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206 6. NEURAL NETWORK SEMIEMPIRICAL MODELING OF AIRCRAFT MOTION

FIGURE 6.6 Empirical (black box) ANN model of the longitudinal angular motion of the aircraft (NARX).

TABLE 6.3 Simulation error on the test set for the semiempirical model and three types of excitation signals.
Problem Point mode Monotonous mode
RMSE α RMSE q RMSE α RMSE q
Doublet 0.0202 0.0417 8.6723 34.943
Random 0.0041 0.0071 0.0772 0.2382
Polyharmonic 0.0029 0.0076 0.0491 0.1169

results given by purely empirical NARX mod- mode” denotes a flight with a monotonically
els. increasing angle of attack. Also, the term “learn-
In Table 6.3 we present a comparison of mag- ing” for the aerodynamic coefficients denotes
nitudes of prediction errors for various kinds the problem of restoring the corresponding un-
of excitation signals used to generate the train- known functions “from scratch,” i.e., under the
ing data set for the semiempirical model of the assumption that there is no information on the
angular longitudinal motion of the aircraft. It possible values of these coefficients. The term
is evident that results given by the empirical “adjusting” refers to the task of improving the
model are much less accurate; for example, in initial approximations of the corresponding co-
the case of a polyharmonic excitation signal, efficients, known, for example, from wind tun-
the NARX model has RMSE α = 1.3293 deg, nel tests.
RMSE q = 2.7445 deg/sec. As noted above, in a number of cases, we
In Tables 6.1, 6.2,and 6.3 the term “point need not only to restore the unknown functions
mode” denotes a straight and level flight at (in this problem, C L (α,q,δ e ) and C m (α,q,δ e )),
a constant speed while the term “monotone but also their derivatives by state variables, for