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pawsen / drillstring-id

(maybe) identification of a drill string

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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

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(maybe) identification of a drill string