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!
