Identification of a drill string.
state space, tutorial
https://lpsa.swarthmore.edu/Representations/SysRepSS.html#Developing_MechR https://lpsa.swarthmore.edu/Systems/MechRotating/RotMechSysModel.html#Free_Body_Diagrams_
Model updating (or tricks)
From prof. Thomas Abrahamsson(thomas.abrahamsson@chalmers.se, https://www.chalmers.se/en/staff/Pages/thab.aspx)
match eigen frequencies
- Minimize diff. in location of eigs
- did not work
- Instead match eigs of same modes
- but difficult for many modes. We want to avoid this
- Also difficult because of damping(different for each mode)
Use modified state space model for comparison
- Do not use raw data. Use state space identified model to compare with
- Modify SS model with artificial damping
- Assign same damping ratio to all modes.
- Use same damping ratio for FE model
- This avoid the difficulty with mode matching
The damping from a SS model is Re(λ₁) = ζᵢIm(λᵢ) Now; instead we chose eg. ζ₀ = 1%, update the eigenvalues and A using the modified λ’s Re(λ₁) = ζ₀Im(λᵢ) That is; update the real part of λ, but keep the imaginary(the oscillating part) Modify FE model, constructing C so it have the same proportional damping.
Use logarithmic cost function
δ = QᴴQ/N, Q = log10(vect(Gₘ(θ)) - log10(vect(Gₑₓₚ)) where Gₘ and and Gₑₓₚ are the transfer functions of the FEM and state space model respectively. θ is the parameter vector of the FEM and N the number of samples in the FFT calculation.
Without log, the biggest difference will be largest around the test- or model resonances. With log, the cost function get smoothed.
- Use logarithmic frequency sampling (WHAT IS THIS?). I wrote p1/2bw in notes.
Maybe it is
s/z, frequency variable in transfer function.- Linear steps gives denser grid at high frequencies modes
- Log steps gives balanced grid for all modes
misc
- Goodness numbers for FRF
- NRMSE - some number from id-toolbox
- Log FRAC - log cost function
- Residual ratio(i think ratio) ?
Reference
Gibanica, M. ; Abrahamsson, T. ; Olsson, M. (2016) Calibration, Validation andUncertainty Quantification of Nominally Identical Car Subframes, IMAC http://dx.doi.org/10.1007/978-3-319-29754-5_31
- 2017 IMAC paper
FEMCALI FEM calibration software, https://www.mathworks.com/matlabcentral/fileexchange/44317-femcali