Impact of fuel supply impedance and fuel staging on gas turbine ...

5.5 Pro<strong>of</strong> <strong>of</strong> concept for the identification <strong>of</strong> the MISO flame model
Phase
Amplitude
1.5
1
0.5
3.14
1.57
−1.57
0
0 2 4 6 8 10
0
−3.14
0 2 4 6 8 10
Strouhal number
Figure 5.16: Flame transfer function F φ,2 identified in the presence <strong>of</strong> noise
(−− Test FTF, -- DRBS (limited frequency range), -· DRBS)
the identification quality. For the present case a DRBS signal with unlimited
frequency range is used as a reference signal. Different numbers <strong>of</strong> time steps
were evaluated ranging from N = 3×M to N = 150×M, where M denotes again
the number <strong>of</strong> UIR coefficients. Three different signal to noise ratios were analyzed
(no noise, S/N = 4, S/N = 10). The results are presented in Fig. 5.17 in
form <strong>of</strong> the ”quality” Q/Q 0 over the time series length, which are shown as
multiple <strong>of</strong> M. Q/Q 0 is determined using Eqn. (5.17), which is normalized by
the maximum possible result <strong>of</strong> Q in presence <strong>of</strong> noise. Taking the case with a
signal to noise ratio <strong>of</strong> 10, a value <strong>of</strong> 97% can be reached when the total simulation
time is 15 times the length <strong>of</strong> the UIR or the longest time lag considered
(M△t ).
The numerical study using the simplified model demonstrated that the proposed
identification method based on correlation analysis <strong>and</strong> the Wiener-
Hopf inversion is able to identify multiple-input single-output (MISO) systems.
Furthermore, it is capable to separate the impact <strong>of</strong> the different input
signals on the response, even if the input signals are correlated to a certain
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