# Does the Multi-Inpu​t-Single-O​utput transfer function estimate obtained from "tfestimate" account for all inputs being active at the same time?

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Philipp Viandt on 1 Nov 2021
Answered: Abhimenyu on 7 Jun 2024
I want to use "tfestimate" to compute the H1-estimation of the transfer behaviour of a gearbox housing. The gearbox housing is excited by six bearing forces (obtained from a multi-body dynamics simulation). The six bearing forces are the inputs to "tfestimate". The housing acceleration is measured experimentally using an acceleration sensor. The acceleration signal is the single output of "tfestimate".
Does "tfestimate" consider that all excitation forces / inputs are exciting the gearbox housing simultaneously? Or is the result, six individual transfer functions for the six transfer paths, valid only if only one of the bearing forces is active at a time? That would mean that the acceleration signal obtained by superposition, Acceleration=H1*F_bearing_1+H2*F_bearing_2...+H6*F_bearing_6, cannot equal the actual measurement signal, but only Acceleration=H1*F_bearing_1+H2*0...+H6*0 would equal the measurement signal.

Abhimenyu on 7 Jun 2024
Hello,
I understand that you have queries regarding the tfestimate function of MATLAB. The tfestimate function in MATLAB computes the transfer function estimate between an input signal and an output signal evaluated at a set of frequencies.
When using the tfestimate, it considers all excitation forces (inputs) simultaneously. If you provide multiple input signals (bearing forces), it computes a multi-input/multi-output (MIMO) transfer function that combines all input and output signals. Therefore, the result includes information about how all bearing forces affect the housing acceleration together. This is explained in this MATLAB R2024a documentation link: https://www.mathworks.com/help/signal/ref/tfestimate.html
The individual transfer functions for each bearing force are not computed separately. Instead, the tfestimate function provides a combined MIMO transfer function that accounts for all inputs. The superposition that you mentioned (Acceleration = H1 * F_bearing_1 + H2 * F_bearing_2 + … + H6 * F_bearing_6) is indeed valid when all forces are active simultaneously.
The acceleration signal obtained from the MIMO transfer function considers the combined effect of all bearing forces. It does not assume that only one force is active at a time. Therefore, the actual measurement signal can be represented by the superposition of all forces, as described in your query.
In summary, the MIMO transfer function estimate obtained from tfestimate accounts for all inputs being active at the same time, allowing you to analyze the combined effect of multiple bearing forces on the gearbox housing acceleration.
I hope this helps!

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