# Advanced system identification techniques for wind turbine structures Page: 7 of 10

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teger. We then solve for the observer Markov parame-

ters

Y=Di CB: CABL... :CA B] (12)

using a least-squares algorithm.

The observer Markov parameters in equation (12) in-

clude the system Markov parameters and the observer

gain Markov parameters. The system Markov parame-

ters are used to compute the system matrices A, B, C,

and D, whereas the observer gain Markov parameters

are used to determine the observer gain matrix G. The

proper algorithm for obtaining these Markov parame-

ters has been introduced by Phan et al. [6] and is also

discussed by Juang [3]. Software implementation of

this identification algorithm was developed at NASA

Langley and is known as the Matlab function OKID.

Finally, the state-space representation (A, B, C, D) of

the system is obtained using the Eigensystem Reali-

zation Algorithm (ERA), based on system realization

theory [3].

It can be proven that the truncated observer model

(12), obtained as a result of the dead beat approxima-

tion of equation (10), produces the same input-output

map as a Kalman filter if the data length is sufficient

so that the truncation error is negligible. In this case,

G, when computed from the combined Markov pa-

rameters of equation (12), gives the steady-state Kal-

man filter gain K = -G.

5 IDENTIFICATION PROCEDURE

The identification of the Observer/Kalman Filter

model of a wind turbine is performed by the MATLAB

program fiokuy.m which uses the MATLAB function

okid. The initial estimate of the number of observer

Markov parameters is specified considering that the

maximum system order that can be identified equals

the product p.m where p is the number of Markov

parameters considered and m is the number of meas-

urements (or outputs). Using the measurement ma-

trix, the Hankel matrix is formed and a plot of its sin-

gular values is displayed to aid in selecting the correct

system order. After selecting system order, the per-

centage of data realized by the model is computed. It

is recommended to choose the lowest system order

resulting in 100% realization of the measurement

data. The corresponding modal parameters are also

displayed on the screen in a tabular form showing the

mode singular values (SV) and modal amplitude co-

herence (MAC) factors. This provides additional

evaluation of the quality of the identified model. Exam-

ining this table, the user can determine the modes

whose contribution to the system dynamics is insig-

nificant. Such modes can be classified as the noise

modes.The identified system matrices A, B, C, D, generated

by the program for the structure model of a selected

order, are available as MATLAB variables Af, Bf, Cf

Df. The identification error is displayed in the Figure

Window.

The next step is to run other identification programs

for all input-output data files. They return the list of

identified eigenvalues and corresponding modal fre-

quencies in [rad/s and [Hz], as well as system zeros

related to the selected output. The frequency re-

sponse plot is also displayed in the Figure Window. A

special program can be used to enlarge a selected

portion of this plot.

All the outlined steps of the above procedure are illus-

trated in the Appendix, where a case study is pre-

sented using simulation data obtained from the

ADAMS model of the Micon 65/13 wind turbine.

6 CONCLUSION

The input-output time-series obtained from the virtual

wind turbine were used to develop and to validate the

identification procedure presented above. It was

found that to identify all vibration modes, we have to

process, repeating the same procedure, the in-

put/output time-series for both in-plane and out-of-

plane excitations applied at various points of the

wind-turbine structure. This has been done for three

data files generated by out-of-plane excitations, collo-

cated with the measurements near the tips of two

blades and at 2/3 of the height of the tower, and for

one data file generated by the in-plane excitation col-

located with the measurement at 2/3 of the height of

the tower.

For each of the four above listed data files, each con-

taining five measurements, the Observer/Kalman Fil-

ter state-space model was identified interactively in

order to determine the model order providing the best

fit for the measurement data. The corresponding set

of modal parameters was generated. Then, for each of

the five input-output pairs, the frequency response

was plotted and the corresponding set of system zeros

and their frequencies determined.

The Appendix presents the scope of the tests per-

formed. It also gives the numerical results of modal

parameter identification, graphically illustrated by

frequency response plots. This graphical illustration

is most distinct on the frequency response plot for the

system output (measurement) collocated with the exci-

tation used to obtain the analyzed data file.

Examining all the capabilities of the developed identi-

fication software tools, it seems that the scope of ap-

plied research this software could support is very

broad.!.

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Bialasiewicz, J.T. & Osgood, R.M. Advanced system identification techniques for wind turbine structures, article, March 1, 1995; Golden, Colorado. (https://digital.library.unt.edu/ark:/67531/metadc688470/m1/7/: accessed April 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.