w)}


  {F(w)} = Input Fourier spectra (m - vector).

  [H(w)] = Transfer Function matrix (n by m).

  {X(w)} = Output Fourier spectra (n - vector).

  m = number of Inputs.

  n = number of Outputs.

  w = frequency variable (radians per second).

NOTE:  Rows of the Transfer Function matrix correspond to Outputs, and columns correspond to Inputs.  Each Input and Output corresponds to a measurement DOF (point & direction).  Each Transfer Function is a Cross-channel function between two DOFs, an Input DOF and an Output DOF.


Transfer Function

Frequency Response Function (FRF)


NOTE:  An FRF and Transmissibility are special cases of a Transfer Function.

MIMO Calculations

Any one of the components of the MIMO model, (Inputs, Outputs, or Transfer Functions) can be calculated from the other two components using commands in the Transform | MIMO menu.

The MIMO model is also used to calculate and display in animation a sinusoidal ODS due to multiple sinusoidal excitation forces at the same frequency.  (See the Transform | MIMO | Sinusoidal ODS command description for details.)