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output value is defined as jq (t) and it is y t (t) in the case other than this unit i is in the input layer.
where I, H, and 0 denote the input unit, intermediate unit, and output unit, respectively. In time t+1,
yj (t+1), the output value of unit i^HUO, is expressed by Eqn. 2, where 85 (t+1) means the internal
state expressed by Eqn. 3. Then, w, j is a weighting coefficient between unit i and unit j. The function
f t is the monotonous increasing function that can be differentiated, and a sigmoid function is used here
(Eqn. 4) (Kitagawa et aL, 1997).
f^t + l)), ieHuO (2)
!>.*,«+ £*W;« = 2X.Z-W (3)
jel jeH(jO ys/utfuO
, ' ; l - + exp(-x) -7—\
As typical learning methods of the recurrent neural network, BPTT (Back Propagation Through Time)
that performs error propagation in the direction of reverse time, and RTRT (Real Time Recurrent
Learning) that performs error propagation in the direction of positive time, are developed. Since the
purpose of this study is the real time learning, RTRT is employed here. The error between the output
value from a network and teaching data in time t is calculated as Eqn. 5 and Eqn. 6.
E(t)=iZ(e t (t)) 2 (5)
(t)=fy k (t)-d t (t),
if keo
kW [0 otherwise
where d k (t) is the teaching data for the input value in time t.
between the output value and the teaching value.
In the output unit, e k (t) is the difference
In this study, the input values of the neural network are current wind velocity, displacement and
velocity of structure, and the control force at the previous time step. Then, learning of recurrent
neural network is performed as follows: the input values in time t 0 are the wind velocity, the
1
displacement and velocity of the structure. Then, the input values at the previous time step are set to
be zero, because ^ is the starting time. The learning is not performed and only the output value is
calculated in order to initialize the information in a neural network. In time t+1, the input data in
time ^ are used as the data before 1 step and set new data with current input value. The next output
values are calculated in the same way and the learning of neural network starts with the minimization
of the square error between output values and teaching data. The similar process is executed in real
time learning method by numerical computation. However, it is difficult for the vibration control to
obtain the teaching data for the learning so that virtual teaching data are used for learning, which are
obtained by solving an approximate differential equation. Fig.l shows learning process of recurrent
neural network.